Broadband Timing and Spectral Study of Accreting Millisecond X-ray Pulsar SAX J1808.4$-$3658 during Its 2022 Outburst

Abstract

We report on our investigation of the NuSTAR and AstroSat observations along with simultaneous NICER observations of the accreting millisecond X-ray pulsar SAX J1808.4$-$3658, obtained during its tenth outburst from 2022. The NuSTAR observation captured the source near the outburst peak, while AstroSat observed it during the decay phase. Coherent pulsations at $\sim$401 Hz were detected throughout the outburst, with the fundamental amplitude in the 3--30 keV range increasing from $\sim$4% near the peak to $\sim$6% during the decay. The pulsations display strong energy dependence and negative time lags of $\sim$0.2--0.3 ms, with harder photons leading softer ones. The broadband spectra in both epochs are well described by a soft thermal component and Comptonized continuum, together with a prominent relativistic reflection component. As the outburst evolved, the continuum softened ($\Gamma$ increasing from $\sim$1.88 to $\sim$1.99) and the coronal electron temperature decreased ($kT_{\rm e}$ from $\sim$31 to $\sim$18 keV), consistent with enhanced Compton cooling at lower accretion rates. The ionization parameter declined ($\log \xi$ from $\sim$3.4 to $\sim$1.8) while the reflection fraction increased, suggesting a changing accretion geometry with a more compact corona and a larger disk covering fraction during the decay phase. The X-ray luminosity decreased by a factor of $\sim$3 between the two epochs. Our results suggest the coupled evolution of the corona, disk, and magnetosphere as the mass accretion rate declines.