Pulse profile modelling of the accretion-powered millisecond pulsar SAX J1808.4-3658 using NICER data from its 2019 and 2022 outbursts

TL;DR

This work applies relativistic pulse-profile modelling (PPM) to NICER data from SAX J1808.4-3658’s 2019 and 2022 outbursts to infer neutron-star and disc parameters. A single circular hotspot fails to reproduce the data; a two-hotspot model with a disc component improves phase residuals but leaves a spectral feature near 1 keV, signaling missing physics in the disc/line treatment. Employing a flexible background (background marginalisation) yields much better spectral fits but introduces parameter degeneracies between non-pulsed background and hotspot emission, limiting robustness of mass and radius estimates. An EoS-informed prior can reduce computational cost and explore consistency with dense-matter constraints, but it does not decisively favor a particular solution; the results underscore the need for improved disc reflection physics and possibly polarimetric/high-energy data to break degeneracies and constrain inclination, hotspot geometry, and the inner disc radius.

Abstract

Pulse profile modelling is a relativistic ray-tracing technique that has provided constraints on parameters, with a focus on mass and radius, of five rotation-powered millisecond pulsars. While the technique can also be applied to accretion-powered millisecond pulsars (AMPs), this requires accounting for the X-rays from the accretion disc and has only been applied to archival data from the Rossi X-ray Timing Explorer. Here, we apply a previously developed neutron star and accretion disc model to the NICER (Neutron star Interior Composition Explorer) data of the 2019 and 2022 outbursts of SAX J1808.4-3658. We find that a single circular hotspot model is insufficient to explain the data. Modelling with two hotspots and an accretion disc model provides better phase-residuals, but a spectral residual at around 1 keV remains. In contrast, we find a good fit with a flexible background approach, replacing the accretion disk. However, the inferred parameters are not robust due to a degeneracy in the origin of the non-pulsed radiation, which can be caused either by the background or a hotspot that is at least partially in view throughout a full rotation. This work represents an important next step in pulse profile modelling of AMPs by analysing NICER data and underlines the need for more accurate accretion disc and hotspot modelling to achieve robust parameter constraints. We expect the inclusion of higher energy and polarimetric data will provide complementary constraints on inclination, hotspot colatitude, and hotspot size, improving the accuracy of pulse profile modelling of AMPs.

Figures (11)

• Figure 1: The outbursts of J1808 in 2019 and 2022. The red band highlights the interval within which data was extracted for this analysis.
• Figure 2: Pulse profiles prepared from the peak of the 2019 and 2022 outbursts of J1808. The top panels display the bolometric pulse profiles while the bottom panels display the energy-phase resolved pulse profiles.
• Figure 3: MAP phase-energy resolved pulse profiles of various models. The panel titled 'model' displays the expected pulse profile with the parameters of the MAP sample. To the right the data and the right-most panel shows the normalized residuals between those two. In the panels left of the model, the decomposition into its constituent parts is shown. For all models, 'hotspot' shows the pulse profile of the hotspot. In the left-most panel(s), the background contributions from various background models are shown: Disc (top), Disc+Line (middle, separated) and the marginalised background (bottom).
• Figure 4: Data and modelled pulse profiles of the MAP samples, where the pulse profiles are also decomposed in their contributions from primary and secondary hotspots, and background contributions.
• Figure 5: Pulse profiles of the MAP samples in three representative NICER channels for the STU-Disc and STU-Marg configurations. In the top panels, the data (in black) and total posterior predicted pulse profiles (i.e. spots and either disk or marginalised background contribution, solid lines) are shown along with the separate contributions of the primary (dash-dotted lines) and secondary hotspots (dotted lines). In the bottom panels, the residual counts (data-model) are shown in each representative channel, with the $\pm1\sigma$ Poisson errors.