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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 |$\ddot{f}_0$| is negative, where |$\ddot{f}_0~=~(-5.38\pm 2.10)\times 10^{-27}$|  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-α 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. [ABSTRACT FROM AUTHOR]

Ultracompact accreting binary systems each consist of a stellar remnant accreting helium-enriched material from a compact donor star. Such binaries include two related sub-classes, AM CVn-type binaries and helium cataclysmic variables, in both of which the central star is a white dwarf. We present a spectroscopic and photometric study of six accreting binaries with orbital periods in the range of 40–70 min, including phase-resolved VLT spectroscopy and high-speed ULTRACAM photometry. Four of these are AM CVn systems and two are helium cataclysmic variables. For four of these binaries we are able to identify orbital periods (of which three are spectroscopic). SDSS J1505+0659 has an orbital period of 67.8 min, significantly longer than previously believed, and longer than any other known AM CVn binary. We identify a Wide-field Infrared Survey Explorer (WISE) infrared excess in SDSS J1505+0659 that we believe to be the first direct detection of an AM CVn donor star in a non-direct impacting binary. The mass ratio of SDSS J1505+0659 is consistent with a white dwarf donor. CRTS J1028–0819 has an orbital period of 52.1 min, the shortest period of any helium cataclysmic variable. MOA 2010-BLG-087 is co-aligned with a K-class star that dominates its spectrum. ASASSN-14ei and ASASSN-14mv both show a remarkable number of echo outbursts following superoutbursts (13 and 10 echo outbursts respectively). ASASSN-14ei shows an increased outburst rate over the years following its superoutburst, perhaps resulting from an increased accretion rate. [ABSTRACT FROM AUTHOR]