Radio Emission from a Young Supernova Remnant Interacting with an Interstellar Cloud: Magnetohydrodynamic Simulation with Relativistic Electrons

We present two-dimensional MHD simulations of the evolution of a young Type Ia supernova remnant (SNR) during its interaction with an interstellar cloud of comparable size at impact. We include for the first time in such simulations explicit relativistic electron transport. This was done using a simplified treatment of the diffusion-advection equation, thus allowing us to model injection and acceleration of cosmic-ray electrons at shocks and their subsequent transport. From this information we also model radio synchrotron emission, including spectral information. The simulations were carried out in spherical coordinates with azimuthal symmetry and compare three different situations, each incorporating an initially uniform interstellar magnetic field oriented in the polar direction on the grid. In particular, we modeled the SNR-cloud interactions for a spherical cloud on the polar axis, a toroidal cloud whose axis is aligned with the polar axis, and, for comparison, a uniform medium with no cloud. We find that the evolution of the overrun cloud qualitatively resembles that seen in simulations of simpler but analogous situations: that is, the cloud is crushed and begins to be disrupted by Rayleigh-Taylor and Kelvin-Helmholtz instabilities. However, we demonstrate here that, in addition, the internal structure of the SNR is severely distorted as such clouds are engulfed. This has important dynamical and observational implications. The principal new conclusions we draw from these experiments are the following. (1) Independent of the cloud interaction, the SNR reverse shock can be an efficient site for particle acceleration in a young SNR. (2) The internal flows of the SNR become highly turbulent once it encounters a large cloud. (3) An initially uniform magnetic field is preferentially amplified along the magnetic equator of the SNR, primarily because of biased amplification in that region by Rayleigh-Taylor instabilities. A similar bias produces much greater enhancement to the magnetic energy in the SNR during an encounter with a cloud when the interstellar magnetic field is partially transverse to the expansion of the SNR. The enhanced magnetic fields have a significant radial component, independent of the field orientation external to the SNR. This leads to a strong equatorial bias in synchrotron brightness that could easily mask any enhancements to electron-acceleration efficiency near the magnetic equator of the SNR. Thus, to establish the latter effect, it will be essential to establish that the magnetic field in the brightest regions are actually tangential to the blast wave. (4) The filamentary radio structures correlate well with "turbulence-enhanced" magnetic structures, while the diffuse radio emission more closely follows the gas-density distribution within the SNR. (5) At these early times, the synchrotron spectral index due to electrons accelerated at the primary shocks should be close to 0.5 unless those shocks are modified by cosmic-ray proton pressures. While that result is predictable, we find that this simple result can be significantly complicated in practice by SNR interactions with clouds. Those events can produce regions with significantly steeper spectra. Especially if there are multiple cloud encounters, this interaction can lead to nonuniform spatial spectral distributions or, through turbulent mixing, produce a spectrum that is difficult to relate to the actual strength of the blast wave. (6) Interaction with the cloud enhances the nonthermal electron population in the SNR in our simulations because of additional electron injection taking place in the shocks associated with the cloud. Together with point 3, this means that SNR-cloud encounters can significantly increase the radio emission from the SNR.