Direct Measurements of Synchrotron-emitting Electrons at Near-Sun Shocks
I. C. Jebaraj1 , O. V. Agapitov2,3 , M. Gedalin4 , L. Vuorinen1,5 , M. Miceli6 , C. M. S. Cohen7 , A. Voshchepynets2,8 ,
A. Kouloumvakos9 , N. Dresing1 , A. Marmyleva10 , V. Krasnoselskikh2,11 , M. Balikhin12 , J. G. Mitchell13 ,
A. W. Labrador13 , N. Wijsen14 , E. Palmerio15 , L. Colomban2 , J. Pomoell10 , E. K. J. Kilpua10 , M. Pulupa2 ,
F. S. Mozer2 , N. E. Raouafi9 , D. J. McComas16 , S. D. Bale2,17 , and R. Vainio1
1 Department of Physics and Astronomy, University of Turku, 20500 Turku, Finland; immanuel.c.jebaraj@gmail.com
2 Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
3 Astronomy and Space Physics Department, National Taras Shevchenko University of Kyiv, 03127 Kyiv, Ukraine
4 Department of Physics, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel
5 Department of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK
6 Dipartimento di Fisica e Chimica E. Segrè, Università degli Studi di Palermo, Palermo, 90134, Italy
7 California Institute of Technology, Pasadena, CA 91125, USA
8 Department of System Analysis and Optimization Theory, Uzhhorod National University, 88000 Uzhhorod, Ukraine
9 The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA
10 University of Helsinki, 00014 Helsinki, Finland
11 LPC2E/CNRS, UMR 7328, 45071 Orléans, France
12 University of Sheffield, Sheffield S10 2TN, UK
13 Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
14 Centre for Mathematical Plasma Astrophysics, KU Leuven, 3001 Leuven, Belgium
15 Predictive Science Inc., San Diego, CA 92121, USA
16 Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
17 Physics Department, University of California, Berkeley, CA 94720, USA
Received 2024 September 16; revised 2024 October 18; accepted 2024 November 2; published 2024 November 14
Abstract
In this study, we present the first-ever direct measurements of synchrotron-emitting heliospheric traveling shocks,
intercepted by the Parker Solar Probe (PSP) during its close encounters. Given that much of our understanding of
powerful astrophysical shocks is derived from synchrotron radiation, these observations by PSP provide an
unprecedented opportunity to explore how shocks accelerate relativistic electrons and the conditions under which
they emit radiation. The probe’s unparalleled capabilities to measure both electromagnetic fields and energetic
particles with high precision in the near-Sun environment has allowed us to directly correlate the distribution of
relativistic electrons with the resulting photon emissions. Our findings reveal that strong quasi-parallel shocks emit
radiation at significantly higher intensities than quasi-perpendicular shocks due to the efficient acceleration of
ultrarelativistic electrons. These experimental results are consistent with theory and recent observations of
supernova remnant shocks and advance our understanding of shock physics across diverse space environments.
Unified Astronomy Thesaurus concepts: Interplanetary shocks (829); Shocks (2086); Non-thermal radiation
sources (1119); Solar radio emission (1522); Radio continuum emission (1340); Radio sources (1358); Solar
coronal mass ejection shocks (1997); Solar particle emission (1517)
1. Introduction
Collisionless shocks are among the most ubiquitous and
strongly nonlinear systems in plasma, spanning spatial scales
from laboratory settings to galaxy clusters (R. Z. Sagd-
eev 1966; A. A. Galeev 1976; C. F. Kennel et al. 1985;
B. Lembege et al. 2004; V. Krasnoselskikh et al. 2013;
O. V. Agapitov et al. 2023; M. Miceli 2023). In the shock
reference frame, most of the directed flowʼs kinetic energy is
converted into plasma heating, particle acceleration, magnetic
compression, and turbulence. Understanding the mechanisms
behind this energy conversion presents a significant chal-
lenge. Electron heating and acceleration to relativistic
energies are key channels of energy redistribution, and the
analysis of the electromagnetic (EM) radiation from these
electrons is crucial for remote study of astrophysical shocks
(J. Vink 2020).
Of particular interest is synchrotron radiation emitted by
relativistic electrons accelerated at shock waves (J. Schwin-
ger 1949; M. Born & E. Wolf 1964; V. L. Ginzburg &
S. I. Syrovatskii 1964), which is the most common EM
emission observed from supernova remnant (SNR) shocks
(A. M. Bykov 2004; E. A. Helder et al. 2009), spanning from
radio to X-ray wavelengths. The energy of these electrons is
given by Ee= γmec
2, where γ (?1) is the Lorentz factor, me is
the electron mass, and c is the speed of light. Consequently,
synchrotron emission is highly beamed within an angle θ∼ 1/γ
around the electron’s velocity direction. The emission power
peaks at the critical frequency, ωm∼Ωeγ
2, where Ωe= eB/mec
is the nonrelativistic electron gyrofrequency, with e being the
electron charge and B the ambient magnetic field (V. L. Ginzb-
urg 1979; M. S. Longair 1992). The synchrotron spectrum is
broadband, with a width Δω∼ ωm, and the total emitted power
scales as 2 g~ . However, this emission typically arises from
a distribution of electrons, often following a power law with an
exponent δ.
The acceleration of such power-law distributed electrons,
which emit broadband radiation, is often described by the
The Astrophysical Journal Letters, 976:L7 (14pp), 2024 November 20 https://doi.org/10.3847/2041-8213/ad8eb8
© 2024. The Author(s). Published by the American Astronomical Society.
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1
diffusive shock acceleration (DSA) theory (W. I. Axford et al.
1977; G. F. Krymskii 1977; A. R. Bell 1978; R. D. Blandford
& J. P. Ostriker 1978). In the strong shock limit (gas
compression ratio, rgas= 4), DSA predicts a power-law
electron energy distribution with δ= (rgas+ 2)/(rgas− 1)= 2
(M. A. Malkov & L. O. Drury 2001; A. M. Bykov et al. 2019).
A typical synchrotron spectrum produced by such an electron
distribution has two main features: a low-frequency turnover
(ωc) separating optically thick and thin regimes (V. L. Ginzburg
& S. I. Syrovatskii 1964; G. B. Rybicki & A. P. Light-
man 1979) and a high-frequency exponential cutoff due to the
maximum electron energy, max e max
2w g~ W , where maxg is the
highest Lorentz factor in the distribution.
In the optically thin regime, the synchrotron spectrum
follows a power law with an exponent α∼ 0.5, which directly
relates to the electron energy distribution (δ= 2) via
α= (δ− 1)/2. This relationship is traditionally used to
estimate particle distributions in astrophysical sources such as
SNRs, though variations are common (D. A. Green 2019).
Despite these insights, uncertainties remain about the detailed
distribution of relativistic electrons, their acceleration mechan-
isms, and the specific conditions under which they emit
radiation. The universality of DSA theory, particularly its scale
invariance in strong shocks (rgas= 4), suggests that under-
standing synchrotron radiation in interplanetary (IP) shocks
could offer a bridge to understanding SNR shocks. Such a
bridge between IP and SNR shocks has long been sought, with
the heliosphere often considered a practical laboratory for
studying remote astrophysical objects (C. F. Kennel et al. 1985;
T. Terasawa 2003). Observations of SNR shocks offer unique
insights into the analysis of global shock structure through
high-resolution radio astronomy, which allows for probing
different regions of a shock with GeV electrons along various
lines of sight. However, certain factors must be considered,
such as the vast difference in system size, with SNR shocks
being more than 6 orders of magnitude larger, and their lifetime
is much longer. Similarly, the energy they carry is at least 15
orders of magnitude greater than that of the most powerful IP
shocks (J. Vink 2020). Furthermore, the nonstationarity of
acceleration, e.g., in traveling IP shocks, may substantially
affect the particle spectrum, making comparison with SNR
shocks more difficult.
