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Sharon Lapiner

Publications and source records attributed to Sharon Lapiner.

At least 19 recordsLinked to original sources

Probing the Cosmic Web with Fast Radio Bursts. I. Scattering

We study the formation of multiphase gas in the post-accretion-shock regions of cosmic sheets, filaments, and the circumgalactic medium (CGM) of haloes, i.e., cosmic web objects (CWOs). Local instabilities in the hot medium result in fragmentation and cooling, eventually forming small-scale overdensities with temperatures of $\sim 10^{4}{\,\rm K}$ in pressure equilibrium with the hot environment. Such dense, ionised inhomogeneities can affect the propagation of radio waves from fast radio bursts (FRBs), thereby offering us a way to probe their presence and properties in CWOs through scattering signatures in the observed FRB flux. We find that high-$z$ filaments \& sheets have a negligible contribution to the total observed scattering. The high rates of FRBs expected even at high redshifts may still allow detection from high-temperature filaments along rare sightlines, and we suggest other methods for such systems in a companion paper. Our model further predicts that if turbulent cloudlets exist in the CGM of intervening massive haloes with a volume-filling fraction of $f_{\rm v}\gtrsim 10^{-3}$, they are expected to cause considerable cumulative scattering along an average sightline, resulting in a significant correlation between the total scattering time and source redshifts. The lack of such a correlation in current observations may imply that the cool gas in the CGM has substantial non-thermal pressure, reducing its density, or significant damping of small-scale density fluctuations. Forthcoming localised FRB samples can map these constraints into bounds on volume-filling fractions, densities, cloud sizes, and the strength of turbulence.

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From Feedback-Free Star Clusters to Little Red Dots via Compaction

We address the origin of the Little Red Dots (LRDs) seen by JWST at cosmic morning ($z \!=\! 4 \!-\! 8$) as compact stellar systems with over-massive black holes (BHs). We propose that LRDs form naturally after feedback-free starbursts (FFB) in thousands of star clusters and following wet compaction. Analytically, we show how the clusters enable efficient dry migration of stars and BHs to the galaxy center by two-body segregation and dynamical friction against the disk. The clusters merge to form compact central stellar systems as observed. Mutual tidal stripping does not qualitatively affect the analysis. The young, rotating clusters are natural sites for the formation of BH seeds via rapid core collapse. The migrating clusters carry the BH seeds, which merge into central super-massive BHs (SMBHs). Compactions are required to deepen the potential wells such that the SMBHs are retained after post-merger gravitational-wave recoils, locked to the galaxy centers. Using cosmological simulations at different epochs, with different codes and physical recipes, we evaluate the additional growth of LRD-matching compact central stellar systems by global compaction events. Adding to the dry growth by cluster mergers, the compactions can increase the escape velocities to retain the SMBHs. The LRDs appear at $z \!\sim\! 8$, after the formation of FFB clusters, and disappear after $z \!\sim\! 4$ when the stellar mass is above $10^9 M_\odot$ by growing post-compaction blue disks around the nuclear LRDs. The LRD abundance is expected to be $\sim\! 10^{-5} \!-\! 10^{-4}\,{\rm Mpc}^{-3}$, increasing from $z \!\sim\! 4$ to $z\!\sim\! 8$.

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From FFB Starbursts at Cosmic Dawn to Quenching at Cosmic Morning: Hi-z Galaxy Bimodality

We propose a mass-dependent bimodality in the early evolution of galaxies. The massive track connects the super-bright galaxies at cosmic dawn ($z > 8$) to the super-massive quiescent galaxies and black holes (BHs) at cosmic morning ($z \sim 4 - 7$). The dark-matter halos $> 10^{10.5} {\rm M}_\odot$ at $z = 10$ are expected to undergo feedback-free starbursts (FFB) with high star-formation efficiency in dense star clusters within compact galaxies. The less massive halos avoid FFB and form stars gradually under stellar feedback, possibly leading to the peak star-forming galaxies at cosmic noon ($z \sim 1-3$). The FFB and non-FFB halos originate from $>4\sigma$ and $2-3\sigma$ density peaks, respectively. The post-FFB galaxies quench their star formation soon after the FFB phase and remain quiescent due to (a) gas depletion by the FFB starbursts and outflows, (b) compaction events driven by angular-momentum loss in colliding streams within the high-sigma-peak FFB halos, (c) turbulent circum-galactic medium (CGM) that suppresses feeding by cold streams, and (d) BH feedback, being a key for complete quenching. BH feedback is enhanced by FFB-driven BH seeding and growth. It seems capable of disrupting the streams by generating CGM turbulence or photo-heating, but this remains an open challenge. The cosmic-morning quiescent galaxies are expected to be massive, compact, showing signatures of compaction, outflows and AGN, with a comoving number density $\sim 10^{-5} {\rm Mpc}^{-3}$, comparable to the super-bright galaxies at cosmic dawn and the AGN at cosmic morning. Their UV luminosity function is predicted to peak about $M_ {\rm uv} \sim -22$ and contribute $\sim 10\%$ of the galaxies there.

