A Precise Benchmark for Cluster Scaling Relations: Fundamental Plane, Mass Plane and IMF in the Coma Cluster from Dynamical Models

We study a sample of 148 early-type galaxies in the Coma cluster using SDSS photometry and spectra, and calibrate our results using detailed dynamical models for a subset of these galaxies, to create a precise benchmark for dynamical scaling relations in high-density environments. For these galaxies, we successfully measured global galaxy properties, modeled stellar populations, and created dynamical models, and support the results using detailed dynamical models of 16 galaxies, including the two most massive cluster galaxies, using data taken with the SAURON IFU. By design, the study provides minimal scatter in derived scaling relations due to the small uncertainty in the relative distances of galaxies compared to the cluster distance. Our results demonstrate low ($\leq$55% for 90$^{th}$ percentile) dark matter fractions in the inner 1$R_{\rm e}$ ~of galaxies. Owing to the study design, we produce the tightest, to our knowledge, IMF-$\sigma_e$ relation of galaxies, with a slope consistent with that seen in local galaxies. Leveraging our dynamical models, we transform the classical Fundamental Plane of the galaxies to the Mass Plane. We find that the coefficients of the mass plane are close to predictions from the virial theorem, and have significantly lower scatter compared to the Fundamental plane. We show that Coma galaxies occupy similar locations in the (M$_*$ - $R_{\rm e}$) and (M$_*$ - $\sigma_e$) relations as local field galaxies but are older. This, and the fact we find only three slow rotators in the cluster, is consistent with the scenario of hierarchical galaxy formation and expectations of the kinematic morphology-density relation.