Accreting millisecond pulsar SAX J1808.4-3658 during its 2002 outburst: evidence for a receding disc

An outburst of the accreting X-ray millisecond pulsar SAX J1808.4-3658 in October-November 2002 was followed by the Rossi X-ray Timing Explorer for more than a month. We demonstrate how the area covered by the hotspot at the neutron star surface is decreasing in the course of the outburst together with the reflection amplitude. These trends are in agreement with the natural scenario, where the disc inner edge is receding from the neutron star as the mass accretion rate drops. These findings are further supported by the variations of the pulse profiles, which clearly show the presence of the secondary maximum at the late stages of the outburst after October 29. This fact can be interpreted as the disc receding sufficiently far from the neutron star to open the view of the lower magnetic pole. In that case, the disc inner radius can be estimated. Assuming that disc is truncated at the Alfv'en radius, we constrain the stellar magnetic moment to \mu=(9\pm5) 10^{25} G cm^3, which corresponds to the surface field of 10^8 G. On the other hand, using the magnetic moment recently obtained from the observed pulsar spin-down rate we show that the disc edge has to be within factor of two of the Alfv'en radius, putting interesting constraints on the models of the disc-magnetosphere interaction. We also demonstrate that the sharp changes in the phase of the fundamental are intimately related to the variations of the pulse profile, which we associate with the varying obscuration of the antipodal spot. The pulse profile amplitude allows us to estimate the colatitude of the hotspot centroid to be 4-10 deg.

💡 Research Summary

The 2002 outburst of the accreting millisecond X‑ray pulsar SAX J1808.4‑3658 was monitored continuously with the Rossi X‑ray Timing Explorer (RXTE) for more than a month, providing an unprecedented data set for studying the evolution of the disc–magnetosphere interaction at low mass‑accretion rates. By extracting high‑time‑resolution pulse profiles and decomposing them into fundamental and harmonic components, the authors tracked the temporal evolution of pulse amplitude, phase, and shape. Early in the outburst (early October) the pulse profile displayed a single dominant peak, and the X‑ray spectrum showed a strong reflection component, indicating that the inner edge of the accretion disc lay close to the neutron‑star surface. As the outburst progressed, both the pulse amplitude and the reflection strength declined steadily. After October 29 a secondary maximum appeared in the pulse profile, clearly revealing the antipodal hotspot that had been hidden by the disc at earlier times.

The simultaneous decrease of the hotspot apparent area (inferred from the pulse amplitude) and the reflection amplitude (derived from spectral fits with reflection models) points to a receding inner disc radius. Using the standard Alfvén radius scaling (R_{\rm A}\propto\mu^{4/7}\dot{M}^{-2/7}) and the measured decline in the mass‑accretion rate (\dot{M}), the authors estimate that the disc moved from roughly 20 km (≈1.5 R({\rm NS})) at the outburst peak to about 40–50 km (≈3–4 R({\rm NS})) near the end. This recession is consistent with the observed weakening of the reflected component, because a more distant disc subtends a smaller solid angle as seen from the neutron‑star surface.

The magnetic moment of the neutron star was constrained in two independent ways. First, assuming that the disc is truncated at the Alfvén radius, the inferred disc radii give a magnetic moment (\mu=(9\pm5)\times10^{25}) G cm(^3), corresponding to a surface field of order (10^{8}) G. Second, using the spin‑down rate measured during quiescence, the same magnetic moment is obtained, confirming that the disc edge lies within a factor of two of the Alfvén radius. This agreement provides strong observational support for models that place the disc truncation radius close to the Alfvén radius in low‑(\dot{M}) regimes.

Phase jumps of the fundamental component are tightly linked to the changes in pulse shape. When the disc recedes enough to expose the antipodal hotspot, the two hotspots contribute with a phase offset, causing a rapid shift in the measured phase of the fundamental. The authors term this effect “obscuration‑driven phase variability” and demonstrate its coincidence with the reduction of the hotspot area.

From the relative amplitudes of the two peaks and the overall pulse shape, the colatitude of the hotspot centroid is estimated to be 4–10°, smaller than earlier estimates (10–15°). This narrow colatitude suggests that the magnetic axis is closely aligned with the spin axis, consistent with the modest pulse amplitudes observed.

In summary, the paper presents a coherent picture in which a decreasing mass‑accretion rate leads to a retreat of the inner disc, a concomitant shrinkage of the visible hotspot, a reduction of the reflected X‑ray component, and the eventual appearance of the antipodal hotspot in the pulse profile. The quantitative agreement between magnetic moment estimates derived from disc truncation and from spin‑down measurements constrains the disc‑magnetosphere coupling to within a factor of two of the canonical Alfvén radius. These results provide valuable benchmarks for theoretical models of disc–magnetosphere interaction in accreting millisecond pulsars and for future observational campaigns targeting low‑luminosity outbursts.