Estimating the evolution of gas in the Fornax dwarf spheroidal galaxy from its star formation history: An illustrative example

We propose that detailed data on the star formation history of a dwarf spheroidal galaxy (dSph) may be used to estimate the evolution of the total mass M_g(t) for cold gas in its star-forming disc. Using Fornax as an illustrative example, we estimate its Mg(t) and the corresponding net gas flow rate ΔF(t) assuming a global star formation rate ψ(t) = λ*(t)[M_g(t)/M_⊙]^α consistent with observations of nearby galaxies. We identify the onset of the transition in ΔF(t) from a net inflow to a net outflow as the time t_sat at which the Fornax halo became a Milky Way satellite and estimate the evolution of its total mass M_h(t) at t < t_sat using the median halo growth history in the current cosmology and its present mass within the half-light radius derived from observations. We examine three different cases of α = 1, 1.5, and 2, and justify the corresponding λ_*(t) by comparing the gas mass fraction f_g(t) = M_g(t)/M_h(t) at t < tsat with results from simulations of gas accretion by haloes in a reionized universe. We find that the Fornax halo grew to M_h(t_sat) ~ 2 × 10⁹M_⊙ at t_sat ~ 5 or 8 Gyr, in broad agreement with previous studies using data on its stellar kinematics and its orbital motion. We describe qualitatively the evolution of Fornax as a satellite and discuss potential extension of our approach to other dSphs.