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Mini-quenching of $z=4-8$ galaxies by bursty star formation

The recent reported discovery of a low-mass $z=5.2$ and an intermediate-mass $z=7.3$ quenched galaxy with JWST/NIRSpec is the first evidence of halted star formation above $z\approx 5$. Here we show how bursty star formation at $z=4-8$ gives rise to temporarily quenched, or mini-quenched galaxies in the mass range $M_{\star} = 10^7-10^9 \ M_{\odot}$ using four models of galaxy formation: the periodic box simulation IllustrisTNG, the zoom-in simulations VELA and FirstLight and an empirical halo model. The main causes for mini-quenching are stellar feedback, lack of gas accretion onto galaxies and galaxy-galaxy interactions. The abundance of (mini-)quenched galaxies agrees across the models: the population first appears below $z\approx 8$, after which their proportion increases with cosmic time, from $\sim 0.5-1.0$% at $z=7$ to $\sim 2-4$% at $z=4$, corresponding to comoving number densities of $\sim 10^{-5}$ Mpc$^{-3}$ and $\sim 10^{-3}$ Mpc$^{-3}$, respectively. These numbers are consistent with star formation rate duty cycles inferred for VELA and FirstLight galaxies. Their star formation histories (SFHs) suggest that mini-quenching at $z=4-8$ is short-lived with a duration of $\sim 20-40$ Myr, which is close to the free-fall timescale of the inner halo. However, mock spectral energy distributions of mini-quenched galaxies in IllustrisTNG and VELA do not match JADES-GS-z7-01-QU photometry, unless their SFHs are artificially altered to be more bursty on timescales of $\sim 40$ Myr. Studying mini-quenched galaxies might aid in calibrating sub-grid models governing galaxy formation, as these may not generate sufficient burstiness at high redshift to explain the SFH inferred for JADES-GS-z7-01-QU.

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Wet Compaction to a Blue Nugget: a Critical Phase in Galaxy Evolution

We utilize high-resolution cosmological simulations to reveal that high-redshift galaxies tend to undergo a robust `wet compaction' event when near a `golden' stellar mass of $\sim 10^{10} M_{\odot}$. This is a gaseous shrinkage to a compact star-forming phase, a `blue nugget' (BN), followed by central quenching of star formation to a compact passive stellar bulge, a `red nugget' (RN), and a buildup of an extended gaseous disc and ring. Such nuggets are observed at cosmic noon and seed today's early-type galaxies. The compaction is triggered by a drastic loss of angular momentum due to, e.g., wet mergers, counter-rotating cold streams, or violent disc instability. The BN phase marks drastic transitions in the galaxy structural, compositional and kinematic properties. The transitions are from star-forming to quenched inside-out, from diffuse to compact with an extended disc-ring and a stellar envelope, from dark matter to baryon central dominance, from prolate to oblate stellar shape, from pressure to rotation support, from low to high metallicity, and from supernova to AGN feedback. The central black hole growth, first suppressed by supernova feedback when below the golden mass, is boosted by the compaction, and the black hole keeps growing once the halo is massive enough to lock in the supernova ejecta.

