NICER timing of the X-ray thermal isolated neutron star RX J0806.4--4123

Abstract: The X-ray thermal isolated neutron star (XTINS) RX J0806.4--4123 shows interesting multiwavelength properties that seemingly deviate from those of similar neutron stars. An accurate determination of the spin frequency change over time can assist in interpreting RX J0806.4-4123's properties in comparison to those of other XTINSs and the wider pulsar population. From 2019 to 2023 we carried out a tailored X-ray timing campaign of RX J0806.4-4123 with the NICER instrument. We used statistical properties of the Fourier coefficients and the $Z_K^2$ test for phase-connecting separate observations and finding a timing solution for the entire dataset. We also developed a simple and universal method for estimating the uncertainties of frequency $\nu$ and its derivative $\dot{\nu}$ from the empirical dependencies of $Z_K^2$ on trial values of these parameters, with account of all significant harmonics of the frequency. Applying this method, we determined a spin-down rate $\dot{\nu} = -7.3(1.2)\times 10^{-17}\,{\rm Hz\, s}^{-1}$. The resulting spin-down power $\dot{E}=2.6\times 10^{29}$ erg s$^{-1}$ is the lowest among the XTINSs, and it is a factor of 60 lower than the X-ray luminosity of this neutron star. RX J0806.4-4123 is also among the pulsars with the lowest measured $\dot{E}$ in general.