virial parameter

The virial parameter is a quantity calculable from the mass, radius and velocity dispersion of a system such as a molecular cloud or dense core, that demonstrates whether it is gravitationally bound. It is essentially the ratio of the cloud's kinetic energy to gravitational potential energy.

     5σ²R
 α = ————
      GM

• α - virial parameter.
• σ - velocity dispersion.
• G - gravitational constant.
• M - mass of the system (e.g., cloud).
• R - radius of the system

If α >> 1, the system is not gravitationally bound, and must be held together by external pressure. If gravitationally bound, α ~ 1. This relation is commonly used to deduce the mass of molecular clouds.