The term hardness is used as a parameter of 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) 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 naturally used as the opposite of hardness). Something making the orbit smaller is said to harden the orbit.
The term has been used in the analysis of the coalescing of binary SMBHs after galaxy mergers.