Hydrostatic equilibrium profiles for gas in elliptical galaxies

TL;DR

This paper develops an analytic model for the gas density profile in elliptical galaxies that includes stellar gravitational effects, improving estimates of baryon and dark matter distributions from X-ray data.

Contribution

It introduces a new hydrostatic equilibrium formulation that accounts for stellar gravity, enhancing the accuracy of galaxy mass and baryon fraction estimates.

Findings

Neglecting stellar gravity underestimates baryonic mass by up to 65%.

Ignoring stars leads to an 80% underestimation of the NFW scale radius.

Standard beta-models are inadequate for high stellar mass fractions.

Abstract

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%.