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

TL;DR

This study presents a simultaneous broadband timing and spectral analysis of SAX J1808.4--3658 during its 2022 outburst, using NICER, NuSTAR, and AstroSat to trace the evolution from the outburst peak to decay. The pulsations at $\sim$401 Hz persist throughout, with the fundamental amplitude increasing as the accretion rate falls and the spectrum softening due to coronal cooling; a strong relativistic reflection component reveals changes in disk ionization and geometry. Spectral modeling with tbabs*(bbodyrad+ nthcomp) and relxillCP shows the corona cooling from $kT_{\rm e}\sim$32 keV to $\sim$18 keV and ionization dropping from $\log\xi\sim3.4$ to $\sim1.8$, while the reflection fraction grows from $\sim$0.1 to $\sim$0.45, suggesting a more compact corona and increased disk covering as luminosity declines. The joint timing–spectral analysis emphasizes a coupled evolution of the corona, disk, and magnetosphere in the hard state and demonstrates the value of strictly simultaneous broadband observations for constraining AMXP outburst physics.

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$0.2--0.3 ms, with harder photons leading softer ones. The broadband spectra in both epochs are well described by a soft thermal component and Comptonized continuum, together with a prominent relativistic reflection component. As the outburst evolved, the continuum softened ($Γ$ 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 ξ$ 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.

Figures (7)

• Figure 1: The light curve of SAX J1808.4--3658 during its 2022 outburst obtained with NICER, NuSTAR and AstroSat/LAXPC binned at 100 s in the energy ranges 0.5--10 keV, 3--30 keV and 3--30 keV, respectively. The lower panel shows the hardness ratio, defined as the count-rate ratios between 3–10 and 0.5–3 keV for NICER, and between 10–30 and 3–10 keV for NuSTAR and AstroSat/LAXPC. The hardness values for NuSTAR have been shifted by $-$1 to match LAXPC. The shaded region marks the NICER segment that was combined for further analysis.
• Figure 2: Pulse profiles of SAX J1808.4--3658 from two observing epochs, obtained by epoch-folding the data with spin frequencies listed in Table \ref{['tab:spin']} after correcting for the orbital motion. Left panel: Epoch 1, showing profiles in the 0.5--10 keV band from NICER and in the 3--30 keV band from NuSTAR. Right panel: Epoch 2, showing profiles in the 0.5--10 keV band from NICER and in the 3--30 keV band from AstroSat/LAXPC. The solid lines denote the best-fitting model, which is the superposition of two sinusoidal functions with harmonically related periods. For clarity, two pulse cycles are shown.
• Figure 3: Energy-resolved pulse properties of SAX J1808.4--3658. Top panels: fractional amplitudes of the fundamental and harmonic components as a function of energy. Bottom panels: corresponding time lags of the fundamental and harmonic components. The left plots correspond to Epoch 1, with the zero lag defined relative to the pulse phase at 0.5 keV, while the right plots correspond to Epoch 2, with the zero lag defined at 3 keV.
• Figure 4: Residuals obtained after modeling the spectrum with absorbed blackbody and Comptonization model. These residuals indicate the broad emission feature at 6--7 keV.
• Figure 5: Best-fit broadband energy spectra from Epoch 1 (left) and 2 (right) using NICER+NuSTAR and NICER+SXT+LAXPC, respectively, fitted with the combined model tbabs*(bbodyrad + relxillCP). The lower panels show residuals from the best-fit model.