A&A 672, A130 (2023)
https://doi.org/10.1051/0004-6361/202243435
c© The Authors 2023
Astronomy
&Astrophysics
Time variability of the core-shift effect in the blazar 3C 454.3?
Wara Chamani1,2 , Tuomas Savolainen1,2,3 , Eduardo Ros3, Yuri Y. Kovalev4,5,3 , Kaj Wiik6 ,
Anne Lähteenmäki1,2, Merja Tornikoski1 , and Joni Tammi1
1 Aalto University Metsähovi Radio Observatory, Metsähovintie 114, 02540 Kylmälä, Finland
e-mail: wara.chamani@aalto.fi
2 Aalto University Department of Electronics and Nanoengineering, PO Box 15500, 00076 Aalto, Finland
3 Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
4 Lebedev Physical Institute of the Russian Academy of Sciences, Leninsky prospekt 53, 119991 Moscow, Russia
5 Moscow Institute of Physics and Technology, Institutsky per. 9, Dolgoprudny, Moscow region 141700, Russia
6 Department of Physics and Astronomy, 20014 University of Turku, Finland
Received 28 February 2022 / Accepted 25 November 2022
ABSTRACT
Measuring and inferring the key physical parameters of jets in active galactic nuclei (AGN) requires high-resolution very long baseline
interferometry (VLBI) observations. Using VLBI to measure a core-shift effect is a common way of obtaining estimates of the jet
magnetic field strength, a key parameter for understanding jet physics. The VLBI core is typically identified as the bright feature at the
upstream end of the jet, and the position of this feature changes with the observed frequency, rcore ∝ ν−1/kr . Due to the variable nature
of AGN, flares can cause variability of the measured core shift. In this work, we investigated the time variability of the core-shift
effect in the luminous blazar 3C 454.3. We employed a self-referencing analysis of multi-frequency (5, 8, 15, 22−24, and 43 GHz)
Very Long Baseline Array (VLBA) data covering 19 epochs from 2005 to 2010. We found significant core-shift variability ranging
from 0.27 to 0.86 milliarcsec between 5 GHz and 43 GHz. These results confirm the core-shift variability phenomenon observed
previously. Furthermore, we also found time variability of the core-shift index, kr, which was typically below one, with an average
value of 0.85±0.08 and a standard deviation of 0.30. Values of kr below one were found during flaring and quiescent states. Our results
indicate that the commonly assumed conical jet shape and equipartition conditions do not always hold simultaneously. Even so, these
conditions are typically assumed when deriving magnetic field strengths from core-shift measurements, which can lead to unreliable
results if kr significantly deviates from unity. Therefore, it is necessary to verify that kr = 1 actually holds before using core-shift
measurements and the equipartition assumption to derive physical conditions in the jets. When kr = 1 epochs are selected in the case
of 3C 454.3, the magnetic field estimates are consistent, even though the core shift varies significantly with time. Subsequently, we
estimated the magnetic flux in the jet of 3C 454.3 and found that the source is in the magnetically arrested disc state, which agrees with
earlier studies. Finally, we found a good correlation of the core position with the core flux density, rcore ∝ S 0.7core, which is consistent
with increased particle density during the flares.
Key words. galaxies: active – galaxies: jets – galaxies: magnetic fields – quasars: individual: 3C454.3 –
techniques: high angular resolution
1. Introduction
The effect known as core shift is an observational fea-
ture of synchrotron-emitting relativistic jets in active galac-
tic nuclei (AGN). Core shift is the change in the radio
core’s distance from the central engine as a function of
frequency. The first observations of the phenomenon were
reported by Marcaide & Shapiro (1984), and since then it
has been detected often in multi-frequency very long base-
line interferometry (VLBI) images of compact extragalactic
sources (e.g. Kovalev et al. 2008; O’Sullivan & Gabuzda 2009;
Sokolovsky et al. 2011; Hada et al. 2011; Pushkarev et al. 2012;
Fromm et al. 2015; Lisakov et al. 2017). The physical nature of
the VLBI core is still a matter of debate, and it has been sug-
gested that at least at millimetre wavelengths it might be due
to a standing shock in the jet (Marscher 2010). In such a case
one would not expect to see a significant frequency dependence
? VLBI maps (FITS) are only available at the CDS via anonymous
ftp to cdsarc.cds.unistra.fr (130.79.128.5) or via https://
cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/672/A130
of the core position. On the other hand, following the predic-
tion of Blandford & Königl (1979, hereafter BK79), the core is
the region where the jet becomes self-absorbed at a given fre-
quency νobs (i.e. the optical depth to synchrotron self-absorption,
τ, becomes approximately one). In the BK79 model the core’s
position along the jet, rcore, varies with frequency as rcore ∝ ν−1/krobs
because of the magnetic field strength and particle density gra-
dients in the jet. The BK79 model assumes a freely expanding,
supersonic, narrow, and conical jet with a constant half-opening
angle, φ, and with a constant Lorentz factor Γ. The magnetic field
strength B and particle number density N within the radiating
cores are assumed to be uniform and constant. Both decay with
the distance r along the jet as B = B1 (r1/r)m and N = N1 (r1/r)n,
where B1 and N1 are the values at the distance of r1 = 1 pc from
the apex of the jet. Assuming energy equipartition between par-
ticle and magnetic energy densities, the indices should be scaled
such that n = 2m. Choosing m = 1 and n = 2 results in kr = 1
irrespective of the optically thin spectral index of the emission
(Königl 1981; Lobanov 1998). Based on these previous mod-
els, a recent study further showed that in microquasars with
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A130, page 1 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
moderately relativistic flow speeds and significant jet opening
angles the core position can also vary with the inclination angle
and different magnetic field configurations (Sharma et al. 2022).
Several studies have confirmed rcore ∝ ν−1obs (Lobanov
1998; Hirotani 2005; O’Sullivan & Gabuzda 2009; Fromm et al.
2010, 2013b, 2015; Sokolovsky et al. 2011; Hada et al. 2011;
Mohan et al. 2015; Lisakov et al. 2017; Pushkarev et al. 2018)
and the amount of core shift together with the equipartition
assumption has been frequently used to infer jet magnetic
field strengths (e.g. Pushkarev et al. 2012; Voitsik et al. 2018;
Plavin et al. 2019b, hereafter PL19; Chamani et al. 2021). How-
ever, there is very little knowledge of the stability of the index
kr over time or how this affects the inferred magnetic field
strength. Knowing the jet magnetic field strength is important
since it is one of the key parameters to test the results from
the general relativistic magnetohydrodynamic (GRMHD) simu-
lations on formation and collimation of jets (e.g. Tchekhovskoy
2015, with references therein). For example, these works show
that when enough magnetic flux is available for accretion,
the magnetic flux surrounding the supermassive black hole
may reach a saturation point and a magnetically arrested disc
(MAD) develops (Narayan et al. 2003). MAD accretion behaves
very differently from the standard weakly magnetized disc,
and it is able to launch very powerful relativistic jets in
simulations (Tchekhovskoy et al. 2011; McKinney et al. 2012).
Zamaninasab et al. (2014) used core shift measurements to infer
magnetic fluxes in 76 jets in blazars and radio galaxies from
the MOJAVE survey, and they concluded that the high-power
jets indeed appear to result from MAD accretion. Core-shift-
inferred magnetic fields can therefore play a major role in our
understanding of accretion and ejection in AGN. Therefore, it is
essential to investigate how reliable these measurements are.
A number of previous works have reported core shift and
magnetic field measurements in a diversity of sources (e.g.
O’Sullivan & Gabuzda 2009; Sokolovsky et al. 2011; Pushkarev
et al. 2012); however, these studies were limited to single-epoch
observations. Recently, a compelling multi-epoch investigation
of the core shift on an extensive AGN data set having more than
ten observing epochs has been reported by PL19. Their results
exhibit a significant variability of the core shift up to 1 mas for
the frequency pair of 2 GHz and 8 GHz on timescales of years.
Although PL19 results show for the first time substantial fluctua-
tion of the core position, dedicated observations at three or more
frequencies are necessary to understand the potential variabil-
ity of the functional form of the core shift, which could provide
information about deviations from the equipartition or effects of
the propagating flares on the physical conditions in the jet. Ide-
ally, such investigations should be done with multi-frequency
and multi-epoch observations of a representative sample of
sources. Examples of such monitoring efforts targeting individ-
ual sources include 3C 273 (Savolainen et al. 2008b), 3C 345
(Lobanov & Zensus 1999), CTA 102 (Fromm et al. 2013b), and
PKS 2233-148 (Pushkarev et al. 2018).
Due to the variable nature of AGN, strong outbursts could
potentially cause time variability of the core-shift effect and pos-
sibly disturb the relation rcore ∝ ν−1 (see e.g. Kovalev et al. 2008;
Fromm et al. 2013b, 2015; Niinuma et al. 2015; Hodgson et al.
2017; Lisakov et al. 2017; PL19). Consequently, magnetic field
strength estimations and astrometry could be significantly
affected. Thus, because blazars are conspicuous flaring sources,
they are attractive targets to study the variability of the core shift
and explore the stability of the magnetic field strength.
An intriguing study case is the very luminous and variable
flat-spectrum radio quasar 3C 454.3 (B 2251+158, 4C +15.76),
also known as the Crazy Diamond, located at redshift z =
0.859 (Jackson & Browne 1991). Blazar 3C454.3 emits a pow-
erful relativistic jet pointing towards us at a small viewing
angle. It has been catalogued as one of the most luminous
astronomical objects and the brightest extragalactic gamma-
ray source. The source exhibits typical flat-spectrum radio-
loud quasar (FSRQ) features, such as non-thermal emission
and variability across the whole electromagnetic spectrum.
Many multi-wavelength observing campaigns of 3C 454.3 rang-
ing from radio to gamma rays have been performed over the
years. The source started an extraordinary flaring behaviour
in early 2005 with the first strong peak in 2006, the second
peak in the mid-2008, and the largest peak in 2010, as seen
in the Metsähovi Radio Observatory single-dish observations
at 37 GHz (see Fig. 9) and in the 15 GHz Owens Valley Radio
Telescope (OVRO) observations (see e.g. Sarkar et al. 2019).
This period corresponds to the major multi-wavelength (radio,
millimetre, optical, X-ray and gamma-ray) flaring events dur-
ing 2005 and 2006 (e.g. Remillard 2005; Giommi et al. 2006;
Villata et al. 2006; Pian et al. 2006; Jorstad et al. 2010), and
in 2007−2010 (e.g. Ghisellini et al. 2007; Raiteri et al. 2008,
2011; Vercellone et al. 2009, 2010; Donnarumma et al. 2009;
Abdo et al. 2009; Jorstad et al. 2010, 2013) with extraordinarily
bright gamma-ray flares in early December 2009 (Bonnoli et al.
2011; Pacciani et al. 2010) and in November 2010 (Abdo et al.
2011). 3C 454.3 continuously flared until 2011, and then
entered a quiescent state in 2012, which lasted until 2014.
Since 2014, small flaring events have been registered although
they are not strong compared to the period prior to 2012
(Sarkar et al. 2019).
Recent studies based on multi-frequency flux density moni-
toring observations and the motion of superluminal components
observed in 3C 454.3 have suggested the existence of a super-
massive binary black hole system in this source (Volvach et al.
2021; Qian et al. 2021). Volvach et al. (2021) performed har-
monic analysis using radio, optical, and gamma-ray flux density
monitoring covering a period from 1966 to 2020 to establish
the precession and orbital periods for what they argue corre-
spond to a close black hole binary system. They report a pos-
sible period of 14 yr based on the light curve analysis. In another
study, a double precessing jet scenario has been proposed for
3C454.3, where two groups of superluminal knots are ejected at
different directions that, according to the authors’ model, orig-
inate from two different jets precessing with the same period
of 10.5 yr (Qian et al. 2021, with references therein). The phys-
ical origin of the observed variability in 3C 454.3 might be
explained in the context of the precessing jet scenario as sug-
gested by Volvach et al. (2021) and Qian et al. (2021). However,
other mechanisms, such as fluctuations in the magnetic field in
the inner disc, variations in the accretion flow, or the develop-
ment of shocks or instabilities in the jet can also be potential
origins of its variability.
In view of its variable nature, 3C 454.3 is an excellent tar-
get for studying whether the core-shift effect is also variable in
this source. Previously, Pushkarev et al. (2012) and Kutkin et al.
(2014) reported core-shift measurements of the jet in 3C 454.3 at
a total of three epochs, but only the measurement in Kutkin et al.
(2014) had enough frequencies to measure kr. Additionally,
radio light curve-based core-shift estimations were reported by
Mohan et al. (2015). However, these data were not enough to
study the time variability of the core shift and kr.
In this paper we present results from three multi-wavelength
Very Long Baseline Array (VLBA) monitoring programmes of
3C 454.3 that we carried out between 2005 and 2010, as well as
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Chamani, W., et al.: A&A 672, A130 (2023)
archival VLBA data. With this rich data set, we aim to test how
stable the core-shift magnitude, the kr index, and the inferred
magnetic field strengths are over time in 3C 454.3. We mea-
sure the frequency-dependent shifts of the core position in a
frequency range spanning from 5 GHz to 43 GHz along with
the core spectrum and core-shift vector directions. We present
a direct measurement of the time variability of the kr index for
the first time. We study how the variable source flux density
affects the core shift and investigate the role played by the flar-
ing events. Using the core-shift measurements, the jet’s mag-
netic field strength at 1 pc is estimated for kr = 1 and kr , 1
cases. We also test whether the source is in a MAD state dur-
ing the observed epochs. Finally, we explore the connection of
core-shift magnitude and kr with core flux densities, the rela-
tion of kr with the jet position angle, and the possible correlation
of magnetic field strength at 1 pc with core-flux density when
kr = 1.
The paper is structured as follows. In Sect. 2 we describe
the observations and data calibration; in Sect. 3 we describe
the analysis method; and in Sect. 4 we present our results.
The discussion and the summary are in Sects. 5 and 6, respec-
tively. We adopt a cosmology with Ωm = 0.27, ΩΛ = 0.73
and H0 = 71 km s−1 Mpc−1 (Komatsu et al. 2009). The source
is at a luminosity distance of 5.49 Gpc; at this distance the scale
is 7.70 pc mas−1. Throughout the paper the spectral index α is
defined as S ν ∝ να, where ν is the observed frequency and S ν is
the flux density.
2. Observations and data calibration
2.1. Observations
2.1.1. Very Long Baseline Array
We analysed a total of 19 epochs of VLBA data dating from
2005 to 2010 and comprising five different frequency bands:
C band (5 GHz), X band (8 GHz), KU band (15 GHz; hereafter
U band), K band (22−24 GHz), and Q band (43 GHz). These
observations include both our own multi-frequency monitoring
programmes1 and archival data2. Table 1 lists the data with all
the epochs and frequencies used in this work. All ten VLBA
antennas were scheduled at all the epochs, and any antennas that
were taken out of the observation for any reason are given in the
table.
The multi-frequency VLBA observations were quasi-
simultaneous (i.e. all the bands were observed in every run).
Individual 4−6 min scans at different bands were interleaved in
order to maximize the (u, v) coverage. The observing runs in
the programmes BS157 and BW086 lasted for 10 h each and
included CTA 102 and 1749+096 as calibrators for bandpass,
polarization leakage, and absolute EVPA. In BS157 the total
integration time per epoch on 3C 454.3 was 49 min at C, X, and
1 The first of these programmes (BS157; PI T. Savolainen) was
triggered by the major multi-wavelength flaring event in May 2005
(Villata et al. 2006). The second programme (BW086; PI K. Wiik)
was a continuation of the monitoring started with BS157. The third
programme (S2087; PI Y. Y. Kovalev) was triggered by the Fermi-
LAT detected γ-ray flare in September 2009. The last monitoring also
covered the large γ-ray outburst of December 2009 (Ackermann et al.
2010).
2 Public data from the project BO033 (PI S. P. O’Sullivan) was down-
loaded from the NRAO archive.
Table 1. VLBA observations of 3C 454.3 used in this work.
Epoch Date Frequency-bands (GHz) Project code
1 2005-05-19 C, X, U, K, Q BS157A
2 2005-07-14 C, X, U, K, Q BS157B
3 2005-09-01 C, X, U, K, Q BS157C
4 2005-12-04 (1) C, X, U, K, Q BS157D
5 2006-08-03 (2) C, X, U, K, Q BW086A
6 2006-10-02 (3) C, X, U, K, Q BW086B
7 2006-12-04 C, X, U, K, Q BW086C
8 2007-01-26 C, X, U, K, Q BW086D
9 2007-04-26 C, X, U, K, Q BW086E
10 2007-06-16 C, X, U, K, Q BW086F
11 2007-07-25 (4) C, X, U, K, Q BW086G
12 2007-09-13 (5) C, X, U, K, Q BW086H
13 2008-01-03 (6) C, X, U, K, Q BW086I
14 2008-12-07 C, X (∗), U, K (∗), Q BO033
15 2009-09-22 C, X, U, K, Q S2087BA
16 2009-10-22 C, X, U, K, Q S2087BB
17 2009-12-03 C, X, U, K, Q S2087BC
18 2010-01-18 (7) C, X, U, K, Q S2087BD
19 2010-02-21 C, X, U, K, Q S2087BE
Notes. (1)Missing antenna(s): Brewster. (2)Missing antenna(s):
Mauna Kea. (3)Missing antenna(s): Brewster missing for half the obser-
vation, due to a focus-rotation mount failure. (4)Missing antenna(s):
Kitt Peak. (5)Missing antenna(s): Hancock and St. Croix. (6)Missing
antenna(s): Hancock and St. Croix; Brewster missing for half the
observation, due to snow problems. (7)Missing antenna(s): Han-
cock. (∗)X-band is split into lower (Xl: 7.9 GHz) and higher (Xh:
8.9 GHz). (∗∗)K-band is split into lower (Kl: 21.8 GHz) and higher
(Kh: 24 GHz).
U bands; 68 min at K band and; 89 min at Q band. In BW086,
more time was spent on CTA 102 and the total integration times
on 3C 454.3 were 36 min at C, X, and U bands; 40 min at
K band; and 54 min at Q band. The recording was made with
dual circular polarization, 4 × 8 MHz sub-bands (IFs) per polar-
ization, and two-bit digitization, which gave a total recording
rate of 256 Mbps. Standard frequency set-ups for continuum
observations were used, except for the X band, which had the
sub-bands spread across the 500 MHz filter in order to facili-
tate a Faraday rotation measurement. The BS157 and BW086
programmes also included observations at 86 GHz, but since the
data quality at this band is highly variable due to tropospheric
phase fluctuations and antenna pointing issues, and since 86 GHz
was not observed in S2087, we do not include these data in the
current analysis.
