Self-gravitating equilibrium models of dwarf galaxies and the minimum mass for star formation

Abstract

Context. We constructed a series of model galaxies in rotational equilibrium consisting of gas, stars, and a fixed dark matter (DM) halo and studied how these equilibrium systems depend on the mass and form of the DM halo, gas temperature, non-thermal and rotation support against gravity, and also on the redshift of galaxy formation. For every model galaxy we found the minimum gas mass M gminrequired to achieve a state in which star formation (SF) is allowed according to contemporary SF criteria. The obtained M gmin-M DM relations were compared against the baryon-to-DM mass relation M b-M DM inferred from the Λ CDM theory and WMAP4 data. Aims. Our aim is to construct realistic initial models of dwarf galaxies (DGs), which take into account the gas self-gravity and can be used as a basis to study the dynamical and chemical evolution of DGs. Methods. Rotating equilibria are found by solving numerically the steady-state momentum equation for the gas component in the combined gravitational potential of gas, stars, and DM halo using a forward substitution procedure. Results. We find that for a given M DM the value of M gmin depends crucially on the gas temperature T g, gas spin parameter α, degree of non-thermal support σ eff, and somewhat on the redshift for galaxy formation z gf. Depending on the actual values of T g, α, σ eff, and z gf, model galaxies may have M gmin that are either greater or smaller than M b. Galaxies with M DM≈10 9 M ⊙ are usually characterized by M gmin≈M b implying that SF in such objects is a natural outcome because the required gas mass is consistent with what is available according to the ΛCDM theory. On the other hand, models with M DM ≈10 9 M ȯ are often characterized by M gminM b M b, implying that they need much more gas than available to achieve a state in which SF is allowed. Conclusions. Our modeling suggests that a star-formation-allowed state is more difficult to achieve in DM halos with mass ≈ 10 9 M ⊙ than in their upper-mass counterparts, because the required gas mass often exceeds both M b and M DM. In the framework of the ΛCDM theory, this implies the existence of a critical DM halo mass below which the likelihood of star formation and hence the total stellar mass may drop substantially, in accordance with the stellar versus DM halo mass relations recently derived from the SDSS survey and millennium simulations. On the other hand, DGs that do not follow the ΛCDM trend are feasible and have recently been identified, which raises questions about the universality of the ΛCDM paradigm. © 2012 ESO.