A combination of remote-sensing observations of synchro-
tron emission and in situ measurements of the emitting
electrons can address key questions about the conditions that
produce accelerated electrons capable of synchrotron radiation.
This approach could help reconcile differences between strong
IP and SNR shocks, where system size and the upstream ion
bulk energy in the shock frame are the primary distinctions.
Earlier studies suggested that heliospheric synchrotron emis-
sion is generated by energetic electrons trapped within the
coronal mass ejections driving the shock, rather than by shock-
accelerated electrons (T. S. Bastian 2007; S. Pohjolainen et al.
2013). However, more recent work has shown that traveling IP
shocks can accelerate electrons to relativistic energies
(I. C. Jebaraj et al. 2023a, 2024; N. Talebpour Sheshvan
et al. 2023).
In this study, we present the first-ever direct observations of
synchrotron-emitting relativistic (γ∼ 2–6 or Ee∼ 1–3MeV)
and ultrarelativistic (γ> 10 or Ee> 5MeV) electrons produced
by fast IP shocks observed by NASAʼs Parker Solar Probe
(PSP; N. J. Fox et al. 2016). We utilize continuous, high-
fidelity electric field measurements in the radio wavelengths
from the Radio Frequency Spectrometer (RFS; M. Pulupa et al.
2017), part of the FIELDS instrument suite (S. D. Bale et al.
2016). These observations are compared with the electron
distributions measured at the time of shock arrival by the Low
and High Energetic Particle Instruments (EPI-Lo and EPI-Hi,
respectively; M. E. Hill et al. 2017; M. E. Wiedenbeck et al.
2017), part of the Integrated Science Investigation of the Sun
(ISeIS) suite (D. J. McComas et al. 2016). The first shock (S1)
was quasi-perpendicular and detected during PSPʼs 13th close
approach to the Sun (Encounter 13) on 2022 September 5 at
15.1 Re (O. M. Romeo et al. 2023; D. Trotta et al. 2024). The
second shock (S2) was near-parallel and detected 49 Re away
during Encounter 15 on 2023 March 13 (I. C. Jebaraj et al.
2024). In the following sections, we present our observations of
synchrotron emission, analyze the spectral characteristics and
polarization, and examine the distribution of the emitting
electrons.
2. Results from the Analysis
2.1. Diffuse and Self-absorbed Continuum-like Emission
Figures 1(A) and (B) display the dynamic radio spectra of
electric field intensity from transverse EM waves, E( f, t)2,
where f= ω/2π (in Hz), recorded by the high (HFR; 19.2–1.6
MHz) and low (LFR; 1.6–0.001MHz) frequency receivers of
FIELDS/RFS on board PSP, both before and during the shock
crossings on 2022 September 5 (S1) and 2023 March 13 (S2),
respectively. The units of measurement are solar flux units
(1 sfu= 10−22 Wm−2 Hz−1), normalized to 1 au, assuming
that the intensity decreases with distance (r) following r−2.
These EM waves, emitted by electrons at some distance from
the spacecraft, propagate toward the observer at the speed of
light, appearing as distinct maxima in the electric field
intensity. The frequencies of these maxima change over time,
and the rate of change, hereafter referred to as “drift,” reflects
variations in plasma density and magnetic field gradients in the
emission region. In regions with negative gradients in plasma
density and magnetic field, both ωpe ( ( ) ( )n e m4e 2 0 ep= ,
where ne is electron density and ò0 is the permittivity of free
space) and Ωe will show negative gradients. As a result,
analyzing spectral drift rates and assuming a model for the
emission mechanism, properties of the emitting electrons and
the surrounding medium can be inferred. The electron plasma
frequency at the observer’s location, fpe= ωpe/2π, is annotated
in both Figures 1(A) and (B). Below fpe, EM waves become
evanescent, resulting in a sharp emission cutoff regardless of
where the emission originates.
Figures 1(A) and (B) also annotate common coherent
emissions generated by plasma instabilities (S. A. Kaplan &
V. N. Tsytovich 1969; A. A. Galeev & V. V. Krasnoselsk-
ikh 1979; K. Papadopoulos & H. P. Freund 1979; A. Voshch-
epynets et al. 2015). This includes type II bursts, produced by
subrelativistic electrons accelerated at shocks. This emission is
characterized by a narrow relative frequency bandwidth
(Δf/f= ( fhigh− flow)/( fcenter)< 0.3, where fcenter= ( fhigh+
flow)/2; I. H. Cairns et al. 2003; I. C. Jebaraj et al. 2020). In
the spectra, type II bursts appear as chains of intense,
fragmented emissions with frequency drift corresponding to
the speed of the shock region where they originate.
Additionally, type III bursts are generated by subrelativistic
electron beams propagating along open magnetic field lines,
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with Δf/f 0.5 (S. Suzuki & G. A. Dulk 1985; I. C. Jebaraj
et al. 2023b). Type III bursts, the most intense heliospheric
radio emissions, exhibit rapid spectral drift rates, reflecting the
high speed of the emitting electrons. While these emissions and
their relationship to solar transient shocks have been exten-
sively studied over the past five decades, this study focuses on
spectral features beyond these well-known emissions.
2022 September 5 (S1). In Figure 1(A), we identify three
distinct emissions that deviate from the characteristics of the
aforementioned coherent emissions, annotated as Syn-1, Syn-2,
and Syn-3. Syn-1 (circle markers) starts at ∼5MHz at 16:20 UT
and drifts down to the local fpe∼ 400 kHz by 17:00 UT, with
some parts observed until shock arrival at 17:27 UT. Syn-2
(square markers) begins at ∼2MHz at 16:30 UT and drifts down
to fpe during shock arrival at 17:27 UT. Syn-3 (diamond
markers) starts at ∼2MHz at 16:50 UT and similarly drifts
down to fpe by 17:27 UT. These emissions are characterized as
diffuse, broadband emissions with Δf/f∼ 1, and the associated
maxima (annotated with distinct markers) correspond to the
turnover frequency ( fc= ωc/2π). The features are indicative of
synchrotron emission with self-absorption (A. Nindos 2020). It
is worth noting that some emission is seen continuing in the
postshock region up until 17:45 UT. Much of it is evanescent
due to the high fpe in the postshock plasma. Analysis in
Appendix B shows that the measured electric field intensity
corresponds to EM waves with phase speeds close to c, with no
detection of Langmuir waves.
2023 March 13 (S2). In Figure 1(B), an emission starts at
05:20 UT from ∼200 kHz and extends until shock arrival at
07:13 UT. This emission is also characterized as diffuse and
broadband withΔf/f∼ 1, with fc annotated with circle markers.
A similar analysis of the EM waves near the shock arrival at
07:12 UT is presented in Appendix B. The estimated phase
speeds for the waves above fpe were close to c. However, unlike
S1, several electrostatic waves were detected at a small fraction
of fpe, annotated as “ES waves” in Figure 1(B). These waves
are not expected to contribute to the generation of coherent
plasma emissions (V. V. Lobzin et al. 2005).
