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

¹ University of Vienna, Institute of Astrophysics, 1180 Vienna, Austria
e-mail: eduard.vorobiev@univie.ac.at
² Research Institute of Physics, Southern Federal University, 344090 Rostov-on-Don, Russia

Received: 24 February 2012
Accepted: 4 May 2012

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_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 were compared against the baryon-to-DM mass relation M_b–M_DM inferred from the ΛCDM 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_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 ≳ 10⁹   M_⊙ are usually characterized by M_g^min ≲ 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 ≲ 10⁹   M_⊙ 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.

Conclusions. Our modeling suggests that a star-formation-allowed state is more difficult to achieve in DM halos with mass  ≲ 10⁹   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.