VLA FRAMEx. II. Radio Spectra of Nearby Active Galactic Nuclei at Subarcsecond Resolution

We present $4-12$ GHz in-band spectral energy distributions with accompanying 6 GHz and 10 GHz imaging results for a volume-complete sample ($<40$ Mpc) of hard X-ray selected active galactic nuclei (AGNs) observed with the Karl G. Jansky Very Large Array (VLA) in its A-array configuration. Despite expectations, only 12 out of 25 of these targets have been detected by the Very Long Baseline Array (VLBA) at milliarcsecond resolution in our previous studies, and we aim to understand the nature of why the circumnuclear radio emission resolves away at the subparsec spatial scales. We find that the sources not detected by the VLBA are also the faintest sources observed with the VLA. We explore the spectral structure derived from the nuclear emission and measure a mean spectral index of $\langle\alpha\rangle=-0.69$ with a scatter of $\sigma_\alpha=0.18$ for the sources not detected by the VLBA, indicative of optically thin synchrotron emission. The 12 sources detected by the VLBA primarily have flat ($-0.5\leq\alpha\leq0.0$) or inverted ($\alpha>0$) spectral indices. Nine of the sources have statistically significant curvature, with only one that was not detected by the VLBA. In NGC~3079, we model an approximately flat spectrum for the excess emission observed by the VLA that is likely produced entirely beyond parsec spatial scales.