Timing analysis of the 2022 outburst of the accreting millisecond X-ray pulsar SAX J1808.4$-$3658: hints of an orbital shrinking

TL;DR

This paper analyzes NICER observations of SAX J1808.4$-$3658 during its 2022 outburst, revealing a long-term spin-down and evidence of orbital shrinking likely due to changes in the companion star's mass quadrupole.

Contribution

First detailed timing analysis of the 2022 outburst showing orbital period decrease and long-term spin-down in SAX J1808.4$-$3658.

Findings

Confirmed long-term spin-down rate of the pulsar

Detected orbital period decrease for the first time in 20 years

Observed an orbital phase modulation consistent with a 21-year cycle

Abstract

We present a pulse timing analysis of NICER observations of the accreting millisecond X-ray pulsar SAX J1808.4$-$3658 during the outburst that started on 2022 August 19. Similar to previous outbursts, after decaying from a peak luminosity of $\simeq 1\times10^{36} \, \mathrm{erg \, s^{-1}}$ in about a week, the pulsar entered in a $\sim 1$ month-long reflaring stage. Comparison of the average pulsar spin frequency during the outburst with those previously measured confirmed the long-term spin derivative of $\dot{\nu}_{\textrm{SD}}=-(1.15\pm0.06)\times 10^{-15} \, \mathrm{Hz\,s^{-1}}$, compatible with the spin-down torque of a $\approx 10^{26} \, \mathrm{G \, cm^3}$ rotating magnetic dipole. For the first time in the last twenty years, the orbital phase evolution shows evidence for a decrease of the orbital period. The long-term behaviour of the orbit is dominated by a $\sim 11 \, \mathrm{s}$ modulation of the orbital phase epoch consistent with a $\sim 21 \, \mathrm{yr}$ period. We discuss the observed evolution in terms of a coupling between the orbit and variations in the mass quadrupole of the companion star.