CHANG-ES XLII: Cosmic-Ray Electron Transport and the Spatially Resolved Radio-SFR Relation in Edge-on Galaxies

Radio continuum emission traces star formation in galaxies, but cosmic-ray electron (CRE) propagation between the disk and halo complicates this connection. We present a wide-band, spatially resolved analysis of 19 nearby edge-on galaxies, combining LOFAR observations at 144 MHz with CHANG-ES VLA imaging at 1.575, 3.0, and 6.0 GHz, and hybrid H α +22 μ m star formation rate (SFR) maps. All maps are convolved to a common 2.1 kpc resolution for pixel-by-pixel analysis of the nonthermal spectral index α nth and the SFR surface density Σ SFR. All 19 galaxies exhibit statistically significant nonthermal spectral flattening with increasing Σ SFR, with a sample median slope of 0.19-0.03+0.09 that traces the contrast between CRE injection in the star-forming disk and cooling in the halo. The galaxy-to-galaxy scatter in this slope shows no dependence on global galaxy properties and instead appears to be modulated by the local dynamical environment, with the largest α nth - Σ SFR slopes appearing in tidally perturbed systems. The resolved radio-SFR slope steepens from 0.57 at 144 MHz to 0.95 at 6 GHz, approaching linearity at high frequencies. This trend is consistent with energy-dependent CRE cooling and transport, with the deviation from linearity most pronounced at low frequencies, where the edge-on line of sight blends midplane and halo CRE populations. These results are robust against thermal contamination, beam smearing, and spectral curvature. Together, our analysis establishes α nth as an observational probe of projected disk-to-halo CRE transport in edge-on galaxies and quantifies how this transport reshapes the frequency dependence of resolved radio-SFR calibrations.