Broad relativistic iron emission line observed in SAX J1808.4-3658

During the September-October 2008 outburst of the accreting millisecond pulsar SAX J1808.4-3658, the source was observed by both Suzaku and XMM-Newton approximately 1 day apart. Spectral analysis reveals a broad relativistic Fe K-alpha emission line which is present in both data-sets, as has recently been reported for other neutron star low-mass X-ray binaries. The properties of the Fe K line observed during each observation are very similar. From modeling the Fe line, we determine the inner accretion disk radius to be 13.2 +/- 2.5 GM/c^2. The inner disk radius measured from the Fe K line suggests that the accretion disk is not very receded in the island state. If the inner disk (as measured by the Fe line) is truncated at the magnetospheric radius this implies a magnetic field strength of ~3E8 G at the magnetic poles, consistent with other independent estimates.

💡 Research Summary

During the September–October 2008 outburst of the accreting millisecond pulsar SAX J1808.4‑3658, the source was observed with Suzaku (October 2, 2008) and XMM‑Newton (September 30, 2008) roughly one day apart. Both observations yielded high‑quality spectra covering the 0.7–45 keV (Suzaku) and 1.2–11 keV (XMM‑Newton) bands. After standard data reduction—using front‑illuminated XIS0 and XIS3 in 1/4‑window mode for Suzaku and the PN detector in timing mode for XMM‑Newton—the authors performed joint spectral fitting with XSPEC. The continuum was modeled as an absorbed multicolor disk blackbody (diskbb) plus a single‑temperature blackbody (bbody) and a power‑law component. A detector feature near 1.85 keV was accounted for with a Gaussian absorption line, and a cross‑normalization constant (c ≈ 1.37) was introduced to reconcile the XIS and PIN fluxes.

Residuals in the 4–7 keV region revealed a broad, asymmetric Fe Kα emission line in both data sets. The line was modeled with the relativistic diskline profile (Fabian et al. 1989), allowing the line centroid (constrained to 6.40–6.97 keV), the emissivity index β, the inner disk radius (R_{\rm in}), and the inclination i to vary freely. The outer radius was fixed at 1000 (GM/c^{2}) because the line profile is dominated by the innermost radii. The inclination was limited to 36°–67°, consistent with optical constraints. By fitting the Suzaku and XMM‑Newton spectra simultaneously and tying the line parameters (except for normalization), the authors obtained a well‑constrained inner radius of (R_{\rm in}=13.2\pm2.5;GM/c^{2}) and an inclination of (55^{+8}_{-4}) degrees. The line centroid was measured at 6.40 keV with an equivalent width of ~130 eV.

Assuming that the disk is truncated at the magnetospheric (Alfvén) radius, the measured (R_{\rm in}) can be used to estimate the neutron‑star magnetic field. Using the formulation of Ibragimov & Poutanen (2009) with a distance of 3.5 kpc, a mass of 1.4 M⊙, a radius of 10 km, an accretion efficiency η = 0.1, and the bolometric flux derived from the 2–25 keV fluxes (average (F_{\rm bol}=2.42\times10^{-9}) erg cm⁻² s⁻¹), the magnetic dipole moment is (\mu=(1.6\pm0.5)\times10^{26}) G cm³. This translates to a polar magnetic field strength of (B=(3.2\pm1.0)\times10^{8}) G, in line with previous estimates from timing and optical studies. The authors note that if the conversion factor (k_A) is reduced to 0.5, the inferred field would be roughly three times larger.

The broadband Suzaku spectrum shows a hard power‑law tail extending to at least 45 keV. Although a self‑consistent relativistic reflection model (reflionx) can fit the data with a reflection fraction of ~0.5, the expected Compton hump is not clearly present, suggesting that the complex thermal components in neutron‑star LMXBs may mask the reflection signature. This contrasts with black‑hole binaries where the hump is more evident.

The measured inner radius is consistent with earlier XMM‑Newton‑only analyses (Papitto et al. 2008b reported (R_{\rm in}=8.7^{+3.7}_{-2.7};GM/c^{2})) once differences in the treatment of the outer disk radius are accounted for. Independent estimates based on pulse‑profile evolution (Ibragimov & Poutanen 2009) also suggest a comparable truncation radius (~19.5 km for a 1.4 M⊙ neutron star), supporting the conclusion that the disk does not recede dramatically even in the hard (island) state.

In summary, the detection of a broad, relativistically broadened Fe Kα line in SAX J1808.4‑3658 with two independent observatories provides a robust measurement of the inner accretion disk radius ((\sim13;GM/c^{2})). Interpreting this radius as the magnetospheric boundary yields a magnetic field strength of a few × 10⁸ G at the poles, corroborating prior magnetic field estimates. The work demonstrates that Fe‑line spectroscopy remains a powerful tool for probing the geometry of the inner disk and the magnetic environment of accreting millisecond pulsars, and it highlights the need for higher‑resolution, higher‑throughput observations to disentangle reflection features from the complex thermal emission typical of neutron‑star low‑mass X‑ray binaries.