Two-component gravitational instability in spiral galaxies

We applied a criterion of gravitational instability, valid for two-component and infinitesimally thin discs, to observational data along the major axis for 7 spiral galaxies of early types. Unlike most papers, the dispersion equation corresponding to the criterion was solved directly without using any approximation. The velocity dispersion of stars in the radial direction $\sigma_R$ was limited by the range of possible values instead of a fixed value. For all galaxies, the outer regions of the disc were analyzed up to $R < 130^{"}$. The maximal and sub-maximal disc models were used to translate surface brightness into surface density. The largest destabilizing disturbance stars can exert on a gaseous disc was estimated. It was shown that the two-component criterion differs a little from the one-fluid criterion for galaxies with a large surface gas density, but it allows to explain large-scale star formation in those regions where the gaseous disc is stable. In the galaxy NGC 1167 star formation is entirely driven by the self-gravity of the stars. A comparison is made with the conventional approximations which also include the thickness effect and with models for different sound speed $c_\mathrm{g}$. It is shown that values of the effective Toomre parameter correspond to the instability criterion of a two-component disc $Q_\mathrm{eff}<1.5-2.5$. This result is consistent with previous theoretical and observational studies.