Gravitational instability and star formation in disc galaxies

We present a general star formation law in which the star formation rate depends upon the efficiency α and the time-scale τ of star formation, and the gas component σg of the surface mass density. The current nominal Schmidt exponent nS for our model is 2<nS<3. Based on a gravitational instability parameter QA and another dimensionless parameter fP=(P/Gcσ2)1/2, where P = pressure and σc = column density of molecular clouds, we suggest a general equation for the star formation rate which depends upon the relative contributions of the two parameters for various physical circumstances. We find that QA turns out to be a better parameter for the star formation scenario than does the Toomre Q-parameter. The star formation rate in the solar neighbourhood is found to be in good agreement with values inferred from previous studies. In the closed box approximation model, we obtain a relationship between the metallicity of the gas and the efficiency of star formation. Our model calculations of metallicity in the solar neighbourhood agree with earlier estimates. We conclude that the metallicity dispersion for stars of the same age may result from a change in the efficiency with which different stars in the sample were processed. For no significant change of metallicity with age, we suggest that all stars in the sample were born with similar efficiencies.