# Virial mass

In the context of dark matter halos of galaxies or galaxy clusters, virial mass refers to the mass within the virial radius ${\displaystyle r_{\rm {vir}}}$, a radius within which a spherical "top hat" density perturbation destined to become a galaxy is collapsing. This radius is defined as where ${\displaystyle \rho ( where ${\displaystyle \rho ( is the halo's average density within that radius, and ${\displaystyle \rho _{c}}$ is the critical density of the universe.[1] (Sometimes in the definition, ${\displaystyle \rho _{c}}$ is replaced with the mean density of matter, ${\displaystyle \rho _{M}=\Omega _{M}\rho _{c}}$, where, at the present day, ${\displaystyle \Omega _{M}\simeq 0.27}$ according to data fitted to the Lambda-CDM model.) The virial mass is the mass within this radius and hence is a reasonable measure of the total mass inside a dark matter halo, because beyond that radius the halo blends into the background matter in the universe. This definition is not universal, however, as the exact value of ${\displaystyle \Delta _{c}}$ depends on the cosmology – in practice, to improve communication, it is sometimes simply assumed that ${\displaystyle \Delta _{c}=200}$ and hence this is sometimes denoted as ${\displaystyle M_{200}=M(, or the total mass contained within the virial radius.