  In the construction of multi-mass King-Michie models of globular clusters, an
approximated central energy equipartition between stars of different masses is
usually imposed by scaling the velocity parameter of each mass class inversely
with the stellar mass, as if the distribution function were isothermal. In this
paper, this 'isothermal approximation' (IA) has been checked and its
consequences on the model parameters studied by a comparison with models
including central energy equipartition correctly. It is found that, under the
IA, the 'temperatures' of a pair of components can differ to a non-negligible
amount for low concentration distributions. It is also found that, in general,
this approximation leads to a significantly reduced mass segregation in
comparison with that given under the exact energy equipartition at the centre.
As a representative example, an isotropic 3-component model fitting a given
projected surface brightness and line-of-sight velocity dispersion profiles is
discussed. In this example, the IA gives a cluster envelope much more
concentrated (central dimensionless potential W=3.3) than under the true
equipartition (W=0.059), as well as a higher logarithmic mass function slope.
As a consequence, the inferred total mass (and then the global mass-to-light
ratio) results a factor 1.4 times lower than the correct value and the amount
of mass in heavy dark remnants is 3.3 times smaller. Under energy
equipartition, the fate of stars having a mass below a certain limit is to
escape from the system. This limit is derived as a function of the mass and W
of the giants and turn-off stars component.
