What assumptions are we making when we infer the mass of a galaxy cluster from observations of the spectra of its constituent galaxies?

The assumptions we make when we infer the mass of a galaxy cluster from observations of the spectra of its constituent galaxies is thermal hydrostatic equilibrium

Explanation:

In galaxy cluster observation, thermal X-ray emission from the hot intracluster gas measures directly the gas density and temperature distributions within the cluster. This hot gas is confined by and expected to trace the underlying three-dimensional gravitational potential. Under the assumption of thermal hydrostatic equilibrium, these gas properties may be used to infer the cluster total mass distribution.

Hence, the assumptions we make when we infer the mass of a galaxy cluster from observations of the spectra of its constituent galaxies is thermal hydrostatic.