2.2. Emission Is Depolarized in Inhomogeneous Plasma
Synchrotron radiation from a homogeneous medium is
highly polarized (V. L. Ginzburg & S. I. Syrovatskii 1964). EM
radiation is emitted as a combination of two transverse wave
modes, distinguished by the orientation of the wave electric
field (E) relative to the background magnetic field (B). These
modes are the ordinary (o-mode, E∥B) and extraordinary (x-
mode, E⊥B) waves. In a cold, unmagnetized plasma, the
propagation of o- and x-modes is independent of each other,
but this is not the case in a magnetoactive plasma. The transfer
of these wave modes through a plasma is best described using
the Stokes parameters: I, Q, U, and V (S. Chandrasekhar 1947;
R. Ramaty 1969). A short description of the Stokes parameters
and the means of estimating them from data can be found in
Appendix D. When wave propagation is quasi-parallel to B, the
Stokes parameters simplify such that Q=U→ 0. As a result,
o- and x-mode waves are circularly polarized in opposite
directions, and Stokes V is given by the difference between the
intensities of the o- and x-modes (V= Io− Ix), resulting in
circular polarization in the direction of the dominant mode. In
the case of quasi-perpendicular wave propagation relative to B,
Stokes Q= Io− Ix, while U= V→ 0, leading to predominantly
linear polarization.
The polarization conventions described above apply strictly
to the region where emission originates. If B changes between
the emitter and observer, the polarization can be altered or lost.
Figure 1. Panels (A) and (B) (top row) show the dynamic spectra of electric field power, E( f, t)2, in the radio frequency range, measured before and at the shock
crossing on 2022 September 5 (S1) and 2023 March 13 (S2), respectively. The units are in solar flux units (1 sfu = 10−22 W m−2 Hz−1). The arrival of both shocks at
PSP is marked by the red (S1) and blue (S2) arrows on top of the figure. The synchrotron emissions, the coherent plasma emissions (type II and type III), and the local
fpe are marked. Panels (A2) and (B2) (middle row) show the degree of circular polarization normalized by total intensity (Stokes V/I; see text for details). Panels (A3)
and (B3) (bottom row) show the magnetic field components and magnitude.
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Stokes V may be converted to Stokes Q (and vice versa) due to
Faraday conversion, potentially reducing or reversing the
observed circular polarization (A. G. Sitenko & Y. A. Kiroch-
kin 1966; V. V. Zheleznyakov 1968). Linear polarization can
undergo Faraday rotation, where the polarization plane rotates
during propagation, possibly leading to depolarization if the
magnetic field is complex (A. G. Sitenko & Y. A. Kiroch-
kin 1966; V. L. Ginzburg & S. I. Syrovatskii 1969; D. B. Mel-
rose 1971). Precise measurement of polarization is impossible,
as the waves may become depolarized while propagating
through a plasma with random fluctuations. Consequently, for a
remote observer, it may differ significantly from what it was at
the region where it is emitted.
Synchrotron radiation is typically emitted over a range of
angles with respect to B, making the x-mode dominant for the
observer. This also makes the emission linearly polarized in the
x-mode when observed along the direction of the electron’s
velocity or from any oblique angles to B. Thus, the degree of
circular polarization is secondary and increases with θ∼ 1/γ,
or when viewed from oblique angles within θ. This can be
reformulated in terms of Stokes parameters as V/Q∼ 1/γ. The
handedness of circular polarization for the o-mode is strictly
clockwise (right-handed) when the magnetic field is pointing
inward (Br< 0) and counterclockwise (left-handed) when it is
pointing outward (Br> 0). For the x-mode, the handedness is
reversed.
The emissions from both S1 and S2 have negligible degrees
of linear polarization and are not presented here. The degree of
circular polarization (( ) ( ) )I I I I V Io x o x- + = for both
events is depicted in Figures 1(A2) and (B2).
2022 September 5 (S1).We observed clear circular polariza-
tion for Syn-2 and Syn-3 when the emission was close to the
local fpe during the shock arrival between 17:15 and 17:27 UT.
Given that V/Q≈ 1/γ, we used the degree of circular
polarization (V/I= 15%–25%) to estimate that the emission
originated from electrons with γ∼ 4–7. Figure 1(A3) shows
the magnetic field components and magnitude, revealing that
S1 is polarized in the left-hand sense, while Br< 0 (inward-
pointing), consistent with emission in the x-mode as predicted
by theory. While remote observations can carry significant
uncertainties when correlating with magnetic field data, our
measurements were made with the emitting region in close
proximity to the observer, thereby reducing much of this
uncertainty.
2023 March 13 (S2). The observations presented in
Figure 1(B2) show no signs of circular polarization. This lack
of polarization is likely due to a combination of observer
position and depolarization caused by a randomly inhomoge-
neous medium. If the conditions at and around the emitting
region are turbulent at scales corresponding to the wavelength
of the EM waves, they may be depolarized within the emitting
region. Even in the presence of large-scale inhomogeneities,
the Faraday effect may significantly depolarize the EM waves.
Indeed, it was demonstrated by I. C. Jebaraj et al. (2024) that
inhomogeneities across a wide range of scales were present.
2.3. Intrinsic Brightness Increases as Shock Approaches PSP
The characteristics of the synchrotron emission may also be
assessed, taking into account the radiation transfer from the
emitting electrons toward the observer (S. Chandrasek-
har 1947). Under the Rayleigh–Jeans approximation
(hf= kBTB, where h is Planck’s constant, f is the frequency
of radiation in Hz, and kB is the Boltzmann constant),
TB≈ (c
2If)/(2kBf
2), where If is the emission intensity. The
intrinsic brightness of the source or brightness temperature TB
of synchrotron emissions cannot exceed the limit set by inverse
Compton scattering (1012 K at 1 GHz; K. I. Kellermann &
I. I. K. Pauliny-Toth 1969; G. B. Rybicki & A. P. Light-
man 1979). Quantifying the solid angle subtended by the
source (Ω in units of steradians) allows us to estimate TB (see
Equation (C3) in Appendix C).
2022 September 5 (S1). In Figure 1(A), the maxima of Syn-
1, Syn-2, and Syn-3 are annotated by the circle, square, and
diamond markers, respectively. They correspond to the self-
absorption cutoff or the fc. If the source of the synchrotron
emission is the relativistic electrons accelerated at the shock
front that rapidly approaches the probe, then Ω increases at a
rate determined by the shock speed. This suggests that the
presence of different synchrotron emissions (Syn-1, Syn-2, and
Syn-3) are likely due to different electron populations at
different regions of the shock, which propagate at different
speeds. Assessing Syn-2 and Syn-3, we find that their intensity
increases with decreasing frequency, indicating a rapid increase
in Ω, such that Ω→ 2π.
The effect of Ω is such that as the region of the shock
accelerating the electron gets closer and closer, emission from
more and more electrons is received. Such an effect would also
be seen in TB, which was estimated for Syn-1, Syn-2, and Syn-
3 in Appendix C. The result suggests that none of them exceed
the inverse Compton scattering limit of 1.3× 1013 K. However,
the TB of Syn-2 and Syn-3 increases rapidly just before the
shock arrival at 17:27 UT, indicating that Ω→ 2π, i.e.,
emission originates from regions in close proximity to the
shock front traversed by the spacecraft. A schematic of the
likely shock encounter is shown on the right in Figure 2, where
the probe encounters the shock flank, which is quasi-
perpendicular. The probe is positioned in close proximity to
the emitting region (marked by the red square on the shock
surface), allowing it to receive portions of the synchrotron
radiation.
2023 March 13 (S2).Here, the intensity of the emission
increases as the shock approaches. Quantifying this using the
solid angle Ω, we find that TB remains relatively stable until
06:55 UT, after which it increases exponentially as the shock
nears the spacecraft, corresponding to Ω→ 2π. Notably, TB
exceeds the inverse Compton limit of 1.7× 1013 K, suggesting
that Ω= 2π at 07:10 UT. This indicates that the spacecraft was
inside the region where electron acceleration and subsequent
emission were being generated. In this scenario, the observer
receives emission from a source that covers the full 4π sr (i.e., a
fully isotropic source), causing the 2π sr assumption to break
down. The schematic on the left in Figure 2 illustrates the likely
encounter between the probe and the shock wave. The probe
encounters the center of the quasi-parallel shock region, where
it receives the bulk of the emitted synchrotron photons, leading
to a higher observed emission intensity. As noted in Figure 6 in
Appendix C, the intrinsic brightness of the radiation from S2 is
an order of magnitude greater than that of S1, supporting the
representation shown in the schematic.
