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

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, f(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 f(0). We exploit two decades of high-speed photometry to precisely quantify the trajectory of HM Cancri, allowing us to find that f(0) is negative, where f(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 Hubble Space Telescope ultra-violet spectra which display Lyman-alpha 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 (approximate to 0.17 M-circle dot) coupled with a high-accretor mass white dwarf (approximate to 1.0 M-circle dot). Our measurements and models affirm that HM Cancri is still one of the brightest verification binaries for the Laser Interferometer Space Antenna spacecraft.