We present an analysis of the properties of the lowest H \alpha -luminosity galaxies ( L _ { H \alpha } \leq 4 \times 10 ^ { 32 } W ; SFR < 0.02 M _ { \odot } yr ^ { -1 } ) in the Galaxy And Mass Assembly ( GAMA ) survey .
These galaxies make up the the rise above a Schechter function in the number density of systems seen at the faint end of the H \alpha luminosity function .
Above our flux limit we find that these galaxies are principally composed of intrinsically low stellar mass systems ( median stellar mass = 2.5 \times 10 ^ { 8 } M _ { \odot } ) with only 5/90 having stellar masses M > 10 ^ { 10 } M _ { \odot } .
The low SFR systems are found to exist predominantly in the lowest density environments ( median density \sim 0.02 galaxy Mpc ^ { -2 } with none in environments more dense than \sim 1.5 galaxy Mpc ^ { -2 } ) .
Their current specific star formation rates ( SSFR ; -8.5 < log ( SSFR [ yr ^ { -1 } ] ) < -12. ) are consistent with their having had a variety of star formation histories .
The low density environments of these galaxies demonstrates that such low-mass , star-forming systems can only remain as low-mass and forming stars if they reside sufficiently far from other galaxies to avoid being accreted , dispersed through tidal effects or having their gas reservoirs rendered ineffective through external processes .