In the programme S2087, 8 h observing sessions were used
with BL Lac scheduled as a calibrator. The total integration times
on 3C 454.3 ranged from 45 min at C and X bands to 82 min at
Q band. The recording set-up was again dual circular polariza-
tion, 4 × 8 MHz sub-bands per polarization, and two-bit digiti-
zation. The K-band centre frequency was moved to 23.8 GHz,
away from the waterline, in order to improve the continuum sen-
sitivity. Data from all three programmes were correlated at the
VLBA correlator in Socorro.
Parts of the data from these three programmes have been
published earlier: Zamaninasab et al. (2013) presented multi-
frequency VLBA polarimetry analysis of 3C 454.3 based obser-
vations made on 2005 May 19 and 2009 September 22, and
Fromm et al. (2013a,b, 2015) analysed the kinematics, spectra,
and core-shift properties of the calibrator CTA 102 based on the
data taken between 2005 May 19 and 2007 April 26.
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2.1.2. Metsähovi Radio Observatory total flux density
monitoring
The 37 GHz observations were made with the 13.7 m diameter
Metsähovi radio telescope. A typical integration time to obtain
one flux density data point is between 1200 and 1400 s. The
detection limit of the telescope at 37 GHz is of the order of 0.2 Jy
under optimal conditions. Data points with a signal-to-noise ratio
<4 are handled as non-detections.
The flux density scale is set by observations of DR 21.
Sources NGC 7027, 3C 274 and 3C 84 are used as secondary cal-
ibrators. A detailed description of the data reduction and analysis
is given in Teräsranta et al. (1998). The error estimate in the flux
density includes the contribution from the measurement rms and
the uncertainty of the absolute calibration.
In our study period from 2005 to 2010, 3C 454.3 went
through multiple large outbursts which are clearly visible in the
37 GHz flux density curve shown in the top panel of Fig. 9.
These outbursts peaked in early 2006, mid-2008, and early 2010.
Furthermore, our VLBA observation epochs (indicated by red
arrows) coincide with the different phases of these flares. These
include the strong rising flare from 2005 May 19 to the short-
lived plateau of 2005 December 04, and the transition from a
quiescent phase from 2006 August 03 to the formation of the
moderate flare in 2008 January 03. The post-flare of 2008 coin-
cides with our VLBA data in 2008 December 07, and the rising
part of the major flare in 2009−2010 includes the epochs from
2009 September 22 to 2010 February 21.
2.2. Calibration and imaging of the VLBA data
We calibrated the VLBA data using standard methods imple-
mented in the Astronomical Image Processing System (AIPS)
software package (Greisen 2003). The procedure followed that
described in Lister et al. (2009) except that we typically did
not use pulse calibration tones to align the phases across the
IFs since the pulse calibration phases often showed unexpected
jumps that may be related to the frequent band changes in our
observing schedules. Instead, we performed fringe fitting of a
single scan of a bright source, either a calibrator or the target
itself, and used the results of the global solution to correct single-
band delays and align the phases across the IFs. We also always
carried out the full global fringe fitting of the whole observa-
tion solving for delays, rates, and phases with solution inter-
vals roughly set according to the expected coherence times at
the individual bands. Atmospheric opacity correction of the a
priori visibility amplitudes was performed for the data taken at
U, K and Q bands. We note that the MOJAVE team calibrated
and imaged a significant fraction of our U-band observations
as a part of their effort to image archival VLBA data in order
to increase the temporal sampling of the MOJAVE programme
sources (Lister et al. 2018). If already processed U-band data
was available from the MOJAVE archive3, it was used instead
of re-doing the calibration.
Imaging (using the standard CLEAN algorithm) and self-
calibration (of both amplitudes and phases) of the VLBA data
sets were performed with the DIFMAP package (Shepherd 1997).
After an initial round of imaging and self-calibration, any sig-
nificant antenna-based gain errors were identified and a sin-
gle correction factor per antenna per experiment was applied
in AIPS, if necessary. Then a new round of imaging and self-
calibration was performed in DIFMAP, this time normalizing the
3 https://www.cv.nrao.edu/MOJAVE/
amplitude self-calibration solutions to unity in order to pre-
vent the flux scale from wandering. The resulting amplitude
calibration accuracy is estimated to be generally ∼5% at C,
X, and U bands and .10% at K and Q bands in accordance
with previous studies (Savolainen et al. 2008a; Sokolovsky et al.
2011; Lister et al. 2018). We used multiple visibility weighting
schemes in imaging, going from super-uniform to uniform and
finally to natural weighting as the model improved. The final
set of CLEAN images was produced with natural weighting;
an example of a set of multi-frequency images at one epoch is
shown in Fig. 1. The images for all the epochs are presented
in Appendix E.
We note the presence of the arc-like structure ∼2 mas down-
stream of the core. This feature was previously reported by
Britzen et al. (2013) and Zamaninasab et al. (2013). The latter
authors modelled the structure as a shock wave and showed
that the structure exhibits a frequency-stratification in its thick-
ness that follows the expectation for a thin particle acceleration
layer, such as a shock wave, from which the accelerated electrons
are advected away, losing their energy to synchrotron radiation.
The arc is visible in our VLBA images mostly at 15 GHz and
22−24 GHz (until late 2009). At 43 GHz, a partial arc, where the
southern side is brighter than the northern one, is visible until
mid-2007.
We note here that we dropped epoch 5 (2006 August 03)
from further analysis because Mauna Kea, the antenna that gives
the longest baselines, did not take part in the observation (see
Table 1). However, the images are still presented in Appendix E.
The core-shift measurement for epoch 13 (2008 January 03)
is still presented but was dropped from the subsequent analy-
sis. There are several missing antennas at this epoch (Hancock,
St. Croix, Brewster partly), which results in a poor (u, v) cov-
erage and a degraded resolution such that the core cannot be
well resolved at the low frequencies. This leads to ambigui-
ties and a very large core-shift value that is unlikely to be real.
Epochs 4, 6, 11, and 18 also had one failed antenna (at least par-
tially) and epoch 12 had two failed antennas, but we kept these
data in the analysis since their core-shift measurements did not
indicate serious issues. However, one should keep in mind that
the (u, v) coverage is degraded at these epochs.
3. Data analysis
3.1. 2D cross-correlation of the images
In order to measure the core shift, it is necessary to first
align the images made at different frequencies. This is non-
trivial since the absolute source positions are lost in the phase
self-calibration procedure during imaging. 3C 454.3 exhibits
an extended parsec-scale jet structure at all the observed fre-
quencies (Fig. 1). The extended structure allows us to align
the images by matching the optically thin parts of the jets
that are assumed to have frequency-independent structures. We
do this by cross-correlating the optically thin jet regions in
the CLEAN images at adjacent frequencies. The 2D cross-
correlation technique has been widely used to align multi-
frequency VLBI images (e.g. Walker et al. 2000; Kovalev et al.
2008; Croke & Gabuzda 2008; O’Sullivan & Gabuzda 2009;
Hovatta et al. 2012; Pushkarev et al. 2012; Kutkin et al. 2014;
Kravchenko et al. 2016; PL19; Chamani et al. 2021).
In order to apply the image cross-correlation analysis, we
first created CLEAN images at the different frequency pairs with
a pixel size of 1/20 of the minor axis of the beam of the higher
frequency image. The pair of images were then convolved with
A130, page 4 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2005-07-14
Peak: 4.98 Jy/beam
Beam: 3.26 × 1.68 mas at -14.3 deg.
0
1
2
3
4
5
Jy/beam
(a)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2005-07-14
Peak: 3.64 Jy/beam
Beam: 2.48 × 1.07 mas at -16.4 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(b)
3 0 -3 -6 -9 -12
12
9
6
3
0
-3
-6
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 15.3 GHz, 2005-07-14
Peak: 2.87 Jy/beam
Beam: 1.25 × 0.59 mas at -18.7 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(c)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2005-07-14
Peak: 2.91 Jy/beam
Beam: 0.81 × 0.37 mas at -17.6 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(d)
1 0 -1 -2 -3 -4 -5 -6 -7
3
2
1
0
-1
-2
-3
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
1 mas
3C454.3 at 43.14 GHz, 2005-07-14
Peak: 6.45 Jy/beam
Beam: 0.43 × 0.19 mas at -16.7 deg.
7.70 pc
0
1
2
3
4
5
6
Jy/beam
(e)
Fig. 1. CLEAN images of 3C 454.3 on 2005 July 14 of the following frequency bands: (a) C, (b) X, (c) U, (d) K and (e) Q with contours at −0.1%,
0.1%, 0.2%, 0.4%, 0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image. The interferometric beam (ellipse) is
displayed in the bottom left corner of each image. The rms noise levels from the lowest to the highest frequency are 0.11, 0.20, 0.35, 0.30 and
0.38 mJy beam−1.
the same restoring beam size (as the lower frequency image).
Next, the image alignment was performed for adjacent pairs of
frequencies (i.e. CX, XU, UK, KQ) using a similar procedure to
that described in Pushkarev et al. (2012). Here, for example, the
CX notation means that the alignment of the C-band image was
done with respect to the X-band image. Finally, to obtain a statis-
tical average of the image shift with associated uncertainty, we
performed the alignments ten times per frequency pair, select-
ing slightly different optically thin features each time, similarly
to the analysis in Chamani et al. (2021). The procedure involved
five alignments with matched common (u, v) range images and
five full (u, v) range images. The resulting spectral index maps
have both the common and full (u, v) range of a frequency pair.
A common (u, v) range means that the lower limit of the (u, v)
distance for both images is the lower limit of the high frequency,
and the upper limit coincides with the upper limit of the low fre-
quency. Spectral index maps with a common (u, v) range should
be used in any analysis of the extended, optically thin emis-
sion since the missing short (u, v) spacings at the higher fre-
quency can result in artificial steepening of the spectrum of the
extended emission features. The common (u, v) range spectral
index images are displayed in Appendix F.
3.2. Visibility plane model fitting
In order to accurately measure the core position, we fitted sim-
ple models of the source structure directly to the visibilities.
We used the (fully self-) calibrated visibility data and model-
fitted the core with 2D Gaussian components consisting of cir-
cular components at each frequency. To model the core, we first
removed the CLEAN components from the nuclear region in the
jet (around the brightest pixel), leaving the extended emission
unchanged. In general, the area removed was one-beam size for
all frequencies; however, at the low frequencies (C, X bands) the
area had to be increased in order to obtain better Gaussian fits,
an approach similar to that performed by Homan et al. (2021).
The model fits were performed minimizing the reduced χ2 with a
Levenberg-Marquardt non-linear least-squares fitting algorithm
implemented in DIFMAP so that a value as close to one as possi-
ble was reached. Then we combined the core coordinates (from
the map centre) with the image shifts measured by 2D cross-
correlation to estimate the core-shift vectors by following the
method described in Pushkarev et al. (2012). We calculated, in
particular, the core-shift vectors for the adjacent frequency pairs:
CX, XU, UK, and KQ.
A typical VLBI image often has the brightest feature at the
upstream end of the jet. This structure is usually assumed to
be the core of the jet; however, in 3C 454.3, at some epochs,
the core region requires several components, reflecting a com-
plex nuclear structure in this source. The emergence of such
features was already found at 2.8 cm (10.7 GHz) in the 1980s
by Pauliny-Toth et al. (1987). Their study suggests that the
additional features near the core may be stationary shocks.
Another alternative includes the possibility of blending the
core with the jet (e.g. Kovalev et al. 2008; Sokolovsky et al.
2011; Algaba et al. 2019). Hence, the presence of several fea-
tures can lead to the misidentification of the true core, and the
identification of the core (i.e. τ = 1 surface) is non-trivial. This
A130, page 5 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
1
0
Re
la
tiv
e 
De
c 
(m
as
)
Peak: 2.19 Jy/beam
Beam: 0.5 × 0.5 mas at 0 deg.
0.0
0.5
1.0
1.5
2.0
Jy/beam
Ca Cb
0
Relative R.A. (mas)
(a)
0 -1
1
Re
la
tiv
e 
De
c 
(m
as
)
0.0
0.5
1.0
1.5
Xa Xb
Relative R.A. (mas)
0
1
Beam: 0.5 × 0.5 mas at 0 deg. Jy/beam
Peak: 1.71 Jy/beam
(b)
Fig. 2. Super-resolved CLEAN images of 3C 454.3 on 2005 July 14 with contours at 0.1%, 0.2%, 0.4%, 0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%,
and 51.2% of the peak intensity at each image. The 2D Gaussian components in the core region are shown in cyan. (a) At the C band (5 GHz), the
features are labelled ‘Ca’ for the upstream feature and ‘Cb’ for the downstream feature or bright component. (b) Similarly, at X band (8.4 GHz),
the components are labelled ‘Xa’ and ‘Xb’.
1
10
1 10 100
Xb
Xa
Ca
Cb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
−0.4−0.3−0.2−0.100.10.20.30.4
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
−0.04
−0.02
0
0.02
0.04
−0.04−0.0200.020.04
(b)
Fig. 3. 2D-Gaussian components at low frequencies. (a) Radio spectrum (5 GHz to 43 GHz) of core and jet features in 3C 454.3 in 2005 July 14. The
flux densities of the upstream components are labelled ‘Ca’ and ‘Xa’ and the downstream components ‘Cb’ and ‘Xb’. (b) Core-shift vectors of each
frequency pair and average vector direction in a polar grid. The dotted lines are given at intervals of 30◦. In the bottom right corner is a zoomed-in
image of the core-shift vector pairs for the high-frequency pairs. All vectors consistently point in the large-scale jet direction towards the west (see
Fig. 1). The true cores are features Cb and Xb at theC and X bands, respectively, since they produce core-shift vectors whose direction is consistent
with the jet direction. Comparisons of the core-shift vectors produced by the other C and X component choices are displayed in Appendix B.
turned out to be an issue at the two lowest frequencies (5 and
8 GHz). An example of this is displayed in Fig. 2, where a mod-
erately bright emission feature is seen upstream of the brightest
emission at the C and X-bands. The two components in the core
region are labelled ‘Ca’ and ‘Cb’ at the C band and ‘Xa’ and
‘Xb’ at the X band. The flux of each component is labelled in
the core spectrum displayed in Fig. 3a.
In order to correctly identify the core at each frequency,
we calculate the CX and XU core-shift vectors by taking the
following combinations: Ca/Xa, Ca/Xb, Cb/Xa, and Cb/Xb. In
many cases it is expected that only one of the combinations will
lead to both the CX and XU core-shift vectors pointing in the
expected jet direction (towards the west) and resulting in a sin-
gle power-law frequency dependence. For example, we found
that the unique combination Cb-Xb leads to correct CX and XU
core-shift directions in the 2005 July 14 epoch, as shown in
Fig. 3b. The other combinations produce CX and/or XU core-
shift vectors that do not align with the jet direction. These com-
binations are displayed in Appendix B. The correct combination
is also verified by the resulting power-law fits. A fit is consid-
ered acceptable as long as the core shifts are not too large to
look unrealistic (which can be driven by the wrong choice of the
core at the low frequencies). Hence, this approach allows us to
identify the most likely core component in each image.
Since the core identification plays a crucial role in accurate
core-shift measurements and consequently the estimation of the
core-shift index kr, we employed the criteria described above as
a sanity check for the observing epochs where the core identifi-
cation at the low frequencies is unclear; these epochs are speci-
fied in Table A. The model fitting of the core for the U, K and
Q bands, in general works well with one single circular Gaus-
sian. However, an emerging new component was identified at
the Q band in our data sets in 2009 and 2010. The ejection of
a new emission feature is possibly related to the strong flar-
ing event in 2009. Although we do not aim to study the jet
kinematics of 3C 454.3 in this paper, we discuss this specific
A130, page 6 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
0.05 0.00 -0.05 -0.10
0.10
0.05
0.00
-0.05
Relative R.A. (mas)
Re
lat
ive
 D
ec
 (m
as
)
Peak: 6.03 Jy/beam
Beam: 0.05 × 0.05 mas at 0 deg.
0
1
2
3
4
5
6
Jy/beam
-0.10
Qa Qb
0.10
September 22, 2009
(a)
0.10 0.05 0.00 -0.05 -0.10
0.10
0.05
0.00
-0.05
-0.10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
Peak: 8.38 Jy/beam
Beam: 0.05 × 0.05 mas at 0 deg.
0
1
2
3
4
5
6
7
8
Jy/beam
Qa
Qb
October 22, 2009
(b)
0.05 0.00 -0.05 -0.10
0.00
-0.10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
Peak: 11.2 Jy/beam
Beam: 0.05 × 0.05 mas at 0 deg.
0
2
4
6
8
10
Jy/beam
-0.05
0.05
0.10
0.10
Qa
Qb
December 3, 2009
(c)
0.10 0.05 0.00 -0.05 -0.10
0.10
0.05
0.00
-0.05
-0.10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
Peak: 9.88 Jy/beam
Beam: 0.05 × 0.05 mas at 0 deg.
0
2
4
6
8
Jy/beam
Qa
Qb
January 18, 2010
(d)
0.00 -0.05 -0.10 -0.15 -0.20
0.15
0.10
0.05
0.00
-0.05
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
Peak: 6.4 Jy/beam
Beam: 0.05 × 0.05 mas at 0 deg.
0
1
2
3
4
5
6
Jy/beam
-0.15
0.10 0.05
-0.10
Qa
Qb
February 21, 2010
(e)
Fig. 4. Super-resolved images of 3C 454.3 at 43 GHz for five different epochs from 2009 to 2010. The contours are given at 0.1%, 0.2%, 0.4%,
0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image. Each map uses a circular convolving beam of 0.05 mas
and the components are displayed in cyan. The restoring beam (circular) is displayed in the bottom left corner of each image. The rms noise level
is in (a) 1.1, (b) 2.4, (c) 4.1, (d) 7.7, and (e) 2.9 mJy beam−1. The core labelled ‘Qa’ and ‘Qb’ denotes a bright, recently ejected component that is
moving downstream.
ejection in the following section, since it significantly affects the
core-shift measurements.
3.3. Ejection of a moving feature downstream at 43 GHz in
the period 2009−2010
In 2009−2010 the nuclear region at 43 GHz was modelled first
with one circular Gaussian; however, the fit became better and
more stable with two circular components, which indicated that
an emission feature had been ejected from the core. Figure 4
shows the two resolved, bright components (in cyan). The core
is labelled ‘Qa’ and the moving feature downstream ‘Qb’. The
feature follows an east−west trajectory. The flux density curves
of each component are shown in Fig. 5. Since the core and the
moving feature are so close to each other they can ‘swap flux’
in model fitting. This means that the flux ratio of the two com-
ponents is uncertain, and the formal flux uncertainties of the fit
(shown in Fig. 5) likely underestimate the errors. Finally, we note
that the moving feature tracked from September 2009 to Febru-
ary 2010 may be cross-identified by the knot K09 in Jorstad et al.
(2013).
