A deep X-ray and UV look into the reflaring stage of the accreting millisecond pulsar SAX J1808.4-3658

Abstract

We present an X-ray and UV high-time-resolution monitoring of the final flaring phase of the 2022 outburst of the AMSP SAX J1808.4-3658, based on simultaneous XMM-Newton and HST observations. The uninterrupted coverage provided by XMM-Newton enabled a detailed characterization of the spectral and temporal evolution of the source X-ray emission, as the flux varied by approximately 1 order of magnitude. We detected coherent X-ray pulsations during the whole X-ray observation, down to a 0.5-10 keV luminosity of $L_{X(low)0.5-10} \simeq 6.21^{+0.20}_{-0.15}\times 10^{34} d^2_{3.5}erg/s$, among the lowest ever observed in this source. At the lowest flux levels, we observed significant variations in pulse amplitude and phase. These variations were anticorrelated with the X-ray source flux. We found a sharp phase jump of $\sim 0.4$ cycles, accompanied by a doubling of the pulse amplitude and a softening of the X-ray emission. We interpreted changes in the X-ray pulse profiles as drifts of emission regions on the neutron-star surface, driven by an increase in the inner-disk radius when the mass-accretion rate decreased. The dependence of the pulse phase on the X-ray flux was consistent with a magnetospheric radius scaling as $R_{m} \propto \dot{M}^{\Lambda}$, with $\Lambda = -0.17(9)$, in broad agreement with theoretical predictions. Simultaneous HST observations confirmed the presence of significant UV pulsations at an X-ray luminosity approximately a factor of two lower than during the 2019 outburst, extending the range of mass accretion rates at which UV pulsations have been detected. The measured pulsed UV luminosity, $L_{pulsed}^{UV}=1.1(3) \times 10^{32}erg/s$, was consistent with that observed during the 2019 outburst. Such a UV luminosity exceeds the predictions of standard emission models, as further confirmed by the shape of the pulsed spectral energy distribution.