Two decades of optical timing of the shortest-period binary star system HM Cancri

Abstract

<p>The shortest-period binary star system known to date, RX J0806.3+1527 (HM Cancri), has now been observed in the optical for more than two decades. Although it is thought to be a double degenerate binary undergoing mass transfer, an early surprise was that its orbital frequency, <em>f</em>₀, is currently increasing as the result of gravitational wave radiation. This is unusual since it was expected that the mass donor was degenerate and would expand on mass loss, leading to a decreasing <em>f</em>₀. We exploit two decades of high-speed photometry to precisely quantify the trajectory of HM Cancri, allowing us to find that <em>f</em>¨₀ is negative, where <em>f</em>¨₀ = (-5.38 ± 2.10) x 10^-27 Hz s^-2. Coupled with our positive frequency derivative, we show that mass transfer is counteracting gravitational-wave dominated orbital decay and that HM Cancri will turn around within 2100 ± 800 yr from now. We present <em>Hubble Space Telescope</em> ultra-violet spectra which display Lyman-<em>α</em> absorption, indicative of the presence of hydrogen accreted from the donor star. We use these pieces of information to explore a grid of permitted donor and accretor masses with the Modules for Experiments in Stellar Astrophysics suite, finding models in good accordance with many of the observed properties for a cool and initially hydrogen-rich extremely low mass white dwarf (≈0.17 M_⊙) coupled with a high-accretor mass white dwarf (≈1.0 M_⊙). Our measurements and models affirm that HM Cancri is still one of the brightest verification binaries for the Laser Interferometer Space Antenna spacecraft.<br></p><p><br></p><p><br></p>