SAX J1808.4-3658: high resolution spectroscopy and decrease of pulsed fraction at low energies

XMM-Newton observed the accreting millisecond pulsar SAX J1808.4-3658 during its 2008 outburst. We present timing and spectral analyses of this observation, in particular the first pulse profile study below 2 keV, and the high-resolution spectral analysis of this source during the outburst. Combined spectral and pulse profile analyses suggest the presence of a strong unpulsed source below 2 keV that strongly reduces the pulsed fraction and a hard pulsed component that generates markedly double peaked profiles at higher energies. We also studied the high-resolution grating spectrum of SAX J1808.4-3658, and found several absorption edges and Oxygen absorption lines with whom we infer, in a model independent way, the interstellar column densities of several elements in the direction of SAX J1808.4-3658.

💡 Research Summary

The paper presents a comprehensive timing and spectral study of the accreting millisecond X‑ray pulsar SAX J1808.4‑3658 using XMM‑Newton data obtained during the 2008 outburst. The observation, performed with the EPIC‑pn camera in timing mode and the Reflection Grating Spectrometer (RGS), provides high‑quality data from 0.3 to 12 keV, allowing the authors to investigate for the first time the pulse profile below 2 keV.

Timing analysis was carried out by barycentering the event times and applying the 2008 outburst ephemeris from Hartman et al. (2009). Pulse profiles were constructed by folding 3500‑second data segments and fitting them with a two‑harmonic model (fundamental ν and second harmonic 2ν) plus a constant unpulsed component. In the full 0.3‑12 keV band the fundamental shows an rms amplitude of 0.98 % and the second harmonic 0.33 %. When the data are divided into nine energy bands, the fractional amplitude rises sharply from the lowest energies up to ≈3 keV and then remains roughly constant up to 12 keV. Below ≈2 keV the pulsed fraction drops to ≈0.4 % rms, indicating that most of the emission in this band is unpulsed. The second harmonic, however, increases monotonically with energy and becomes comparable to the fundamental above ≈6 keV, producing a clearly double‑peaked pulse shape at higher energies. A linear correlation between pulse phase residuals of the fundamental and the total X‑ray count rate is also reported, with a slope of (9.9 ± 1.2) × 10⁻⁴ cycle (ct s⁻¹)⁻¹.

Spectral analysis combined the EPIC‑pn spectrum (0.6‑12 keV) with the first‑order RGS spectra (0.4‑1.8 keV). After accounting for inter‑instrument calibration offsets (≤4 %) and adding a 1.5 % systematic error to each bin, the authors fitted the continuum with an absorbed multi‑component model: phabs × (diskbb + bbody + powerlaw) plus a relativistic diskline to describe the broad Fe Kα emission around 6.4–6.5 keV. The best‑fit parameters are N_H ≈ 1.4 × 10²¹ cm⁻², inner disc temperature kT_disc ≈ 0.20 keV, hot‑spot blackbody temperature kT_bb ≈ 0.33 keV, photon index Γ ≈ 2.11, and a diskline with inner radius ≈20 km, outer radius ≈190 km, and inclination >30°. The power‑law component dominates the flux above ≈2 keV, while the disc contributes roughly 30 % of the flux below that energy.

The high‑resolution RGS data were used to measure interstellar absorption edges in a model‑independent way. By fixing the continuum and fitting individual edges with the vphabs model, the authors derived optical depths for O K (0.542 keV, τ ≈ 0.66), Fe L, Ne K, Mg K, and Si K. Converting these depths using photo‑electric cross sections yields column densities for each element; the O K edge implies a hydrogen column N_H = (1.4 ± 0.2) × 10²¹ cm⁻², consistent with radio H I measurements. Additionally, narrow 1s‑2p absorption lines of O I, O II, and O III were identified and their equivalent widths measured, providing an independent check on the oxygen abundance via curve‑of‑growth analysis.

In the discussion, the authors interpret the low‑energy suppression of the pulsed fraction as the result of a strong, essentially unpulsed disc blackbody component that dilutes the pulsations originating from the neutron‑star hot spot. The hard blackbody and power‑law components remain pulsed, explaining the persistence of ≈2 % rms pulsations up to 12 keV. The double‑peaked pulse shape at higher energies reflects the comparable contributions of the fundamental and second harmonic, likely caused by asymmetric emission from the two magnetic poles and relativistic beaming. The broad Fe Kα line, modeled with a relativistic diskline, indicates reflection from the inner accretion disc, providing constraints on the disc geometry and inclination.

Overall, this work delivers the first detailed low‑energy pulse profile of SAX J1808.4‑3658, demonstrates the coexistence of pulsed and unpulsed spectral components, and supplies precise interstellar column density measurements through high‑resolution spectroscopy. These results advance our understanding of pulse formation mechanisms in accreting millisecond pulsars and offer valuable constraints on the surrounding interstellar medium.