Chemical Abundance Ratios of Nitrogen Rich Galaxies Identified at zsim 6-12: Observational Demographics and Models

We present chemical abundance ratios of 8 nitrogen-rich ([N/O]$>0.3$) galaxies at $z\sim 6-12$ identified by the first 4 years of the JWST observations, and compare these ratios with chemical evolution models. We reanalyze the JWST/NIRSpec data of these galaxies in the self-consistent manner for line fluxes and upper limits including those previously unconstrained. We derive the abundance ratios and constraints of [N/O], [C/O], [Ne/O], [Ne/C], [Ar/O], [S/O] and [Fe/O], characterizing the nebulae in the galaxies with the electron temperatures and densities measured with {\sc[Oiii]}$\lambda4363$ and {\sc[Oii]}$\lambda\lambda3727, 3729$ lines, respectively. We develop the chemical evolution models for the three major scenarios, Wolf-Rayet stars, supermassive stars, and tidal disruption events (TDEs) with the AGB star contribution, integrating the ejecta of the stars and core-collapse supernovae (CCSNe) over the age with yields calculated by numerical simulations. We compare the models with the [N/O] measurements and stellar ages, and find that all of the scenarios reproduce [N/O] as high as those of our galaxies. However, the time-scales of the high [N/O] ratios are too short to explain our galaxies in any of the scenarios, suggestive of very frequent failed supernovae that do not increase oxygen against nitrogen. We find that the three scenarios are distinguished in the plane of [Ne/C] vs. [N/O] due to Ne production outside CNO cycle, and that the observed abundance ratios are explained by the Wolf-Rayet models better than supermassive-star and TDE models. We argue that abundance ratios of various elements and time scales are clues for understanding nitrogen-rich galaxies.