Search

Magnetars are neutron stars that host huge, complex magnetic fields which require supporting currents to flow along the closed field lines. This makes magnetar atmospheres different from those of passively cooling neutron stars because of the heat deposited by backflowing charges impinging on the star surface layers. This particle bombardment is expected to imprint the spectral and, even more, the polarisation properties of the emitted thermal radiation. We present solutions for the radiative transfer problem for bombarded plane-parallel atmospheres in the high magnetic field regime. The temperature profile is assumed a priori, and selected in such a way to reflect the varying rate of energy deposition in the slab (from the impinging currents and/or from the cooling crust). We find that thermal X-ray emission powered entirely by the energy released in the atmosphere by the magnetospheric back-bombardment is linearly polarised and X-mode dominated, but its polarisation degree is significantly reduced (down to $10-50\%$) when compared with that expected from a standard atmosphere heated only from the cooling crust below. By increasing the fraction of heat flowing in from the crust the polarisation degree of the emergent radiation increases, first at higher energies ($\sim 10$ keV) and then in the entire soft X-ray band. We use our models inside a ray-tracing code to derive the expected emission properties as measured by a distant observer and compare our results with recent IXPE observations of magnetar sources., Comment: 9 pages, 9 figures, accepted for publication in MNRAS

We present a phase-dependent analysis of the polarized emission from the Crab pulsar based on three sets of observations by the Imaging X-ray Polarimetry Explorer (IXPE). We found that a phenomenological model involving a simple linear transformation of the Stokes parameters adequately describes the IXPE data. This model enables us to establish, for the first time, a connection between the polarization properties of the Crab pulsar in the optical and soft X-ray bands, suggesting a common underlying emission mechanism across these bands. In particular, the phase-dependent polarization degree in X-rays for pure pulsar emission shows similar features but is reduced by a factor $\approx (0.46-0.56)$ compared to the optical band, implying an energy-dependent polarized emission. In addition, using this model, we study the polarization angle swing in X-rays and identify a potentially variable phase-shift at the interpulse relative to the optical band, alongside a phase-shift marginally consistent with zero persisting at the main pulse. While the variability presents a new challenge for theoretical interpretation, our findings suggest that the emission mechanism for the main pulse is likely located far from the neutron star surface, perhaps near or beyond the light cylinder, rather than operating in the inner magnetosphere where vacuum birefringence is expected to be at work. Ignoring the phase-shifts would result in identical phase-dependent polarization angles between the optical and X-ray bands for pure pulsar emission., Comment: 16 pages, 11 figures, submitted to A&A

We develop two new highly efficient estimators to measure the polarization (Stokes parameters) in experiments that constrain the position angle of individual photons such as scattering and gas-pixel-detector polarimeters, and analyse in detail a previously proposed estimator. All three of these estimators are at least fifty percent more efficient on typical datasets than the standard estimator used in the field. We present analytic estimates of the variance of these estimators and numerical experiments to verify these estimates. Two of the three estimators can be calculated quickly and directly through summations over the measurements of individual photons., Comment: 4 pages, accepted by the Open Journal of Astrophysics

In an accreting X-ray pulsar, a neutron star accretes matter from a stellar companion through an accretion disk. The high magnetic field of the rotating neutron star disrupts the inner edge of the disc, funneling the gas to flow onto the magnetic poles on its surface. Hercules X-1 is in many ways the prototypical X-ray pulsar; it shows persistent X-ray emission and it resides with its companion HZ Her, a two-solar-mass star, at about 7~kpc from Earth. Its emission varies on three distinct timescales: the neutron star rotates every 1.2~seconds, it is eclipsed by its companion each 1.7~days, and the system exhibits a superorbital period of 35~days which has remained remarkably stable since its discovery. Several lines of evidence point to the source of this variation as the precession of the accretion disc, the precession of the neutron star or both. Despite the many hints over the past fifty years, the precession of the neutron star itself has yet not been confirmed or refuted. We here present X-ray polarization measurements with the Imaging X-ray Polarimetry Explorer (IXPE) which probe the spin geometry of the neutron star. These observations provide direct evidence that the 35-day-period is set by the free precession of the neutron star crust, which has the important implication that its crust is somewhat asymmetric fractionally by a few parts per ten million. Furthermore, we find indications that the basic spin geometry of the neutron star is altered by torques on timescale of a few hundred days., Comment: 37 pages

We report on IXPE, NICER and XMM-Newton observations of the magnetar 1E 2259+586. We find that the source is significantly polarized at about or above 20% for all phases except for the secondary peak where it is more weakly polarized. The polarization degree is strongest during the primary minimum which is also the phase where an absorption feature has been identified previously (Pizzocaro et al. 2019). The polarization angle of the photons are consistent with a rotating vector model with a mode switch between the primary minimum and the rest of the rotation of the neutron star. We propose a scenario in which the emission at the source is weakly polarized (as in a condensed surface) and, as the radiation passes through a plasma arch, resonant cyclotron scattering off of protons produces the observed polarized radiation. This confirms the magnetar nature of the source with a surface field greater than about 1015 G, Comment: 13 pages, 13 figures, 5 tables

