Spin-down rate of the transitional millisecond pulsar PSR J1023+0038 in the optical band with Aqueye+

We present a timing analysis of the transitional millisecond pulsar PSR J1023+0038 using observations taken between January 2018 and January 2020 with the high time resolution photon counter Aqueye+ mounted at the 1.82 m Copernicus telescope in Asiago. We report the first measurement of the timing solution and the frequency derivative of PSR J1023+0038 based entirely on optical data. The spin-down rate of the pulsar is $(-2.53 \pm 0.04) \times 10^{-15}$ Hz$^2$, which is $\sim$20% slower than that measured from the X-ray observations taken in 2013-2016 and $\sim$5% faster than that measured in the radio band during the rotation-powered state.