2.4. Relativistic Electron Distribution and the Optically Thin
Synchrotron Spectra
The observations of synchrotron emission from shocks that
traversed PSP provide a unique opportunity to directly probe
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the energetic electron distribution and compare it with the
synchrotron spectrum. This comparison may be approached
from DSA theory, as the power-law exponents of the
synchrotron spectrum (α) and that of the electrons (δ) are
directly related through α∼ (δ− 1)/2.18 While the shock
structure is relatively unimportant for high-energy ions under-
going DSA, it plays an important role for electron acceleration
(M. A. Riquelme & A. Spitkovsky 2011). Furthermore,
investigating the characteristics of the accelerated electrons
such as their anisotropy may also improve our understanding of
the process. In the presence of a well-developed ion foreshock,
electrons scatter and their pitch angles become diffused,
leading to an isotropic distribution (M. A. Malkov &
L. O. Drury 2001).
If these shock characteristics play a significant role, we
would expect to see differences between S1 and S2, given their
distinct properties that have been discussed in O. M. Romeo
et al. (2023) and I. C. Jebaraj et al. (2024). S1 was a fast shock
that was propagating quasi-perpendicularly to the background
B and had moderate gas compression, rgas∼ 2.5. S2 was also a
fast shock but propagating nearly parallel to B with maximum
compression, rgas= 4. While shock geometry is not a direct
factor in DSA estimations, it plays a crucial role in creating the
conditions that enable efficient particle acceleration via
DSA, such as the development of a wave foreshock
(L. O. Drury 1983; R. Vainio 2003). The formation of a
foreshock is particularly effective in quasi-parallel shocks due
to ion-streaming instabilities, which generate waves that act as
scattering centers for both ions and relativistic electrons,
thereby enhancing DSA (R. Vainio & R. Schlickeiser 1999).
According to DSA theory, the predicted electron energy
spectral index δ would be around 3 for S1 and closer to 2 for
S2, corresponding to synchrotron spectral slopes of α∼ 1 for
S1 and α= 0.5 for S2. However, a limitation of DSA’s
applicability to electrons is that only those with γ 2 or
Ee 1MeV can participate effectively, as these electrons are
able to interact with the waves generated by ions (G. P. Zank &
T. K. Gaisser 1992; M. A. Malkov & L. O. Drury 2001). The
technical requirement for electron involvement in DSA is less
stringent than for their injection into it. The primary condition
is that their speed must exceed that of the shock along the field
line, which imposes additional constraints on DSA efficiency in
quasi-perpendicular shocks, even in the presence of ion-scale
waves.
While this study does not specifically address how and why
subrelativistic electrons reach relativistic energies, the process
remains poorly understood and presents a barrier to fully
understanding electron acceleration. Previous studies have
shown that electron energization is linked to the scale of the
EM fields at the shock transition layer (M. Balikhin et al.
1993, 1998), which determines the contributions from both
adiabatic and nonadiabatic processes (M. Gedalin 2020). In
the case of S1, where the shock is quasi-perpendicular, much
of the subrelativistic electron acceleration is likely to be
adiabatic (M. A. Balikhin et al. 1989; I. C. Jebaraj et al.
2023b), although nonadiabatic processes may also play a role
when the shock is supercritical (M. Gedalin et al. 1995;
T. Katou & T. Amano 2019). In the case of S2, I. C. Jebaraj
et al. (2024) found that the transition consisted of a series of
large-amplitude quasi-perpendicular waves, with a wide range
of electron-scale waves present in the foreshock. This
combination makes it difficult to pinpoint a single mechanism,
though adiabatic, nonadiabatic, and other diffusive mechan-
isms could coexist.
2022 September 5 (S1). To directly compare the accelerated
electrons and the synchrotron radiation they emit, we fit the
emission peaks fc, marked with distinct indicators in
Figure 2. Schematic of the synchrotron emission from S1 and S2. The curved purple front represents the traveling shock wave, with magnetic field lines shown in
blue. The shock geometry along the reference field lines is labeled as Q⊥ (quasi-perpendicular) and Q∥ (quasi-parallel). The finite region on the shock surface where
relativistic electrons are accelerated and subsequently emit synchrotron radiation is indicated by the red square. The emitted photons are represented by yellow markers
and the notation γ.
18 It is worth noting that for mildly relativistic electrons, G. A. Dulk &
K. A. Marsh (1982) propose a modified form, α ∼ 0.9δ − 1.22, resulting in a
steeper spectrum.
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Figure 1(A), using power laws. For the same time interval, we
present the time evolution of the relativistic electron intensity
(in unprocessed units of counts s−1) measured by EPI-Hi High
Energy Telescope (HET). The relativistic electron intensity
rapidly increases approximately 5 minutes before the shock
crossing and remains substantial and nearly constant up to the
crossing itself. This suggests that relativistic electrons are
found in a relatively small region upstream of the shock. In the
postshock region, the relativistic electron intensity decreases
significantly, suggesting that emission must be produced by
electrons in the upstream. We construct the electron energy
spectra shown in Figure 3(B) using data collected by the EPI-
Lo and EPI-Hi/HET instruments during the shock crossing,
between 17:17 and 17:27 UT. Both detectors of EPI-Hi/HET,
namely, the Sun-facing HET-A and the anti-Sun-facing HET-
B, are used. Unlike in Figure 3(A), the data used to construct
the energy–intensity spectra are processed in units of intensity,
i.e., particles cm−2 s−1 sr−1 keV−1. We use a 10 minute
average of the data to reduce large uncertainties that may arise
due to low statistics. Detailed information about the unfolding
procedure used to construct the energy spectra and the
associated errors is provided in Appendix A.2.
The energy spectra shown in Figure 3(B) span from
subrelativistic energies, where γ∼ 1 or Ee∼ 50 keV, to 4MeV
(or γ∼ 8). Due to missing energy channels between 200
and 500 keV, we approximately fit a single power law from
50 keV up to 1MeV, yielding an exponent δ∼ 2.85. However,
these electrons, with γ∼ 1−2, do not contribute significantly to
synchrotron power, which scales as 2 g~ . Beyond 1MeV,
uncertainties in HET measurements increase (see Appendix A.2),
making precise determination of δ challenging. Despite these
uncertainties, we observe a deviation from the power law
obtained for lower energies beyond 1MeV. A new power-law fit,
combining data from HET-A and HET-B between 1 and 5MeV,
yields an exponent δ∼ 4.5. However, when assessed separately,
HET-A and HET-B do not follow the same trend and can be fit
with separate power laws, with exponents δ∼ 4.4 for HET-A
(shown in red) and δ∼ 5 for HET-B (shown in green).
Figure 3. Characteristics of the synchrotron emission from S1 and the corresponding electron distribution. Panel (A) presents the time evolution of the electron
intensity in units of counts s−1 observed between 16:00 UT and 18:00 UT. The arrival of the shock at PSP is marked by the vertical black line at 17:27 UT and the red
arrow on top. Panel (B) shows the 10 minute averaged electron energy distribution between 17:17 and 17:27 UT in units of particles cm−2 s−1 sr−1 keV−1. The
different detectors of ISeIS used to construct the electron spectrum are annotated with colored markers. The approximate power-law fits and the exponents are also
shown in the legend. Panel (C) shows the intensity–frequency profiles at specific times leading up to the shock arrival, along with approximate power-law fits to the
optically thin regime. The fc for Syn-1, Syn-2, and Syn-3 are indicated by the distinct markers introduced in Figure 1(A).
