Virial mass

In astrophysics, the virial mass is the mass of a gravitationally bound astrophysical system, assuming the virial theorem applies. In the context of galaxy formation and dark matter halos, the virial mass is defined as the mass enclosed within the virial radius r v i r {displaystyle r_{ m {vir}}} of a gravitationally bound system, a radius within which the system obeys the virial theorem. The virial radius is determined using a 'top-hat' model. A spherical 'top hat' density perturbation destined to become a galaxy begins to expand, but the expansion is halted and reversed due to the mass collapsing under gravity until the sphere reaches virial equilibrium–it is said to be virialized. Within this radius, the sphere obeys the virial theorem which says that the average kinetic energy is equal to minus one half times the average potential energy, ⟨ T ⟩ = − 1 2 ⟨ V ⟩ {displaystyle langle T angle =-{frac {1}{2}}langle V angle } , and this radius defines the virial radius. In astrophysics, the virial mass is the mass of a gravitationally bound astrophysical system, assuming the virial theorem applies. In the context of galaxy formation and dark matter halos, the virial mass is defined as the mass enclosed within the virial radius r v i r {displaystyle r_{ m {vir}}} of a gravitationally bound system, a radius within which the system obeys the virial theorem. The virial radius is determined using a 'top-hat' model. A spherical 'top hat' density perturbation destined to become a galaxy begins to expand, but the expansion is halted and reversed due to the mass collapsing under gravity until the sphere reaches virial equilibrium–it is said to be virialized. Within this radius, the sphere obeys the virial theorem which says that the average kinetic energy is equal to minus one half times the average potential energy, ⟨ T ⟩ = − 1 2 ⟨ V ⟩ {displaystyle langle T angle =-{frac {1}{2}}langle V angle } , and this radius defines the virial radius. The virial radius of a gravitationally bound astrophysical system is the radius within which the virial theorem applies. It is defined as the radius at which the density is equal to the critical density ρ c {displaystyle ho _{c}} of the Universe at the redshift of the system, multiplied by an overdensity constant Δ c {displaystyle Delta _{c}} : where ρ ( < r v i r ) {displaystyle ho (