We use cosmological simulations to study a characteristic evolution pattern of high redshift galaxies. Early, stream-fed, highly perturbed, gas-rich discs undergo phases of dissipative contraction into compact, star-forming systems ("blue" nuggets) at z ∼ 4 − 2. The peak of gas compaction marks the onset of central gas depletion and inside-out quenching into compact ellipticals (red nuggets) by z ∼ 2. These are sometimes surrounded by gas rings or grow extended dry stellar envelopes. The compaction occurs at a roughly constant specific starformation rate (SFR), and the quenching occurs at a constant stellar surface density within the inner kpc (Σ 1 ). Massive galaxies quench earlier, faster, and at a higher Σ 1 than lower-mass galaxies, which compactify and attempt to quench more than once. This evolution pattern is consistent with the way galaxies populate the SFR-size-mass space, and with gradients and scatter across the main sequence. The compaction is triggered by an intense inflow episode, involving (mostly minor) mergers, counter-rotating streams or recycled gas, and is commonly associated with violent disc instability. The contraction is dissipative, with the inflow rate >SFR, and the maximum Σ 1 anti-correlated with the initial spin parameter . The central quenching is triggered by the high SFR and stellar/supernova feedback (maybe also AGN feedback) due to the high central gas density, while the central inflow weakens as the disc vanishes. Suppression of fresh gas supply by a hot halo allows the longterm maintenance of quenching once above a threshold halo mass, inducing the quenching downsizing.

Using cosmological simulations, we address the properties of high-redshift starforming 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. Stellarstructure gradients are negligible. The SFGs oscillate about the MS ridge on timescales ∼ 0.4 t Hubble (∼ 1 Gyr at z ∼ 3). 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 (±0.3 dex) MS. Full quenching occurs in massive haloes (M vir > 10 11.5 M ) 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.

Although giant clumps of stars are thought to be crucial to galaxy formation and evolution, the most basic demographics of clumps are still uncertain, mainly because the definition of clumps has not been thoroughly discussed. In this paper, we carry out a study of the basic demographics of clumps in star-forming galaxies at 0.5 < z < 3, using our proposed physical definition that UV-bright clumps are discrete star-forming regions that individually contribute more than 8% of the rest-frame UV light of their galaxies. Clumps defined this way are significantly brighter than the HII regions of nearby large spiral galaxies, either individually or blended, when physical spatial resolution and cosmological dimming are considered. Under this definition, we measure the fraction of star-forming galaxies that have at least one off-center clump (f clumpy ) and the contributions of clumps to the rest-frame UV light and star formation rate (SFR) of star-forming galaxies in the CANDELS/GOODS-S and UDS fields, where our mass-complete sample consists of 3239 galaxies with axial ratio q > 0.5. The redshift evolution of f clumpy changes with the stellar mass (M * ) of the galaxies. Low-mass (log(M * /M ⊙ ) < 9.8) galaxies keep an almost constant f clumpy of ∼60% from z ∼ 3 to z ∼ 0.5. Intermediate-mass and massive galaxies drop their f clumpy from 55% at z ∼ 3 to 40% and 15%, respectively, at z ∼ 0.5. We find that (1) the trend of disk stabilization predicted by violent disk instability matches the f clumpy trend of massive galaxies; (2) minor mergers are a viable explanation of the f clumpy trend of intermediate-mass galaxies at z < 1.5, given a realistic observability timescale; and (3) major mergers are unlikely responsible for the f clumpy trend in all masses at z < 1.5. The clump contribution to the rest-frame UV light of star-forming galaxies shows a broad peak around galaxies with log(M * /M ⊙ ) ∼ 10.5 at all redshifts. The clump contribution in the intermediate-mass and massive galaxies is possibly linked to the molecular gas fraction of the galaxies. The clump contribution to the SFR of star-forming galaxies, generally around 4-10%, also shows dependence on the galaxy M * , but for a given galaxy M * , its dependence on the redshift is mild.

