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 $R_{m} \propto \dot{M}^Λ$, with $Λ= -0.17(9)$, 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.

Figures (12)

• Figure 1: Light curve of 2022 outburst of SAX J1808 in 0.5--10 keV energy band, using $\mathrm{1\,ks}$ bins. NICER observations are shown in black, and XMM-Newton observations are given in red. The blue star marks the epoch of the HST/STIS observation (2022 September 10). We rescaled the XMM-Newton count rate to the NICER count rate using a conversion factor of 1.44, which was calculated with the WebPIMMS tool and a power-law model with a photon index of $\Gamma = 2.04$ (Table \ref{['tab:spectra']}).
• Figure 2: Background-subtracted 0.5--10 keV XMM-Newton/EPIC-pn light curve of 2022 outburst of SAX J1808 measured using $200\,\text{s}$-long bins. A red band indicates the low-flux interval, and a blue band shows the interval of the HST observation discussed in this paper (see Sect. \ref{['sec:UV']} for details). Two Type I X-ray bursts, detected at 59831.87 and 59832.82 MJD, are not plotted. Green dash-dotted lines indicate the epochs of their occurrence.
• Figure 3: X-ray pulse profiles obtained by folding the high- and low-flux intervals of XMM-Newton observation into 16 phase bins at a spin frequency of $\nu_F = 400.975209557\,\text{Hz}$. The solid line represents the best-fit model (constant plus two harmonics), while the dashed red and blue lines indicate the first and second harmonic contributions, respectively. For clarity, two cycles are shown.
• Figure 4: Top panel: 0.5--10 keV XMM-Newton/EPIC-pn light curve using 1 ks bins, with Type I X-ray bursts removed. The dashed blue line shows the spline interpolation obtained with the UnivariateSpline function from scipy.interpolate. The blue band indicates the interval of the HST observation discussed in this paper (see Sect. \ref{['sec:UV']} for details). Second panel: Pulse fractional amplitude for the first harmonic (black dots) and the second harmonic (red dots). Third and fourth panels: Phase residuals relative to a linear model and a model that includes a phase-flux correlation term, respectively. Note that, where not visible, the error bars are smaller than the data points.
• Figure 5: Contour levels of $\chi^2$ obtained by varying both parameters $b$ and $\Lambda$ in the flux-adjusted phase fit. The contour levels are shown for $\chi^2_{\min} + 2.3$ (blue) and $\chi^2_{\min} + 4.61$ (red), corresponding to confidence levels of 68% and 90%, respectively, for a fit with two parameters Lampton_1976. The black dot indicates the values of $b$ and $\Lambda$ corresponding to the minimum $\chi^2$, while the dashed black line represents the contour corresponding to the constant value given by the product $b \times \Lambda$.