A Real-time View of Orbital Evolution in HM Cancri

HM Cancri is a double-degenerate binary with the shortest orbital period presently known. The 5.36 minute period is seen as a large amplitude, soft X-ray modulation, likely resulting from a hot spot produced by direct impact accretion. With such a short orbital period it is expected to have a gravitational wave luminosity comparable to or larger than that in the X-ray, and its orbital frequency is known to be increasing at a rate consistent with the expected loss of angular momentum due to gravitational radiation. We use recent Neutron Star Interior Composition Explorer observations to extend its long-term X-ray timing baseline to almost 20 yr. Phase coherent timing of these new data combined with existing Chandra data demonstrates conclusively that the rate of orbital frequency increase is slowing, and we measure a non-zero d²f/dt² = -9.0 ± 1.2 x 10^-27 Hz s^-2, which is to our knowledge the first such measurement of its kind for any compact astrophysical binary. With the simultaneous high precision measurement of df/dt = 3.557 ± 0.005 x 10^-16 Hz s^-1, we estimate that the system will reach its maximum orbital frequency of f_max = 3.1172091 mHz in 1,260 ± 200 yr, indicating that the system is close to its epoch of maximum orbital frequency. Beyond that epoch, increasing accretion will push the components apart. Assuming mass transfer is conservative, the measurement of d²f/dt² < 0 implies that the accretion rate from the donor is growing, with -5.4 x 10^-10 < d²M/dt² < -4.0 x 10^-10 M_sun yr^-2. Further quantitative comparisons with theoretical models should enable more precise inferences regarding its evolutionary history.