Are Gravitational Waves Spinning Down PSR $\mathrm{J}1023+0038$?

The pulsar $\mathrm{J}1023+0038$ rotates with a frequency $\nu \approx 592\mathrm{Hz}$ and has been observed to transition between a radio state, during which it is visible as a millisecond radio pulsar, and a low-mass x-ray binary (LMXB) state, during which accretion powered x-ray pulsations are visible. Timing during the two phases reveals that during the LMXB phase the neutron star is spinning down at a rate of $\dot{\nu }\approx -3\times {10}^{-15}\mathrm{Hz}/\mathrm{s}$, which is approximately 27% faster than the rate measured during the radio phase, $\dot{\nu }\approx -2.4\times {10}^{-15}\mathrm{Hz}/\mathrm{s}$, and is at odds with the predictions of accretion models. We suggest that the increase in spin-down rate is compatible with gravitational wave emission, particularly with the creation of a “mountain” during the accretion phase. We show that asymmetries in pycnonuclear reaction rates in the crust can lead to a large enough mass quadrupole to explain the observed spin-down rate, which thus far has no other self-consistent explanation. We also suggest two observational tests of this scenario, involving radio timing at the onset of the next millisecond radio pulsar phase, when the mountain should dissipate, and accurate timing during the next LMXB phase to track the increase in torque as the mountain builds up. Another possibility is that an unstable $r$ mode with an amplitude $\alpha \approx 5\times {10}^{-8}$ may be present in the system.