Are gravitational waves spinning down PSR J1023+0038?

The pulsar J1203+0038 rotates with a frequency $\nu\approx 592$ Hz and has been observed to transition between a radio state, during which it is visible as a millisecond radio pulsar, and and a Low Mass X-ray Binary 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 $\dot{\nu}\approx -3 \times 10^{-15}$ Hz/s, which is approximately 27\% faster than the rate measured during the radio phase, $\dot{\nu}\approx -2.4 \times 10^{-15}$ Hz/s, and at odds with the predictions of accretion models. In this letter we suggest that the increase in spin-down rate is compatible with gravitational wave emission, and in particular to the creation of a `mountain' during the accretion phase. We show that asymmetries in pycno-nuclear reaction rates in the crust can lead to a large enough mass quadrupole to explain the observed spin-down rate, which so far has no other self-consistent explanation, and that radio timing at the onset of the next millisecond radio pulsar phase can test this scenario. Another possibility is that an unstable $r$-mode with amplitude $\alpha\approx 5\times10^{-8}$ may be present in the system.