Timing Analysis of the 2022 Outburst of the Accreting Millisecond X-Ray Pulsar SAX J1808.4-3658: Hints of an Orbital Shrinking

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 ≃1 × 10³⁶ erg s^-1 in about a week, the pulsar entered a ~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 ${\dot{\nu }}_{\mathrm{SD}}=-(1.15\,\pm \,0.06)\times \,{10}^{-15}$ Hz s^-1, compatible with the spin-down torque of a ≈10²⁶ G cm³ 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 behavior of the orbit is dominated by an ~11 s modulation of the orbital phase epoch consistent with a ~21 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.