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 r_50 we use r_80, the
radius containing 80% of the stellar light. We find that the r_80 -- M_star
relation has the form of a broken power law, with a clear change of slope at a
pivot mass M_p. Below the pivot mass the relation is shallow (r_80 \propto
M_star^0.15) and above it it is steep (r_80\propto M_star^0.6). The pivot mass
increases with redshift, from log(M_p/M_sun)~ 10.2 at z=0.4 to log(M_p/M_sun)~
10.9 at z=1.7-3. We compare these r_80-M_star relations to the M_halo-M_star
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_halo \propto
r_80^3. The implied scaling factor to relate galaxy size to halo size is r_80 /
R_vir = 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 ratio is relatively small for massive
halos (~0.2 dex for M_halo>10^12.5 M_sun).
