X-ray Analysis and Photon-transport Simulations of SMC X-1: A Warped-disc Origin of the Superorbital Modulation

TL;DR

This work probes the origin of SMC X-1's superorbital modulation by combining broadband Suzaku and NuSTAR spectroscopy with three-dimensional radiative transfer simulations of a warped accretion disc. The analysis shows increasing absorption and Fe $K\alpha$ line EW at low superorbital phases, consistent with obscuration by a precessing warped disc rather than intrinsic luminosity changes. Photon-transport Monte Carlo simulations (MONACO) reproduce the observed flux suppression, Fe line behavior, and double-peaked pulse profiles when the disc precesses by about $\sim 30^{\circ}$ with a mildly misaligned magnetic geometry ($\delta\approx 30^{\circ}$, $\sigma\approx 30^{\circ}$, $\gamma\lesssim 10^{\circ}$). The results support a geometry in which a warped inner disc periodically attenuates the central X-ray source, providing a physically consistent explanation for both spectral and timing variability and informing accretion geometry in high-luminosity X-ray pulsars.

Abstract

The luminous accreting pulsar SMC X-1 is an appropriate target to explore the accretion dynamics. SMC X-1 shows unique quasi-periodic flux variability of 40-65$\,$days known as superorbital modulation. To constrain the accretion structure of SMC X-1 based on timing and spectral study, we have analysed X-ray data of SMC X-1 observed by Suzaku and NuSTAR at various epochs between 2011 and 2022. The spectral analysis shows that the hydrogen column density ($N_\mathrm{H}$) increases from $1.1 \times 10^{22}\,\mathrm{cm^{-2}}$ to $1.24 \times 10^{23}\,\mathrm{cm^{-2}}$ as the flux decreases with the superorbital modulation. The neutral iron K$α$ line at 6.4$\,$keV has a broad width of 0.3$\,$keV, and its equivalent width increases as toward superorbital low states. The line broadening is consistent with Keplerian motion at the inner disc rather than the stellar wind velocity of the donor star. These findings support that the superorbital modulation is a consequence of X-ray attenuation by the warped accretion disc. To test this interpretation, we have conducted photon transport simulations of a system consisting of a neutron star, a warped disc, and optically-thin disc atmosphere. Occultation of the central source by the disc successfully reproduces the observed variations in the equivalent width of neutral iron K$α$ line, pulse profiles, and flux in hard X-rays. Notably, a disc precession angle of approximately $30^\circ$ can account for the observational features. For the radiation pattern of the photon source, the preferred beam width corresponds to a standard deviation of $30^\circ$.

Figures (18)

• Figure 1: A light curve of SMC X-1 observed by MAXI (2--20 keV). Blue data indicate observations out of eclipse ($0.15\leq \phi_\mathrm{orb} \leq 0.85$) while green ones, which appear in dips, correspond to the eclipse. Magenta (red) lines point to Suzaku (NuSTAR) observations.
• Figure 2: X-ray spectra of all the Suzaku SMC X-1 observations. Low energy region ($\leq\,10\,\mathrm{keV}$) and higher one ($\geq 15\,\mathrm{keV}$) correspond to data XIS0 and HXD PIN observed, respectively.
• Figure 3: X-ray spectra from all NuSTAR observations and the best-fit models are shown in the top panel. The bottom panel displays the residuals, i.e., the difference between the data and the model normalized by the statistical uncertainty.
• Figure 4: MAXI light curve (top), superorbital phases (second), and all 16 IMFs (the other panels) between MJD 55600 and 56100.
• Figure 5: Dependence of the hydrogen column density derived from the Suzaku spectral analysis on the superorbital phase ($\phi_\mathrm{SO}$).