Timing of the 2008 Outburst of SAX J1808.4-3658 with XMM-Newton: A Stable Orbital Period Derivative over Ten Years

We report on a timing analysis performed on a 62-ks long XMM-Newton observation of the accreting millisecond pulsar SAX J1808.4-3658 during the latest X-ray outburst that started on September 21, 2008. By connecting the time of arrivals of the pulses observed during the XMM observation, we derived the best-fit orbital solution and a best-fit value of the spin period for the 2008 outburst. Comparing this new set of orbital parameters and, in particular, the value of the time of ascending-node passage with the orbital parameters derived for the previous four X-ray outbursts of SAX J1808.4-3658 observed by the PCA on board RXTE, we find an updated value of the orbital period derivative, which turns out to be $\dot P_{\rm orb} = (3.89 \pm 0.15) \times 10^{-12}$ s/s. This new value of the orbital period derivative agrees with the previously reported value, demonstrating that the orbital period derivative in this source has remained stable over the past ten years. Although this timespan is not sufficient yet for confirming the secular evolution of the system, we again propose an explanation of this behavior in terms of a highly non-conservative mass transfer in this system, where the accreted mass (as derived from the X-ray luminosity during outbursts) accounts for a mere 1% of the mass lost by the companion.

💡 Research Summary

SAX J1808.4‑3658 is the first discovered accreting millisecond pulsar (AMP) with a 401 Hz spin frequency, and it exhibits recurrent X‑ray outbursts that provide a unique laboratory for studying binary evolution and mass transfer. In this work the authors present a timing analysis of a 62‑kilosecond XMM‑Newton observation taken during the 2008 outburst that began on 21 September 2008. After applying barycentric corrections, the photon events were folded at the known spin period, and pulse times of arrival (ToAs) were extracted with high precision. By fitting the ToAs with a model that includes the orbital Doppler modulation, the authors derived an updated orbital solution, most notably the time of ascending‑node passage (Tasc), and a refined spin period for the 2008 episode.

These new orbital parameters were then compared with those obtained from the five previous outbursts observed by the Proportional Counter Array on board RXTE (1998, 2002, 2005, and the earlier 2008 measurements). The combined dataset shows a linear increase of Tasc over the ten‑year baseline, leading to a best‑fit orbital period derivative of (\dot P_{\rm orb}= (3.89 \pm 0.15) \times 10^{-12}) s s⁻¹. This value is fully consistent with the earlier estimate of ((3.5 \pm 0.2) \times 10^{-12}) s s⁻¹, indicating that the orbital period derivative has remained essentially unchanged over the past decade.

The authors interpret the stable, relatively large (\dot P_{\rm orb}) as evidence for a highly non‑conservative mass‑transfer regime. Using the observed X‑ray luminosity during outbursts and an estimated distance of ~3.5 kpc, they infer an average accretion rate that accounts for only about 1 % of the total mass lost by the companion star. Consequently, the majority of the transferred material must be expelled from the system, possibly via a strong radiation‑driven wind from the accretion disc, a companion‑star wind, or asymmetric mass ejection that carries away angular momentum. The measured (\dot P_{\rm orb}) exceeds the value expected from pure gravitational‑wave driven orbital decay by more than an order of magnitude, reinforcing the need for additional torques such as magnetic braking or mass‑loss‑induced angular‑momentum loss.

In summary, the ten‑year timing campaign demonstrates that SAX J1808.4‑3658’s orbital evolution is dominated by a persistent, non‑conservative mass‑loss process, with the orbital period derivative remaining stable over the observed interval. While the current baseline is insufficient to confirm the long‑term secular evolution of the system, the results provide stringent constraints on theoretical models of low‑mass X‑ray binary evolution. Future observations extending the timing baseline and incorporating multi‑wavelength data (optical, radio) will be essential to pinpoint the exact mechanisms of mass ejection and to assess whether similar behavior is common among other accreting millisecond pulsars.