Radio polarization maps of shell-type supernova remnants – I. Effects of a random magnetic field component and thin-shell models

Abstract

The maps of intensity and polarization of the radio synchrotron emission from shelltype supernova remnants (SNRs) contain a considerable amount of information, although of not easy interpretation. With the aim of deriving constraints on the 3-D spatial distribution of the emissivity, as well as on the structure of both ordered and random magnetic fields (MFs), we present here a scheme to model maps of the emission and polarization in SNRs.We first generalize the classical treatment of the synchrotron emission to the case in which the MF is composed by an ordered MF plus an isotropic random component, with arbitrary relative strengths. In the case of a power-law particle energy distribution, we derive analytic formulae that formally resemble those for the classical case. We also treat the case of a shock compression of a fully random upstream field and we predict that the polarization fraction in this case should be higher than typically measured in SNRs. We implement the above treatment into a code, which simulates the observed polarized emission of an emitting shell, taking into account also the effect of the internal Faraday rotation.Finally, we show simulated maps for different orientations with respect to the observer, levels of the turbulent MF component, Faraday rotation levels, distributions of the emissivity (either barrel-shaped or limited to polar caps), and geometries for the ordered MF component (either tangential to the shell, or radial). Their analysis allows us to outline properties useful for the interpretation of radio intensity and polarization maps.

A laminar model for the magnetic field structure in bow-shock pulsar wind nebulae

“…8), with a polarized fraction of 40-50%, and extending for several parsecs. Using the subgrid model by Bandiera & Petruk (2016) recently applied to PWNe (Bucciantini et al 2017;Bucciantini & Olmi 2018), we can estimate a typical turbulence with δB/B ∼ 0.3. On the other hand low polarization systems like the Mouse G359.23-0.82 (Yusef-Zadeh & Gaensler 2005), with polarized fraction below 10% are likely characterized by strong turbulence, in part already evident in the rapid change of polarization pattern.…”

Modeling the effect of small-scale magnetic turbulence on the X-ray properties of Pulsar Wind Nebulae

“…A cautionary remark is here in order: the corrections derived by Bandiera & Petruk (2016), are formally valid only in the limit β → 0, when the isotropic assumption in the comoving frame corresponds to the isotropic assumption in the observer's frame. In case of strongly relativistic motions this is in general not true.…”

“…In a recent paper Bandiera & Petruk (2016) have shown that the effect of the small scale magnetic field fluctuations on the total and the polarized emissivity can be computed analytically, considering a fluid element with a net average field and assuming that the small scale fluctuations can be described by an isotropic random Gaussian field with variance (B ′ σ) 2 in each direction. The emission is computed considering the electrons to be distributed in the nebula with a power-law distribution function, as specified in Eq.…”

Future X-ray Polarimetry of Relativistic Accelerators: Pulsar Wind Nebulae and Supernova Remnants

“…Based on the idea that small-scale turbulence can be present, we have developed a formalism to include it, as a sub-grid effect [50][51][52], into large scale models for the global structure of the field, either simplified toy models on the line of [53], which are easy and fast to compute and allow us to deeply scan the possible parameter space in order to optimize the agreement with observations, or more sophisticated time-dependent numerical models that can take into account the interplay between the pulsar wind and the environment. These models have been recently applied to the Crab and Vela nebulae [52].…”