Galaxy And Mass Assembly (GAMA): Bivariate functions of H$α$ star forming galaxies

Abstract: We present bivariate luminosity and stellar mass functions of H$\alpha$ star forming galaxies drawn from the Galaxy And Mass Assembly (GAMA) survey. While optically deep spectroscopic observations of GAMA over a wide sky area enable the detection of a large number of $0.001<{SFR}{H\alpha}$ (M${\odot}$ yr$^{-1}$)$<100$ galaxies, the requirement for an H$\alpha$ detection in targets selected from an $r$-band magnitude limited survey leads to an incompleteness due to missing optically faint star forming galaxies. Using $z<0.1$ bivariate distributions as a reference we model the higher-$z$ distributions, thereby approximating a correction for the missing optically faint star forming galaxies to the local SFR and stellar mass densities. Furthermore, we obtain the $r$-band LFs and stellar mass functions of H$\alpha$ star forming galaxies from the bivariate LFs. As our sample is selected on the basis of detected H$\alpha$ emission, a direct tracer of on-going star formation, this sample represents a true star forming galaxy sample, and is drawn from both photometrically classified blue and red sub-populations, though mostly from the blue population. On average 20-30% of red galaxies at all stellar masses are star forming, implying that these galaxies may be dusty star forming systems.