We have measured the H \alpha + [ N II ] fluxes of the I -selected Canada - France Redshift Survey ( CFRS ) galaxies lying at a redshift z below 0.3 , and hence derived the H \alpha luminosity function .
The magnitude limits of the CFRS mean that only the galaxies with M _ { B } \gtrsim - 21 mag were observed at these redshifts .
We obtained a total H \alpha luminosity density of at least 10 ^ { 39.44 \pm 0.04 } erg s ^ { -1 } Mpc ^ { -3 } at a mean z = 0.2 for galaxies with rest-fame EW ( H \alpha + [ N~ { } II ] ) \gtrsim 10 Å .
This is twice the value found in the local universe by [ Gallego et al .
1995 ] .
Our H \alpha star formation rate , derived from Madau ( 1997 ) is higher than the UV observations at same z , implying a UV dust extinction of \sim 1 mag .
We found a strong correlation between the H \alpha luminosity and the absolute magnitude in the B -band : M ( B _ { AB } ) = 46.7 - 1.6 \log L ( H \alpha ) .
This work will serve as a basis of future studies of H \alpha luminosity distributions measured from optically-selected spectroscopic surveys of the distant universe , and it will provide a better understanding of the physical processes responsible for the observed galaxy evolution .