  In this note, I suggest that the beta-model used to fit the X-ray surface
brightness profiles of extended sources, like groups and clusters of galaxies,
has to be corrected when the counts are collected in a wide energy band
comparable to the mean temperature of the source and a significant gradient in
the gas temperature is observed. I present a revised version of the beta-model
for the X-ray brightness that applies to a intracluster gas with temperature
and density related by a polytropic equation and extends the standard version
that is strictly valid for an isothermal gas. Given a temperature gradient
observed through an energy window of 1--10 keV typical for the new generation
of X-ray observatories, the beta parameter can change systematically up to 20
per cent from the value obtained under isothermal assumption, i.e. by an amount
larger that any statistical uncertainty obtained from the present data. Within
the virial regions of typical clusters of galaxies, these systematic
corrections affect the total gravitating mass estimate by 5--10 per cent, the
gas mass by 10--30 per cent and the gas fraction value up to 50 per cent, when
compared to the measurements obtained under the isothermal assumption.
