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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 back-flowing charges impinging on the star surface layers. This particle bombardment is expected to imprint the spectral and, even more, the polarization 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 polarized and X-mode dominated, but its polarization degree is significantly reduced (down to 10 per cent–50 per cent) 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 polarization degree of the emergent radiation increases, first at higher energies (⁠|${\sim} 10\ \mathrm{keV}$|⁠) 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. [ABSTRACT FROM AUTHOR]

Magnetars, the most strongly magnetized neutron stars, are among the most promising targets for X-ray polarimetry. Imaging X-ray Polarimetry Explorer (IXPE), the first satellite devoted to exploring the sky in polarized X-rays, has observed four magnetars to date. A proper interpretation of IXPE results requires the development of new atmospheric models that can take into proper account the effects of the magnetized vacuum on par with those of the plasma. Here we investigate the effects of mode conversion at the vacuum resonance on the polarization properties of magnetar emission by computing plane-parallel atmospheric models under varying conditions of magnetic field strength/orientation, effective temperature, and allowing for either complete or partial adiabatic mode conversion. Complete mode conversion results in a switch of the dominant polarization mode, from the extraordinary (X) to the ordinary (O) one, below an energy that decreases with increasing magnetic field strength, occurring at |$\approx 0.5\, \mathrm{keV}$| for a magnetic field strength of |$B=10^{14}\, \mathrm{G}$|⁠. Partial adiabatic mode conversion results in a reduced polarization degree when compared with a standard plasma atmosphere. No dominant mode switch occurs for |$B=10^{14}\, \mathrm{G}$|⁠ , while there are two switches for lower fields of |$B=3\times 10^{13}\, \mathrm{G}$|⁠. Finally, by incorporating our models in a ray-tracing code, we computed the expected polarization signal at infinity for different emitting regions on the star surface and for different viewing geometries. The observability of quantum electrodynamics signatures with IXPE and with future soft X-ray polarimeters as Rocket Experiment Demonstration of a Soft X-ray Polarimeter is discussed. [ABSTRACT FROM AUTHOR]