X-ray polarimetry

Introduction

Electromagnetic radiation that we observe from various sources is intrinsically polarized. Polarization depends on the source geometry and specifically on its asymmetry. The symmetry can be broken by the magnetic field, which introduces polarization into synchrotron radiation. Scattering is yet another source of polarization. Polarimetry provides an independent approach to explore physics and astrophysics of cosmic sources in addition to traditionally used imaging, spectroscopy, and timing. It allows to determine the geometry of the otherwise unresolved sources, i.e. to determine the position of the symmetry axis or the magnetic field on the sky, thus providing us with the information that no other technique can obtain.

X-ray binaries hosting black holes (BH) or neutron stars (NS) emit large fraction of their radiation in the X-ray spectral band. These X-rays are expected to be strongly polarized, as they are produced either by Compton scattering or cyclo-synchrotron radiation in the accretion disc, an accretion shock or a boundary layer in the case of NSs, or jets. All these alternatives have specific polarization signatures. For example, in accreting millisecond pulsars (AMPs, NSs rotating with ms periods and having magnetic field B=10⁸–10⁹ G), variations of the polarization angle with the pulsar phase allow us to measure source inclination and magnetic obliquity (Viironen & Poutanen 2004) which in their turn give a possibility to measure NS mass-radius relation from the pulse profiles with a much better accuracy (Salmi, Nättilä, Poutanen 2018), to constrain the equation of state of cold ultra-dense matter and to test nuclear physics models. In X-ray pulsars and magnetars (NSs with B=10¹²–10¹⁵ G) the presence of strong magnetic field leads to dramatic changes in propagation properties of photons of different polarizations, in turn resulting in high polarization degree of tens of per cent. Variations of polarization as a function of the pulsar phase allow us to constrain the magnetic field geometry, inclination and the physics of the emitting region, e.g. study quantum electrodynamics effects in the strong B-field regime.

In the very vicinity of the BH, strong gravity causes rotation of the polarization plane, resulting in characteristic swing of polarization angle with energy. This is a unique signature of a BH and allows us to measure the accretion disc geometry and the BH spin. Thus polarization provides us with invaluable tool to study physics of accretion in X-ray binaries.

Although polarization measurements in radio and optical bands are commonly used in astrophysics, polarized X-rays have not been utilized much so far because of the absence of the X-ray polarimeters. The only satellite having X-ray polarimetric capabilities was OSO-8 (launched in 1975), which measured significant polarization of the Crab nebulae and black hole Cyg X-1 (Weisskopf et al. 1976, 1977, Long et al. 1980). The situation has changed in December 2021, when NASA launched the first satellite specifically designed for X-ray polarimetry Imaging X-ray Polarimetry Explorer (IXPE, PI M. Weisskopf, Marshall Space Flight Center) to study polarization from astrophysical sources. The instrument is two orders of magnitude more sensitive than OSO-8 and is measuring polarization as small as 1% in bright X-ray sources, such as such as X-ray pulsars, rotation-powered pulsars, magnetars, supernovae remnants and pulsar-wind nebulae, stellar-mass BHs, and super-massive BHs both Seyferts and blazars. In the field of accreting BHs, it has resolved a three-decade long debate on the accretion geometry. IXPE has opened a new window to studying the physics of X-ray sources. Our group is heavily involved in the IXPE project. Poutanen is the leader of the Topical Working Group (TWG) on Accreting Neutron Stars and we are also members of other TWGs on Accreting black holes and AGNs.

Among the projects that we have worked on recently, one can mention detailed modelling of the pulse profiles and polarization properties of rapidly rotating neutron stars (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 developed formalism to compute Compton scattering in strong magnetic field (Mushtukov et al. 2012, 2016) to be used for calculations of polarization properties of strong-field X-ray pulsars.

We have developed recently an analytical theory to compute polarization from accretion disks around black holes and neutron stars (Loktev et al. 2022). This simplifies calculations dramatically since no ray-tracing is needed. This theory can be applied to the future observations of black hole X-ray binaries with IXPE and also to modelling radio polarization images produced by the Event Horizon Telescope. Similar approach was recently developed by Narayan et al. (2021).

Results from IXPE

Stellar-mass black holes

For the last two years we were involved in the analysis of the X-ray polarimetric data obtained with the Imaging X-ray Polarimeter Explorer. The first massive stellar remnant studied with this mission was the prototypical black hole X-ray binary Cygnus X-1, which is also the first X-ray source discovered in Cygnus constellation during a rocket flight in 1964, and the first source that was widely accepted to be a black hole. Polarimetric measurements from Cyg X-1, reported on 2022 November 3 volume of Science, revealed a 4% polarization parallel to the radio jet imaged in earlier radio observations (see Fig. 1). This univocally proved that the X-ray emitting gas extends perpendicular to the jet.  The data thus rule out previously considered spherical or lamppost models.

The detected high polarization degree also imply that the hot flow might be seen more edge-on than previously thought indicating the misalignment between the black hole spinning axis and the axis of the orbit in which the black hole is rotating around the massive companion. In order to verify this assumption, we performed an observational campaign with the high-precision optical polarimeter DIPol-2, which can say about the direction of the orbital axis on the plane of the sky. However, unlike in MAXI J1820+070, where we have been able to identify a large misalignment seen in the plane of the sky, the binary orbit in Cyg X-1 is very well aligned with the black hole spin axis. Alternatively, the large polarization may indicate that the X-rays are scattered in the outflow that moves away from the black hole at a mildly relativistic velocity. Then due to relativistic aberration, we actually see the scattering region at a different angle in its comoving frame, this increases polarization.

Figure 1: Direction of X-ray polarization of Cyg X-1 as observed by IXPE (orange contours) together with the radio contours identifying the direction of the jet.

X-ray pulsars