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Effects of feedback on galaxies in the VELA simulations: elongation, clumps and compaction

The evolution of star-forming galaxies at high redshifts is very sensitive to the strength and nature of stellar feedback. Using two sets of cosmological, zoom-in simulations from the VELA suite, we compare the effects of two different models of feedback: with and without kinetic feedback from the expansion of supernovae shells and stellar winds. At a fixed halo mass and redshift, the stellar mass is reduced by a factor of 1-3 in the models with stronger feedback, so the stellar-mass-halo-mass relation is in better agreement with abundance matching results. On the other hand, the three-dimensional shape of low-mass galaxies is elongated along a major axis in both models. At a fixed stellar mass, Ms<10^10 Msun, galaxies are more elongated in the strong-feedback case. More massive, star-forming discs with high surface densities form giant clumps. However, the population of round, compact, old (age_c > 300 Myr), quenched, stellar (or gas-poor) clumps is absent in the model with strong feedback. On the other hand, giant star-forming clumps with intermediate ages (age_c= 100 - 300 Myr) can survive for several disc dynamical times, independently of feedback strength. The evolution through compaction followed by quenching in the plane of central surface density and specific star-formation rate is similar under the two feedback models.

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Evaluating Galaxy Dynamical Masses From Kinematics and Jeans Equilibrium in Simulations

We provide prescriptions to evaluate the dynamical mass ($M_{\rm dyn}$) of galaxies from kinematic measurements of stars or gas using analytic considerations and the VELA suite of cosmological zoom-in simulations at $z=1-5$. We find that Jeans or hydrostatic equilibrium is approximately valid for galaxies of stellar masses above $M_\star \!\sim\! 10^{9.5}M_\odot$ out to $5$ effective radii ($R_e$). When both measurements of the rotation velocity $v_ϕ$ and of the radial velocity dispersion $σ_r$ are available, the dynamical mass $M_{\rm dyn} \!\simeq\! G^{-1} V_c^2 r$ can be evaluated from the Jeans equation $V_c^2= v_ϕ^2 + ασ_r^2$ assuming cylindrical symmetry and a constant, isotropic $σ_r$. For spheroids, $α$ is inversely proportional to the Sérsic index $n$ and $α\simeq 2.5$ within $R_e$ for the simulated galaxies. The prediction for a self-gravitating exponential disc, $α= 3.36(r/R_e)$, is invalid in the simulations, where the dominant spheroid causes a weaker gradient from $α\!\simeq\! 1$ at $R_e$ to 4 at $5R_e$. The correction in $α$ for the stars due to the gradient in $σ_r(r)$ is roughly balanced by the effect of the aspherical potential, while the effect of anisotropy is negligible. When only the effective projected velocity dispersion $σ_l$ is available, the dynamical mass can be evaluated as $M_{\rm dyn} = K G^{-1} R_e σ_l^2$, where the virial factor $K$ is derived from $α$ given the inclination and $v_ϕ/σ_r$. We find that the standard value $K=5$ is approximately valid only when averaged over inclinations and for compact and thick discs, as it ranges from 4.5 to above 10 between edge-on and face-on projections.

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Compaction-Driven Black Hole Growth

We study the interplay between galaxy evolution and central black-hole (BH) growth using the {NewHorizon} cosmological simulation. BH growth is slow when the dark-matter halo is below a golden mass of $M_{\rm v} \sim 10^{12} \rm M_\odot$, and rapid above it. The early suppression is primarily due to gas removal by supernova (SN) feedback in the shallow potential well, predicting that BHs of $\sim 10^5 \rm M_\odot$ tend to lie below the linear relation with bulge mass. Rapid BH growth is allowed when the halo is massive enough to lock in the SN ejecta by its deep potential well and its heated circum-galactic medium (CGM). The onset of BH growth between these two zones is triggered by a wet-compaction event, caused, e.g., by mergers or counter-rotating streams. It brings gas that lost angular momentum into the inner-$1\rm kpc$ "blue nugget" and causes major transitions in the galaxy structural, kinematic and compositional properties, including the onset of star-formation quenching. The compaction events are confined to the golden mass by the same mechanisms of SN feedback and hot CGM. The onset of BH growth is associated with its sinkage to the center due to the compaction-driven deepening of the potential well and the associated dynamical friction. The galaxy golden mass is thus imprinted as a threshold for rapid BH growth, allowing the AGN feedback to keep the CGM hot and maintain long-term quenching. AGN feedback is not causing the onset of quenching; they are both caused by a compaction event when the mass is between the SN and hot-CGM zones.

