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 data set. We also developed a simple and universal method for estimating the uncertainties of the frequency ν and its derivative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>7.3</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1.2</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>17</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:mi>Hz</mml:mi> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> . The resulting spin-down power <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> <mml:mo>=</mml:mo> <mml:mn>2.6</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>29</mml:mn> </mml:mrow> </mml:msup> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> in general.