Figure 6 displays the feature separation from the core as a
function of time. The errors of the core separation are small
since both components are very bright. The uncertainties in the
component position were derived from Gaussian model fitting
by moving the component by small amounts around the best-fit
position, fixing the component position, and finding the set of
remaining parameters that minimize the χ2. The errors are found
1
10
2009.7 2009.8 2009.9 2010 2010.1 2010.2
S
4
3
G
H
z
(J
y
)
Time (years)
core
moving feature
Fig. 5. Flux density at 43 GHz of the core and the moving feature down-
stream as a function of time. The error bars include the uncertainty in
the flux scale which is ∼10%.
by requiring ∆χ2 = χ2 − χ2min < Cαp , where χ2min is the minimum
χ2 corresponding to the best-fit model andCαp is the critical value
of χ2 distribution for p degrees of freedom and a significance
level α (we use α = 0.32 corresponding to 1σ errors; for details,
see Chamani et al. 2021).
A130, page 7 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
150 200 250 300 350 400 450
S
ep
ar
at
io
n
fr
om
th
e
co
re
(m
as
)
Time (days)
Fig. 6. Separation of the moving feature (see Fig. 4) from the core
as a function of time at 43 GHz. The first day is counted from
2009 January 01. The black circles indicate the observations on 2009
September 22, 2009 October 22, 2009 December 03, 2010 January 18,
and 2010 February 21. The red and blue curves indicate linear and accel-
erating fitting functions, respectively.
A linear function was fitted to the data to follow the tra-
jectory of the moving feature. The fitting model gives d =
−(0.06±0.02)+(3±0.5)×10−4 t, where d is the separation (mas)
from the core and t the time (days from 2009 January 01). Hence,
the feature has a proper motion of (0.11 ± 0.02) mas yr−1 corre-
sponding to an apparent superluminal speed of βapp = 5.0 ± 1.0.
The new feature’s extrapolated ejection time (T0) is 179±66 days
corresponding to 2009 June 28, or equivalently to 2009.49±0.18.
On the other hand, fitting an accelerating model gives d =
(0.17 ± 0.08) − (1 ± 0.5) × 10−3 t + (2 ± 0.7) × 10−6 t2, where the
acceleration of the feature is (0.26±0.09) mas yr−2. We note that
in Jorstad et al. (2013), the new component K09 is tracked only
from January 2010 on, and it moves at (0.21 ± 0.02) mas yr−1,
corresponding to βapp = 9.6 ± 0.6 and T0 = 2009.86 ± 0.05
(using 24 epochs). In their study, they estimated two accelera-
tion components both along and perpendicular to the jet given
by (0.10 ± 0.01) and (0.13 ± 0.02) mas yr−2, respectively. Addi-
tionally, the flux density of the moving feature in early 2010
is comparable to the flux density of K09 shown in Fig. 13
in Jorstad et al. (2013). The separation from the core is below
0.1 mas and is similar to our observed values. Hence, we con-
clude that K09 is likely the same feature we detected in late 2009
and early 2010. If this is the case, the moving feature has expe-
rienced acceleration, which can explain the factor of two differ-
ence in the average speeds.
4. Results
In previous sections we described our method to identify the
core and the estimations of the core shifts for adjacent frequency
pairs. Here we present and analyse the resulting core shifts.
4.1. Core-shift measurements and variability
We list in Table A.1 the core-shift vectors with components in
right ascension (RA) and declination (Dec), as well as the core-
shift absolute values and projected absolute values. The pro-
jected absolute values were obtained by projecting the core-
shift vectors onto the average vector direction, as described in
Sect. 4.1 in Chamani et al. (2021). This is done to diminish the
effect of random errors on core-shift vector directions, and it is
implicitly assumed that the jet is straight at any given epoch. The
total positional uncertainties of the core shifts (for both coordi-
nates) are estimated as
∆θtotal,core−shift =
√
∆θ22DCC + ∆θ
2
core−position , (1)
where ∆θ2DCC is the error obtained from the 2D image cross-
correlation analysis, and ∆θcore−position is the error of the core
position obtained from the 2D Gaussian model fitting. For the
latter we employed the same method as used by Chamani et al.
(2021), and also described in Sect. 3.3.
By following the method and notation for the core identifi-
cation described in the previous section (see Figs. 2 and 3), we
present in Appendix D the core spectrum, the core-shift vectors,
and the core-shift power-law fit for each epoch. Using the abso-
lute (projected) core shifts in Appendix A we fitted the data with
power-law curves using 43 GHz as the reference frequency,
∆r = a (ν−1/krGHz − 43−1/kr ), (2)
where ∆r represents the core shift in mas, ν is the observing
frequency, a is a fitting parameter, and kr is the core-shift power-
law index. The fitting parameters are summarized in Table 2.
We found, in general, that all core-shift vectors point towards
the west−north−west direction, which agrees well with the jet
direction downstream of the 3C 454.3 jet. Changes in the direc-
tion towards the south-west are seen in some core-shift vectors,
for instance in Figs. D.1, D.13–D.18. Major flaring events were
registered for instance in May 2005 and from late 2009 to early
2010, which might have affected the direction of some core-shift
vectors.
We note that the core shift at the U band is off the fit-
ting curve in the observation on 2008 December 07; thus, we
dropped 15 GHz from the fit at this epoch. The data set with-
out the U-band data point yields a better fit at this epoch (see
Fig. D.13). A similar case is seen in the observation on 2009
September 22 (see Fig. D.14). Furthermore, the outburst start-
ing in late 2009 appears to affect the core-shift measurements
of the last five epochs. In these observations, the core-shift vec-
tors changed the direction significantly towards the south−west,
and the functional form of the core shift changed significantly
with kr, increasing to values above one, and the typical core-
shift behaviour became distorted in some cases. This effect is
evident on 2009 December 03, where the core-shift for the
K band increased by a factor of two from the previous epoch.
As a consequence, the fit became poor, deviating greatly from a
power law (see Fig. D.16c). Hence, we did not include this epoch
for the further analysis described in the next subsections. Even
though the core shifts are not greatly distorted on 2010 January
18 and 2010 February 21, the uncertainties are large and the fits
exhibit considerable deviations from kr = 1 (see Figs. D.17d
and D.18d).
We plot the core-shift variability in Fig. 7. The plots show
the absolute values of the XU and CQ core shifts as a function
of time. For comparison, we included the XU core-shift values
measured by Pushkarev et al. (2012). Their values lie well within
the range of our measurements between 0.05 mas and 0.34 mas.
The mean XU core shift is 0.14± 0.02 mas with a standard devi-
ation, σ, of 0.09 mas. In order to test whether the XU core shift
is variable given the measurement uncertainties, we set up a null
hypothesis stating that the core shift does not vary and remains
A130, page 8 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Table 2. Core-shift power-law fit parameters.
Epoch Date kr a
1 2005-05-19 0.70± 0.10 2.6± 1.1
2 2005-07-14 0.45± 0.05 29.4± 12.5
3 2005-09-01 0.52± 0.07 19.6± 9.2
4 2005-12-04 0.70± 0.10 7.2± 2.7
6 2006-10-02 1.0± 0.3 1.7± 0.8
7 2006-12-04 0.67± 0.07 4.4± 1.3
8 2007-01-26 0.65± 0.06 3.8± 1.1
9 2007-04-26 0.80± 0.10 2.8± 1.0
10 2007-06-16 0.60± 0.10 5.9± 2.5
11 2007-07-25 0.69± 0.05 4.5± 0.8
12 2007-09-13 0.90± 0.10 4.2± 0.8
14 2008-12-07 1.4± 0.4 (a) 1.7± 0.6
2008-12-07 1.1± 0.1 (b) 2.3± 0.4
15 2009-09-22 1.1± 0.6 (c) 1.7± 1.2
2009-09-22 0.8± 0.3 (d) 2.4± 1.7
16 2009-10-22 1.1± 0.3 3.4± 1.4
17 2009-12-03 (†) – –
18 2010-01-18 1.7± 0.7 1.6± 0.5
19 2010-02-21 1.3± 0.3 1.7± 0.5
Notes. kr is the core-shift index, a is a fitting parameter. Rounded values
are given here. The 13th observing epoch (2008-01-03) was dropped
from the analysis. (a)Using all frequency bands, see D.13c. (b)Without
the U band, see Fig. D.13e. (c)Using all frequency bands, see D.14e.
(d)Without the U band, see Fig. D.14f. (†)No good power-law fit, see
Fig. D.16d.
stable around the mean value and calculated the χ2 statistic,
χ2 =
N∑
i
(
∆r(ν1ν2)i − ∆rν1ν2
)2
σ′i
2 , (3)
where ∆r(ν1ν2)i represents the core shift of the ith observation
between two frequencies, ν1 and ν2 (ν2 > ν1); σ′i is the core-shift
error; ∆rν1ν2 is the mean core shift; and N(= 17) is the number of
observations. At the 99.9% confidence level for N −1 degrees of
freedom (d.o.f.), χ2critical = 39.25 is the critical value for reject-
ing the null hypothesis. For XU core shift (∆rXU), χ2 results in
312.5, which is above the critical value, confirming that the XU
core shift significantly varies with time.
A similar analysis was also performed for the CQ core shifts
(∆rCQ; see Fig. 7b) where the mean value is 0.49±0.05 mas with
a standard deviation of 0.18 mas. The core shifts vary between
0.27 mas and 0.86 mas. There is one extreme core-shift value,
1.64 ± 0.04 mas, on 2008 January 03. Since this observation
misses both St. Croix and Hancock for the whole observation, as
well as Brewster for half of the observation, the resulting poor
(u, v) coverage makes this result suspect, and we drop it from our
analysis and from Fig. 7. The χ2 test for the CQ core shift gives
279.02 (for N = 17), above the critical level. Thus, the CQ core
shift also shows significant variability. Overall, the variability
curves of both the XU and CQ core shifts exhibit similar trends,
although there is no one-to-one correspondence.
Additionally, we studied the mean core-shift direction vari-
ability, which represents approximately the overall inner jet
direction (PA) in the core region. The mean jet PA was mea-
sured by averaging the direction of the core-shift vectors of all
frequency pairs. The PA variability plot is presented in Fig. 8.
For the study period, the mean jet PA is −80◦ ± 3◦, σ ∼ 10.8,
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
2005 2006 2007 2008 2009 2010
A
b
so
lu
te
X
U
co
re
-s
h
if
t
(m
as
)
Time (years)
Pushkarev+2012
(a)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
2005 2006 2007 2008 2009 2010
A
b
so
lu
te
C
Q
co
re
-s
h
if
t
(m
as
)
Time (years)
(b)
Fig. 7. Variability of the core shift in 3C 454.3. (a) Core shift between
the X (8 GHz) and U (15 GHz) bands vs. time. The purple triangles rep-
resent the core shifts derived by Pushkarev et al. (2012). (b) Core shift
between the C (5 GHz) and Q (43 GHz) bands vs. time. In both panels
the mean value is represented by the blue line and ±σ is displayed by
the shaded cyan background. The epoch 2008 January 03, which had
three missing antennas, was dropped from this plot as an outlier with a
CQ core shift of 1.64 ± 0.04 mas. Zero core shift physically means that
the cores at two frequencies coincide at the same location.
χ2 = 13.66 (for N = 17). The last is below the critical value
(χ2critical = 39.25) indicating no significant jet PA variability. That
means that even if there is significant core-shift variability, the
jet vector direction stayed relatively stable in our study period.
While the changes in jet PA are not statistically significant, it is
interesting to note an increasing trend in the PA from mid-2005
to early 2006, corresponding to a major millimetre wavelength
flare, and then more or less stable PA from late 2006 to late 2007.
Possibly related to the strong outburst, PA decreased to lower
values from late 2009 to early 2010.
4.2. Variability of the core-shift index kr
Core-shift indices kr are listed in Table 2, and the variability
plot of kr is displayed in the bottom panel of Fig. 9. For com-
parison, we included the result obtained by Kutkin et al. (2014)
for a single observation. We find that kr varies in the range
0.45 < kr < 1.7, with an average value of 0.85 ± 0.08 and
A130, page 9 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
−120
−110
−100
−90
−80
−70
−60
−50
−40
2005 2006 2007 2008 2009 2010
P
A
(d
eg
re
es
)
Epoch
Fig. 8. Time variability of the jet position angle (PA) from the model fit-
ting to the core. The PA values (black open circles) represent the average
PA per epoch using all core-shift vectors per frequency pair (CX, XU,
UK, KQ). The blue line is the mean PA for the whole data set. The area
in light cyan represents ±1σ.
with a standard deviation σ = 0.30. We note that we dropped
the observation on 2009 December 03 since the fitting result
gives an unreasonably large kr value that is due to the ongoing
flare significantly increasing the KQ core-shift value, while the
lower frequencies are not affected (see Fig. D.16d). It is impor-
tant to point out that kr indices in the period of 2009 to 2010 have
large uncertainties due to the strong flare affecting the core-shift
measurements (see Figs. D.14–D.18). It appears that the flare
increases the distance between the 24 and 43 GHz cores. This
may be due to several reasons, including increased particle den-
sity and/or magnetic field strength due to the flare that increases
the synchrotron opacity and moves the 24 GHz core downstream.
It is also possible that the blending of the newly ejected compo-
nent with the core at 24 GHz drags the apparent core position
downstream. In any case, the power-law dependences measured
during this period are disrupted by the flare and the measured kr
values are affected.
Similarly to the variability test of the core shift, we set up
a null hypothesis that kr = 1 and does not vary over time. We
also included in the analysis the result from (Kutkin et al. 2014).
The chi-square test resulted in χ2 = 146.50, which is above
the critical value (for N = 17). If we exclude the epochs from
2009 to 2010, the mean of kr is 0.74 ± 0.05 with σ = 0.18, and
χ2 = 67.16, which is still above the corresponding critical value
of χ2critical = 32.91 (12 d.o.f.). Hence we reject the null hypothesis
and conclude that kr is indeed also a variable parameter. These
results could indicate that the jet in 3C 454.3 does not always
stay in equipartition or does not follow the classical Blandford
& Königl jet model. The last explanation also includes the pos-
sibility that the core is not strictly a τ = 1 surface at our highest
observing frequencies during the strong flares.
The variability plot of kr is displayed in the bottom panel of
Fig. 9; kr indices below 1 can occur either during flaring (2005
to 2006) or quiescent episodes (2007). These results indicate
that the jet in 3C 454.3 cannot be described with the ideal BK79
model with equipartition and conical jet assumptions even dur-
ing the quiescent period. On the other hand, kr values close to
one within the uncertainties are found in a quiescent state (late
2006 and late 2007), post-flare (December 2008), and during
flaring periods (late 2009 to early 2010).
0.5
1
1.5
2
2.5
2005 2006 2007 2008 2009 2010
In
d
ex
k
r
Time (years)
Conical jet
Kutkin+2014
0
5
10
15
20
25
30
35
40
F
lu
x
d
en
si
ty
(J
y
)
37 GHz
Fig. 9. Comparisons of the source activity and the core-shift index.
Top: Total flux density at 37 GHz for 3C 454.3 observed at the Met-
sähovi Radio Observatory. The red arrows show the time correspon-
dence with our VLBA observations. Bottom: Core-shift power-law kr
index vs. time. The measured kr values are represented as black open
circles. The purple square, 0.7 ± 0.1, represents the value obtained by
Kutkin et al. (2014). The observation epoch on 2009 December 03 is
not included. The blue dashed line shows the mean for the whole data
set. The area in cyan represents ±1σ. The red line represents the ideal
BK79 conical jet with kr = 1.
4.3. Core position
The core position or distance from the central engine, rcore, at
frequency ν is given by
rcore(νGHz) =
Ωrν
ν1/krGHz sin θ
[pc], (4)
where Ωrν is the core offset; θ is the source’s viewing angle,
which is a fixed constant parameter here (Lobanov 1998); Ωrν
is formulated as
Ωrν = 4.85 · 10−9 ∆rν1ν2 DL(1 + z)2
ν1/kr1 ν
1/kr
2
ν1/kr2 − ν1/kr1
[pc GHz1/kr ], (5)
where DL denotes the luminosity distance; ∆rν1 ν2 is the core shift
measured in mas at two frequencies, and z is the redshift.
To measure rcore at each frequency, we employed the mean
value of Ωrν per epoch given by (Ωr,CX + Ωr,XU + Ωr,UK+ Ωr,KQ +
Ωr,CQ +Ωr,XQ +Ωr,UQ)/7. The uncertainties of rcore were obtained
via error propagation of Eq. (5), and the details are presented
in Appendix C. We use rcore for a further analysis presented in
Sect. 4.5.
A130, page 10 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Table 3. Physical properties of 3C 454.3.
Name Parameter Value
Redshift (a) z 0.859
Luminosity distance (b) DL 5.49 Gpc
Doppler factor (c) δ 24.6 ± 4.5
Lorentz factor (c) Γ 15.6 ± 2.2
Viewing angle (c) θ 1.3◦ ± 1.2◦
Half-opening angle (c) θj 0.8◦ ± 0.2◦
Black hole mass (d) MBH 4.9 × 108 M
Accretion disc luminosity (d) Lacc 7.2 × 1046 erg s−1
Notes. (a)Observed by Sargent et al. (1988), Jackson & Browne (1991).
(b)Using the online calculator of Wright (2006). (c)Global jet param-
eters adopted from Jorstad et al. (2005). We assumed that parameters
remain constant during the period 2005–2010. (d)Values adopted from
Zamaninasab et al. (2014, with references therein).
4.4. Magnetic field parameters
The magnetic field at 1 pc from the jet apex, B1pc, can be
estimated from the measured core shift as long as the energy
equipartition between the magnetic field and radiating parti-
cles at the radio core holds (Lobanov 1998; Hirotani 2005).
The expression for B1pc used in several previous works (e.g.
Hirotani 2005; O’Sullivan & Gabuzda 2009; Zamaninasab et al.
2014) misses one (1 + z) term, as shown by Zdziarski et al.
(2015). We take into account this factor and use the corrected
version,
B1pc ≈ 0.025
σrel Ω3krrν (1 + z)3
δ2 θj sin3kr−1θ
 14 [G], (6)
where σrel is the ratio of magnetic to particle energy densities
and is taken as unity, δ is the Doppler factor, and θj is the jet’s
half opening angle. The physical properties of 3C 454.3 rele-
vant for the magnetic field parameter estimations are summa-
rized in Table 3. We adopted from Jorstad et al. (2005) the aver-
age values for δ, Γ, and θ. We note that Jorstad et al. (2010, 2013)
obtained δ, Γ, and θ for several ejected components named K1,
K2, K3, K09, and K10. Jorstad et al. (2010) shows that K1, K2,
and K3 were ejected in 2005.5, 2007.49, and 2007.93, respec-
tively. Component K09 (described in Sect. 3.3) was ejected in
mid-2009, and K10 appeared to be ejected at the end of 2010
according to Jorstad et al. (2013). Components K1, K2, and K09
have measured δ, Γ, and θ values, which are similar and in good
agreement with the parameter values measured by Jorstad et al.
