A Mass-dependent Slope of the Galaxy Size–Mass Relation out to z ∼ 3: Further Evidence for a Direct Relation between Median Galaxy Size and Median Halo Mass

We reassess the galaxy size–mass relation out to z ∼ 3 using a new definition of size and a sample of >29,000 galaxies from the 3D-HST, CANDELS, and COSMOS-DASH surveys. Instead of the half-light radius r50 we use r80, the radius containing 80% of the stellar light. We find that the r80–M* relation has the form of a broken power law, with a clear change of slope at a pivot mass Mp. Below the pivot mass the relation is shallow (${r}_{80}\propto {M}_{* }^{0.15}$); above it, it is steep (${r}_{80}\propto {M}_{* }^{0.6}$). The pivot mass increases with redshift, from $\mathrm{log}({M}_{{\rm{p}}}/{M}_{\odot })\approx 10.2$ at z = 0.4 to $\mathrm{log}({M}_{{\rm{p}}}/{M}_{\odot })\approx 10.9$ at z = 1.7–3. We compare these ${r}_{80}\mbox{--}{M}_{* }$ relations to the ${M}_{\mathrm{halo}}\mbox{--}{M}_{* }$ relations derived from galaxy–galaxy lensing, clustering analyses, and abundance matching techniques. Remarkably, the pivot stellar masses of both relations are consistent with each other at all redshifts, and the slopes are very similar both above and below the pivot when assuming ${M}_{\mathrm{halo}}\propto {r}_{80}^{3}$. The implied scaling factor to relate galaxy size to halo size is r80/Rvir = 0.047, independent of stellar mass and redshift. From redshift 0 to 1.5, the pivot mass also coincides with the mass where the fraction of star-forming galaxies is 50%, suggesting that the pivot mass reflects a transition from dissipational to dissipationless galaxy growth. Finally, our results imply that the scatter in the stellar-to-halo mass is relatively small for massive halos (∼0.2 dex for ${M}_{\mathrm{halo}}\gt {10}^{12.5}{M}_{\odot }$).