  We present an analytic formulation for the equilibrium gas density profile of
early-type galaxies that explicitly includes the contribution of stars in the
gravitational potential. We build a realistic model for an isolated elliptical
galaxy and explore the equilibrium gas configurations as a function of multiple
parameters. For an assumed central gas temperature k_B*T_0=0.6 keV, we find
that neglecting the gravitational effects of stars, which can contribute
substantially in the innermost regions, leads to an underestimate of the
enclosed baryonic gas mass by up to ~65% at the effective radius, and by up to
~15% at the NFW scale radius, depending on the stellar baryon fraction. This
formula is therefore important for estimating the baryon fraction in an
unbiased fashion. These new hydrostatic equilibrium solutions, derived for the
isothermal and polytropic cases, can also be used to generate more realistic
initial conditions for simulations of elliptical galaxies. Moreover, the new
formulation is relevant when interpreting X-ray data. We compare our composite
isothermal model to the standard beta-model used to fit X-ray observations of
early-type galaxies, to determine the value of the NFW scale radius r_s.
Assuming a 10% stellar baryon fraction, we find that the exclusion of stars
from the gravitational potential leads to (i) an underestimate of r_s by ~80%,
and to (ii) an overestimate of the enclosed dark matter at r_s by a factor of
~2, compared to the equivalent beta-model fit results when stars are not taken
into account. For higher stellar mass fractions, a beta-model is unable to
accurately reproduce our solution, indicating that when the observed surface
brightness profile of an isolated elliptical galaxy is found to be well fitted
by a beta-model, the stellar mass fraction cannot be much greater than ~10%.

Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies;High Energy Astrophysical Phenomena