We report on Imaging X-ray polarimetry explorer (IXPE) observations of the Be-transient X-ray pulsar LS V +44 17/RX J0440.9+4431 made at two luminosity levels during the giant outburst in January--February 2023. Considering the observed spectral variability and changes in the pulse profiles, the source was likely caught in supercritical and subcritical states with significantly different emission-region geometry, associated with the presence of accretion columns and hot spots, respectively. We focus here on the pulse-phase-resolved polarimetric analysis and find that the observed dependencies of the polarization degree and polarization angle (PA) on the pulse phase are indeed drastically different for the two observations. The observed differences, if interpreted within the framework of the rotating vector model (RVM), imply dramatic variations in the spin axis inclination, the position angle, and the magnetic colatitude by tens of degrees within the space of just a few days. We suggest that the apparent changes in the observed PA phase dependence are predominantly related to the presence of an unpulsed polarized component in addition to the polarized radiation associated with the pulsar itself. We then show that the observed PA phase dependence in both observations can be explained with a single set of RVM parameters defining the pulsar's geometry. We also suggest that the additional polarized component is likely produced by scattering of the pulsar radiation in the equatorial disk wind., Comment: 10 pages, 7 figures, accepted in A&A

The phase- and energy-resolved polarization measurements of accreting X-ray pulsars (XRPs) allow us to test different theoretical models of their emission, and they also provide an avenue to determine the emission region geometry. We present the results of the observations of the XRP GX 301-2 performed with the Imaging X-ray Polarimetry Explorer (IXPE). A persistent XRP, GX 301-2 has one of the longest spin periods known: $\sim$680s. A massive hyper-giant companion star Wray 977 supplies mass to the neutron star via powerful stellar winds. We did not detect significant polarization in the phase-averaged data when using spectro-polarimetric analysis, with the upper limit on the polarization degree (PD) of 2.3% (99% confidence level). Using the phase-resolved spectro-polarimetric analysis, we obtained a significant detection of polarization (above 99% confidence level) in two out of nine phase bins and a marginal detection in three bins, with a PD ranging between $\sim$3% and $\sim$10% and a polarization angle varying in a very wide range from $\sim$0 degree to $\sim$160 degree. Using the rotating vector model, we obtained constraints on the pulsar geometry using both phase-binned and unbinned analyses, finding excellent agreement. Finally, we discuss possible reasons for a low observed polarization in GX 301-2., Comment: 10 pages, 10 figures, accepted for publication in A&A

Cen X-3 is the first X-ray pulsar discovered 50 years ago. Radiation from such objects is expected to be highly polarized due to birefringence of plasma and vacuum associated with propagation of photons in presence of the strong magnetic field. Here we present results of the observations of Cen X-3 performed with the Imaging X-ray Polarimetry Explorer. The source exhibited significant flux variability and was observed in two states different by a factor of ~20 in flux. In the low-luminosity state no significant polarization was found either in pulse phase-averaged (with the 3$\sigma$ upper limit of 12%) or phase-resolved data (the 3$\sigma$ upper limits are 20-30%). In the bright state the polarization degree of 5.8$\pm$0.3% and polarization angle of $49.6\deg\pm1.5\deg$ with significance of about 20$\sigma$ was measured from the spectro-polarimetric analysis of the phase-averaged data. The phase-resolved analysis showed a significant anti-correlation between the flux and the polarization degree as well as strong variations of the polarization angle. The fit with the rotating vector model indicates a position angle of the pulsar spin axis of about 49$\deg$ and a magnetic obliquity of 17$\deg$. The detected relatively low polarization can be explained if the upper layers of the neutron star surface are overheated by the accreted matter and the conversion of the polarization modes occurs within the transition region between the upper hot layer and a cooler underlying atmosphere. A fraction of polarization signal can also be produced by reflection of radiation from the neutron star surface and the accretion curtain., Comment: Submitted to ApJL. 18 pages, 12 figures

We present a systematic study of the unbinned, photon-by-photon likelihood technique which can be used as an alternative method to analyse phase-dependent, X-ray spectro-polarimetric observations obtained with IXPE and other photo-electric polarimeters. We apply the unbinned technique to models of the luminous X-ray pulsar Hercules X-1, for which we produce simulated observations using ixpeobssim package. We consider minimal knowledge about the actual physical process responsible for the polarized emission from the accreting pulsar and assume that the observed phase-dependent polarization angle can be described by the rotating vector model. Using the unbinned technique, the detector's modulation factor, and the polarization information alone, we found that both the rotating vector model and the underlying spectro-polarimetry model can reconstruct equally well the geometric configuration angles of the accreting pulsar. However, the measured polarization fraction becomes biased with respect to underlying model unless the energy dispersion and effective area of the detector are also taken into account. To this end, we present an energy-dispersed likelihood estimator that is proved to be unbiased. For different analyses, we obtain posterior distributions from multiple ixpeobssim realizations and show that the unbinned technique yields $\sim 10\%$ smaller error bars than the binned technique. We also discuss alternative sources, such as magnetars, in which the unbinned technique and the rotating vector model might be applied., Comment: 11 pages, 9 figures. Accepted for publication in MNRAS. Source code available at https://github.com/UBC-Astrophysics/Unbinned-Xray-polarimetry

