The Velocity Dispersion Function for Quiescent Galaxies in Massive Clusters from IllustrisTNG

We derive the central stellar velocity dispersion function for quiescent galaxies in 280 massive clusters with $\log (M_{200} / M_{\odot}) > 14$ in IllustrisTNG300. The velocity dispersion function is an independent tracer of the dark matter mass distribution of subhalos in galaxy clusters. Based on the IllustrisTNG cluster catalog, we select quiescent member subhalos with a specific star formation rate $< 2 \times 10^{-11}$ yr${^-1}$ and stellar mass $\log (M_{*} / M_{\odot}) > 9$. We then simulate fiber spectroscopy to measure the stellar velocity dispersion of the simulated galaxies; we compute the line-of-sight velocity dispersions of star particles within a cylindrical volume that penetrates the core of each subhalo. We construct the velocity dispersion functions for quiescent subhalos within $R_{200}$. The simulated cluster velocity dispersion function exceeds the simulated field velocity dispersion function for $\log \sigma_{*} > 2.2$, indicating the preferential formation of large velocity dispersion galaxies in dense environments. The excess is similar in simulations and in the observations. We also compare the simulated velocity dispersion function for the three most massive clusters with $\log (M_{200} / M_{\odot}) > 15$ with the observed velocity dispersion function for the two most massive clusters in the local universe, Coma and A2029. Intriguingly, the simulated velocity dispersion functions are significantly lower for $\log \sigma_{*} > 2.0$. This discrepancy results from 1) a smaller number of subhalos with $\log (M_{*} / M_{\odot}) > 10$ in TNG300 compared to the observed clusters, and 2) a significant offset between the observed and simulated $M_{*} - \sigma_{*}$ relations. The velocity dispersion function offers a unique window on galaxy and structure formation in simulations.