6
The Astrophysical Journal Letters, 976:L7 (14pp), 2024 November 20 Jebaraj et al.
Isolating the theoretically predicted shape of the synchrotron
spectra is impossible in the presence of elevated background
radiation from thermal and nonthermal sources during PSP’s
close encounters (M. Liu et al. 2023). Therefore, in what
follows, we focus on identifying fc as seen in Figure 1(A) and
estimating α in the optically thin regime to infer the
corresponding δ. Figure 3(C) shows temporal cuts of spectral
power as a function of frequency at selected times between
16:42 UT and the shock arrival at 17:27 UT. We focus on Syn-
2 (square markers) and Syn-3 (diamond markers), as Syn-1
(circle markers) reaches the local fpe early and is not relevant to
the locally measured electrons. For Syn-2 and Syn-3, fc is well
defined by intensity peaks, allowing for the estimation of the
spectral slope α above fc. Between 16:42 UT and 17:15 UT, we
find α∼ 2 (δ∼ 5) for both Syn-2 and Syn-3, consistent with
the δ∼ 4.5 estimated from the in situ electron measurements
(Figure 3(B)). After 17:15 UT, as fc approaches fpe, the
minimum electron energy ming required to emit above fpe
increases. In this case, emission originates from the steep tail of
the electron distribution resulting in a steep α 8 or δ 17.
Alternatively, this may be a result of the high-frequency
exponential synchrotron cutoff, f 2max maxw p= , at maxg of the
electron distribution.
Interpreting these observations from a DSA perspective, we
find that the power-law exponent of the low-energy electrons
δ∼ 2.85 aligns reasonably well with the prediction for S1,
δ∼ 3. However, DSA is not particularly effective for the
acceleration of subrelativistic electrons, and it is likely that only
electrons with energy Ee 1MeV can efficiently participate in
the process. The observations presented here show that at
1 MeV and above, the power-law exponent steepens to δ∼ 4.5,
suggesting that even if DSA is active, it is inefficient. The
steepening of α also suggests that there is a cutoff in DSA close
to Ee∼ 4MeV. Here, we find varying electron intensities
measured by HET-A and HET-B above 1.5 MeV. When the
magnetic field is nominally oriented, the Sun (HET-A) and
anti-Sun (HET-B) directions correspond to parallel (0◦) and
antiparallel (180◦) pitch angles of the electrons. Since the
electron intensity measured by HET-A is more than an order of
magnitude higher than HET-B, it indicates strong anisotropy in
the electrons observed from the Sun direction, where the shock
is approaching the observer. Anisotropy is generally found
when the accelerated particles do not partake in efficient DSA
or in the absence of a well-developed foreshock.
2023 March 13 (S2). We present the temporal evolution of
the relativistic electron population in Figure 4(A), which shows
an increase in particle counts leading up to the shock arrival.
Unlike in S1, the relativistic electron intensity in S2 is
relatively high, with a noticeable increase starting at
∼06:40 UT and continuing until the shock’s arrival at
07:13 UT. Figure 4(B) illustrates the average electron
energy–intensity spectrum in a 10 minute interval upstream of
the shock arrival. Using a similar power-law fitting as for S1,
we found an exponent of δ∼ 2.7 between 50 keV and 2.5 MeV
(γ∼ 4). Unlike S1, the power law extends beyond subrelati-
vistic energies up to γ∼ 4, making it more relevant for
synchrotron emission. Beyond ∼2.5 MeV, the spectrum
transitions into a much steeper power law or exhibits an
exponential rollover. Despite increased uncertainties due to the
instrument’s dynamic threshold mode (see Appendix A.2), we
approximate a power-law fit for these data and obtain an
exponent of δ∼ 4.18.
Next, we isolate the maxima fc of the synchrotron emission,
shown with circle markers in Figure 1(B), and construct the
spectra of the optically thin emission above fc, as displayed in
Figure 4(C). We follow the evolution of this spectrum over a
72 minute period from 06:00 to 07:12 UT, up until the shock
arrives at the observer. Between 06:00 UT and 07:00 UT, α
remains constant at approximately 3 (δ∼ 7), which is steeper
than the δ∼ 4.18 measured in situ. This discrepancy may arise
from large uncertainties in the δ estimated from the data in
Figure 4(B). Alternatively, it could indicate that the emission is
produced by electrons in the steeper part of the electron
distribution, such that fc corresponds to 4ming > or
Ee∼ 2MeV, where the power law breaks in Figure 4(B).
After 07:00 UT, as the shock approaches the observer and fc
approaches fpe, ming increases, further steepening α to
approximately 5 (δ∼ 11). Between 07:10 UT and 07:12 UT,
just before the shock arrives and when the observer is within
the emitting region, α 8 (δ 17). Similar to S1, this may be a
result of the high-frequency exponential synchrotron cut off
at maxg .
Unlike S1, we can directly compare DSA predictions with
observations, as the power law extends up to γ∼ 5, the energy
range where electrons are affected by the DSA process. DSA
predicts δ= 2, which differs from the observed power-law
exponent of δ∼ 2.7, suggesting the presence of additional
factors that reduce DSA efficiency. Regarding anisotropy, both
HET-A and HET-B detect similar intensities and energies up to
∼6.7 MeV ( 13maxg ~ ). This indicates that the electrons are
isotropic, likely due to the presence of a well-developed
foreshock that enables efficient DSA. A final important
observation from Figure 4(B) is the order-of-magnitude higher
intensity of the entire population of electrons, from subrelati-
vistic to relativistic, compared to what was estimated for S1 in
Figure 3(B).
3. Discussion
In this study, we present the first-ever in situ observations of
shocks that produced an accelerated power-law distribution of
electrons with γ? 1 capable of emitting synchrotron radiation.
Unlike the previous remote-sensing study by T. S. Bastian
(2007), we experimentally verified the properties of synchro-
tron emission and the conditions under which it is generated.
This was made possible by the unique trajectory of the PSP,
which, for the first time, allowed us to study the strongest and
fastest IP shocks near their origin at the Sun. Our detailed
analysis of both the relativistic electron distribution and the
characteristics of the synchrotron radiation led to several key
findings, summarized below.
We first demonstrated that the observed radiation character-
istics, including spectral morphology and brightness temper-
ature, align with theoretical predictions. For S1, we measured
circular polarization in the x-mode, consistent with plasma
theory, and found further agreement in the relationship between
circular polarization and the γ of the emitting electrons.
However, both S1 and S2 exhibited significant deviations from
the expected maximum polarization. The theoretical maximum
polarization, 3 3
3 7
P = dd
+
+ , using δ values from S1 and S2, yields
Π∼ 80%. Notably, emission from S2 was completely
depolarized, suggesting that in strongly coupled plasma with
multiscale inhomogeneities (both parallel and perpendicular to
B), such as those found in the solar wind or interstellar
medium, the emitted EM wave characteristics may be lost near
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The Astrophysical Journal Letters, 976:L7 (14pp), 2024 November 20 Jebaraj et al.
the emission region. This result is consistent with recent X-ray
polarimetric studies of SNRs (J. Vink et al. 2022). These
studies show only a small degree of polarization due to a
mixture of tangential magnetic field alignment near the shock
front and a radially aligned magnetic field structure further
from it (A. M. Bykov et al. 2020).
Second, both shocks exhibited similar power-law exponents
(δ∼ 2.7–2.9) in the low-energy regime before breaking or
transitioning to an exponential cutoff. S1 showed partial
agreement with DSA predictions for rgas∼ 2.5, yielding δ∼ 3.
