The Confinement of Star-Forming Galaxies into a Main Sequence through
  Episodes of Gas Compaction, Depletion, and Replenishment
  Using cosmological simulations, we address the properties of high-redshift
star-forming galaxies (SFGs) across their main sequence (MS) in the plane of
star-formation rate (SFR) versus stellar mass. We relate them to the evolution
of galaxies through phases of gas compaction, depletion, possible
replenishment, and eventual quenching. We find that the high-SFR galaxies in
the upper envelope of the MS are compact, with high gas fractions and short
depletion times ("blue nuggets"), while the lower-SFR galaxies in the lower
envelope have lower central gas densities, lower gas fractions and longer
depletion times, consistent with observed gradients across the MS.
Stellar-structure gradients are negligible. The SFGs oscillate about the MS
ridge on timescales $\sim0.4~t_{\mathrm{Hubble}}$ ($\sim1$ Gyr at $z\sim3$).
The propagation upwards is due to gas compaction, triggered, e.g., by mergers,
counter-rotating streams, and/or violent disc instabilities. The downturn at
the upper envelope is due to central gas depletion by peak star formation and
outflows while inflow from the shrunken gas disc is suppressed. An upturn at
the lower envelope can occur once the extended disc has been replenished by
fresh gas and a new compaction can be triggered, namely as long as the
replenishment time is shorter than the depletion time. The mechanisms of gas
compaction, depletion and replenishment confine the SFGs to the narrow
($\pm0.3$ dex) MS. Full quenching occurs in massive haloes
($M_{\mathrm{vir}}>10^{11.5}~M_\odot$) and/or at low redshifts ($z<3$), where
the replenishment time is long compared to the depletion time, explaining the
observed bending down of the MS at the massive end.