(2005). Since these appear to be relatively stable at least for our
period of study, we kept them as constants. Component K3 has a
significantly higher Lorentz factor and a smaller viewing angle,
and consequently significantly higher δ. However, we consider
K3 here as a likely outlier since it faded away much closer to
the core (<0.2 mas; Jorstad et al. 2013) compared to the other
components.
To estimate B1pc, we employ the CQ core shift per epoch
together with the kr measurements. The uncertainties on B1pc are
evaluated by error-propagating Eq. (6) and taking into account
the uncertainties on δ, θ, and θj (see Appendix C). The B1pc
values as a function of time are shown in Fig. 10. The results
show an evident discrepancy in B1pc, meaning that there is up
to an order of magnitude difference in B1pc between kr = 1 and
kr , 1. Furthermore, B1pc varies more than two orders of mag-
nitude when kr , 1. These results suggest that reliable B1pc esti-
0.1
1
10
100
2005 2006 2007 2008 2009 2010
B
1
p
c
(G
)
Time (years)
kr=1
kr 6=1
Fig. 10. Magnetic field B1pc at one parsec by employing the CQ core
shift pair. We use here the (projected) core shift absolute values. The
blue open circles represent the results assuming kr = 1. The black open
circles represent the results using measured kr values.
Table 4. B1pc values using kr = 1.
Epoch B1pc(G)
2006-10-02 1.3 ± 0.6
2007-09-13 2.0 ± 0.9
2008-12-07 1.5 ± 0.7
2009-10-22 2.0 ± 0.9
Notes. The epochs selected have measured kr indices near one.
mations can be obtained only as long as kr = 1, which is under-
standable remembering the assumptions underlying Eq. (6) (i.e.
an ideal Blandford & Königl conical jet and equipartition). If we
cannot reasonably assume that these hold, then the resulting B1pc
values are suspect.
We assume the B1pc estimations to be more reliable when
our measured kr indices are near one and consistent within the
error bars. From our results shown in Fig. 10, only four obser-
vations satisfy this condition. Thus, using kr = 1, the magnetic
fields for the four epochs are displayed in Table 4. In this table,
the weighted mean B1pc is (1.5 ± 0.4) G, which is comparable
with the value of 1.1 G obtained by Pushkarev et al. (2012). We
note that Hu et al. (2021) made recent estimations of the mag-
netic field in 3C 454.3 based on the spectral fitting of six SEDs
with a one-zone leptonic jet model concentrated around the time
of the strong gamma-ray flares in 2009. For the two epochs, they
can constrain the distance of the emission region from the cen-
tral engine. They obtain 0.7−1.0 G at the distance of 0.3−0.4 pc,
which means that their inferred magnetic field strength is smaller
by a factor of about five compared to what is expected based on
our results if the magnetic field strength scales as r−1.
We further use the observations listed in Table 4 to esti-
mate the jet’s magnetic flux in 3C 454.3. We examined whether
the magnetic flux value is consistent with the source having
developed a magnetically arrested disc (MAD). We adopted
the formula for jet magnetic flux derived by Zdziarski et al.
(2015), who considered the observed condition of Γθj ∼ 0.1
and Γθ , 1 for blazars and radio galaxies, respectively, instead
of Γθj = 1 assumed in the original Zamaninasab et al. (2014)
paper. The updated formula for the magnetic flux used by
A130, page 11 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1030
1031
1032
1033
1034
1035
1027 1028 1029 1030 1031 1032 1033 1034
M
A
D
pr
ed
ic
ti
on
M87
Φ
je
t
[G
cm
2 ]
L1/2acc M [erg
1/2 s−1/2 M]
3C454.3
1032.8
1033
1033.2
1033.4
1033.6
1033.8
1034
1034.2
1034.4
1034.6
1032.05 1032.1 1032.15 1032.2
Fig. 11. Measured Φjet vs. L1/2acc M for radio galaxies (open circles)
and blazars (filled circles) shown in green. The plot is adapted
from Zamaninasab et al. (2014), and it uses the corrections from
Zdziarski et al. (2015; see also Chamani et al. 2021). The blazar
3C 454.3 is marked with the green diamond. The plot on the right zooms
in on the values only for 3C 454.3 for four epochs. The light blue dia-
monds represent the Φjet values using B1pc with measured CQ core shifts
and with kr = 1. If 3C 454.3 harbours a maximally rotating (a = 1) black
hole, then the source appears to remain near the magnetically arrested
disc state in the four observing epochs.
Chamani et al. (2021) is
Φjet = 8 × 1033 f (a) [1 + σ]1/2
[
MBH
109 M
] [
B1pc
G
]
[G cm2], (7)
with a the black hole (BH) spin and f (a) = 1+(1−a
2)1/2
a . Assum-
ing that 3C 454.3 hosts a fast spinning BH (a = 1), f (a) = 1.
Setting the jet magnetization parameter as σ = (Γ θj )
2, the Φjet
values are readily obtained. We compare the measured Φjet val-
ues with the predicted magnetic flux threading the BH, ΦBH, at
the magnetically arrested disc (MAD) state,
ΦBH = 2.4 × 1034
[
η
0.4
]−1/2 [ MBH
109 M
] [
Lacc
1.26 × 1047 erg s−1
]1/2
(8)
given in units of G cm2 (e.g. Tchekhovskoy et al. 2011;
Zamaninasab et al. 2014). The parameters η and Lacc respec-
tively indicate the radiative efficiency of the accretion disc and
the accretion disc luminosity.
Figure 11 displays the Φjet values for 3C 454.3 for the four
epochs that have kr = 1. The plot of the jet’s magnetic flux as a
function of the accretion luminosity and BH mass was adapted
from Zamaninasab et al. (2014) (who assumed Γθj = 1). We
used the corrections given for radio galaxies (Γθj , 1) and
blazars (Γθj = 0.13) presented in Chamani et al. (2021). Our
result appears to be very close to the predicted MAD limit, even
closer than the measurement given in Zamaninasab et al. (2014).
4.5. Light curves and correlation analysis
The long-term light curve of 3C 454.3 at 37 GHz obtained from
the Metsähovi Radio Observatory is displayed in Fig. 9. In this
period, three remarkable flux density peaks were observed, and
they are linked to major gamma-ray flare events such as the one
observed on 2009 December 02 (Pacciani et al. 2010).
0
1
2
3
4
5
6
C
or
e
fl
u
x
d
en
si
ty
,
S
co
re
(J
y
)
5 GHz
0
1
2
3
4
5
6
7
8 GHz
0
2
4
6
8
10
12
14
16
15 GHz
0
5
10
15
20 22-24 GHz
0
5
10
15
20
25
2005 2006 2007 2008 2009 2010
Time (years)
43 GHz
Fig. 12. VLBA core flux density of 3C 454.3 at 5, 8, 15, 22−24, and
43 GHz estimated from Gaussian model fitting (see Sect. 3.2). The error
bars include the uncertainty on the flux scale, which is 10%.
The core flux density at each frequency as a function of time
is shown in Fig. 12. At 43 GHz the core flux density from 2009
to 2010 corresponds to the sum of flux densities of the compo-
nents Qa and Qb. Due to opacity effects, the 2009 flare starts at
43 GHz and then progresses to lower frequencies; no flux density
increase is seen at 5 GHz yet. The first three VLBA observations
in 2005 at 22 and 43 GHz bands coincide well with the rising
side of the flux at 37 GHz, whereas our last observing epoch
in 2005 coincides with the short-lived plateau at 37 GHz. All
multi-frequency core flux density observations from mid-2006 to
mid-2007 coincide with the low state at 37 GHz. After that, the
core flux density increases moderately until January 2008. The
last observation in December 2008 coincides with the declin-
ing or post-flare phase at 37 GHz. Finally, the last five observa-
tions at the 8, 15, 24, and 43 GHz bands from September 2009
to February 2010 coincide with the sudden increase in flux den-
sity at 37 GHz. The peak in the 43 GHz core flux density closely
matches the 37 GHz peak in January 2010.
To understand the influence of flares on the core shift effect,
we explored the possible dependence of the core shift (between
a pair of frequencies), ∆rν1ν2 , the core position, rcore, with the
core flux density, S core, and with the total flux density, SMRO, at
37 GHz. We calculated Spearman’s rank correlation coefficient
(ρ) and the p-value in R; p-values below 0.05 are taken as possi-
ble correlations and those below 0.01 as correlations (all shown
in boldface in Table 5). We also include Pearson’s correlation
coefficient to evaluate the strength of the possible linear correla-
tions. For the core shift versus core flux density correlations, we
used a generic fitting function of the form ∆rν1ν2 ∝ S tcore, where
t is the power-law index.
In Figs. 13–17 we present scatter-plots of ∆rν1ν2 – S core at
each frequency. The scatter-plots are given for the following
relationships: ∆rCX – S core at 5 GHz and 8 GHz, ∆rXU – S core
A130, page 12 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Table 5. Spearman’s rank and Pearson correlation coefficients.
Relations Spearman Pearson Fitting function
Correlation coefficient (ρ) p-value Correlation coefficient (r) Power-law
∆rCX – S core at 5 GHz 0.37 0.14
∆rCX – S core at 8 GHz 0.19 0.46
∆rXU – S core at 8 GHz −0.48 0.05 -0.46 (0.24 ± 0.06) S −0.7±0.3core
∆rXU – S core at 15 GHz −0.12 0.66
∆rUK – S core at 15 GHz 0.59 0.01 0.37 (0.05 ± 0.01) S 0.3±0.2core
∆rUK – S core at 22−24 GHz 0.60 0.01 0.40 (0.05 ± 0.01) S 0.3±0.2core
∆rKQ – S core at 22−24 GHz 0.77 0.0003 0.60 (0.02 ± 0.01) S 0.7±0.2core
∆rKQ – S core at 43 GHz 0.64 0.006 0.71 (0.010 ± 0.004) S 0.7±0.2core
∆rCQ – SMRO at 37 GHz 0.63 0.008 0.22 (0.3 ± 0.1) S 0.2±0.2core
∆rCQ – S core at 43 GHz 0.52 0.03 0.23 (0.35 ± 0.09) S 0.1±0.1core
rcore – S core at 5 GHz 0.40 0.12
rcore – S core at 8 GHz 0.61 0.02 (∗) 0.75 (58.3 ± 9.3) S 0.6±0.2core
rcore – S core at 15 GHz 0.84 0.0003 0.71 (19.3 ± 2.8) S 0.6±0.1core
rcore – S core at 22−24 GHz 0.74 0.001 0.77 (7.9 ± 1.7) S 0.8±0.2core
rcore – S core at 43 GHz 0.49 0.05 0.77 (2.1 ± 2.0) S 0.5±0.5core
kr – S core at 5 GHz 0.28 0.30
kr – S core at 8 GHz 0.67 0.006 0.80 (0.55 ± 0.05) S 0.5±0.1core
(0.5 ± 0.1)+(0.15 ± 0.03) S core
kr – S core at 15 GHz 0.44 0.12 0.74
kr – S core at 22−24 GHz 0.56 0.03 0.81 (0.48 ± 0.06) S 0.3±0.1core
(0.6 ± 0.1)+(0.04 ± 0.01) S core
kr – SMRO at 37 GHz 0.50 0.05 0.77 (0.39 ± 0.08) S 0.30±0.09core (†)
(0.5 ± 0.1)+(0.03 ± 0.01) S core
kr – S core at 43 GHz 0.52 0.04 0.76 (0.52 ± 0.09) S 0.21±0.09core (†)
(0.5 ± 0.1)+(0.04 ± 0.01) S core
PA – kr −0.42 0.11
Correlations with B1pc values assuming kr=1
BCQ,1pc – S core at 5 GHz 0.54 0.03 0.47
BCQ,1pc – S core at 8 GHz 0.29 0.26
BCQ,1pc– S core at 15 GHz 0.56 0.02 0.05
BCQ,1pc – S core at 22−24 GHz 0.61 0.01 0.12
BCQ,1pc – S core at 43 GHz 0.52 0.03 0.23
BCQ,1pc – SMRO at 37 GHz 0.63 0.008 0.24
Notes. Power-law fits are given only for the relations with p-values< 0.05. Additional linear fits are provided for the kr − S core relationship.
(∗)Excluding the data point of 37 pc. (†)The fits do not include the data at kr = 0.45 and kr = 0.52. These are taken as outliers in the scatter plots.
By including these points, the power-law fits become much less steep with indices: 0.05 ± 0.18 at 37 GHz and 0.04 ± 0.14 at 43 GHz.
at 8 GHz and 15 GHz, ∆rUK – S core at 15 GHz and 22−24 GHz,
and ∆rKQ – S core at 22−24 GHz and 43 GHz. With regard to
∆rCX – S core no correlations were found. A negative but weak
correlation was obtained for ∆rXU – S core at 8 GHz, but not at
15 GHz. Positive and moderate correlations were found for ∆rUK
– S core at 15 GHz and 22−24 GHz. A strong correlation was
found at the higher frequencies for ∆rKQ – S core at 22−24 GHz
with a power-law index t = 0.7 ± 0.2. A moderate correla-
tion at 43 GHz was also found, although the correlation is less
robust than at 22−24 GHz. Additionally, we searched for pos-
sible correlations of the full CQ core shift with the core flux at
43 GHz and at 37 GHz. The results suggest possible correlations,
although there is not a clear monotonic relationship between the
two variables, as seen in Fig. 17.
Figure 18 displays the scatter-plots of the core positions as
a function of the core flux at different frequencies, rcore–S core.
As is evident from the plots, there is no correlation between the
variables at 5 GHz, but there are moderate to strong positive cor-
relations at all the other frequencies. Taking only the strongest
correlations at 8, 15, and 22−24 GHz, the fitted power laws have
indices from 0.6 to 0.8 with an average of 0.7. This indicates that
the core position appears to follow approximately rcore ∝ S 2/3
0.1
1
1 10
∆
r C
X
(m
as
)
Score at 5 GHz (Jy)
1 10
Score at 8 GHz (Jy)
Fig. 13. CX core shifts vs core flux density at different frequencies. No
correlations are found with the core flux at 5 and 8 GHz.
as expected in the BK79 model if the flares are mainly due to
increased particle density (Lobanov 1998; Kovalev et al. 2008).
We discuss this in Sect. 5.1.
We also searched for correlations between the index kr and
the core flux density, kr – S core, at all the VLBA frequencies and
at 37 GHz, as shown in Fig. 19. A significant correlation was
A130, page 13 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
0.1
1
1 10
∆
r X
U
(m
as
)
Score at 8 GHz (Jy)
1 10
Score at 15 GHz (Jy)
Fig. 14. XU core shifts vs. core flux density at different frequencies.
A negative correlation with the core flux at 8 GHz is found, but not at
15 GHz. The green line indicates a power-law fit; see Table 5 for further
details.
0.01
0.1
1 10
∆
r U
K
(m
as
)
Score at 15 GHz (Jy)
1 10
Score at 22-24 GHz (Jy)
Fig. 15. UK core shifts vs. core flux density at different frequencies.
Positive correlations are found at 15 and 22−24 GHz. The green line
indicates a power-law fit; see Table 5 for further details.
0.01
0.1
1 10
∆
r K
Q
(m
as
)
Score at 22-24 GHz (Jy)
1 10
Score at 43 GHz (Jy)
Fig. 16. KQ core shifts vs. core flux density at different frequencies.
Positive correlations are found at 22−24 and 43 GHz. The green line
indicates a power-law fit; see Table 5 for further details.
found at 8 GHz. Possible correlations were found at 22−24, 37,
and 43 GHz. In all the cases, the fitted power-law indices are in
the range from 0.2 to 0.5 (see Table 5), and the Pearson correla-
tion coefficients are high; therefore, we also fitted the data with
a linear function. This interesting new finding may be driven by
the flaring behaviour, which is further discussed in Sect. 5.1.
In addition, correlations of index kr with jet PA have also
been investigated. The scatter plot is displayed in Fig. 20.
Although the scatter plot appears to show hints of a negative
trend for kr with the PA, there is no statistically significant cor-
relation. Furthermore, correlation studies of jet PA and flux den-
sity have also been considered. Still, we have not found evident
correlations for the PA – S core, PA – SMRO at 37 GHz and PA –
0.1
1
1 10
∆
r C
Q
(m
as
)
SMRO at 37 GHz (Jy)
1 10
Score at 43 GHz (Jy)
Fig. 17. Full CQ core shifts vs. MRO 37 GHz flux density and core
flux density at 43 GHz at different frequencies. Positive correlations are
found at both frequencies. The green line indicates a power-law fit; see
Table 5 for further details.
∆r relationships. In general, the data appears scattered and dis-
ordered. A monotonic function cannot describe the relations.
Finally, for curiosity, we searched for possible correlations
of B1pc with the core flux density and MRO 37 GHz flux density
assuming entirely kr = 1. The results show positive Spearman
correlation coefficients, although the data do not follow strong
monotonic relationships, as seen in the scatter plots of Fig. 21.
It is evident from these plots that the B1pc values are relatively
stable at all frequencies. Since we used kr = 1, and the same δ, θ,
and θ j at all the epochs, B1pc depends only on Ωrν, which in turn
depends on rcore. Hence, the B1pc − S core correlation is a direct
consequence of the rcore − S core correlation.
5. Discussion
5.1. Core shift and flares
In our search for correlations between core shift and core flux
density, we found that rcore depends approximately on S 0.7core. This
relationship closely matches the theoretical prediction by BK79
that the observed radius, rmax,ob, where the maximum brightness
temperature is achieved, scales with the synchrotron luminos-
ity, Ls, as rmax,ob ∝ L2/3s ∝ L0.7s and consequently has the same
dependence on flux density.
The connection between the core position and core flux den-
sity during jet flares has been previously investigated by PL19.
They use a phenomenological model of the form rcore = bS
KrS
core
and independent of any physical assumptions model the core-
shift variability at 2.3/8.4 GHz in a sample of 40 AGN. Using a
general time-dependent model, they determine KrS = 0.28±0.05
for the whole sample. Our results show a mean KrS = 0.7 for
rcore ∝ S KrScore, which differs significantly from the results in PL19.
On the other hand, our ∆r shows a weaker dependence on S core
with KrS = 0.3 ± 0.2 at 15 and 22−24 GHz and even a negative
KrS at 8 GHz (see Table 5). This discrepancy may be related to (i)
varying kr in our case, (ii) lower observing frequencies used in
PL19, or (iii) 3C 454.3 possibly having a behaviour that differs
significantly from a typical AGN.
As pointed out by PL19, and references therein, the phys-
ical mechanisms producing variations of core flux density can
be associated with variations in particle density, magnetic field
strength or bulk Doppler factor as S core ∝ Ncore B1−αcore δ3−α, where
α is the optically thin spectral index. Thus, flares and con-
sequently core position variations can be due to variations in
any of these parameters. PL19 list four basic scenarios for the
flares: (i) Flaring emission is in equipartition (i.e. Ncore ∝ B2core)
A130, page 14 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
100
101
102
103
1 10
r c
or
e
(p
c)
Score at 5 GHz (Jy)
1 10
Score at 8 GHz (Jy)
1 10
Score at 15 GHz (Jy)
1 10
Score at 22-24 GHz (Jy)
1 10
Score at 43 GHz (Jy)
Fig. 18. Core position vs. core flux density at different frequencies. Positive correlations are found at 8, 15, 22−24, 43 GHz. The green line indicates
a power-law fit; see Table 5 for further details.
