Accreting and transitional millisecond pulsars

The research field of accreting NS in low-mass X-ray binaries (LMXBs) has changed dramatically during the last 15 years with the launch of the Rossi X-ray Timing Explorer (RXTE). In 1996, the first evidence of millisecond periods in NS systems came with the detection of highly coherent oscillation in the 200–600 Hz range during X-ray bursts. By now about 20 NS show such oscillations. These are called nuclear-powered millisecond pulsars since the emission during the bursts is produced by thermonuclear burning at the NS surface. In 1998 RXTE also discovered coherent ms pulsations in the persistent emission of SAX J1808.4–3658. Now there are about 20 such sources showing oscillations in the frequency range 180–600 Hz. These are called accreting millisecond pulsars (AMPs, see Table 1 and Fig.1). In addition, a few dozen NS show kHz quasi-periodic oscillations (QPOs).

Table 1: List of accreting millisecond pulsars with their orbital periods, rotational frequencies, minimum companion masses and time of discovery.

Figure 1: Artist impression of accreting millisecond pulsars. ©Marek Gierlinski.

AMPs are exceptional physical laboratories for studying extreme gravity effects as well as plasma physics of the interaction between the NS magnetosphere and the accretion disc. Coherent ms pulsations in the persistent emission allow us to produce highly accurate pulse profiles by folding the data over a long observational period (days or even weeks). By detailed modelling the folded pulse profiles, one is able to determine the physical parameters such as the NS mass and radius, inclination of the system, position of the emitting region (hotspot) at the NS surface as well as the emission pattern from the hotspot responsible for the observed radiation. We have developed a theory of formation of pulse profiles from rapidly spinning NS including all relativistic effects, and proposed to use pulse profiles to obtain constraints on the NS radius as a function of its mass (Poutanen & Gierlinski 2003). Sometimes, pulse profiles of AMPs show significant deviations from a sine wave showing double-peak structure, which can be interpreted as a signature of the secondary magnetic pole (Ibragimov & Poutanen 2009, Poutanen et al. 2009). Studying the evolution of the profile with the accretion rate then gives us a possibility to geometrically constrain the inner disc radius as a function of accretion rate. The results will allow us to determine the energy dissipation profile in the region between the disc and the magnetosphere and thus use AMPs as laboratories to study the complicated plasma physics of the disc-magnetosphere interaction (Kajava et al. 2011).

Among the projects that we have worked on recently, one can mention detailed modelling of the pulse profiles and polarization properties (Poutanen 2020) accounting for the non-sphericity of the NS (Loktev et al. 2020) also accounting for deviations of the metric from the Schwarzschild one (Nättilä & Pihajoki 2018). Determining the NS parameters such as their masses and radii from the detailed models of the AMPs’ pulse profiles is one of the primary goals of the enchanced X-ray Timing Polarimeter (eXTP) mission to be launched in 2028 (Watts et al. 2019).

We have also analysed timing and spectral properties of a number of AMPs. Already for more than 15 years, we had a TOO program at the INTEGRAL observatory to study these sources during outbursts.

In the near future we are aiming at studying the geometry of AMPs using X-ray polarimetric means with the Imaging X-ray Polarimetry Explorer (IXPE) that wass lauched in December 2021. As of now (August 2023), no AMPs was observed. However, we are ready for the analysis of the upcoming data and in the mean time have developed the most advanced model for X-ray polarization from rapidly rotating AMPs (Bobrikova et al. 2023).

Transitional millisecond pulsars constitute a subclass of neutron stars that swing between the radio-pulsar state (when there is no active flow of matter from the companion star) and accretion state (when the matter dragged from the companion comes close to the neutron star). They provide strong evidence for the recycling scenario, where occasional accretion episodes can spin-up the neutron star to millisecond periods. Transitional millisecond pulsars also provide a unique set of observational data for understanding accretion at low rates onto magnetized neutron stars. For one of these sources, PSR J1023+0038, the pulsations at millisecond timescales have been found both in the X-rays and at optical wavelengths. This discovery challenged all previous low-rate accretion models, as the optical emission has to be coming from a very compact region. We proposed that the multiwavelength emission in this system originates from the area of interaction between the relativistic pulsar wind and the accretion stream (Fig. 2). Powerful wind is capable of stopping the stream, preventing its penetration towards the neutron star surface, and creating a standing shock. As the neutron star rotates, the shock slides along the matter leading to variations of the optical and X-ray fluxes with the period equal to half of the neutron star spin period, consistent with the observations. This scenario opens new prospects to study microphysical processes of interaction between the low-density relativistic beam with the matter.

Figure 2: Geometry of the interaction between the pulsar wind and the accretion disc in two different modes. From Veledina et al. (2019).

Selected publications (theory, simulation):