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Core Formation in High-z Massive Haloes: Heating by Post Compaction Satellites and Response to AGN Outflows

Observed rotation curves in star-forming galaxies indicate a puzzling dearth of dark matter in extended flat cores within haloes of mass $\geq\! 10^{12}M_\odot$ at $z\!\sim\! 2$. This is not reproduced by current cosmological simulations, and supernova-driven outflows are not effective in such massive haloes. We address a hybrid scenario where post-compaction merging satellites heat up the dark-matter cusps by dynamical friction, allowing AGN-driven outflows to generate cores. Using analytic and semi-analytic models (SatGen), we estimate the dynamical-friction heating as a function of satellite compactness for a cosmological sequence of mergers. Cosmological simulations (VELA) demonstrate that satellites of initial virial masses $>\!10^{11.3}M_\odot$, that undergo wet compactions, become sufficiently compact for significant heating. Constituting a major fraction of the accretion onto haloes $\geq\!10^{12}M_\odot$, these satellites heat-up the cusps in half a virial time at $z\!\sim\! 2$. Using a model for outflow-driven core formation (CuspCore), we demonstrate that the heated dark-matter cusps develop extended cores in response to removal of half the gas mass, while the more compact stellar systems remain intact. The mergers keep the dark matter hot, while the gas supply, fresh and recycled, is sufficient for the AGN outflows. AGN indeed become effective in haloes $\geq\!10^{12}M_\odot$, where the black-hole growth is no longer suppressed by supernovae and its compaction-driven rapid growth is maintained by a hot CGM. For simulations to reproduce the dynamical-friction effects, they should resolve the compaction of the massive satellites and avoid artificial tidal disruption. AGN feedback could be boosted by clumpy black-hole accretion and clumpy response to AGN.

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The Dekel-Zhao profile: A mass-dependent dark-matter density profile with flexible inner slope and analytic potential, velocity dispersion, and lensing properties

We explore a function with two shape parameters for the dark-matter halo density profile subject to baryonic effects, which is a special case of the general Zhao family of models applied to simulated dark matter haloes by Dekel et al. This profile has variable inner slope and concentration parameter, and analytic expressions for the gravitational potential, velocity dispersion, and lensing properties. Using the NIHAO cosmological simulations, we find that it provides better fits than the Einasto profile and the generalized NFW profile with variable inner slope, in particular towards the halo centers. We show that the profile parameters are correlated with the stellar-to-halo mass ratio $M_{\rm star}/M_{\rm vir}$. This defines a mass-dependent density profile describing the average dark matter profiles in all galaxies, which can be directly applied to observed rotation curves of galaxies, gravitational lenses, and semi-analytic models of galaxy formation or satellite-galaxy evolution. The effect of baryons manifests itself by a significant flattening of the inner density slope and a 20\% decrease of the concentration parameter for $M_{\rm star}/M_{\rm vir} = 10^{-3.5}$ to $10^{-2}$, corresponding to $M_{\rm star} \sim 10^{7-10} M_\odot$. The accuracy by which this profile fits simulated galaxies is similar to certain multi-parameter, mass-dependent profiles, but its fewer parameters and analytic nature make it most desirable for many purposes.

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Origin of Star-Forming Rings around Massive Centres in Massive Galaxies at $z\!<\!4$

Using analytic modeling and simulations, we address the origin of an abundance of star-forming, clumpy, extended gas rings about massive central bodies in massive galaxies at $z \!<\! 4$. Rings form by high-angular-momentum streams and survive in galaxies of $M_{\rm star} \!>\! 10^{9.5-10} M_\odot$ where merger-driven spin flips and supernova feedback are ineffective. The rings survive after events of compaction to central nuggets. Ring longevity was unexpected based on inward mass transport driven by torques from violent disc instability. However, evaluating the torques from a tightly wound spiral structure, we find that the timescale for transport per orbital time is long and $\propto\! δ_{\rm d}^{-3}$, with $δ_{\rm d}$ the cold-to-total mass ratio interior to the ring. A long-lived ring forms when the ring transport is slower than its replenishment by accretion and the interior depletion by SFR, both valid for $δ_{\rm d} \!<\! 0.3$. The central mass that lowers $δ_{\rm d}$ is a compaction-driven bulge and/or dark matter, aided by the lower gas fraction at $z \!<\! 4$, provided that it is not too low. The ring is Toomre unstable for clump and star formation. The high-$z$ dynamic rings are not likely to arise form secular resonances or collisions. AGN feedback is not expected to affect the rings. Mock images of simulated rings through dust indicate qualitative consistency with observed rings about bulges in massive $z\!\sim\!0.5\!-\!3$ galaxies, in $H_α$ and deep HST imaging. ALMA mock images indicate that $z\!\sim\!0.5\!-\!1$ rings should be detectable. We quote expected observable properties of rings and their central nuggets.