0.1
1
1 10
In
d
ex
k
r
Score at 5 GHz (Jy)
1 10
Score at 8 GHz (Jy)
1 10
Score at 15 GHz (Jy)
0.1
1
1 10
In
d
ex
k
r
Score at 22-24 GHz (Jy)
1 10
SMRO at 37 GHz (Jy)
1 10
Score at 43 GHz (Jy)
Fig. 19. Core-shift index kr vs. flux density
at each frequency. No evident correlation is
found at 5 and 15 GHz. Positive and mod-
erate correlations were found at 8, 22−24,
37, and 43 GHz, respectively. Power-law fits
are shown with the green line, and linear
fits with a blue line. It appears that the kr
index increases modestly when the core flux
rises. All fitting parameters are displayed in
Table 5.
while δ is constant; (ii) Flares are mainly due to particle den-
sity variability; (iii) Flares are mainly due to variations in mag-
netic field strength; and (iv) Flares are due to variations in
the jet Doppler factor. The fact that kr , 1 in 3C 454.3 for
most of the observing epochs, also outside of the flaring peri-
ods, indicates that the source is unlikely to be in equiparti-
tion, making scenario (i) also unlikely. Scenario (ii) is perhaps
the simplest case matching our observed relationship rcore ∝
S 0.7core since it gives rcore ∝ N2/3core ∝ S 2/3core. Scenario (iii) can-
not be ruled out. Scenario (iv) appears unlikely since, consid-
ering that in blazars in general (Savolainen et al. 2002), and
in 3C 454.3 in particular (Jorstad et al. 2010, 2013) the flares
are connected to travelling disturbances in the VLBI jet, it is
likely that changes in the jet Doppler factor alone do not pro-
duce them. Furthermore, rcore ∝ Γ−4/3β−2/3δ2/3 sin−1/3 θ S 2/3core
in BK79, and thus one would expect KrS to differ from
2/3 in scenario (iv). In a general case, both Ncore and
Bcore likely vary simultaneously (e.g. Niinuma et al. 2015), but
results from PL19 and, for example, from Lobanov & Zensus
(1999) suggest that variations in Ncore dominate the flaring
behaviour.
−100
−90
−80
−70
−60
−50
0.5 1 1.5 2 2.5
P
A
(d
eg
re
es
)
Index kr
Fig. 20. Jet position angle (PA) vs. index kr. The correlation between the
variables is very weak, although the negative trend suggests that when
kr > 1 the PA values decrease.
5.2. Frequency dependence of the core shift
We found that most of the time, the frequency dependence of
the core position does not follow ν−1obs in 3C 454.3. Instead, the
A130, page 15 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
0.3
0.5
0.7
1
3
5
1 10
B
1p
c
(G
)
Score at 5 GHz (Jy)
1 10
Score at 8 GHz (Jy)
1 10
Score at 15 GHz (Jy)
0.3
0.5
0.7
1
3
5
1 10
B
1p
c
(G
)
Score at 22-24 GHz (Jy)
1 10
SMRO at 37 GHz (Jy)
1 10
Score at 43 GHz (Jy)
Fig. 21. B1pc as a function of the core flux
density. The results are displayed assuming
kr = 1 and using CQ core shifts.
index kr was found to be a variable parameter in the period
of our study. We have demonstrated here the variability of kr
by direct measurements using multi-epoch quasi-simultaneous
multi-band VLBI data for the first time. Frequency dependence
with kr < 1 values were found during flaring and quiescent
states. This would mean that either energy equipartition or con-
ical shape assumptions do not always hold or the jet cannot be
described by the BK79 model. For a BK79 jet, we might assume
that kr should be close to one and stable in quiescent states.
During flaring episodes, the parsec-scale jet would temporar-
ily become particle-dominated and deviation from equipartition
would be natural, implying a consequent deviation from kr = 1.
This, however, does not seem to be the case in 3C 454.3. Instead,
it appears that kr is typically below one in this source.
We note that, in general, core shift and core position mea-
surements can be positively biased due to the use of a Gaussian
template, which is only a crude model for the actual jet bright-
ness distribution, and consequently bias the ν−1/kr dependence
when kr , 1 as shown by Pashchenko et al. (2020). Their results
show that this bias leads to observed kr values closer to one than
the true kr. Hence, the deviation of kr from one in 3C 454.3 can
be even larger than is observed here.
We note that the large uncertainties of kr from 2009 to 2010
were produced by the strong flares that disrupted the core-shift
effect. The ejection of a new moving feature at 43 GHz led
to ambivalence in measuring the kr parameter, judging by the
results demonstrated in Figs. D.14−D.18. In these strong flar-
ing epochs, the core-shift data are not always compatible with
a single power-law dependence, which supports the findings of
Kutkin et al. (2019) and PL19.
We found a significant correlation of kr with the core flux
density, S core, as shown in Fig. 19. The figure shows that the
index kr tends to become larger when the flux density is higher.
This effect appears to be steeper and pronounced at 8 GHz
(kr − S 0.5core) and less pronounced from 22−24 to 43 GHz where
the power-law indices range from 0.2 to 0.3. This would mean
that dependence of the core position on frequency (ν−1/kr ) is less
steep when flux density is higher. This could be explained by
the fact that flares start at high frequencies, affecting the core
shift first at the high-frequency end of the spectrum and later
at the low frequencies. Furthermore, if the KQ core shift first
increases due to a higher particle density while the lower fre-
quency core position remains the same (since the flare has not yet
propagated there), this could make kr look larger. For example,
Fig. D.16 shows a situation in which the shift between 24 GHz
and 43 GHz is suddenly very large during the rising part of a
large flare. This effect agrees well with the flaring jet model pre-
sented by PL19. More observations are necessary to closely fol-
low changes in the core position at different frequencies and,
consequently, kr during pre-flare, peak, and post-flare, and also
extensive observations during quiescent states. Furthermore, it is
important to note that the increase in kr with flux density has also
been observed in 3C 345 at 14.5 GHz for a few observing epochs
(Kudryavtseva et al. 2011).
5.3. Consequences to the magnetic field estimation
Significant deviations of kr from one imply that this parameter
can also be variable in other radio sources. This should be con-
sidered when measuring magnetic field strengths using just a pair
of frequencies and assuming a priori kr = 1. In general, having
three or more frequencies in core-shift measurements in order to
verify the kr = 1 condition is important if these measurements
are used to calculate magnetic field strengths. Furthermore, mak-
ing the measurements outside of flaring periods is likely to yield
‘undisturbed’ core-shift measurements.
A key problem found in this study is the large differences
in B1pc with kr = 1 and kr , 1. Using the same formula for
both cases indicates that the current expression for B1pc is not
applicable and fails for high or low kr values. This is not sur-
prising since the deviations from kr = 1 indicate that one of the
assumptions used to derive B1pc does not hold. The expression
A130, page 16 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
for B1pc in equipartition with a conical jet holds strictly as long
as kr is near one. When kr = 1 epochs are selected, the magnetic
field estimates are quite consistent, even though the amount of
core shift varies significantly with time.
Since the equipartition expression for B1pc does not hold
when measured kr is different from one, we should con-
sider measuring the magnetic field strength by incorporating
the core flux density in the core-shift measurements, as done
by Zdziarski et al. (2015), or by measuring the synchrotron
self-absorption turnover frequency and turnover flux density
of a resolved jet (Marscher 1983; Savolainen et al. 2008a).
In both cases, we can estimate the magnetic field strength
without assuming equipartition. The known downside of these
approaches is the high sensitivity of the derived magnetic field
values to the accuracy of the measured quantities. In 3C 454.3,
the core spectrum is inverted in nearly all observations, which in
most cases does not constrain well the turnover frequency (see
the results in Appendix D).
5.4. Consequences to astrometry and geodetic VLBI
High-accuracy astrometric VLBI measurements of extragalactic
radio sources are the basis of the International Celestial Refer-
ence Frame (ICRF). In its third realization (ICRF3; Charlot et al.
2020) and in the independently produced Radio Fundamental
Catalog (RFC4), the absolute source positions are measured at
submilliarcsecond accuracy. Together with other space geodetic
techniques, VLBI is also essential for realizing the International
Terrestrial Reference Frame (ITRF) and obtaining the full set
of Earth Orientation Parameters that provide a link between the
ITRF and the ICRF (e.g. Petrov et al. 2009). In astrometric and
geodetic VLBI observations, core shift adds another frequency-
dependent phase term (Kovalev et al. 2008) that behaves like an
extra path through a dispersive medium. Porcas (2009) showed
that if kr = 1, the contribution of the core shift to the measured
group delays is, in fact, zero, and the source coordinates derived
from the group delays refer to the jet base, a fiducial point
upstream of the core. If kr , 1, this is not the case, and the core-
shift-induced group delays are non-zero. On the other hand, the
coordinates measured from the single-band phase delays refer to
the position of the radio emission at the given observing band
and always depend on the core shift.
As PL19 point out, the core shift variability can affect the
astrometric measurements using the group delays, even if for-
mally kr = 1 and strong flares can disrupt any regular frequency
dependence of kr. Our results further show that in 3C 454.3
kr , 1 even during quiescent periods (i.e. the core shift can
affect the measured group delays even outside of the flaring peri-
ods in this source). Therefore, unless 3C 454.3 is an exceptional
case, knowing the core shift, including the actual kr, is important
for improving the accuracy of VLBI astrometry. The significant
core-shift variability observed here and in PL19 indicates that
ideally, the core shift in the ICRF3 defining sources should be
regularly monitored.
Several studies have established that systematic effects due
to the non-point-like structure of extragalactic radio sources are
currently the major source of errors in geodetic VLBI mea-
surements (e.g. Xu et al. 2017, 2021a; Anderson & Xu 2018;
Bolotin et al. 2019). With the advent of the new broad-band (four
512 MHz wide bands over 2−14 GHz) observing system known
as VGOS (VLBI Global Observing System; Niell et al. 2018),
the source structure effects now dominate the thermal errors by
4 http://astrogeo.org/rfc/
about an order of magnitude and are of the same order or larger
than the errors due to uncertainties in the atmospheric modelling
(Xu et al. 2021a). VGOS has an ambitious goal of 1 mm accu-
racy for the station positions on the ground, which translates to
∼30 µas accuracy of the source positions in the sky. Therefore,
it is clear that accurate modelling of the time and frequency-
dependent source structure is crucial for VGOS. This has led to
active efforts to remove the source structure effects by imaging
the geodetic VLBI data at the four bands of the VGOS (Xu et al.
2021c). In order to use these images to correct the visibility data,
it is necessary to align them accurately, which amounts to deter-
mining the core-shift effect. Our results presented in this paper
directly demonstrate the variability of the magnitude of the core
shift that was shown in PL19 and the variability of kr which
PL19 deduced from a model analysis of two-frequency core-shift
time series. The former means that core shift should also be regu-
larly monitored for the geodetic VLBI purposes, and preferably
at more than two frequencies. The latter should be taken into
account when attempting, for example, to fit the core shift to the
geodetic VLBI measurements: an a priori assumption of kr = 1
may not always hold.
Finally, we comment on the offsets between the optical and
radio positions of AGN. The European Space Agency’s astrom-
etry mission Gaia has recently provided submilliarcsecond posi-
tions in optical band (Gaia Collaboration 2021) for well over a
billion celestial sources with a limiting magnitude of G ≈ 21.
While a good overall agreement exists between the ICRF3 and
RFC radio positions and the Gaia optical positions, statisti-
cally significant offsets are seen for about 10% of the match-
ing AGN (e.g. Petrov & Kovalev 2017a,b; Gaia Collaboration
2018; Petrov et al. 2019). Kovalev et al. (2017) found that the
significant VLBI-Gaia offsets are preferentially parallel to the
direction of the radio jet. This result was later confirmed
and studied by Plavin et al. (2019a), Kovalev et al. (2020), and
Xu et al. (2021b), among others. The offsets, therefore, consti-
tute a genuine astrophysical effect and core shift; the source
structure can also contribute to this effect, at least in some
cases (Petrov & Kovalev 2017b). If kr , 1, as we report here
for 3C 454.3, the radio source position derived from the group
delays does not correspond to the jet base, and one can have
an offset from the nucleus-dominated optical position. On the
other hand, if the optical emission is dominated by the jet, offsets
are also expected for the kr = 1 case, but in the opposite direc-
tion (Kovalev et al. 2017; Plavin et al. 2019a). Knowing both the
amount of the core shift as well as its time and frequency depen-
dence is useful for interpreting the offsets and highlights the
importance of such measurements.
6. Summary and conclusions
The core-shift effect has been broadly used for a variety of
studies which include jet geometry (e.g. Pushkarev et al. 2018),
astrometry, and estimation of particle densities, magnetic field
strengths, and magnetic fluxes in a broad range of AGN (e.g.
Pushkarev et al. 2012; Zamaninasab et al. 2014; PL19). These
studies have been made possible by employing the VLBI tech-
nique that allows the highest angular resolution measurements.
Identifying the surface where the opacity is near unity is essen-
tial for locating the core and measuring the core shift.
We studied the time variability of the core-shift effect in the
jet of 3C 454.3 by analysing multi-epoch and multi-frequency
VLBA data from 2005 to 2010 (19 epochs). Core-shift mea-
surements were performed for the following adjacent frequency
bands: CX (5 GHz and 8 GHz), XU (8 GHz and 15 GHz), UK
A130, page 17 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
(15 GHz and 22−24 GHz), KQ (22−24 GHz and 43 GHz). These
data allowed us to examine the time variability of the core shift
and core-shift index, kr, for the first time. The current study
found significant variability of the core shift from 0.27 mas up
to 0.86 mas for the frequencies between 5 and 43 GHz.
Investigation of the variable nature of the core-shift effect
was carried out previously by PL19, who found significant
core-shift variability in a sample of 40 sources (not including
3C 454.3), although only between two frequencies, 2 GHz and
8 GHz. In this paper we confirm the time variability of the core-
shift effect found by PL19 and present for the first time direct
evidence of the variability of the index kr. We found signifi-
cant deviations from the ideal Blandford & Königl conical jet in
equipartition (kr = 1). The full range of measured kr values goes
from 0.45 to 1.7. The large values are, however, related to the
flaring period in 2009−2010 and have large uncertainties. Typi-
cally kr was below one with a mean value of kr = 0.85±0.08 for
the entire study period.
The disorder of the core shifts in the observations from late
2009 to the beginning of 2010 is attributable to the strong out-
bursts that took place in that period (Pacciani et al. 2010). Such
a substantial variability of the core shift connected with nuclear
flares was also observed by PL19. In addition to this, the emer-
gence of a new moving feature detected at 43 GHz has also
shifted the core position, hampering the accurate localization
of the core. These disturbances introduce additional shifts at
the high frequencies, hindering accurate estimations of the kr
indices. The nuclear region model fitting at 43 GHz revealed that
the new feature was moving in the direction of the jet at an appar-
ent speed of βapp = 5.0 ± 1.0 from 2009 September 22 to 2010
February 21.
Using core-shift measurements and the expression for the
magnetic field strength at one parsec in equipartition, we esti-
mated B1pc when kr = 1 and kr , 1. The results showed sig-
nificant discrepancies, which highlights the importance of first
observationally validating the equipartition assumption before
using the core-shift measurements to obtain magnetic field
strength estimates. Thus, B1pc values were calculated only for
the observations when kr was close to one, leading to B1pc val-
ues that ranged from 1.3 G to 2.0 G. Subsequently, we estimated
the magnetic flux of 3C 454.3. We found that the source was in
the MAD state, which agrees with Zamaninasab et al. (2014).
To identify a link between the core-shift effect and outbursts,
we searched for correlations between the core shift, core flux
density, and the 37 GHz total flux density from single-dish obser-
vations. We generally encountered a good correlation of the UK
core shift with the core flux density at 15 and 22−24 GHz and the
KQ core shift with the core flux density at 22−24 and 43 GHz.
A good correlation was also found for the full CQ core shift
with the single-dish flux density at 37 GHz and core flux den-
sity at 43 GHz. The relationships follow a generic power law as
∆rν1ν2 ∝ S tcore, with t ranging from 0.1 to 0.7. A large index
of 0.7 was found for the high-frequency pair, KQ. Hence, there
seems to be a tendency of increasing dependence between core
shift and flux density. The relationship becomes steeper for the
higher frequency pair, which suggests that strong flares increase
the core shift at high frequencies.
We also found correlations between the core position (at a
given frequency) and the core flux, rcore − S core. At most fre-
quencies except at 5 GHz, there are moderate to strong positive
correlations between the variables. The data can be fitted well
by a power law with indices ranging from 0.6 to 0.8 (for 8, 15
and 22−24 GHz) and with a mean of 0.7. This matches closely
the rcore ∝ S 2/3core relationship predicted for a Blandford & Königl
type jet when flares are due to changes in particle density (or
magnetic field strength).
An interesting finding is the correlation of the kr index with
core flux density: kr tends to increase as the source flares. This
would mean that extreme and drastic outbursts in 3C 454.3 tend
to increase the core shift at the high frequencies. On the other
hand, we did not find any evident correlation between the jet PA
and kr.
The present study suggests that full multi-frequency core-
shift measurements should be carried out to measure kr before
assuming a priori anything about equipartition for the calculation
of B1pc, for example, since deviations from kr = 1 indicate that
the assumptions of Eq. (6) may not hold, and this can affect the
jet’s magnetic field strength calculations.
Acknowledgements. We thank Ming H. Xu for useful discussions regarding the
astrometric aspects of the core-shift effect. This work was partly supported by
the Academy of Finland under the project “Physics of Black Hole Powered Jets”
(numbers 274477, 284495, and 312496) and the project “NT-VGOS” (number
315721). YYK is supported in the framework of the State project “Science” by
the Ministry of Science and Higher Education of the Russian Federation under
contract 075-15-2020-778. The Very Long Baseline Array and the National
Radio Astronomy Observatory are facilities of the National Science Founda-
tion operated under a cooperative agreement by Associated Universities, Inc.
This work made use of the Swinburne University of Technology software cor-
relator (Deller et al. 2011), developed as part of the Australian Major National
Research Facilities Programme and operated under licence. This paper has made
use of data from the MOJAVE database that is maintained by the MOJAVE team
(Lister et al. 2018) and data obtained at Metsähovi Radio Observatory, operated
by Aalto University in Finland.
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A130, page 19 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Appendix A: Core-shift magnitudes
Table A.1. Core-shift values per epoch and frequency pair.
