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 Hα 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_⊙ yr⁻¹, but with no evolution in the faint-end slope, α ≈ −1.6. The stellar mass function of SFGs, however, reveals little evolution: α ≈ −1.4, M* ∼ 10^{11.2 ± 0.2} M_⊙ and just a slight increase of ∼2.3× in Φ* from z = 2.23 to z = 0.4. The stellar mass density within SFGs has been roughly constant since z = 2.23 at ∼10^{7.65 ± 0.08} M_⊙ Mpc⁻³, comprising ≈100 per cent of the stellar mass density in all galaxies at z = 2.23, and declining to ≈20 per cent by z = 0.40, driven by the rise of the passive population. We find that SFGs with ∼10^{10.0 ± 0.2} M_⊙ contribute most to the SFR density (ρ_SFR) per d log₁₀M, and that there is no significant evolution in the fractional contribution from SFGs of different masses to ρ_SFR or ρ_SFR(d log₁₀M)⁻¹ since z = 2.23. Instead, we show that the decline of SFR* and of ρ_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 ∼66 M_⊙ yr⁻¹ to 5 M_⊙ yr⁻¹ since z ∼ 2.23.