Gravitational instability and star formation in disk galaxies

We present a general star formation law where star formation rate depends upon efficiency $\alpha$, timescale $\tau$ of star formation, gas component $\sigma_{g}$ of surface mass density and a real exponent $n$. A given exponent $n$ determines $\tau$ which however yields the corresponding star formation rate. Current nominal Schmidt exponent $n_{s}$ for our model is $2<n_{s}<3$. Based on a gravitational instability parameter $Q_{A}$ and another dimensionless parameter $f_{P}\equiv (P/G\sigma_{c}^{2})^{1/2}$, where $P$ = pressure, $\sigma_{c}$ = column density of molecular clouds, we suggest a general equation for star formation rate which depends upon relative competence of the two parameters for various physical circumstances. We find that $Q_{A}$ emerges to be a better parameter for star formation scenario than Toomre Q-parameter. Star formation rate in the solar neighbourhood is found to be in good agreement with values inferred from previous studies. Under closed box approximation model, we obtain a relation between metallicity of gas and the efficiency of star formation. Our model calculations of metallicity in the solar neighbourhood agree with earlier estimates. We conclude that metallicity dispersion for stars of same age may result due to a change in efficiency through which different sample stars were processed. For no significant change of metallicity with age, we suggest that all sample stars were born with almost similar efficiency.