Date Frequency pair R.A. (mas) Dec (mas) Absolute values (mas) Projected absolute values (mas)
2005-05-19a CX −0.15 ± 0.06 0.03 ± 0.07 0.15 ± 0.06 0.15 ± 0.06
XU −0.06 ± 0.02 −0.04 ± 0.02 0.07 ± 0.02 0.06 ± 0.03
UK −0.04 ± 0.01 0.04 ± 0.01 0.06 ± 0.01 0.05 ± 0.02
KQ −0.020 ± 0.005 −0.003 ± 0.005 0.020 ± 0.005 0.020 ± 0.005
CQ −0.27 ± 0.06 0.03 ± 0.07 0.27 ± 0.06 0.27 ± 0.06
2005-07-14a CX −0.42 ± 0.06 0.04 ± 0.07 0.42 ± 0.06 0.42 ± 0.06
XU −0.29 ± 0.03 0.10 ± 0.02 0.31 ± 0.03 0.30 ± 0.03
UK −0.04 ± 0.01 0.004 ± 0.009 0.04 ± 0.01 0.04 ± 0.01
KQ −0.020 ± 0.006 0.003 ± 0.005 0.020 ± 0.006 0.020 ± 0.006
CQ −0.77 ± 0.06 0.15 ± 0.07 0.78 ± 0.06 0.78 ± 0.06
2005-09-01a CX −0.41 ± 0.03 0.10 ± 0.03 0.42 ± 0.03 0.42 ± 0.03
XU −0.35 ± 0.02 0.06 ± 0.02 0.35 ± 0.02 0.35 ± 0.02
UK −0.06 ± 0.02 0.01 ± 0.01 0.06 ± 0.02 0.06 ± 0.02
KQ −0.02 ± 0.01 0.02 ± 0.01 0.02 ± 0.01 0.02 ± 0.01
CQ −0.84 ± 0.04 0.18 ± 0.04 0.86 ± 0.04 0.86 ± 0.04
2005-12-04b CX −0.34 ± 0.03 0.07 ± 0.03 0.35 ± 0.03 0.35 ± 0.03
XU −0.16 ± 0.02 0.01 ± 0.02 0.16 ± 0.02 0.16 ± 0.02
UK −0.09 ± 0.02 0.09 ± 0.01 0.13 ± 0.02 0.12 ± 0.02
KQ −0.02 ± 0.02 0.03 ± 0.01 0.03 ± 0.01 0.02 ± 0.02
CQ −0.62 ± 0.04 0.20 ± 0.04 0.65 ± 0.04 0.65 ± 0.04
2006-10-02b CX −0.23 ± 0.03 0.07 ± 0.03 0.24 ± 0.03 0.24 ± 0.03
XU −0.06 ± 0.02 −0.001 ± 0.017 0.06 ± 0.02 0.05 ± 0.02
UK −0.03 ± 0.01 0.02 ± 0.01 0.04 ± 0.01 0.04 ± 0.01
KQ −0.046 ± 0.005 0.007 ± 0.005 0.046 ± 0.005 0.046 ± 0.005
CQ −0.36 ± 0.03 0.09 ± 0.03 0.37 ± 0.03 0.37 ± 0.03
2006-12-04 CX −0.19 ± 0.03 0.09 ± 0.03 0.21 ± 0.03 0.21 ± 0.03
XU −0.11 ± 0.02 −0.01 ± 0.02 0.11 ± 0.02 0.10 ± 0.02
UK −0.05 ± 0.02 0.04 ± 0.02 0.06 ± 0.02 0.06 ± 0.02
KQ −0.021 ± 0.007 0.008 ± 0.006 0.02 ± 0.01 0.02 ± 0.01
CQ −0.36 ± 0.04 0.13 ± 0.04 0.38 ± 0.04 0.38 ± 0.04
2007-01-26b CX −0.11 ± 0.03 0.11 ± 0.03 0.15 ± 0.03 0.13 ± 0.03
XU −0.11 ± 0.02 −0.02 ± 0.02 0.12 ± 0.02 0.10 ± 0.02
UK −0.04 ± 0.01 0.01 ± 0.01 0.04 ± 0.01 0.04 ± 0.01
KQ −0.020 ± 0.005 −0.010 ± 0.005 0.022 ± 0.005 0.016 ± 0.005
CQ −0.28 ± 0.04 0.08 ± 0.03 0.29 ± 0.04 0.29 ± 0.04
2007-04-26b CX −0.09 ± 0.03 0.08 ± 0.03 0.12 ± 0.03 0.11 ± 0.04
XU −0.13 ± 0.02 −0.001 ± 0.014 0.13 ± 0.02 0.12 ± 0.02
UK −0.05 ± 0.01 0.02 ± 0.01 0.05 ± 0.01 0.05 ± 0.01
KQ −0.022 ± 0.007 0.006 ± 0.005 0.023 ± 0.007 0.023 ± 0.007
CQ −0.29 ± 0.04 0.10 ± 0.04 0.31 ± 0.04 0.31 ± 0.04
2007-06-16 CX −0.18 ± 0.03 0.08 ± 0.03 0.19 ± 0.03 0.19 ± 0.03
XU −0.16 ± 0.02 0.006 ± 0.015 0.16 ± 0.02 0.16 ± 0.02
UK −0.06 ± 0.01 0.02 ± 0.01 0.07 ± 0.01 0.07 ± 0.01
KQ −0.020 ± 0.005 0.007 ± 0.005 0.021 ± 0.005 0.021 ± 0.005
CQ −0.42 ± 0.04 0.11 ± 0.03 0.43 ± 0.04 0.43 ± 0.04
2007-07-25b CX −0.20 ± 0.03 0.03 ± 0.03 0.20 ± 0.03 0.20 ± 0.03
XU −0.16 ± 0.02 0.03 ± 0.02 0.16 ± 0.02 0.16 ± 0.02
UK −0.02 ± 0.01 −0.002 ± 0.008 0.02 ± 0.01 0.02 ± 0.01
KQ −0.04 ± 0.01 0.004 ± 0.011 0.04 ± 0.01 0.04 ± 0.01
CQ −0.42 ± 0.04 0.06 ± 0.03 0.42 ± 0.04 0.42 ± 0.04
2007-09-13b CX −0.31 ± 0.04 0.06 ± 0.04 0.32 ± 0.04 0.32 ± 0.04
XU −0.23 ± 0.02 0.04 ± 0.02 0.23 ± 0.02 0.23 ± 0.02
UK −0.04 ± 0.02 0.02 ± 0.02 0.04 ± 0.02 0.04 ± 0.02
KQ −0.08 ± 0.01 0.05 ± 0.01 0.09 ± 0.01 0.09 ± 0.01
CQ −0.66 ± 0.05 0.16 ± 0.04 0.68 ± 0.05 0.68 ± 0.05
2008-01-03b CX −0.92 ± 0.03 0.21 ± 0.04 0.94 ± 0.03 0.92 ± 0.04
XU −0.26 ± 0.02 0.18 ± 0.03 0.32 ± 0.02 0.32 ± 0.03
UK −0.13 ± 0.01 0.14 ± 0.02 0.19 ± 0.02 0.18 ± 0.01
KQ −0.15 ± 0.01 0.21 ± 0.02 0.26 ± 0.02 0.23 ± 0.01
CQ −1.47 ± 0.04 0.74 ± 0.05 1.64 ± 0.04 1.64 ± 0.05
2008-12-07 CXl −0.22 ± 0.03 −0.01 ± 0.03 0.22 ± 0.03 0.22 ± 0.03
XlXh −0.05 ± 0.03 0.007 ± 0.026 0.05 ± 0.03 0.05 ± 0.03
XhU −0.02 ± 0.03 −0.05 ± 0.02 0.05 ± 0.02 0.02 ± 0.03
UKl −0.11 ± 0.01 0.05 ± 0.02 0.12 ± 0.01 0.10 ± 0.01
KlKh −0.02 ± 0.01 0.001 ± 0.010 0.02 ± 0.01 0.02 ± 0.01
KhQ −0.05 ± 0.01 0.007 ± 0.008 0.05 ± 0.01 0.05 ± 0.01
CQ −0.46 ± 0.05 0.002 ± 0.046 0.46 ± 0.05 0.46 ± 0.05
2009-09-22 CX −0.10 ± 0.03 −0.03 ± 0.05 0.10 ± 0.04 0.09 ± 0.03
XU −0.09 ± 0.02 −0.02 ± 0.02 0.09 ± 0.02 0.08 ± 0.02
A130, page 20 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Table A.1. continued.
Date Frequency pair R.A. (mas) Dec (mas) Absolute values (mas) Projected absolute values (mas)
UK −0.11 ± 0.01 0.09 ± 0.01 0.14 ± 0.01 0.13 ± 0.02
KQ −0.005 ± 0.011 0.029 ± 0.007 0.029 ± 0.007 0.01 ± 0.01
CQ −0.30 ± 0.04 0.07 ± 0.05 0.31 ± 0.04 0.31 ± 0.04
2009-10-22 CX −0.34 ± 0.04 0.13 ± 0.06 0.37 ± 0.04 0.35 ± 0.04
XU −0.13 ± 0.02 −0.05 ± 0.02 0.13 ± 0.02 0.12 ± 0.02
UK −0.16 ± 0.02 0.01 ± 0.02 0.16 ± 0.02 0.16 ± 0.02
KQ −0.06 ± 0.02 −0.04 ± 0.01 0.07 ± 0.02 0.06 ± 0.02
CQ −0.69 ± 0.05 0.05 ± 0.06 0.69 ± 0.05 0.69 ± 0.05
2009-12-03 CX −0.13 ± 0.03 −0.05 ± 0.03 0.14 ± 0.03 0.14 ± 0.03
XU −0.13 ± 0.02 −0.02 ± 0.02 0.13 ± 0.02 0.13 ± 0.02
UK −0.07 ± 0.02 0.05 ± 0.01 0.08 ± 0.02 0.07 ± 0.02
KQ −0.120 ± 0.007 −0.007 ± 0.018 0.120 ± 0.007 0.120 ± 0.007
CQ −0.45 ± 0.03 −0.04 ± 0.04 0.45 ± 0.03 0.45 ± 0.04
2010-01-18b CX −0.25 ± 0.03 −0.08 ± 0.03 0.26 ± 0.03 0.25 ± 0.03
XU −0.06 ± 0.02 −0.02 ± 0.02 0.06 ± 0.02 0.06 ± 0.02
UK −0.11 ± 0.02 0.021 ± 0.009 0.11 ± 0.02 0.10 ± 0.02
KQ −0.07 ± 0.01 0.032 ± 0.007 0.08 ± 0.01 0.07 ± 0.01
CQ −0.48 ± 0.04 −0.04 ± 0.03 0.49 ± 0.04 0.49 ± 0.04
2010-02-21b CX −0.21 ± 0.03 −0.09 ± 0.03 0.23 ± 0.03 0.22 ± 0.03
XU −0.09 ± 0.02 −0.02 ± 0.01 0.09 ± 0.02 0.09 ± 0.02
UK −0.075 ± 0.008 0.05 ± 0.01 0.09 ± 0.01 0.07 ± 0.01
KQ −0.060 ± 0.007 0.025 ± 0.007 0.065 ± 0.007 0.058 ± 0.007
CQ −0.44 ± 0.03 −0.04 ± 0.03 0.44 ± 0.03 0.44 ± 0.03
Notes. the nuclear region at the Q band can be model fitted by two components where a bright moving feature has been identified at all epochs
in the period 2009-2010. aThe nuclear region at both C and X bands can be fitted with two components. bOnly the C band can be fitted with two
components.
A130, page 21 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Appendix B: Core-shift pair vector choice
As described in Figure 3 we show in Figure B.1 a comparison of
the core-shift vectors produced by the other choices. The optimal
core choice at the C and X bands is the pair: Cb-Xb. This leads
both CX and XU core-shift vectors to point in the jet direction
(towards the west), as already demonstrated in Figure 3b.
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
−0.15−0.1−0.0500.050.10.15
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
−0.04
−0.02
0
0.02
0.04
−0.04−0.0200.020.04
(a)
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.3−0.2−0.100.10.20.3
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
−0.04
−0.02
0
0.02
0.04
−0.04−0.0200.020.04
(b)
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
−0.8−0.6−0.4−0.200.20.40.60.8
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
−0.04
−0.02
0
0.02
0.04
−0.04−0.0200.020.04
(c)
Fig. B.1. Core-shift vector directions by combining the alternative options for the core at the low-frequency C−X bands. These are a) Ca−Xa, b)
Ca−Xb, and c) Cb−Xa. In all options, at least one vector points in the opposite direction, contrary to the jet direction that is towards the west.
A130, page 22 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Appendix C: Parameter uncertainties
C.1. Uncertainty of Ωrν
The uncertainty of Ωrν, denoted by ∆Ωrν is obtained by propagat-
ing uncertainty in Equation 5 with both ∆rν1ν2 and kr as variable
parameters. For simplification purposes, we set here ∆rν1ν2 = l
and the uncertainty of ∆rν1ν2 = ∆l. The uncertainty of index kr is
∆kr. The expression for ∆Ωrν is given as
∆Ωrν =
√(
∂Ω
∂l
· ∆l
)2
+
(
∂Ω
∂kr
· ∆kr
)2
, (C.1)
where
∂Ωrν
∂l
=
Ωrν
l
, (C.2)
and
∂Ωrν
∂kr
= Ωrν
(
ν1/kr1 ln(ν2) − ν1/kr2 ln(ν1)
)
k2r (ν
1/kr
2 − ν1/kr1 )
. (C.3)
Plugging C.2 and C.3 into C.1, the uncertainty of Ωrν is given by
∆Ωrν = Ωrν
√√(
∆l
l
)2
+
ν1/kr1 ln(ν2) − ν1/kr2 ln(ν1)
k2r (ν
1/kr
2 − ν1/kr1 )
· ∆kr
2. (C.4)
Equation C.4 is a generic formula to estimate the uncertainties
in Ωrν for each frequency pair: ∆ΩCX , ∆ΩXU , ∆ΩUK and ∆ΩKQ.
C.2. Uncertainty of rcore
The uncertainty of rcore is denoted by ∆rcore. The measured
uncertainties are propagated in Equation 4 having Ωrν and kr as
variable parameters. We note that Ωrν is an average-mean value
per epoch; therefore, the expression for ∆rcore is
∆rcore =
√(
∂rcore
∂Ωrν
· ∆Ωrν
)2
+
(
∂rcore
∂kr
· ∆kr
)2
, (C.5)
with
∂rcore
∂Ωrν
=
rcore
Ωrν
, (C.6)
and
∂rcore
∂kr
= rcore
ln(ν)
k2r
. (C.7)
Plugging C.6 and C.7 into C.5, the uncertainty of rcore is given
by
∆rcore = rcore
√(
∆Ωrν
Ωrν
)2
+
(
ln(ν)
k2r
∆kr
)2
. (C.8)
C.3. Uncertainty of B1pc
The uncertainty of B1pc is denoted by ∆B1pc. The measured
uncertainties are propagated in Equation 6 with respect to the CQ
core shift, ∆rCQ, δ, θj, θ, and kr. Below M = 4.85 · 10−9 DL/(1 +
z)2. Inserting equation 5 into equation 6, the formula for B1pc
transforms to
B1pc ≈ 0.025
 σrel (1 + z)3δ2 θj sin3kr−1θ ν31ν32
 M∆rCQ
ν1/kr2 − ν1/kr1
3kr

1
4
[G]. (C.9)
For simplification purposes, we set here ∆rCQ = A and the uncer-
tainty of the CQ core shift as ∆A. The error of B1pc is denoted by
∆B1pc and is obtained as
∆B1pc =
[ (
∂B1pc
∂A
· ∆A
)2
+
(
∂B1pc
∂δ
· ∆δ
)2
+
(
∂B1pc
∂θj
· ∆θj
)2
+
(
∂B1pc
∂θ
· ∆θ
)2
+
(
∂B1pc
∂kr
· ∆kr
)2 ]1/2
, (C.10)
where
∂B1pc
∂A
=
3
4
kr
B1pc
∆A
, (C.11)
∂B1pc
∂δ
= −1
2
B1pc
δ
, (C.12)
∂B1pc
∂θj
= −1
4
B1pc
θj
, (C.13)
∂B1pc
∂θ
= −1
4
(3kr − 1)cos θsin θ B1pc, (C.14)
∂B1pc
∂kr
=
3
4
1
kr
B1pc
1
ν1/kr2 − ν1/kr1[
kr(ν
1/kr
2 − ν1/kr1 )
(
ln
(
MA
ν1/kr2 − ν1/kr1
)
− ln(sin θ)
)
+ ν1/kr2 ln(ν2) − ν1/kr1 ln(ν1)
]
(C.15)
Finally, plugging all the partial derivatives into C.10, the error of
B1pc is readily obtained.
A130, page 23 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Appendix D: Core spectrum, core-shift vectors, and
power-law fits
The main results of the core-shift analysis for individual epochs
(listed in Table 1) are shown in Figures D.1−D.18. The results
for each epoch include the core spectrum, the core-shift vectors
in polar coordinates, and the core-shift power-law fit. Projected
values of the core shifts onto the average direction are used. All
fitting parameters are summarized in Table 2.
We note that we still present the core-shift analysis for the
observation on 2008 January 03 (epoch 13, Figure D.12) as a
demonstration of the case when large core shifts are measured
due to lack of resolution. Furthermore, as emphasized in the
main text, this observation was not included in the variability
analysis.
1
10
1 10 100
Xb
Xa
Ca
Cb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
−0.15−0.1−0.0500.050.10.15
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 10 20 30 40 50
kr=0.7 ± 0.1
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.1. Epoch 1, 2005 May 19. (a) Core spectrum, Ca−Xa represent the core. (b) Core-shift vectors of all frequency pairs. The choice of Ca−Xa
cores leads to the correct direction of vectors CX and XU. (c) The power-law fit is shown with the red curve.
A130, page 24 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Xb
Xa
Ca
Cb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
−0.4−0.3−0.2−0.100.10.20.30.4
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
−0.04
−0.02
0
0.02
0.04
−0.04−0.0200.020.04
(b)
0
0.2
0.4
0.6
0.8
0 10 20 30 40 50
kr=0.45 ± 0.04
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.2. Epoch 2, 2005 July 14: (a) Core spectrum, Cb−Xb represent the core. (b) Core-shift vectors of all frequency pairs. The choice of Cb−Xb
cores leads to the correct direction of vectors CX and XU. (c) The power-law fit is shown with the red curve.
A130, page 25 of 58
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1
10
1 10 100
Xb
Xa
Ca
Cb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.4
−0.2
0
0.2
0.4
−0.4−0.200.20.4
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
−0.04
−0.02
0
0.02
0.04
−0.04−0.0200.020.04
(b)
0
0.2
0.4
0.6
0.8
0 10 20 30 40 50
kr=0.52 ± 0.07
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.3. Epoch 3, 2005 September 01: (a) Core spectrum, Cb−Xb represent the core. (b) Core-shift vectors of all frequency pairs. The choice of
Cb−Xb cores leads to the correct direction of vectors CX and XU. (c) The power-law fit is shown with the red curve.
