Introduction to Cosmology Ryden · Problem 11.5

Structure Formation: Gravitational Instability

Physics — Astrophysics · coma-cluster-formation-dynamical-time

Problem

Within the Coma cluster, as discussed in Section 7.3, galaxies have a root mean square velocity of

\langle v^2 \rangle^{1/2} \approx 1520\,\rm km\,s^{-1}

relative to the center of mass of the cluster; the half-mass radius of the Coma cluster is

r_h \approx 1.5\,\rm Mpc

. Using arguments similar to those of the previous problem, compute the minimum time

t_{\rm min}

required for the Coma cluster to form by gravitational collapse.