Atmosphere models of magnetized neutron stars: QED effects, radiation spectra and polarization signals

Abstract

Observations of surface emission from isolated neutron stars (NSs) provide unique challenges to theoretical modelling of radiative transfer in magnetized NS atmospheres. Recent work has demonstrated the critical role of vacuum polarization effects in determining NS spectra and polarization signals, in particular the conversion of photon modes (due to the ‘vacuum resonance’ between plasma and vacuum polarization) propagating in the density gradient of the NS atmosphere. Previous NS atmosphere models incorporated the mode conversion effect approximately, relying on transfer equations for the photon modes. Such treatments are inadequate near the vacuum resonance, particularly for magnetic field strengths around B∼Bl≃ 7 × 1013 G, where the vacuum resonance occurs near the photosphere. In this paper, we provide an accurate treatment of the mode conversion effect in magnetized NS atmosphere models, employing both the modal radiative transfer equations coupled with an accurate mode conversion probability at the vacuum resonance, and the full evolution equations for the photon Stokes parameters. In doing so, we are able to quantitatively calculate the effects of vacuum polarization on atmosphere structure, emission spectra and beam patterns, and polarizations for the entire range of magnetic field strengths, B= 1012–1015 G. In agreement with previous works, we find that for NSs with magnetic field strength B≳ 2 Bl, vacuum polarization reduces the widths of spectral features, and softens the hard spectral tail typical of magnetized atmosphere models. For B≲Bl/2, vacuum polarization does not change the emission spectra, but can significantly affect the polarization signals. Our new, accurate treatment of vacuum polarization is particularly important for quantitative modelling of NS atmospheres with ‘intermediate’ magnetic fields, B≃ (0.5–2) Bl. We provide fitting formulae for the temperature profiles for a suite of NS atmosphere models with different field strengths, effective temperatures and chemical compositions (ionized H or He). These analytical profiles are useful for direct modelling of various observed properties of NS surface emission. As an example, we calculate the observed intensity and polarization light curves from a rotating NS hotspot, taking into account the evolution of photon polarization in the magnetosphere. We show that vacuum polarization induces a unique energy‐dependent linear polarization signature, and that circular polarization can be generated in the magnetosphere of rapidly rotating NSs. We discuss the implications of our results to recent observations of thermally emitting isolated NSs and magnetars, as well as the prospects of future spectral and polarization observations.

Model X‐Ray Spectra of Magnetic Neutron Stars with Hydrogen Atmospheres

“…Thermal radiation has been detected from radio pulsars and radio-quiet neutron stars (NSs; see Kaspi et al 2006;Haberl 2007;van Kerkwijk & Kaplan 2007;Zavlin 2007 for reviews) and from soft gamma-ray repeaters and anomalous X-ray pulsars, which form the magnetar class of NSs endowed with superstrong (B k 10 14 G) magnetic fields (see Woods & Thompson 2006 for a review). Radiation from the surface of these NSs can provide invaluable information on the physical properties and evolution of the NSs.…”

Modelling of the surface emission of the low magnetic field magnetar SGR 0418+5729

“…On the other hand, the distance to SGR 0418 is rather uncertain. If located in the Perseus arm (which is in its direction), then the distance would be about 2 kpc (van der Horst et al 2010). However, there is no independent observational link to such an association.…”

“…While the magnetar model has been very successful in explaining some general features of the triggering mechanism of bursts and flares, the discovery in 2010 of an outburst from SGR 0418+5729 (SGR 0418 hereafter, van der Horst et al 2010;Esposito et al 2010), a NS with dipolar magnetic field B dip = (6 ± 2) ×10 12 G (Rea et al 2010, lower than those of most magnetars, clearly showed that the overall picture was not complete. Following this discovery, two more sources showing magnetar-like activity, but with "non-magnetar"-like B fields have then been discovered (Rea et al 2012;Scholz et al 2012;Rea et al 2014;Zhou et al 2014).…”

Atmospheres and radiating surfaces of neutron stars

“…• [377] (see also [378]). These calculations have thus fully confirmed the early analysis by Gnedin and Sunyaev [11].…”