A130, page 26 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Ca
CbF
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.3−0.2−0.100.10.20.3
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 10 20 30 40 50
kr=0.7 ± 0.1
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.4. Epoch 4, 2005 December 04. (a) Core spectrum, Ca represents the core. (b) Core-shift vectors of all frequency pairs. The choice of Ca
core leads to the correct direction of the CX vector. (c) The power-law fit is shown with the red curve.
A130, page 27 of 58
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1
2
3
4
1 10 100
Cb
Ca
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.2
−0.1
0
0.1
0.2
−0.2−0.100.10.2
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
0
0.1
0.2
0.3
0.4
0 10 20 30 40 50
kr=1.0 ± 0.3
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.5. Epoch 6, 2006 October 02. (a) Core spectrum, Ca represents the core. (b) Core-shift vectors of all frequency pairs. The choice of Ca core
leads to the correct direction of the CX vector. (c) The power-law fit is shown with the red curve.
A130, page 28 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
2
3
1 10 100
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
−0.2−0.15−0.1−0.0500.050.10.150.2
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
0
0.1
0.2
0.3
0.4
0 10 20 30 40 50
kr=0.67 ± 0.07
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.6. Epoch 7, 2006 December 04. (a) Core spectrum. (b) Core-shift vectors of all frequency pairs. (c) The power-law fit is shown with the red
curve.
A130, page 29 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
2
3
4
1 10 100
Ca
Cb
Xb
Xa
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
−0.15−0.1−0.0500.050.10.15
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 10 20 30 40 50
kr=0.65 ± 0.06
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.7. Epoch 8, 2007 January 26. (a) Core spectrum, Ca−Xb represent the core. (b) Core-shift vectors of all frequency pairs. The choice of
Ca−Xb cores leads to the correct direction of vectors CX and XU. (c) The power-law fit is shown with the red curve.
A130, page 30 of 58
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1
2
3
4
1 10 100
Ca
Cb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
−0.15−0.1−0.0500.050.10.15
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 10 20 30 40 50
kr=0.8 ± 0.1
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.8. Epoch 9, 2007 April 26. (a) Core spectrum, Ca represents the core. (b) Core-shift vectors of all frequency pairs. The choice of Ca core
leads to the correct direction of the CX vector. (c) The power-law fit is shown with the red curve.
A130, page 31 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
−0.2−0.15−0.1−0.0500.050.10.150.2
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.1
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50
kr=0.6 ± 0.1
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.9. Epoch 10, 2007 June 16. (a) Core spectrum. (b) Core-shift vectors of all frequency pairs. (c) The power-law fit is shown with the red
curve.
A130, page 32 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Ca
Cb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
−0.2−0.15−0.1−0.0500.050.10.150.2
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50
kr=0.69 ± 0.05
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.10. Epoch 11, 2007 July 25. (a) Core spectrum, Ca represents the core. (b) Core-shift vectors of all frequency pairs. The choice of Ca core
leads to the correct direction of the CX vector. (c) The power-law fit is shown with the red curve.
A130, page 33 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Ca
Cb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.3−0.2−0.100.10.20.3
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
kr=0.9 ± 0.1
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.11. Epoch 12, 2007 September 13. (a) Core spectrum, Cb represents the core. (b) Core-shift vectors of all frequency pairs. The choice of
Cb core leads to the correct direction of the CX vector. (c) The power-law fit is shown with the red curve.
A130, page 34 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Ca
CbF
lu
x
[J
y
]
Frequency [GHz]
(a)
−1
−0.5
0
0.5
1
−1−0.500.51
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 10 20 30 40 50
kr=1.1 ± 0.2
∆
r
[m
as
]
Frequency [GHz]
(c)
Fig. D.12. Epoch 13, 2008 January 03. (a) Core spectrum, Cb possibly represents the core. (b) Core-shift vectors of all frequency pairs. (c) Power-
law fit is shown with the red curve. Due to the poor (u, v) coverage, the core at the C band cannot be well resolved, producing ambiguities on its
location. As a result, very large core-shift values above 1 mas were measured. This observation was not included in the variability analysis.
A130, page 35 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
10 100
F
lu
x
d
en
si
ty
[J
y
]
Frequency [GHz]
(a)
−0.2
−0.1
0
0.1
0.2
−0.2−0.100.10.2
R.A. (mas)
Dec (mas)
Average
direction
CXl
XlXh
XhU
UKl
KlKh
KhQ
−0.02
−0.01
0
0.01
0.02
−0.02−0.0100.010.02
(b)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 10 20 30 40 50
kr=1.4 ± 0.4
∆
r
[m
as
]
Frequency [GHz]
(c)
−0.2
−0.1
0
0.1
0.2
−0.2−0.100.10.2
R.A. (mas)
Dec (mas)
Average
direction
CXl
XlXh
XhKl
KlKh
KhQ
−0.04
−0.02
0
0.02
0.04
−0.04−0.0200.020.04
(d)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 10 20 30 40 50
kr=1.1 ± 0.1
∆
r
[m
as
]
Frequency [GHz]
(e)
Fig. D.13. Epoch 14, 2008 December 07. (a) Core spectrum. (b) Core-shift vectors of all frequency pairs, including intermediate frequencies
denoted by Xl (7.9 GHz), Xh (8.9 GHz), Kl (21.8 GHz) and Kh (24 GHz). (c) Power-law fit (red curve) using all bands. (d) Core-shift vectors
without the U band, (e) Power-law fit (red curve) using all bands except the U band. This approach leads to a better fit.
A130, page 36 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Qa
Qb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
−0.15−0.1−0.0500.050.10.15
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.1
0
0.1
0.2
0.3
0.4
0 10 20 30 40 50
kr=0.7 ± 0.4
∆
r
[m
as
]
Frequency [GHz]
(c)
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
−0.15−0.1−0.0500.050.10.15
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(d)
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 10 20 30 40 50
kr=1.1 ± 0.6
∆
r
[m
as
]
Frequency [GHz]
(e)
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 10 20 30 40 50
kr=0.8 ± 0.3
∆
r
[m
as
]
Frequency [GHz]
(f)
Fig. D.14. Epoch 15, 2009 September 22. a) Core spectrum, where Qa represents the core and Qb the feature moving downstream. For comparisons,
see Figure 4a. b) Core-shift vectors of all frequency pairs. Using component Qb makes the KQ core-shift vector point in the opposite direction. c)
Power-law fit (red curve) using the Qb component. d) Core-shift vectors of all frequency pairs. Using component Qa, labelled as the core, gives a
reasonable direction of the KQ core-shift vector. e) Power-law fit (red curve) using Qa as the core, but a better fit is obtained f) when the U band
is excluded.
A130, page 37 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Qb
Qa
F
lu
x
[J
y
]
Frequency [GHz]
(a) .
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
−0.4−0.3−0.2−0.100.10.20.30.4
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
−0.4−0.3−0.2−0.100.10.20.30.4
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(c)
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
kr=1.1 ± 0.3
∆
r
[m
as
]
Frequency [GHz]
(d)
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
kr=0.8 ± 0.2
∆
r
[m
as
]
Frequency [GHz]
(e)
Fig. D.15. Epoch 16, 2009 October 22. a) Core spectrum, where Qa represents the core and Qb the feature moving downstream. For comparisons,
see Figure 4b. Core-shift vectors of all frequency pairs using b) Qa and c) Qb. In this case, the two components have a similar impact on the
direction of KQ core-shift vector. Power-law fits (red curve) using d) Qa and e) Qb. In this epoch, the flare appears to hinder the correct location
of the core at the Q-band (43 GHz).
A130, page 38 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Qa
Qb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
−0.15−0.1−0.0500.050.10.15
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
−0.15−0.1−0.0500.050.10.15
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(c)
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50
∆
r
[m
as
]
Frequency [GHz]
kr=1
(d)
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50
kr=2.2 ± 0.3
∆
r
[m
as
]
Frequency [GHz]
(e)
Fig. D.16. Epoch 17, 2009 December 03. a) Core spectrum, where Qa represents the core and Qb the feature moving downstream. For comparisons,
see Figure 4c. Core-shift vectors of all frequency pairs using b) Qa and c) Qb. Similarly, as in the previous epoch, the two components have a
similar impact on the direction of KQ core-shift vector. Power-law fits (red curve) using d) Qa and e) Qb. In this epoch the flare appears to hinder
the correct location of the core at the Q-band (43 GHz). This ultimately disrupts the core-shift effect by increasing the core-shift values at the high
frequencies, as seen in d). Therefore, this observation is not included in the variability analysis of index kr.
A130, page 39 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Cb
Ca
Qb
Qa
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.3−0.2−0.100.10.20.3
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.3−0.2−0.100.10.20.3
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(c)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 10 20 30 40 50
kr=1.7± 0.7
∆
r
[m
as
]
Frequency [GHz]
(d)
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50
kr=0.8 ± 0.2
∆
r
[m
as
]
Frequency [GHz]
(e)
Fig. D.17. Epoch 18, 2010 January 18. a) Core spectrum, where Cb and Qa represent the core at the C and Q bands. Qb is the feature moving
downstream. For comparisons, see Figure 4d. Core-shift vectors of all frequency pairs using b) Qa and c) Qb. Similarly, as in the previous epoch,
the two components have a similar impact on the direction of KQ core-shift vector. Power-law fits (red curve) using d) Qa and e) Qb. Again, the
flare appears to hinder the correct location of the core at the Q band (43 GHz). The effect is less pronounced than in the previous epoch, but it
disorders the core-shift effect by increasing the core-shift values at the high frequencies, as seen in d).
A130, page 40 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1
10
1 10 100
Qa
Qb
Ca
Cb
F
lu
x
[J
y
]
Frequency [GHz]
(a)
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
−0.2−0.15−0.1−0.0500.050.10.150.2
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
(b)
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
−0.2−0.15−0.1−0.0500.050.10.150.2
R.A. (mas)
Dec (mas)
Average
direction
CX
XU
UK
KQ
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
−0.03−0.02−0.0100.010.020.03
(c)
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50
kr=1.3 ± 0.3
∆
r
[m
as
]
Frequency [GHz]
(d)
0
0.1
0.2
0.3
0.4
0 10 20 30 40 50
kr=0.5 ± 0.1
∆
r
[m
as
]
Frequency [GHz]
(e)
Fig. D.18. Epoch 19, 2010 February 21. a) Core spectrum, where Cb and Qa represent the core at the C and Q bands. Qb is the feature moving
downstream. For comparisons, see Figure 4e. Core-shift vectors of all frequency pairs using b) Qa and c) Qb. In this epoch it is clear that Qa
and Qb have different effects on the KQ core-shift vector direction. The use of Qb leads to the wrong core-shift direction. Power-law fits (red
curve) using d) Qa and e) Qb. Similarly, as in previous epochs, the flare appears to affect the location of the core at the Q band (43 GHz). In this
observation, the flare effect is less pronounced but increases the core-shift values at the high frequencies, as seen in d).
A130, page 41 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Appendix E: VLBA multi-epoch and multi-frequency
images
The CLEAN images after self-calibration in amplitudes and in
phases are presented here for all epochs. C-band images are dis-
played in Figures E.1 and E.2, X-band images in Figures E.3 and
E.4. For the U band, we present only the epochs not published
in the MOJAVE website shown in Figure E.5. K-band images
are shown in Figures E.6 and E.7. Finally, Q-band images are
displayed in Figures E.8 and E.9.
10 0 -10 -20 -30 -40
30
20
10
0
-10
Right Ascension (mas)
Re
la
tiv
e 
De
cli
na
tio
n 
(m
as
)
3C454.3 at 5.0 GHz, 2005-05-19
Peak: 5.51 Jy/beam
Beam: 3.39 × 1.67 mas at -19.1 deg.
0
1
2
3
4
5
Jy/beam
(a)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2005-07-14
Peak: 4.98 Jy/beam
Beam: 3.26 × 1.68 mas at -14.3 deg.
0
1
2
3
4
5
Jy/beam
(b)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Right Ascension (mas)
Re
la
tiv
e 
De
cli
na
tio
n 
(m
as
)
3C454.3 at 5.0 GHz, 2005-09-01
Peak: 5.05 Jy/beam
Beam: 3.36 × 1.77 mas at -13.6 deg.
0
1
2
3
4
5
Jy/beam
(c)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2005-12-04
Peak: 4.76 Jy/beam
Beam: 3.75 × 1.71 mas at -16.7 deg.
0
1
2
3
4
Jy/beam
(d)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Right Ascension (mas)
Re
la
tiv
e 
De
cli
na
tio
n 
(m
as
)
3C454.3 at 5.0 GHz, 2006-08-03
Peak: 4.59 Jy/beam
Beam: 4.06 × 2.16 mas at 17.4 deg.
0
1
2
3
4
Jy/beam
(e)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2006-10-02
Peak: 3.91 Jy/beam
Beam: 3.46 × 1.62 mas at -10.7 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(f)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2006-12-04
Peak: 3.79 Jy/beam
Beam: 3.21 × 1.72 mas at -7.67 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(g)
10 0 -10 -20 -30 -40 -50
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2007-01-26
Peak: 3.5 Jy/beam
Beam: 3.23 × 1.62 mas at -7.26 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(h)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2007-04-26
Peak: 3.38 Jy/beam
Beam: 3.29 × 1.72 mas at -7.86 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Jy/beam
(i)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2007-06-16
Peak: 3.21 Jy/beam
Beam: 3.19 × 1.67 mas at -8.06 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Jy/beam
(j)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2007-07-25
Peak: 2.92 Jy/beam
Beam: 3.16 × 1.57 mas at -7.67 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(k)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2007-09-13
Peak: 3.49 Jy/beam
Beam: 4.71 × 2.05 mas at -23.9 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(l)
Fig. E.1. C-band (5 GHz) CLEAN images of 3C454.3 from 2005 May 19 to 2007 September 13 with contours at -0.1%, 0.1%, 0.2%, 0.4%, 0.8%,
1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image.
A130, page 42 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
-20
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2008-01-03
Peak: 2.71 Jy/beam
Beam: 6.47 × 2.05 mas at -22.3 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(a)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 4.85 GHz, 2008-12-07
Peak: 3.57 Jy/beam
Beam: 3.38 × 1.95 mas at 4.51 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(b)
10 0 -10 -20 -30 -40 -50
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2009-09-22
Peak: 4.18 Jy/beam
Beam: 3.50 × 1.76 mas at 0.5 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(c)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2009-10-22
Peak: 4.27 Jy/beam
Beam: 4.27 × 2.10 mas at 20.1 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(d)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2009-12-03
Peak: 4.12 Jy/beam
Beam: 3.55 × 1.79 mas at 1.74 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(e)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2010-01-18
Peak: 4.14 Jy/beam
Beam: 3.55 × 1.78 mas at 7.35 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(f)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 5.0 GHz, 2010-02-21
Peak: 4.6 Jy/beam
Beam: 3.31 × 1.65 mas at 6.07 deg.
0
1
2
3
4
Jy/beam
(g)
Fig. E.2. C-band (5 GHz) CLEAN images of 3C454.3 from 2008 January 03 to 2010 February 21 with contours at -0.1%, 0.1%, 0.2%, 0.4%,
0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image.
A130, page 43 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2005-05-19
Peak: 4.84 Jy/beam
Beam: 2.24 × 1.13 mas at -13.9 deg.
0
1
2
3
4
Jy/beam
(a)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2005-07-14
Peak: 3.64 Jy/beam
Beam: 2.48 × 1.07 mas at -16.4 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(b)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Right Ascension (mas)
Re
la
tiv
e 
De
cli
na
tio
n 
(m
as
)
3C454.3 at 8.35 GHz, 2005-09-01
Peak: 3.45 Jy/beam
Beam: 2.04 × 1.06 mas at -8.07 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Jy/beam
(c)
5 0 -5 -10 -15 -20 -25
20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2005-12-04
Peak: 2.86 Jy/beam
Beam: 2.32 × 1.06 mas at -12.7 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(d)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2006-08-03
Peak: 3.08 Jy/beam
Beam: 2.62 × 1.35 mas at 18.2 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Jy/beam
(e)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2006-10-02
Peak: 2.5 Jy/beam
Beam: 2.11 × 1.00 mas at -4.76 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(f)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2006-12-04
Peak: 2.71 Jy/beam
Beam: 2.12 × 1.17 mas at -2.96 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(g)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2007-01-26
Peak: 2.19 Jy/beam
Beam: 2.01 × 1.07 mas at 0.49 deg.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Jy/beam
(h)
5 0 -5 -10 -15 -20 -25 -30
25
20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2007-04-26
Peak: 2.14 Jy/beam
Beam: 2.27 × 1.19 mas at -1.58 deg.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Jy/beam
(i)
5 0 -5 -10 -15 -20 -25 -30
20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2007-06-16
Peak: 1.9 Jy/beam
Beam: 2.14 × 1.12 mas at -6.06 deg.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
Jy/beam
(j)
5 0 -5 -10 -15 -20 -25 -30
25
20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2007-07-25
Peak: 1.67 Jy/beam
Beam: 2.10 × 1.02 mas at -6.44 deg.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Jy/beam
(k)
5 0 -5 -10 -15 -20 -25 -30
25
20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2007-09-13
Peak: 2.19 Jy/beam
Beam: 3.05 × 1.30 mas at -23.2 deg.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Jy/beam
(l)
Fig. E.3. X-band (8 GHz) CLEAN images of 3C454.3 from 2005 May 19 to 2007 September 13 with contours at -0.1%, 0.1%, 0.2%, 0.4%, 0.8%,
1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image.
A130, page 44 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
5 0 -5 -10 -15 -20 -25 -30 -35
30
25
20
15
10
5
0
-5
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.35 GHz, 2008-01-03
Peak: 2.35 Jy/beam
Beam: 4.36 × 1.28 mas at -21.4 deg.
0.0
0.5
1.0
1.5
2.0
Jy/beam
(a)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 7.92 GHz, 2008-12-07
Peak: 5.67 Jy/beam
Beam: 2.11 × 1.21 mas at 1.69 deg.
0
1
2
3
4
5
Jy/beam
(b)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.89 GHz, 2008-12-07
Peak: 6.15 Jy/beam
Beam: 1.94 × 1.11 mas at 1.95 deg.
0
1
2
3
4
5
6
Jy/beam
(c)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.43 GHz, 2009-09-22
Peak: 3.81 Jy/beam
Beam: 2.14 × 0.97 mas at -2.55 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(d)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.45 GHz, 2009-10-22
Peak: 4.03 Jy/beam
Beam: 2.48 × 1.24 mas at 18.1 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(e)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.43 GHz, 2009-12-03
Peak: 4.1 Jy/beam
Beam: 2.12 × 1.01 mas at -1.61 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(f)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.43 GHz, 2010-01-18
Peak: 5.13 Jy/beam
Beam: 2.00 × 0.99 mas at 6.4 deg.
