CHANG-ES VI: Probing Supernova Energy Deposition in Spiral Galaxies
  Through Multi-Wavelength Relationships
  How a galaxy regulates its SNe energy into different
interstellar/circumgalactic medium components strongly affects galaxy
evolution. Based on the JVLA D-configuration C- (6 GHz) and L-band (1.6 GHz)
continuum observations, we perform statistical analysis comparing
multi-wavelength properties of the CHANG-ES galaxies. The high-quality JVLA
data and edge-on orientation enable us for the first time to include the halo
into the energy budget for a complete radio-flux-limited sample. We find tight
correlations of $L_{\rm radio}$ with the mid-IR-based SFR. The normalization of
our $I_{\rm 1.6GHz}/{\rm W~Hz^{-1}}-{\rm SFR}$ relation is $\sim$2-3 times of
those obtained for face-on galaxies, probably a result of enhanced IR
extinction at high inclination. We also find tight correlations between $L_{\rm
radio}$ and the SNe energy injection rate $\dot{E}_{\rm SN(Ia+CC)}$, indicating
the energy loss via synchrotron radio continuum accounts for $\sim0.1\%$ of
$\dot{E}_{\rm SN}$, comparable to the energy contained in CR electrons. The
integrated C-to-L-band spectral index is $\alpha\sim0.5-1.1$ for non-AGN
galaxies, indicating a dominance by the diffuse synchrotron component. The
low-scatter $L_{\rm radio}-{\rm SFR}$/$L_{\rm radio}-\dot{E}_{\rm SN (Ia+CC)}$
relationships have super-linear logarithmic slopes at $\sim2~\sigma$ in L-band
($1.132\pm0.067$/$1.175\pm0.102$) while consistent with linear in C-band
($1.057\pm0.075$/$1.100\pm0.123$). The super-linearity could be naturally
reproduced with non-calorimeter models for galaxy disks. Using Chandra halo
X-ray measurements, we find sub-linear $L_{\rm X}-L_{\rm radio}$ relations.
These results indicate that the observed radio halo of a starburst galaxy is
close to electron calorimeter, and a galaxy with higher SFR tends to distribute
an increased fraction of SNe energy into radio emission (than X-ray).
