Half-mass radii for ~7,000 galaxies at 1.0 < z < 2.5: most of the
  evolution in the mass-size relation is due to color gradients
  Radial mass-to-light ratio gradients cause the half-mass and half-light radii
of galaxies to differ, potentially biasing studies that use half-light radii.
Here we present the largest catalog to date of galaxy half-mass radii at z > 1:
7,006 galaxies in the CANDELS fields at 1.0 < z < 2.5. The sample includes both
star-forming and quiescent galaxies with stellar masses 9.0 < log(M_* /
M_\odot) < 11.5. We test three methods for calculating half-mass radii from
multi-band PSF-matched HST imaging: two based on spatially-resolved SED
modeling, and one that uses a rest-frame color profile. All three methods
agree, with scatter <~0.3 dex. In agreement with previous studies, most
galaxies in our sample have negative color gradients (the centers are redder
than the outskirts, and r_e,mass < r_e,light). We find that color gradient
strength has significant trends with increasing stellar mass, half-light
radius, U-V color, and stellar mass surface density. These trends have not been
seen before at z>1. Furthermore, color gradients of star-forming and quiescent
galaxies show a similar redshift evolution: they are flat at z>~2, then steeply
decrease as redshift decreases. This affects the galaxy mass-size relation. The
normalizations of the star-forming and quiescent r_mass-M_* relations are
10-40% smaller than the corresponding r_light-M_* relations; the slopes are
~0.1-0.3 dex shallower. Finally, the half-mass radii of star-forming and
quiescent galaxies at M_* = 10^{10.5}M_\odot only grow by ~1%$ and ~8% between
z~2.25 and z~1.25. This is significantly less than the ~37% and ~47% size
increases found when using the half-light radius.
