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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 $α\sim0.5-1.1$ 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 $\sim2~σ$ 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).