However, because electrons with γ 2 are required to
participate in DSA, and the power law did not extend beyond
γ∼ 2 for S1, it is unclear if DSA was fully active or efficient.
Additionally, we observed significant anisotropy, likely due to
minimal pitch angle scattering, which suggests that DSA was
inefficient. For S2, we found δ∼ 2.7, steeper than the DSA
prediction of δ= 2 for rgas∼ 4. Despite this, the power law
extended up to γ∼ 5 before breaking. The electron distribution
in S2 was isotropic, a hallmark of efficient DSA.
Lastly, our analysis of the in situ relativistic electron
distributions revealed that a quasi-parallel shock like S2 is far
more efficient at accelerating electrons than a quasi-perpend-
icular shock like S1. Electron intensities near the shock where
synchrotron emission was generated were an order of
magnitude higher for S2 than for S1, resulting in much
stronger synchrotron radiation from S2. A plausible explana-
tion is that in quasi-perpendicular shocks, adiabatic accelera-
tion mechanisms likely dominate, resulting in low efficiency
for producing relativistic particles (e.g., I. C. Jebaraj et al.
2023b). This suggests that additional mechanisms are required
for producing larger populations of relativistic electrons. If
DSA were the additional mechanism, its efficiency would be
limited by the growth of ion-scale waves through ion-streaming
instabilities, a process that is highly inefficient in quasi-
Figure 4. Characteristics of the synchrotron emission from S2 and the corresponding electron distribution. Panel (A) presents the time evolution of the electron
intensity in units of counts s−1 observed between 04:00 UT and 07:30 UT. The arrival of the shock at PSP is marked by the vertical black line at 07:13 UT and the
blue arrow on top. Panel (B) shows the 10 minute averaged electron energy distribution between 07:03 and 07:13 UT in units of particles cm−2 s−1 sr−1 keV−1. The
different detectors of ISeIS used to construct the electron spectrum are annotated with colored markers. The approximate power-law fits and the exponents are also
shown in the legend. Panel (C) shows the intensity–frequency profiles at distinct times leading up to the shock arrival, and approximate power-law fits to the optically
thin regime are shown.
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The Astrophysical Journal Letters, 976:L7 (14pp), 2024 November 20 Jebaraj et al.
perpendicular shocks like S1 (G. P. Zank & T. K. Gais-
ser 1992). In contrast, I. C. Jebaraj et al. (2024) found that S2
can locally provide quasi-perpendicular conditions while
supporting the efficient growth of ion-scale waves due to its
large-scale quasi-parallel geometry making it an efficient
accelerator of relativistic electrons.
The last result also experimentally confirms what was
observed in the bilateral SNR SN 1006, where the analysis of
remote-sensing observations demonstrates that synchrotron
emissions from quasi-parallel SNR shocks were significantly
brighter than those from oblique and quasi-perpendicular
shocks (e.g., R. Rothenflug et al. 2004; R. Giuffrida et al.
2022). This consistency is expected, as the structure of quasi-
parallel shocks aligns with theoretical predictions (M. A. Bali-
khin et al. 2023). Consequently, the nonthermal radiation
resulting from the evolutionary behavior of quasi-parallel SNR
and IP shocks is likely similar.
The experimental results presented here are the first of their
kind, showing that certain IP shocks are capable of persistently
accelerating electrons to relativistic energies—a phenomenon
previously considered unlikely. The mechanisms by which
these shocks accelerate particles and produce radiation
resemble those seen in SNR shocks. While detailed quantifica-
tion of differences between IP and SNR shocks is beyond the
scope of this Letter, our work suggests that efficient
acceleration is directly related to the upstream bulk flow
energy dissipated at the shock in its rest frame.
Acknowledgments
Author contributions. The study was initiated by I.C.J. and
conceptualized together with O.V.A., V.V.K., M.G., M.B., and
M.M. The methodologies for data analysis were provided by
I.C.J., O.V.A., L.V., M.G., A.V., N.D., and R.V. Data analysis
was performed by I.C.J., O.V.A., L.V., and A.V. The
results were interpreted by I.C.J., O.V.A., M.G., R.V., M.M.,
V.V.K., J.P., and M.B. The data were visualized by I.C.J.,
O.V.A., L.V., and A.V. A.M. prepared the schematic. I.C.J.
wrote the manuscript and prepared the final draft with significant
revisions from M.G. All authors have read the manuscript and
agreed to the presented results. The science operations of PSP
are led by N.E.R. The operations of the ISeIS instrument suite
are led by D.J.M., and the data were processed by C.M.S.C.,
J.G.M., and A.L. The operation of the FIELDS instrument suite
is led by S.D.B. and M.P.
Funding Information
The Parker Solar Probe spacecraft was designed and built
and is now operated by the Johns Hopkins Applied Physics
Laboratory as part of NASAʼs Living with a Star (LWS)
program (contract NNN06AA01C). Support from the LWS
management and technical team has played a critical role in the
success of the Parker Solar Probe mission. The authors express
their gratitude to all the instrument teams for their work in
processing and publishing the publicly available data from the
Parker Solar Probe. The data used in this study are available at
the NASA Space Physics Data Facility (SPDF), https://spdf.
gsfc.nasa.gov. This research was supported by the International
Space Science Institute (ISSI) in Bern through ISSI Interna-
tional Team project No. 23-575, “Collisionless Shock as a Self-
Regulatory System.” This research was supported through the
Visiting Scientist program of the International Space Science
Institute (ISSI) in Bern. I.C.J., L.V., and N.D. are grateful for
support by the Research Council of Finland (SHOCKSEE,
grant No. 346902) and the European Unionʼs (EU’s) Horizon
2020 research and innovation program under grant agreement
No. 101004159 (SERPENTINE) and No. 101134999
(SOLER). The study reflects only the authors’ view, and the
European Commission is not responsible for any use that may
be made of the information it contains. O.V.A. was partially
supported by NSF grant No. 1914670, NASAʼs Living with a
Star (LWS) program (contract 80NSSC20K0218), and NASA
grant contracts 80NNSC19K0848, 80NSSC22K0433, and
80NSSC22K0522. O.V.A. and V.V.K. were supported by
NASA grants 80NSSC20K0697 and 80NSSC21K1770. L.V.
acknowledges the financial support of the University of Turku
Graduate School. V.V.K. also acknowledges financial support
from CNES through grants “Parker Solar Probe” and “Solar
Orbiter.” A.K. acknowledges financial support from a NASA
NNN06AA01C (PSP EPI-Lo) contract. N.W. acknowledges
funding from the Research Foundation—Flanders (FWO—
Vlaanderen, fellowship no. 1184319N). E.P. acknowledges
support from NASA’s Parker Solar Probe Guest Investigators
(PSP-GI; grant No. 80NSSC22K0349) and Living With a Star
(LWS; grant No. 80NSSC19K0067) programs. E.K. and J.P.
acknowledge the Finnish Center of Excellence in Research of
Sustainable Space, Project 352850, for supporting this research
J.P. acknowledges support from the Research Council of
Finland (SWATCH, grant No. 343581). The FIELDS experi-
ment was developed and is operated under NASA contract
NNN06AA01C.
Appendix A
Experimental Details
A.1. FIELDS
Our study primarily utilizes the high-frequency electric field
measurements from both the HFR and LFR of the RFS
(M. Pulupa et al. 2017). These measurements are made by the
FIELDS instrument suite on board the PSP spacecraft
(S. D. Bale et al. 2016). RFS includes four electric antennas
(V V V V, , , and1 2 3 4) and measures over a wide frequency range,
spanning from 20MHz to 1 kHz at a 3.5 s cadence during close
encounters. The frequency resolutions is 4% at any given time
over 64 channels in LFR and 64 in HFR.
