Central Velocity Dispersion being the Primary Driver of Abundance Patterns in Quenched Galaxies

The element abundances of galaxies provide crucial insights into their formation and evolution. Using high-resolution IFU data from the MaNGA survey, we analyze the central spectra (0-0.5 $R_{\rm e}$) of 1,185 quenched galaxies ($z = 0.012-0.15$) to study their element abundances and stellar populations. We employ the full-spectrum fitting code {\tt alf} to derive stellar ages and element abundances from synthetic spectra and empirical libraries. Our key findings are: (1) Central velocity dispersion ($\sigma_*$) is the most effective parameter correlating with (relative) element abundances, especially [Na/Fe], [Mg/Fe], [C/Fe], and [N/Fe], outperforming $M_\ast$ and $M_\ast/R_{\rm e}$. (2) When binned by $\sigma_*$, the relative abundances of Na, Mg, C, and N remain stable across different formation times ($T_{\rm form}$), suggesting these elements are primarily influenced by the burstiness of star formation (traced by $\sigma_*$) rather than prolonged evolutionary processes. (3) Fe and Ca show little variation with $\sigma_*$, indicating weaker sensitivity to $\sigma_*$-driven processes. However, $T_{\rm form}$ has a global influence on all elements, contributing to their overall chemical evolution, albeit secondary to $\sigma_*$ for most elements. These results support the primary role of $\sigma_*$ in shaping the abundance patterns, likely stemming from the connection between central massive black holes and possibly dark matter halos, which influences the burstiness of star formation histories.