0
1
2
3
4
5
Jy/beam
(g)
5 0 -5 -10 -15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 8.43 GHz, 2010-02-21
Peak: 6.87 Jy/beam
Beam: 1.89 × 0.94 mas at 5.2 deg.
0
1
2
3
4
5
6
Jy/beam
(h)
Fig. E.4. X-band (8 GHz) CLEAN images of 3C454.3 from 2008 January 03 to 2010 February 21 with contours at -0.1%, 0.1%, 0.2%, 0.4%,
0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image.
A130, page 45 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
3 0 -3 -6 -9 -12 -15
12
9
6
3
0
-3
-6
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 15.3 GHz, 2006-08-03
Peak: 3.14 Jy/beam
Beam: 1.45 × 0.82 mas at 17.6 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Jy/beam
(a)
3 0 -3 -6 -9 -12 -15
12
9
6
3
0
-3
-6
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 15.3 GHz, 2007-09-13
Peak: 3.46 Jy/beam
Beam: 1.79 × 0.69 mas at -24.1 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Jy/beam
(b)
3 0 -3 -6 -9 -12 -15
12
9
6
3
0
-3
-6
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 15.3 GHz, 2008-01-03
Peak: 3.22 Jy/beam
Beam: 2.30 × 0.67 mas at -22.1 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Jy/beam
(c)
3 0 -3 -6 -9 -12 -15
12
9
6
3
0
-3
-6
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 15.4 GHz, 2009-10-22
Peak: 4.35 Jy/beam
Beam: 1.36 × 0.74 mas at 10.5 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(d)
Fig. E.5. U-band (15 GHz) CLEAN images of 3C454.3 from 2006 August 03 to 2009 October 22 with contours at -0.2%, 0.2%, 0.4%, 0.8%, 1.6%,
3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image. The missing images for the other epochs have already been published
by the MOJAVE team.
A130, page 46 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2005-05-19
Peak: 2.21 Jy/beam
Beam: 0.91 × 0.41 mas at -23.3 deg.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Jy/beam
(a)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2005-07-14
Peak: 2.91 Jy/beam
Beam: 0.81 × 0.37 mas at -17.6 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(b)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2005-09-01
Peak: 4.38 Jy/beam
Beam: 0.83 × 0.37 mas at -18.7 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(c)
2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2005-12-04
Peak: 6.06 Jy/beam
Beam: 1.10 × 0.42 mas at -23.2 deg.
0
1
2
3
4
5
6
Jy/beam
(d)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2006-08-03
Peak: 2.67 Jy/beam
Beam: 0.98 × 0.53 mas at 23 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(e)
2 0 -2 -4 -6 -8 -10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2006-10-02
Peak: 2.12 Jy/beam
Beam: 0.81 × 0.38 mas at -9.07 deg.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Jy/beam
(f)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2006-12-04
Peak: 1.97 Jy/beam
Beam: 0.87 × 0.42 mas at -14.2 deg.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
Jy/beam
(g)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2007-01-26
Peak: 1.97 Jy/beam
Beam: 0.76 × 0.40 mas at -6.85 deg.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
Jy/beam
(h)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2007-04-26
Peak: 2.14 Jy/beam
Beam: 0.99 × 0.41 mas at -15.6 deg.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Jy/beam
(i)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2007-06-16
Peak: 2.5 Jy/beam
Beam: 0.83 × 0.39 mas at -9.67 deg.
0.0
0.5
1.0
1.5
2.0
2.5
Jy/beam
(j)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2007-07-25
Peak: 3.7 Jy/beam
Beam: 0.78 × 0.35 mas at -12.5 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(k)
2 0 -2 -4 -6 -8 -10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2007-09-13
Peak: 5.23 Jy/beam
Beam: 1.14 × 0.47 mas at -23.2 deg.
0
1
2
3
4
5
Jy/beam
(l)
Fig. E.6. K-band (22−24 GHz) CLEAN images of 3C454.3 from 2005 May 19 to 2007 September 13 with contours at -0.1%,0.1%, 0.2%, 0.4%,
0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image.
A130, page 47 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 22.24 GHz, 2008-01-03
Peak: 4.3 Jy/beam
Beam: 1.64 × 0.41 mas at -20.8 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(a)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 21.78 GHz, 2008-12-07
Peak: 9.25 Jy/beam
Beam: 0.86 × 0.44 mas at -12.9 deg.
0
2
4
6
8
Jy/beam
(b)
2 0 -2 -4 -6 -8
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 24 GHz, 2008-12-07
Peak: 10.8 Jy/beam
Beam: 0.77 × 0.41 mas at -12.8 deg.
0
2
4
6
8
10
Jy/beam
(c)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 23.8 GHz, 2009-09-22
Peak: 3.93 Jy/beam
Beam: 0.91 × 0.33 mas at -13.4 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jy/beam
(d)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 23.8 GHz, 2009-10-22
Peak: 6.43 Jy/beam
Beam: 0.92 × 0.49 mas at 15.4 deg.
0
1
2
3
4
5
6
Jy/beam
(e)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 23.8 GHz, 2009-12-03
Peak: 9.91 Jy/beam
Beam: 0.88 × 0.41 mas at -12.1 deg.
0
2
4
6
8
Jy/beam
(f)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 23.8 GHz, 2010-01-18
Peak: 16 Jy/beam
Beam: 0.75 × 0.35 mas at -7.47 deg.
0
2
4
6
8
10
12
14
16
Jy/beam
(g)
2 0 -2 -4 -6 -8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 23.8 GHz, 2010-02-21
Peak: 18.7 Jy/beam
Beam: 0.65 × 0.29 mas at -10.1 deg.
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
Jy/beam
(h)
Fig. E.7. K-band (22−24 GHz) CLEAN images of 3C454.3 from 2008 January 03 to 2010 February 21 with contours at -0.1%, 0.1%, 0.2%, 0.4%,
0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image.
A130, page 48 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9
4
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2005-05-19
Peak: 4.24 Jy/beam
Beam: 0.49 × 0.21 mas at -21 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Jy/beam
(a)
1 0 -1 -2 -3 -4 -5 -6 -7
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2005-07-14
Peak: 6.45 Jy/beam
Beam: 0.43 × 0.19 mas at -16.7 deg.
0
1
2
3
4
5
6
Jy/beam
(b)
1 0 -1 -2 -3 -4 -5 -6 -7
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2005-09-01
Peak: 9.61 Jy/beam
Beam: 0.42 × 0.20 mas at -18.4 deg.
0
2
4
6
8
Jy/beam
(c)
1 0 -1 -2 -3 -4 -5 -6 -7 -8
4
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2005-12-04
Peak: 9.61 Jy/beam
Beam: 0.42 × 0.20 mas at -18.4 deg.
0
2
4
6
8
Jy/beam
(d)
1 0 -1 -2 -3 -4 -5 -6 -7
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2006-08-03
Peak: 2.39 Jy/beam
Beam: 0.52 × 0.29 mas at -21.9 deg.
0.0
0.5
1.0
1.5
2.0
Jy/beam
(e)
2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
6
5
4
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2006-10-02
Peak: 2.39 Jy/beam
Beam: 0.43 × 0.22 mas at -8.76 deg.
0.0
0.5
1.0
1.5
2.0
Jy/beam
(f)
1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11
5
4
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2006-12-04
Peak: 2.44 Jy/beam
Beam: 0.44 × 0.22 mas at -10.8 deg.
0.0
0.5
1.0
1.5
2.0
Jy/beam
(g)
1 0 -1 -2 -3 -4 -5 -6 -7 -8
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2007-01-26
Peak: 3.23 Jy/beam
Beam: 0.40 × 0.21 mas at -9.19 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Jy/beam
(h)
1 0 -1 -2 -3 -4 -5 -6 -7 -8
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2007-04-26
Peak: 3.24 Jy/beam
Beam: 0.47 × 0.21 mas at -14.4 deg.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Jy/beam
(i)
1 0 -1 -2 -3 -4 -5 -6 -7 -8
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2007-06-16
Peak: 5.46 Jy/beam
Beam: 0.41 × 0.21 mas at -9.74 deg.
0
1
2
3
4
5
Jy/beam
(j)
1 0 -1 -2 -3 -4 -5 -6 -7
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2007-07-25
Peak: 6.74 Jy/beam
Beam: 0.37 × 0.19 mas at -10.3 deg.
0
1
2
3
4
5
6
Jy/beam
(k)
2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9
5
4
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2007-09-13
Peak: 6.79 Jy/beam
Beam: 0.56 × 0.27 mas at -27.4 deg.
0
1
2
3
4
5
6
Jy/beam
(l)
Fig. E.8. Q-band (43 GHz) CLEAN images of 3C454.3 from 2005 May 19 to 2007 September 13 with contours at -0.1%, 0.1%, 0.2%, 0.4%, 0.8%,
1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image. For 2007 September 13 the contours are at -0.05%, 0.05%, 0.1%,
0.2%, 0.4%, 0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity.
A130, page 49 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
2 1 0 -1 -2 -3 -4 -5 -6 -7 -8
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2008-01-03
Peak: 6.15 Jy/beam
Beam: 0.84 × 0.28 mas at -24 deg.
0
1
2
3
4
5
6
Jy/beam
(a)
1 0 -1 -2 -3 -4 -5 -6 -7
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.14 GHz, 2008-12-07
Peak: 12.9 Jy/beam
Beam: 0.43 × 0.28 mas at -4.21 deg.
0
2
4
6
8
10
12
Jy/beam
(b)
1 0 -1 -2 -3 -4 -5 -6 -7
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.22 GHz, 2009-09-22
Peak: 9.55 Jy/beam
Beam: 0.49 × 0.20 mas at -14.6 deg.
0
2
4
6
8
Jy/beam
(c)
1 0 -1 -2 -3 -4 -5 -6 -7
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.22 GHz, 2009-10-22
Peak: 14.6 Jy/beam
Beam: 0.57 × 0.29 mas at 21.3 deg.
0
2
4
6
8
10
12
14
Jy/beam
(d)
1 0 -1 -2 -3 -4 -5 -6 -7
3
2
1
0
-1
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.22 GHz, 2009-12-03
Peak: 20 Jy/beam
Beam: 0.47 × 0.23 mas at -10.9 deg.
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
Jy/beam
(e)
1 0 -1 -2 -3 -4
1
0
-1
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.22 GHz, 2010-01-18
Peak: 20.8 Jy/beam
Beam: 0.38 × 0.17 mas at 4.62 deg.
0
5
10
15
20
Jy/beam
(f)
1 0 -1 -2 -3 -4 -5
2
1
0
-1
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 43.22 GHz, 2010-02-21
Peak: 17.4 Jy/beam
Beam: 0.33 × 0.15 mas at -2.91 deg.
0.0
2.5
5.0
7.5
10.0
12.5
15.0
Jy/beam
(g)
Fig. E.9. Q-band (43 GHz) CLEAN images of 3C454.3 from 2008 January 03 to 2010 February 21. The contours are given at -0.1%, 0.1%, 0.2%,
0.4%, 0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity at each image. For 2008 December 7 the contours are at -0.05%,
0.05%, 0.1%, 0.2%, 0.4%, 0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and 51.2% of the peak intensity.
A130, page 50 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
Appendix F: Spectral index maps
Spectral index maps are obtained after alignment using matched
common-uvrange images per frequency pair at all epochs. CX
spectral index maps are displayed in Figures F.1 and F.2. XU
spectral index maps are displayed in Figures F.3 and F.4. UK
spectral index maps are displayed in Figures F.5 and F.6, and
KQ spectral index maps are displayed in Figures F.7 and F.8.
10 0 -10 -20 -30 -40
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-05-19,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(a)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-07-14,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(b)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-09-01,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(c)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-12-04,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(d)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2006-10-02,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(e)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2006-12-04,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(f)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-01-26,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(g)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-04-26,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(h)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-16-06,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(i)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-07-25,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(j)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-09-13,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(k)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2008-01-03,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(l)
Fig. F.1. Spectral index maps for the frequency pair CX (5 - 8 GHz). The colour bar indicates the spectral index. The ellipse in the bottom left
corner represents the interferometric beam. The contour lines are given at -0.1%, 0.1% 0.2%, 0.4%, 0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and
51.2% of the peak intensity at each image.
A130, page 51 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2008-12-07,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(a)
0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-09-22,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(b)
10 0 -10 -20 -30 -40 -50
40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-10-22,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(c)
10 0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-12-03,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(d)
0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2010-01-18,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(e)
0 -10 -20 -30 -40
30
20
10
0
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2010-02-21,
Spectral index: 5.00 - 8.35 GHz.
Contours: 5.00 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(f)
Fig. F.2. Continuation of Figure F.1.
A130, page 52 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-05-19,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(a)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-07-14,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(b)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-09-01,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(c)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-12-04,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(d)
5 0 -5 -10 -15
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2006-10-02,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(e)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2006-12-04,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(f)
5 0 -5 -10 -15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-01-26,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(g)
5 0 -5 -10 -15
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-04-26,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(h)
5 0 -5 -10 -15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-06-16,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(i)
5 0 -5 -10 -15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-07-25,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(j)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-09-13,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(k)
5 0 -5 -10 -15 -20
20
15
10
5
0
-5
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2008-01-03,
Spectral index: 8.35 - 15.3 GHz.
Contours: 8.35 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(l)
Fig. F.3. Spectral index maps for the frequency pair XU (8 - 15 GHz). The colour bar indicates the spectral index. The ellipse in the bottom left
corner represents the interferometric beam. The contour lines are given at -0.1%, 0.1% 0.2%, 0.4%, 0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and
51.2% of the peak intensity at each image.
A130, page 53 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2008-12-07,
Spectral index: 8.89 - 15.3 GHz.
Contours: 8.89 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(a)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-09-22,
Spectral index: 8.4 - 15.3 GHz.
Contours: 8.4 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(b)
5 0 -5 -10 -15 -20 -25
20
15
10
5
0
-5
-10
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-10-22,
Spectral index: 8.4 - 15.3 GHz.
Contours: 8.4 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(c)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-12-03,
Spectral index: 8.4 - 15.3 GHz.
Contours: 8.4 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(d)
5 0 -5 -10 -15 -20
15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2010-01-18,
Spectral index: 8.4 - 15.3 GHz.
Contours: 8.4 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(e)
0 -5 -10 -15
10
5
0
-5
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2010-02-21,
Spectral index: 8.4 - 15.3 GHz.
Contours: 8.4 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
(f)
Fig. F.4. Continuation of Figure F.3.
A130, page 54 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
4 2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-05-19,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(a)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-07-14,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(b)
2 0 -2 -4 -6 -8 -10 -12 -14
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-09-01,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(c)
4 2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-12-04,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(d)
2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2006-10-02,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(e)
4 2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2006-12-04,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(f)
4 2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-01-26,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(g)
4 2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-04-26,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(h)
4 2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-06-16,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(i)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-07-25,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(j)
4 2 0 -2 -4 -6 -8 -10-12-14-16
12
10
8
6
4
2
0
-2
-4
-6
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-09-13,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(k)
4 2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2008-03-01,
Spectral index: 15.3 - 22.2 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(l)
Fig. F.5. Spectral index maps for the frequency pair UK (15 − 22) GHz. The colour bar indicates the spectral index. The ellipse in the bottom left
corner represents the interferometric beam. The contour lines are given at -0.1%, 0.1% 0.2%, 0.4%, 0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and
51.2% of the peak intensity at each image.
A130, page 55 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
4 2 0 -2 -4 -6 -8 -10 -12 -14 -16
10
8
6
4
2
0
-2
-4
-6
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2008-12-07,
Spectral index: 15.3 - 21.8 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(a)
2 0 -2 -4 -6 -8 -10 -12
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-09-22,
Spectral index: 15.4 - 24.0 GHz.
Contours: 15.4 GHz.
2
1
0
1
2
3
(b)
2 0 -2 -4 -6 -8 -10 -12 -14
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-10-22,
Spectral index: 15.4 - 24.0 GHz.
Contours: 15.4 GHz.
2
1
0
1
2
3
(c)
2 0 -2 -4 -6 -8 -10 -12
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-12-03,
Spectral index: 15.4 - 24.0 GHz.
Contours: 15.4 GHz.
2
1
0
1
2
3
(d)
2 0 -2 -4 -6 -8 -10 -12
10
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2010-01-18,
Spectral index: 15.4 - 24.0 GHz.
Contours: 15.4 GHz.
2
1
0
1
2
3
(e)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2010-02-21,
Spectral index: 15.4 - 24.0 GHz.
Contours: 15.3 GHz.
2
1
0
1
2
3
(f)
Fig. F.6. Continuation of Figure F.5. Spectral index maps for the frequency pair UK (15 − 24) GHz.
A130, page 56 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
2 0 -2 -4 -6 -8 -10
8
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-05-19,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(a)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-07-14,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(b)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-09-01,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(c)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2005-12-04,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(d)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2006-10-02,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(e)
2 0 -2 -4 -6 -8 -10
8
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2006-12-04,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(f)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-01-26,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(g)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-04-26,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(h)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-06-16,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(i)
2 0 -2 -4 -6 -8
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-07-25,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(j)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2007-09-13,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(k)
2 0 -2 -4 -6 -8 -10 -12
8
6
4
2
0
-2
-4
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2008-01-03,
Spectral index: 22.2 - 43.1 GHz.
Contours: 22.2 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(l)
Fig. F.7. Spectral index maps for the frequency pair KQ (22−43 GHz). The colour bar indicates the spectral index. The ellipse in the bottom left
corner represents the interferometric beam. The contour lines are given at -0.1%, 0.1% 0.2%, 0.4%, 0.8%, 1.6%, 3.2%, 6.4%, 12.8%, 25.6%, and
51.2% of the peak intensity at each image.
A130, page 57 of 58
Chamani, W., et al.: A&A 672, A130 (2023)
2 0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2008-12-07,
Spectral index: 24.0 - 43.1 GHz.
Contours: 24.0 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(a)
0 -2 -4 -6 -8 -10 -12
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-09-22,
Spectral index: 24.0 - 43.1 GHz.
Contours: 24.0 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(b)
2 0 -2 -4 -6 -8 -10
8
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-10-22,
Spectral index: 24.0 - 43.2 GHz.
Contours: 24.0 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(c)
0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2009-12-03,
Spectral index: 24.0 - 43.2 GHz.
Contours: 24.0 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(d)
0 -2 -4 -6 -8 -10
6
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2010-01-18,
Spectral index: 24.0 - 43.2 GHz.
Contours: 24.0 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(e)
0 -2 -4 -6 -8
4
2
0
-2
Relative R.A. (mas)
Re
la
tiv
e 
De
c 
(m
as
)
3C454.3 at 2010-02-21,
Spectral index: 24.0 - 43.2 GHz.
Contours: 24.0 GHz.
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
(f)
Fig. F.8. Continuation of Figure F.7. Spectral index maps for the frequency pair KQ (24−43 GHz).
A130, page 58 of 58