We argue that measurements of X-ray polarization using the recently launched Imaging X-ray Polarimetry Explorer will answer many open questions about magnetars in particular the physical state of their surfaces, whether vacuum birefringence exists, and the nature of the hard X-ray emission from these objects. We outline the capabilities of the instrument, specific models and the results of simulations for the magnetar 4U~0142+61., Comment: 12 pages, 7 figures, Neutron Star Astrophysics at the Crossroads: Magnetars and the Multimessenger Revolution, Proceedings IAU Symposium No. 363, 2022, E. Troja & M. Baring, eds

Over the next year, a new era of observations of compact objects in X-ray polarization will commence. Among the key targets for the upcoming Imaging X-ray Polarimetry Explorer mission, will be the magnetars 4U 0142+61 and 1RXS J170849.0-400910. Here we present the first detailed predictions of the expected polarization from these sources that incorporate realistic models of emission physics at the surface (gaseous or condensed), the temperature distribution on the surface, general relativity, quantum electrodynamics and scattering in the magnetosphere, and also account for the broadband spectral energy distribution of these sources from below 1 keV to nearly 100 keV. We find that either atmospheres or condensed surfaces can account for the emission at a few keV; in both cases either a small hot polar cap or scattering is required to account for the emission at 5-10 keV, and above 10 keV scattering by a hard population of electrons can account for the rising power in the hard X-rays observed in many magnetars in quiescence. Although these different scenarios result in very similar spectral energy distributions, they generate dramatically different polarization signatures from 2-10 keV, which is the range of sensitivity of the Imaging X-ray Polarimetry Explorer. Observations of these sources in X-ray polarization will therefore probe the emission from magnetars in an essentially new way., Comment: 11 pages, 5 figures, 1 table

The X-ray Polarization Probe (XPP) is a second generation X-ray polarimeter following up on the Imaging X-ray Polarimetry Explorer (IXPE). The XPP will offer true broadband polarimetery over the wide 0.2-60 keV bandpass in addition to imaging polarimetry from 2-8 keV. The extended energy bandpass and improvements in sensitivity will enable the simultaneous measurement of the polarization of several emission components. These measurements will give qualitatively new information about how compact objects work, and will probe fundamental physics, i.e. strong-field quantum electrodynamics and strong gravity., Comment: submitted to Astrophysics Decadal Survey as a State of the Profession white paper

We analyzed the thermal emission from the entire surface of the millisecond pulsar PSR J0437-4715 observed in the ultraviolet and soft X-ray bands. For this, we calculated non-magnetized, partially ionized atmosphere models of hydrogen, helium, and iron compositions and included plasma frequency effects that may affect the emergent spectrum. This is particularly true for the coldest atmospheres composed of iron (up to a few percent changes in the soft X-ray flux). Employing a Markov chain Monte Carlo method, we found that the spectral fits favour a hydrogen atmosphere, disfavour a helium composition and rule out iron atmosphere and blackbody models. By using a Gaussian prior on the dust extinction, based on the latest 3D map of Galactic dust, and accounting for the presence of hot polar caps found in previous work, we found that the hydrogen atmosphere model results in a well-constrained neutron star radius $R_\mathrm{NS} = 13.6^{+0.9}_{-0.8}~\mathrm{km}$ and bulk surface temperature $T^{\infty}_\mathrm{eff}=\left(2.3\pm0.1\right)\times10^5~\mathrm{K}$. This relatively large radius favours a stiff equation of state and disfavours a strange quark composition inside neutron stars., Comment: Accepted for publication in MNRAS

In this paper we present the science potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission for studies of strongly magnetized objects. We will focus on the physics and astrophysics of strongly magnetized objects, namely magnetars, accreting X-ray pulsars, and rotation powered pulsars. We also discuss the science potential of eXTP for QED studies. Developed by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Sciences, the eXTP mission is expected to be launched in the mid 2020s., Comment: Accepted for publication on Sci. China Phys. Mech. Astron. (2019)

The magnetosphere of strongly magnetized neutron stars, such as magnetars, can sustain large electric currents. The charged particles return to the surface with large Lorentz factors, producing a particle bombardment. We investigate the transport of radiation in the atmosphere of strongly magnetized neutron stars, in the presence of particle bombardment heating. We solve the radiative transfer equations for a gray atmosphere in the Eddington approximation, accounting for the polarization induced by a strong magnetic field. The solutions show the formation of a hot external layer and a low (uniform) temperature atmospheric interior. This suggests that the emergent spectrum may be described by a single blackbody with the likely formation of a optical/infrared excess (below ~ 1 eV). We also found that the polarization is strongly dependent on both the luminosity and penetration length of the particle bombardment. Therefore, the thermal emission from active sources, such as transient magnetars, in which the luminosity decreases by orders of magnitude, may show a substantial variation in the polarization pattern during the outburst decline. Our results may be relevant in view of future X-ray polarimetric missions such as IXPE and eXTP., Comment: 16 pages, 9 figures, accepted for publication in MNRAS