The stellar mass function of star-forming galaxies and the mass-dependent SFR function since z=2.23 from HiZELS

We explore a large uniformly selected sample of H alpha selected star-forming galaxies (SFGs) at z = 0.40, 0.84, 1.47, 2.23 to unveil the evolution of the star formation rate (SFR) function and the stellar mass function. We find strong evolution in the SFR function, with the typical SFR of SFGs declining exponentially in the last 11 Gyr as SFR*(T[Gyr]) = 10(4.23/T + 0.37) M-circle dot yr(-1), but with no evolution in the faint-end slope, alpha approximate to -1.6. The stellar mass function of SFGs, however, reveals little evolution: alpha approximate to -1.4, M* similar to 10(11.2 +/- 0.2) M-circle dot and just a slight increase of similar to 2.3x in Phi* from z = 2.23 to z = 0.4. The stellar mass density within SFGs has been roughly constant since z = 2.23 at similar to 10(7.65 +/- 0.08) M-circle dot Mpc(-3), comprising approximate to 100 per cent of the stellar mass density in all galaxies at z = 2.23, and declining to approximate to 20 per cent by z = 0.40, driven by the rise of the passive population. We find that SFGs with similar to 10(10.0 +/- 0.2) M-circle dot contribute most to the SFR density ((SFR)) per d log(10)M, and that there is no significant evolution in the fractional contribution from SFGs of different masses to (SFR) or (SFR)(d log(10)M)(-1) since z = 2.23. Instead, we show that the decline of SFR* and of (SFR) is primarily driven by an exponential decline in SFRs at all masses. Our results have important implications not only on how SFGs need to be quenched across cosmic time, but also on the driver(s) of the exponential decline in SFR* from similar to 66 M-circle dot yr(-1) to 5 M-circle dot yr(-1) since z similar to 2.23.