Demography of stellar radio population within 500 pc: A VLASS-Gaia DR3 study

In this work, we have carried out a systematic analysis of the VLASS quick look catalogs together with \textit{Gaia DR3} to identify the optical counterparts of 3~GHz radio emitters within 500~pc to obtain a homogeneous statistical sample of stellar radio sources. We have identified distinct populations of 3 GHz emitters across the \textit{Gaia DR3} color-magnitude diagram. We also present candidate sources (transient, highly variable or background artifacts) which can be confirmed by follow-up observations. A majority of the detected sources constitute main sequence G, K and M-type stars including ultra-cool dwarfs. Pinning down the origin of radio emission from these populations can help us gain further insights into the origin of stellar and planetary magnetic fields. By analyzing the variation of brightness temperature of the sources with their spectral type, we have tentatively associated possible emission mechanisms with different object types. We inspected the correlation between quiescent radio and X-ray emission for our sample that can provide crucial insights into the current understanding of the Gudel-Benz relationship, which is essential for modeling steady radio emission and coronal heating. This VLASS-\textit{\textit{Gaia DR3}} analysis acts as a pilot study for follow-up observations at multiple wavelengths to better understand stellar structure, model flaring activities and detect radio emission caused by star-planet interactions.