We analyze the star-forming and structural properties of 45 massive (log(M/Msun)>10) compact star-forming galaxies (SFGs) at 2<z<3 to explore whether they are progenitors of compact quiescent galaxies at z~2. The optical/NIR and far-IR Spitzer/Herschel colors indicate that most compact SFGs are heavily obscured. Nearly half (47%) host an X-ray bright AGN. In contrast, only about 10% of other massive galaxies at that time host AGNs. Compact SFGs have centrally-concentrated light profiles and spheroidal morphologies similar to quiescent galaxies, and are thus strikingly different from other SFGs. Most compact SFGs lie either within the SFR-M main sequence (65%) or below (30%), on the expected evolutionary path towards quiescent galaxies. These results show conclusively that galaxies become more compact before they lose their gas and dust, quenching star formation. Using extensive HST photometry from CANDELS and grism spectroscopy from the 3D-HST survey, we model their stellar populations with either exponentially declining (tau) star formation histories (SFHs) or physically-motivated SFHs drawn from semi-analytic models (SAMs). SAMs predict longer formation timescales and older ages ~2 Gyr, which are nearly twice as old as the estimates of the tau models. While both models yield good SED fits, SAM SFHs better match the observed slope and zero point of the SFR-M main sequence. Some low-mass compact SFGs (log(M/Msun)=10-10.6) have younger ages but lower sSFRs than that of more massive galaxies, suggesting that the low-mass galaxies reach the red sequence faster. If the progenitors of compact SFGs are extended SFGs, state-of-the-art SAMs show that mergers and disk instabilities are both able to shrink galaxies, but disk instabilities are more frequent (60% versus 40%) and form more concentrated galaxies. We confirm this result via high-resolution hydrodynamic simulations.
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