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

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 ZK² 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 ν and its derivative ν̇ from the empirical dependencies of ZK² on trial values of these parameters, with account of all significant harmonics of the frequency. Applying this method, we determined a spin-down rate ν̇ = -7.3(1.2)× 10⁻¹⁷\, Hz\, s⁻¹. The resulting spin-down power Ė=2.6× 10²⁹ 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 Ė in general.