Additionally, PSP measures the full EM fields for which, the
coordinate system used throughout the manuscript is the
inertial radial–tangential–normal system, where the radial
component R is oriented along the Sun–spacecraft line, the
transverse component T is defined to be orthogonal to the
rotational axis of the Sun and the radial component, i.e.,
T=Ωe× R, while the normal component N completes the
orthogonal right-handed triad and, in this case, is aligned with
the normal of the ecliptic plane. The electric field measure-
ments are made using the electric fields instrument consisting
of two pairs of dipole electric field antennas oriented in the TN
plane and extending beyond the PSP heat shield and a fifth
antenna located behind the heat shield on the instrument boom;
the location of antenna V5 in the wake of PSP means the R
component is susceptible to detrimental interference by the
wake electric field and cannot be reliably interpreted
(S. D. Bale et al. 2016). Two three-component flux-gate
magnetometers measure the magnetic field from DC up to 293
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The Astrophysical Journal Letters, 976:L7 (14pp), 2024 November 20 Jebaraj et al.
vector measurements per second during 2–4 days around close
encounter. The latter is used in the present study.
The Time Domain Sampler (TDS) provides high-frequency
measurements of waveforms at a rate of about 1.92 million
samples s−1. Waveform events captured by TDS consist
of 15 ms of the electric (two components) and magnetic (one
component) field measurements (S. D. Bale et al. 2016). TDS
recorded 66 events on 2022 September 5 between 16:00 and
17:30 UT and 66 events on 2023 March 13 between 04:00 and
07:30 UT. These events were used to compliment the HFR/
LFR data.
A.2. ISeIS
To analyze the energetic electron spectra close to the shock,
we used the ISeIS instrument suite (D. J. McComas et al.
2016). It measures energetic particles from ∼20 keV to over
100MeV nuc–1 with two EPIs, EPI-Lo (M. E. Hill et al. 2017)
and EPI-Hi (M. E. Wiedenbeck et al. 2017). EPI-Lo measures
energetic electrons primarily through the “ChanE” data
product, which utilizes a single silicon solid-state detector
(SSD) for the energy measurement and a secondary SSD in
anticoincidence with the front SSD to reject penetrating
electrons. The HET within EPI-Hi provides measurements of
higher-energy electrons with minimal contamination from
incident ions. HET is a double-ended dE/dx versus residual
energy telescope with one aperture (HET-A) pointed toward
the Sun along a nominal Parker spiral and HET-B pointing the
opposite direction. For both EPI-Lo and EPI-Hi/HET, the
measured electron spectra were unfolded using the response
matrix technique to account for the contribution of higher-
energy electrons being measured in a lower-energy bin. Full
details of the Monte Carlo simulations utilized to construct
these response matrices are provided in J. G. Mitchell (2022)
and A. Labrador et al. (2023). While EPI-Hi/HET electron
measurements are essentially unaffected by ion contamination,
EPI-Lo ChanE can have substantial contamination from high-
energy ions when there is a significant Solar Energetic Particle
(SEP) ion foreground (J. G. Mitchell et al. 2021). The EPI-Lo
response matrix factors in contamination from high-energy ions
and reliably separates them from the electron signals
(J. G. Mitchell 2022). As such, only the filled markers in
Figure 3 should be interpreted as being produced by electrons.
During normal operation, all detector segments in EPI-Hi/
HET are sensitive to protons, alphas, electrons, and heavier
ions. In periods of high energetic particle intensity, the EPI-Hi
instruments employ automated “dynamic threshold” states that
raise the trigger thresholds of some detector segments such that
they are sensitive only to Z 6 ions. This lowers the effective
geometry factor of the instrument for protons, alphas, and
electrons and keeps the instrument livetime from dropping to
low levels while also preserving the ability to measure heavy
ions during large events. In the case of the most restrictive
dynamic threshold state, HET electron sensitivity is reduced in
the energy range of ∼2–5MeV.
Appendix B
Transverse EM Wave Properties
Figure 5 displays a waveform captured by the FIELDS/TDS
on 2023 March 13. The electric field measurements depicted in
panels (a) and (b) reveal the presence of a wave with a
frequency of approximately 60 kHz, which aligns with the
synchrotron emission illustrated in Figure 1. Magnetic field
measurements in panel (c) exhibit only 150 kHz noise,
indicating that the magnetic aspect of the wave is too faint
for detection by the Search Coil Magnetometer.
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For further insights into the wave characteristics, we have
performed processing of the plasma potential recorded by V1
and V2 in panel (d). Notably, the absence of a phase difference
in the time profiles allows for estimations of the lower limits of
the wavelength and phase velocity of the recorded wave. Given
the separation distance between the antennas, denoted as
L∼ 4 m, and the time step Δt∼ 0.5× 10−6 s, the wavelength
is estimated to exceed L/( fΔt)∼ 133 m. Consequently, the
resulting phase velocity greatly exceeds ∼7.8× 103 km s−1.
These derived values surpass those anticipated for any
electrostatic plasma wave under the prevailing plasma condi-
tions. Analysis of the waveforms recorded on 2022 September
5 gave similar results. Example of waves with a frequency of
approximately 420 kHz (consistent with the synchrotron
emission illustrated Figure 1) are shown in panels (e)–(h).
Appendix C
Estimating Brightness Temperature
The brightness temperatures of synchrotron sources have an
upper limit at low frequencies due to synchrotron self-
absorption, limiting the maximum brightness temperature to
that of the kinetic temperature of the emitting electrons. For a
nonthermal source where the electron energy distribution
follows a power law, the brightness temperature cannot exceed
the effective temperature of the relativistic electrons respon-
sible for the emission at a given frequency.
At sufficiently low frequencies, the brightness temperature
TB approaches the effective electron temperature Te, calculated
as
( )⎛
⎝
⎞
⎠
T
m cf
eB
m c
k
2 2
3
. C1e
e
1 2
e
2
B
p~
The brightness temperature in the Rayleigh–Jeans limit is
defined as
( )T I c
k f2
. C2
f
B
2
B
2
=
For an optically thick synchrotron source, TB cannot exceed Te,
and the flux density S relates to TB through
( )S k T f c2 , C3B B 2 2= W
Figure 5. The potential waveforms recorded by TDS on 2023 March 13, 07:04:17.301. (a) and (b) Two components of the electric field. (c) The magnetic field. (d)
The potential recorded on antenna 1 (black) and 2 (red). Panels (e)–(h): waveforms recorded by FIELDS/TDS on 2022 September 5, 17:27:13.222.
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The Astrophysical Journal Letters, 976:L7 (14pp), 2024 November 20 Jebaraj et al.
where Ω is the solid angle subtended by the source. In order to
estimate the brightness temperature of the radiation, this solid
angle needs to be estimated. The solid angle for distant
astrophysical sources is approximated to be Ω= πθ2, but for
sources much closer, this approximation falls apart. For large
angles subtended by the source, ( )2 1 cosp qW = - (S. Chan-
drasekhar 1960). Here, we estimate ( )s Darctanq = by taking
the distance between the shock at r∼ VshockΔt and the observer
at rsc as D= rsc− r and the source width as s∼ r. For S1, we
assume Vshock= 1800 km s
−1, and for S2, Vshock= 2500 km s
−1
based on simple transit time estimations.
TB of a synchrotron source that absorbs its own radiation is
restricted by inverse Compton scattering, with a theoretical
maximum around 1012 K, as noted by K. I. Kellermann &
I. I. K. Pauliny-Toth (1969). This limit is given by the ratio of
inverse Compton to synchrotron cooling and depends primarily
on ( )dfTB5 , being highly sensitive to brightness temperature.