We address the internal support against total free-fall collapse of the giant clumps that form by violent gravitational instability in high-z disc galaxies. Guidance is provided by an analytic model, where the protoclumps are cut from a rotating disc and collapse to equilibrium while preserving angular momentum. This model predicts prograde clump rotation, which dominates the support if the clump has contracted to a surface density contrast 10. This is confirmed in hydro adaptive mesh refinement zoom-in simulations of galaxies in a cosmological context. In most high-z clumps, the centrifugal force dominates the support, R ≡ V 2 rot /V 2 circ > 0.5, where V rot is the rotation velocity and the circular velocity V circ measures the potential well. The clump spin indeed tends to be in the sense of the global disc angular momentum, but substantial tilts are frequent, reflecting the highly warped nature of the high-z discs. Most clumps are in Jeans equilibrium, with the rest of the support provided by turbulence, partly driven by the gravitational instability itself. The general agreement between model and simulations indicates that angular momentum loss or gain in most clumps is limited to a factor of 2. Simulations of isolated gas-rich discs that resolve the clump substructure reveal that the cosmological simulations may overestimate R by ∼30 per cent, but the dominance of rotational support at high z is not a resolution artefact. In turn, isolated gas-poor disc simulations produce at z = 0 smaller gaseous non-rotating transient clouds, indicating that the difference in rotational support is associated with the fraction of cold baryons in the disc. In our current cosmological simulations, the clump rotation velocity is typically more than twice the disc dispersion, V rot ∼ 100 km s −1 , but when beam smearing of ≥0.1 arcsec is imposed, the rotation signal is reduced to a small gradient of ≤30 km s −1 kpc −1 across the clump. The velocity dispersion in the simulated clumps is comparable to the disc dispersion so it is expected to leave only a marginal signal for any beam smearing. Retrograde minor-merging galaxies could lead to massive clumps that do not show rotation even when marginally resolved. A testable prediction of the scenario as simulated is that the mean stellar age and the stellar fraction of the clumps are declining linearly with distance from the disc centre.

Using cosmological simulations, we address the interplay between structure and star formation in high-redshift galaxies via the evolution of surface density profiles. Our sample consists of 26 galaxies evolving in the redshift range z = 7−1, spanning the stellar mass range (0.2−6.4)×10 10 M at z = 2. We recover the main trends by stacking the profiles in accordance to their evolution phases. Following a wet compaction event that typically occurs when the stellar mass is ∼ 10 9.5 M at z ∼ 2 − 4, the gas develops a cusp inside the effective radius, associated with a peak in star-formation rate (SFR). The SFR peak and the associated feedback, in the absence of further gas inflow to the centre, marks the onset of gas depletion from the central 1 kpc, leading to quenching of the central SFR. An extended, star-forming ring that forms by fresh gas during the central quenching process shows as a rising specific SFR (sSFR) profile, which is interpreted as inside-out quenching. Before quenching, the stellar density profile grows self-similarly, maintaining its log-log shape because the sSFR is similar at all radii. During the quenching process, the stellar density saturates to a constant value, especially in the inner 1 kpc. The stellar mass and SFR profiles deduced from observations show very similar shapes, consistent with the scenario of wet compaction leading to inside-out quenching and the subsequent saturation of a dense stellar core. We predict a cuspy gas profile during the blue nugget phase, and a gas-depleted core, sometimes surrounded by a ring, in the post-blue nugget phase.

We study the properties of giant clumps and their radial gradients in high-z disc galaxies using AMR cosmological simulations. Our sample consists of 770 snapshots in the redshift range z = 4 − 1 from 29 galaxies that at z = 2 span the stellar mass range (0.2 − 3) × 10 11 M ⊙ . Extended gas discs exist in 83% of the snapshots. Clumps are identified by gas density in 3D and their stellar and dark matter components are considered thereafter. While most of the overdensities are diffuse and elongated, 91% of their mass and 83% of their star-fromation rate (SFR) are in compact round clumps. Nearly all galaxies have a central, massive bulge clump, while 70% of the discs show off-center clumps, 3-4 per galaxy. The fraction of clumpy discs peaks at intermediate disc masses. Clumps are divided based on dark-matter content into in-situ and ex-situ, originating from violent disc instability (VDI) and minor mergers respectively. 60% of the discs are in a VDI phase showing off-center in-situ clumps, which contribute 1-7% of the disc mass and 5-45% of its SFR. The in-situ clumps constitute 75% of the off-center clumps in terms of number and SFR but only half the mass, each clump containing on average 1% of the disc mass and 6% of its SFR. They have young stellar ages, 100−400 Myr, and high specific SFR (sSFR), 1−10 Gyr −1 . They exhibit gradients resulting from inward clump migration, where the inner clumps are somewhat more massive and older, with lower gas fraction and sSFR and higher metallicity. Similar observed gradients indicate that clumps survive outflows. The ex-situ clumps have stellar ages 0.5 − 3 Gyr and sSFR ∼ 0.1 − 2 Gyr −1 , and they exhibit weaker gradients. Massive clumps of old stars at large radii are likely ex-situ mergers, though half of them share the disc rotation.

