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

We construct a series of model galaxies in rotational equilibrium consisting of gas, stars, and a fixed dark matter (DM) halo and study 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 find the minimum gas mass M_g^min required to achieve a state in which star formation (SF) is allowed according to contemporary SF criteria. The obtained M_g^min--M_DM relations are compared against the baryon-to-DM mass relation M_b--M_DM inferred from the \LambdaCDM theory and WMAP4 data. 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. 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. We find that for a given M_DM the value of M_g^min 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_g^min that are either greater or smaller than M_b. Galaxies with M_DM \ga 10^9 M_sun are usually characterized by M_g^min \la M_b, implying that SF in such objects is a natural outcome as the required gas mass is consistent with what is available according to the \LambdaCDM theory. On the other hand, models with M_DM \la 10^9 M_sun are often characterized by M_g^min >> M_b, implying that they need much more gas than available to achieve a state in which SF is allowed. Abridged.