Here
( )⎜ ⎟⎛
⎝
⎞
⎠
d
f
f
1
1
, C4max
c
1
a= -
a-
where α is the spectral index of the synchrotron spectrum, fmax
is the maximum frequency of the synchrotron emission, and fc
is the turnover frequency below which self-absorption is active.
d is a dimensionless parameter that is of order 10 for
astronomical sources and becomes critical for determining the
inverse Compton scattering limit. For typical values of d and f,
the brightness temperature limit to prevent the Compton
catastrophe is
( )⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
T
f d
1.5 10
10 Hz 10
K. C5B 12 9
1 5 1 5
< ´
- -
It should be noted that the 1012 K limit is given for 1 GHz
and for d of order 10, and both f and d scale weakly as f−1/5
and d−1/5. Given that the frequency at which the synchrotron
radiation is observed is ∼4 orders of magnitude smaller, the
limit becomes ≈1013 K.
Assessing the TB for Syn-1, Syn-2, and Syn-3 in
Figure 6(A), we find that Syn-1 maintains a nearly constant
TB, while the TB of Syn-2 and Syn-3 increase rapidly prior to
shock arrival at 17:27 UT. However, this increase does not
exceed the inverse Compton scattering limit of 1.3× 1013 K,
with f= 400 kHz, and for α= 3. Figure 6(B) shows the
brightness temperature TB of the emission, which rises
exponentially as the shock nears the spacecraft. The TB even
exceeds the inverse Compton limit of 1.7× 1013 K at 07:10,
suggesting that Ω= 2π, at which point the estimation of TB
becomes unreliable. This indicates that at 07:10 UT, the
spacecraft should have been in the region where the electrons
emitting synchrotron radiation were being accelerated. This is
in line with the conclusions of G. A. Dulk & K. A. Marsh
(1982), who find that the TB of the signal at a specific
frequency will be strong only under two conditions. The first is
the presence of a substantial population of nonthermal electrons
along the line of sight, leading to a high optical depth. Second,
the magnetic field is either relatively weak (which necessitates
higher harmonics and, therefore, more energetic electrons) or
aligned at a small angle to the line of sight, where only high-
energy electrons contribute significantly to the emission.
The limit is widely accepted, and it is important to
distinguish synchrotron radiation, which is incoherent, from
coherent plasma emissions. The defining characteristic of
coherent emissions is their very high intensities (S. Suzuki &
G. A. Dulk 1985; V. Krasnoselskikh et al. 2019), which in TB
units greatly exceed 1012 K and can reach 1018 K (P. Saint-Hi-
laire et al. 2012). This suggests that coherent emissions have far
greater TB than what is allowed for a hypothetical blackbody
radiation of the emitting electrons. Estimating and analyzing
the TB can help in the identification of the emission mechanism.
When TB exceeds the limits found here, it rules out synchrotron
radiation as the primary emission process.
Appendix D
Polarization
A monochromatic EM wave of the frequency ω is observed
at a receiver by measuring the electric field E that lies in the
plane perpendicular to the line of sight, i.e., the direction of
propagation. This electric field is conveniently represented as
( ˆ )E eE eRe .i t= w- The real amplitude E determines the
intensity, while the complex unit polarization vector eˆ fully
determines the axes of the polarization ellipse and the direction
of the electric vector rotation for the completely polarized
wave. If the emission comes from many sources, the receiver
measures a superposition of many waves,
( ˆ ) ( )E eE eRe , D1
i
i i
i tå= w-
where the summation is over the ensemble of the emitters. Since
all Ei and eˆi may be different and independent, it is not possible
to describe the emission with a single polarization axis. Instead,
the Stokes parameters are widely used (S. Chandrasekhar 1947;
G. B. Rybicki & A. P. Lightman 1979). These parameters are
the differences of average intensities projected onto several
sets of unit vectors. Let the plane of the electric field be the x
−y plane. Consider the following pairs of unit vectors: (a)
ˆ ˆe xx = , ˆ ˆe y ;y = (b) ˆ ( ˆ ˆ)e x y 2a = + , ˆ ( ˆ ˆ)e x y 2 ;b = - and
(c) ˆ ( ˆ ˆ)e x iy 2R = + , ˆ ( ˆ ˆ)e x iy 2L = - . Then the Stokes
Figure 6. The brightness temperatures (TB) of the synchrotron emission for S1
and S2 are shown in panels (A) and (B). The inverse Compton scattering limit
is explicitly stated in both panels and also represented by the blue dotted–
dashed in panel (B).
12
The Astrophysical Journal Letters, 976:L7 (14pp), 2024 November 20 Jebaraj et al.
parameters are defined as follows:
∣ · ˆ ∣ ∣ · ˆ ∣ ( )E e E eI , D2x y2 2= á ñ + á ñ
∣ · ˆ ∣ ∣ · ˆ ∣ ( )E e E eQ , D3x y2 2= á ñ - á ñ
∣ · ˆ ∣ ∣ · ˆ ∣ ( )E e E eU , D4a b2 2= á ñ - á ñ
∣ · ˆ ∣ ∣ · ˆ ∣ ( )E e E eV , D5R L2 2= á ñ - á ñ
where á¼ñ means ensemble averaging, which corresponds to
the averaging of the observations over the time much larger
than 1/ω. Accordingly, the linear polarization degree is
Q U Ilin 2 2P = + , the circular polarization degree is
Πcir=V/I, and the total polarization degree is totP =
Q U V I2 2 2+ + .
This final expression, Πtot, is important since it is used in
observational astronomy to determine the characteristics of the
cosmic object and the medium in which it is situated
(A. M. Bykov et al. 2012). In radio astronomy, Stokes
parameters are often calculated by converting incident electric
fields into voltages, where the detection process yields power
proportional to the square of these voltages. The raw data,
initially in arbitrary units, is calibrated to brightness temper-
ature (K) or flux density (Wm−2 Hz−1), with a constant factor
accounting for intensity calibration. The exact details of how
PSP data are calibrated and the polarization is estimated can be
found in M. Pulupa et al. (2017).
ORCID iDs
I. C. Jebaraj https://orcid.org/0000-0002-0606-7172
O. V. Agapitov https://orcid.org/0000-0001-6427-1596
M. Gedalin https://orcid.org/0000-0003-1236-4787
L. Vuorinen https://orcid.org/0000-0002-2238-109X
M. Miceli https://orcid.org/0000-0003-0876-8391
C. M. S. Cohen https://orcid.org/0000-0002-0978-8127
A. Voshchepynets https://orcid.org/0000-0001-8307-781X
A. Kouloumvakos https://orcid.org/0000-0001-6589-4509
N. Dresing https://orcid.org/0000-0003-3903-4649
A. Marmyleva https://orcid.org/0000-0003-1175-7124
V. Krasnoselskikh https://orcid.org/0000-0002-6809-6219
M. Balikhin https://orcid.org/0000-0002-8110-5626
J. G. Mitchell https://orcid.org/0000-0003-4501-5452
A. W. Labrador https://orcid.org/0000-0001-9178-5349
N. Wijsen https://orcid.org/0000-0001-6344-6956
E. Palmerio https://orcid.org/0000-0001-6590-3479
L. Colomban https://orcid.org/0000-0001-6016-7548
J. Pomoell https://orcid.org/0000-0003-1175-7124
E. K. J. Kilpua https://orcid.org/0000-0002-4489-8073
M. Pulupa https://orcid.org/0000-0002-1573-7457
F. S. Mozer https://orcid.org/0000-0002-2011-8140
N. E. Raouafi https://orcid.org/0000-0003-2409-3742
D. J. McComas https://orcid.org/0000-0001-6160-1158
S. D. Bale https://orcid.org/0000-0002-1989-3596
R. Vainio https://orcid.org/0000-0002-3298-2067
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