Unveiling the Coma Cluster Structure: From the Core to the Hubble Flow

The Coma cluster, embedded in a cosmic filament, is a complex and dynamically active structure in the local Universe. Applying a density-based member selection dbscan to data from the Sloan Digital Sky Survey (SDSS), we identify cluster member galaxies from its virialised core out to the zero-velocity boundary in the least model-dependent way. From dbscan, we infer a projected virial radius of $r_{\rm vir} = \left(1.95 \pm 0.12\right)\,h^{-1}~\text{Mpc}$ and projected zero-velocity radius of $r_{\rm ta} \geq 4.87~{h}^{-1}~\mbox{Mpc}$. Assuming that the barycentre of Coma has zero peculiar velocity, its distance from us is $r_\mathrm{c}=(69.959 \pm 0.012_\mathrm{stat}) \, h^{-1}~\text{Mpc}$ determined from the redshifts of 1092 member galaxies. Cross-correlating with the Cosmicflows-4 (CF4) catalogue enables a velocity-distance analysis. This reveals, for the first time, the Hubble flow surrounding Coma, a first step to investigate the entanglement between Coma's dark matter halo and the dark energy driving the expansion of the surroundings. If $v_\mathrm{c}$ is moving with the cosmic expansion, the CF4 distances yield a Hubble constant $H_0 = (73 \pm {1_\mathrm{stat} \pm 7_\mathrm{sys}})~\mbox{km}/\mbox{s}/\mbox{Mpc}$ with a dominating systematic error from different calibrations for the distance moduli. Mass estimates via caustics, the virial theorem, and the Hubble-flow method yield $M = [0.77, 2.0] \times 10^{15}\,h^{-1}\,M_{\odot}$ consistent with prior mass estimates. Our mass estimates are based on fewer model assumptions in the member selection and require $\sim20\%$ members to attain the same precision. Our approach maps the structure of Coma into its Hubble flow and shows degeneracies between the Hubble constant, the virial radius, and the total mass only using data and models from the single line-of-sight towards Coma.