Unbiased Differential Size Evolution and the Inside-out Growth of Galaxies in the Deep CANDELS GOODS Fields at 1 ≤ z ≤ 7

We present a size analysis of a sample of similar to 49,000 galaxies from the Cosmic Assembly Near-infrared Deep Extragalactic Survey GOODS North and South fields, using redshift-independent relative surface-brightness metrics to determine an unbiased measure of the differential size evolution of galaxies at 1 <= z <= 7. We introduce a novel method of removing foreground objects from distant galaxy (z > 3) images that makes use of the Lyman break at 912 angstrom, in what we call 2D Lyman-break imaging. The images used are in the rest-frame optical at z < 3 and progressively bluer bands at z > 3. They are therefore subject to K-correction and cosmological dimming effects, which are tested and corrected for. We separately consider a mass-selected sample (with masses in the range 10(9) M-circle dot <= M-* <= 10(10.5) M-circle dot) and a number-density-selected sample (using a constant number density of n = 1 x 10(-4) Mpc(-3)). Instead of utilizing the commonly used, but potentially biased, effective radii for size measurements, we measure the redshift-independent Petrosian radius, defined by the parameter eta, for each galaxy for three values of eta, and use this as a proxy for size. The evolution of the measured radii can be described by a power law of the form R-Petr = alpha(1+z)(beta) kpc where beta < 0. We find that the outer radius increases more rapidly, suggesting that as a galaxy grows, mass is added to its outer regions via an inside-out growth. This growth is stronger for the number-density-selected sample, with a growth rate of nearly three in the outer radii compared to the inner. We test and confirm these results using a series of image simulations.