Reconciling the observed star-forming sequence with the observed stellar mass function

We examine the connection between the observed star-forming sequence (SFR $\propto$ $M^{\alpha}$) and the observed evolution of the stellar mass function between $0.2 < z < 2.5$. We find the star-forming sequence cannot have a slope $\alpha$ $\lesssim$ 0.9 at all masses and redshifts, as this would result in a much higher number density at $10 < \log(\mathrm{M/M_{\odot}}) < 11$ by $z=1$ than is observed. We show that a transition in the slope of the star-forming sequence, such that $\alpha=1$ at $\log(\mathrm{M/M_{\odot}})<10.5$ and $\alpha=0.7-0.13z$ ({Whitaker} {et~al.} 2012) at $\log(\mathrm{M/M_{\odot}})>10.5$, greatly improves agreement with the evolution of the stellar mass function. We then derive a star-forming sequence which reproduces the evolution of the mass function by design. This star-forming sequence is also well-described by a broken-power law, with a shallow slope at high masses and a steep slope at low masses. At $z=2$, it is offset by $\sim$0.3 dex from the observed star-forming sequence, consistent with the mild disagreement between the cosmic SFR and recent observations of the growth of the stellar mass density. It is unclear whether this problem stems from errors in stellar mass estimates, errors in SFRs, or other effects. We show that a mass-dependent slope is also seen in other self-consistent models of galaxy evolution, including semi-analytical, hydrodynamical, and abundance-matching models. As part of the analysis, we demonstrate that neither mergers nor hidden low-mass quiescent galaxies are likely to reconcile the evolution of the mass function and the star-forming sequence. These results are supported by observations from {Whitaker} {et~al.} (2014).