The auto and cross angular power spectrum of the Cas A supernova remnant in radio and X-ray

The shell type supernova remnant (SNR) Cas A exhibits structures at nearly all angular scales. Previous studies show the angular power spectrum $(C_{\ell})$ of the radio emission to be a broken power law, consistent with MHD turbulence. The break has been identified with the transition from 2D to 3D turbulence at the angular scale corresponding to the shell thickness. Alternatively, this can also be explained as 2D inverse cascade driven by energy injection from knot-shock interactions. Here we present $C_{\ell}$ measured from archival VLA $5$GHz (C band) data, and Chandra X-ray data in the energy ranges ${\rm A}=0.6-1.0 \, \, {\rm keV}$ and ${\rm B} =4.2-6.0 \, \, {\rm keV}$, both of which are continuum dominated. The different emissions all trace fluctuations in the underlying plasma and possibly also the magnetic field, and we expect them to be correlated. We quantify this using the cross $C_{\ell}$ between the different emissions. We find that X-ray B is strongly correlated with both radio and X-ray A, however X-ray A is only very weakly correlated with radio. This supports a picture where X-ray A is predominantly thermal bremsstrahlung whereas X-ray B is a composite of thermal bremsstrahlung and non-thermal synchrotron emission. The various $C_{\ell}$ measured here, all show a broken power law behaviour. However, the slopes are typically shallower than those in radio and the position of the break also corresponds to smaller angular scales. These findings provide observational inputs regarding the nature of turbulence and the emission mechanisms in Cas A.