We study the evolution and properties of giant clumps in high-z disc galaxies using AMR cosmological simulations at redshifts z ∼ 6 − 1. Our sample consists of 34 galaxies, of halo masses 10 11 − 10 12 M ⊙ at z = 2, run with and without radiation pressure (RP) feedback from young stars. While RP has little effect on the sizes and global stability of discs, it reduces the amount of star-forming gas by a factor of ∼ 2, leading to a similar decrease in stellar mass by z ∼ 2. Both samples undergo extended periods of violent disc instability (VDI) continuously forming giant clumps of masses 10 7 − 10 9 M ⊙ at a similar rate, though RP significantly reduces the number of long-lived clumps (LLCs). When RP is (not) included, clumps with circular velocity 3 )M ⊙ are short-lived, disrupted in a few free-fall times. More massive and dense clumps survive and migrate toward the disc centre over a few disc orbital times. In the RP simulations, the distribution of clump masses and star-formation rates (SFRs) normalized to their host disc is similar at all redshifts, exhibiting a truncated power-law with a slope slightly shallower than −2. The specific SFR (sSFR) of the LLCs declines with age as they migrate towards the disc centre, producing gradients in mass, stellar age, gas fraction, sSFR and metallicity that distinguish them from the short-lived clumps which tend to populate the outer disc. Ex situ mergers comprise ∼ 37% of the mass in clumps and ∼ 29% of the SFR. They are more massive and with older stellar ages than the in situ clumps, especially near the disc edge. Roughly half the galaxies at redshifts z = 4 − 1 are clumpy, with ∼ 3 − 30% of their SFR and ∼ 0.1 − 3% of their stellar mass in clumps.

Studying giant star-forming clumps in distant galaxies is important to understand galaxy formation and evolution. At present, however, observers and theorists have not reached a consensus on whether the observed "clumps" in distant galaxies are the same phenomenon that is seen in simulations. In this paper, as a step to establish a benchmark of direct comparisons between observations and theories, we publish a sample of clumps constructed to represent the commonly observed "clumps" in the literature. This sample contains 3193 clumps detected from 1270 galaxies at z 0.5 3.0  < . The clumps are detected from rest-frame UV images, as described in our previous paper. Their physical properties (e.g., rest-frame color, stellar mass (M * ), star formation rate (SFR), age, and dust extinction) are measured by fitting the spectral energy distribution (SED) to synthetic stellar population models. We carefully test the procedures of measuring clump properties, especially the method of subtracting background fluxes from the diffuse component of galaxies. With our fiducial background subtraction, we find a radial clump U−V color variation, where clumps close to galactic centers are redder than those in outskirts. The slope of the color gradient (clump color as a function of their galactocentric distance scaled by the semimajor axis of galaxies) changes with redshift and M * of the host galaxies: at a fixed M * , the slope becomes steeper toward low redshift, and at a fixed redshift, it becomes slightly steeper with M * . Based on our SED fitting, this observed color gradient can be explained by a combination of a negative age gradient, a negative E(B−V ) gradient, and a positive specific SFR gradient of the clumps. We also find that the color gradients of clumps are steeper than those of intra-clump regions. Correspondingly, the radial gradients of the derived physical properties of clumps are different from those of the diffuse component or intra-clump regions.