A study of Kepler supernova remnant: angular power spectrum estimation from radio frequency data

Supernova remnants (SNRs) have a variety of overall morphology as well as rich structures over a wide range of scales. Quantitative study of these structures can potentially reveal fluctuations of density and magnetic field originating from the interaction with ambient medium and turbulence in the expanding ejecta. We have used $1.5$GHz (L band) and $5$GHz (C band) VLA data to estimate the angular power spectrum $C_{\ell}$ of the synchrotron emission fluctuations of the Kepler SNR. This is done using the novel, visibility based, Tapered Gridded Estimator of $C_{\ell}$. We have found that, for $\ell = (1.9 - 6.9) \times 10^{4}$, the power spectrum is a broken power law with a break at $\ell = 3.3 \times 10^{4}$, and power law index of $-2.84\pm 0.07$ and $-4.39\pm 0.04$ before and after the break respectively. The slope $-2.84$ is consistent with 2D Kolmogorov turbulence and earlier measurements for the Tycho SNR. We interpret the break to be related to the shell thickness of the SNR ($0.35 $ pc) which approximately matches $\ell = 3.3 \times 10^{4}$ (i.e., $0.48$ pc). However, for $\ell > 6.9 \times 10^{4}$, the estimated $C_{\ell}$ of L band is likely to have dominant contribution from the foregrounds while for C band the power law slope $-3.07\pm 0.02$ is roughly consistent with $3$D Kolmogorov turbulence like that observed at large $\ell$ for Cas A and Crab SNRs.