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A mass threshold for galactic gas discs by spin flips

We predict, analytically and by simulations, that gas discs tend to survive only in haloes above a threshold mass $\sim 2 \times 10^{11} M_\odot$ (stellar mass $\sim 10^9 M_\odot$), with only a weak redshift dependence. At lower masses, the disc spins typically flip in less than an orbital time due to mergers associated with a change in the pattern of the feeding cosmic-web streams. This threshold arises from the halo merger rate when accounting for the mass dependence of the ratio of galactic baryons and halo mass. Above the threshold, wet compactions lead to massive central nuggets that allow the longevity of extended clumpy gas rings. Supernova feedback has a major role in disrupting discs below the critical mass, by driving the stellar-to-halo mass ratio that affects the merger rate, by stirring up turbulence and suppressing high-angular-momentum gas supply, and by confining major compactions to the critical mass. Our predictions seem consistent with current observed fractions of gas discs, to be explored by future observations that will resolve galaxies below $10^9 M_\odot$ at high redshifts, e.g. by JWST.

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A model for core formation in dark matter haloes and ultra diffuse galaxies by outflow episodes

We present a simple model for the response of a dissipationless spherical system to an instantaneous mass change at its center, describing the formation of flat cores in dark matter haloes and ultra-diffuse galaxies (UDGs) from feedback-driven outflow episodes in a specific mass range. This model generalizes an earlier simplified analysis of an isolated shell into a system with continuous density, velocity and potential profiles. The response is divided into an instantaneous change of potential at constant velocities due to a given mass loss or gain, followed by energy-conserving relaxation to a new Jeans equilibrium. The halo profile is modeled by a two-parameter function with a variable inner slope and an analytic potential profile (Dekel et al. 2017), which enables determining the associated kinetic energy at equilibrium. The model is tested against NIHAO cosmological zoom-in simulations, where it successfully predicts the evolution of the inner dark-matter profile between successive snapshots in about 75% of the cases, failing mainly in merger situations. This model provides a simple understanding of the formation of dark-matter halo cores and UDGs by supernova-driven outflows, and a useful analytic tool for studying such processes.

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Multi-Filament Inflows Fueling Young Star Forming Galaxies

Theory suggests that there are two primary modes of accretion through which dark matter halos acquire the gas to form and fuel galaxies, hot and cold mode accretion. In cold mode accretion, gas streams along cosmic web filaments to the center of the halo, allowing for the efficient delivery of star-forming fuel. Recently, two QSO-illuminated HI Lyman alpha (Lyα) emitting objects were reported to have properties of cold, rotating structures (Martin et al. 2015, Martin et al. 2016). However, the spatial and spectral resolution available was insufficient to constrain radial flows associated with connecting filaments. With the Keck Cosmic Web Imager (KCWI) we now have eight times the spatial resolution, permitting the detection of these in-spiraling flows. In order to detect these inflows, we introduce a suite of models which incorporate zonal radial flows, demonstrate their performance on a numerical simulation that exhibits coldflow accretion, and show that they are an excellent match to KCWI velocity maps of two Lyα emitters observed around high-redshift quasars. These Multi-Filament Inflow models kinematically isolate zones of radial inflow that correspond to extended filamentary emission. The derived gas flux and inflow path is sufficient to fuel the inferred central galaxy star formation rate and angular momentum. Thus, our kinematic emission maps provide strong evidence for the inflow of gas from the cosmic web building galaxies at the peak of star formation.

