The term hardness is used for a parameter regarding the orbit of a binary star expressing the binding energy, specifically compared to the kinetic energy of the surrounding stars. The term is used (along with hardening rate, the rate of change of hardness) in discussing whether and when the binary is likely to coalesce (collide), particularly based upon their orbits being modified by interactions with passing stars. A binary star with a small orbit is described as hard (e.g., hard binary) as opposed to a pair with a looser orbit, described as soft (e.g., soft binary, the term softness used as the opposite of hardness). Something making the orbit smaller is said to harden the orbit.
The term is often used in analysis of the dynamics of globular clusters, and also that of binary SMBHs, such as analyzing the possibility of black hole mergers.
The term hardness is also used to refer to the frequency (and equivalent photon energy) of X-rays (and sometimes gamma rays), harder being higher.