Self-regulated growth of galaxy sizes along the star-forming main sequence

We present a systematic analysis of the spatially-resolved star formation histories (SFHs) using Hubble Space Telescope imaging data of $\sim 997$, intermediate redshifts $0.5 \leq z \leq 2.0$ galaxies from GOODS-S field, with stellar mass range $9.8 \leq \log \mathrm{M}_{\star}/\mathrm{M}_{\odot} \leq 11.5$. We estimate the SFHs in three spatial regions (central region within the half-mass radii $\mathrm{R}_{50s}$, outskirts between $1-3 \mathrm{R}_{50s}$, and the whole galaxy) using pixel-by-pixel spectral-energy distribution (SED) fitting, assuming exponentially declining tau model in individual pixels. The reconstructed SFHs are then used to derive and compare the physical properties such as specific star-formation rates (sSFRs), mass-weighted ages (t$_{\mathrm{50}}$), and the half mass-radii to get insights on the interplay between the structure and star-formation in galaxies. The correlation of sSFRs ratio of the centre and outskirts with the distance from the main sequence (MS) indicates that galaxies on the upper envelope of the MS tend to grow outside-in, building up their central regions, while those below the MS grow inside-out, with more active star-formation in the outskirts. The findings suggest a self-regulating process in galaxy size growth when they evolve along the MS. Our observations are consistent with galaxies growing their inner bulge and outer disc regions, where they appear to oscillate about the average MS in cycles of central gas compaction, which leads to bulge growth, and subsequent central depletion possibly due to feedback from the starburst resulting in more star formation towards the outskirts from newly accreted gas.