MASS AND ENVIRONMENT AS DRIVERS OF GALAXY EVOLUTION. III. THE CONSTANCY OF THE FAINT-END SLOPE AND THE MERGING OF GALAXIES

Using our continuity approach, we explore the underlying connections between the evolution of the faint-end slope as of the stellar mass function of star-forming galaxies, the logarithmic slope beta of the specific star formation rate (sSFR)-mass relation, and the merging of galaxies. We derive analytically the consequences of the observed constancy of alpha(s) since redshifts of at least z similar to 2. If the logarithmic slope beta of the sSFR-mass relation is negative, then the faint-end slope alpha(s) should quickly diverge due to the differential mass increase of galaxies on the star-forming main sequence, and this will also quickly destroy the Schechter form of the mass function. This problem can be solved by removing low-mass galaxies by merging them into more massive galaxies. We quantify this process by introducing the specific merger mass rate (sMMR) as the specific rate of mass added to a given galaxy through mergers. For a modest negative value of beta similar to-0.1, an average sMMR similar to 0.1 sSFR across the population is required to keep alpha(s) constant with epoch, as observed. This in turn implies a merger rate of beta 0.2 sSFR for major mergers, which is consistent with the available observational estimates. More negative values of beta require higher sMMR and higher merger rates, and the steepening of the mass function becomes impossible to control for beta <-(alpha(s) + 2). The close link that is required between the in situ sSFR and the sMMR probably arises because both are closely linked to the buildup of dark matter halos. These new findings further develop the formalism for the evolving galaxy population that we introduced earlier and show how striking symmetries in the galaxy population can emerge as the result of deep links between the physical processes involved.