  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.