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Origin of the Golden Mass of Galaxies and Black Holes

We address the origin of the golden mass and time for galaxy formation and the onset of rapid black-hole growth. The preferred dark-halo mass of ~$10^{12}M_\odot$ is translated to a characteristic epoch, z~2, at which the typical forming halos have a comparable mass. We put together a coherent picture based on existing and new simple analytic modeling and cosmological simulations. We describe how the golden mass arises from two physical mechanisms that suppress gas supply and star formation below and above the golden mass, supernova feedback and virial shock heating of the circum-galactic medium (CGM), respectively. Cosmological simulations reveal that these mechanisms are responsible for a similar favored mass for the dramatic events of gaseous compaction into compact star-forming "blue nuggets", caused by mergers, counter-rotating streams or other mechanisms. This triggers inside-out quenching of star formation, to be maintained by the hot CGM, leading to today's passive early-type galaxies. The blue-nugget phase is responsible for transitions in the galaxy structural, kinematic and compositional properties, e.g., from dark-matter to baryon central dominance and from prolate to oblate shape. The growth of the central black hole is suppressed by supernova feedback below the critical mass, and is free to grow once the halo is massive enough to lock the supernova ejecta by its deep potential well and the hot CGM. A compaction near the golden mass makes the black hole sink to the galactic center and triggers a rapid black-hole growth. This ignites feedback by the Active Galactic Nucleus that helps keeping the CGM hot and maintaining long-term quenching.

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Is the dark-matter halo spin a predictor of galaxy spin and size?

The similarity between the distributions of spins for galaxies ($λ_{\rm g}$) and for dark-matter haloes ($λ_{\rm h}$), indicated both by simulations and observations, is naively interpreted as a one-to-one correlation between the spins of a galaxy and its host halo. This is used to predict galaxy sizes in semi-analytic models via $R_{\rm e}\simeqλ_{\rm h} R_{\rm v}$, with $R_{\rm e}$ the half-mass radius of the galaxy and $R_{\rm v}$ the halo radius. Utilizing two different suites of zoom-in cosmological simulations, we find that $λ_{\rm g}$ and $λ_{\rm h}$ are in fact only barely correlated, especially at $z\geq 1$. A general smearing of this correlation is expected based on the different spin histories, where the more recently accreted baryons through streams gain and then lose significant angular momentum compared to the gradually accumulated dark matter. Expecting the spins of baryons and dark matter to be correlated at accretion into $R_{\rm v}$, the null correlation at the end reflects an anti-correlation between $λ_{\rm g}/λ_{\rm h}$ and $λ_{\rm h}$, which can partly arise from mergers and a compact star-forming phase that many galaxies undergo. On the other hand, the halo and galaxy spin vectors tend to be aligned, with a median $\cosθ=0.6$-0.7 between galaxy and halo, consistent with instreaming within a preferred plane. The galaxy spin is better correlated with the spin of the inner halo, but this largely reflects the effect of the baryons on the halo. Following the null spin correlation, $λ_{\rm h}$ is not a useful proxy for $R_{\rm e}$. While our simulations reproduce a general relation of the sort $R_{\rm e}=AR_{\rm vir}$, in agreement with observational estimates, the relation becomes tighter with $A=0.02(c/10)^{-0.7}$, where $c$ is the halo concentration, which in turn introduces a dependence on mass and redshift.

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Evolution of Galaxy Shapes from Prolate to Oblate through Compaction Events

We study the evolution of global shapes of galaxies using cosmological simulations. The shapes refer to the components of dark matter (DM), stars and gas at the stellar half-mass radius. Most galaxies undergo a characteristic compaction event into a blue nugget at $z\sim2-4$, which marks the transition from a DM-dominated central body to a self-gravitating baryonic core. We find that in the high-$z$, DM-dominated phase, the stellar and DM systems tend to be triaxial, preferentially prolate and mutually aligned. The elongation is supported by an anisotropic velocity dispersion that originates from the assembly of the galaxy along a dominant large-scale filament. We estimate that torques by the dominant halo are capable of inducing the elongation of the stellar system and its alignment with the halo. Then, in association with the transition to self-gravity, small-pericenter orbits puff up and the DM and stellar systems evolve into a more spherical and oblate configuration, aligned with the gas disc and associated with rotation. This transition typically occurs when the stellar mass is $\sim 10^9$ M$_\odot$ and the escape velocity in the core is $\sim 100$ km s$^{-1}$, indicating that supernova feedback may be effective in keeping the core DM-dominated and the system prolate. The early elongated phase itself may be responsible for the compaction event, and the transition to the oblate phase may be associated with the subsequent quenching in the core.

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Evolution of Density Profiles in High-z Galaxies: Compaction and Quenching Inside-Out

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 $(0.2-6.4)\times 10^{10}M_\odot$ 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 $\sim10^{9.5}~M_{\odot}$ at $z\sim2-4$, 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.

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