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Gabriella De Lucia

Publications and source records attributed to Gabriella De Lucia.

At least 37 records · Page 2Linked to original sources

Do z>6 quasars reside in protoclusters?

We discuss the properties of a sample of z>6 bright (bolometric luminosity L$_{\rm bolo}$>10$^{46.25}$ erg/s) Quasars drawn from a realisation of the GAlaxy Evolution and Assembly (GAEA) model coupled with the Planck Millennium Simulation. We focus on the properties and environment of host galaxies on a physical scale of 10 cMpc, and their evolution down to z=0, with the aim of assessing how well the bright high redshift QSOs population traces the progenitors of the most massive haloes in the local Universe. GAEA predicts that z>6 bright QSOs live in a variety of environments, and that secular processes like disc instability are responsible for triggering roughly the same number of QSOs as galaxy mergers. We consider mock fields built around these high-z QSOs, and we show that roughly half of them include other active galaxies (with L$_{\rm bolo}$>10$^{44}$ erg/s). The predicted large field-to-field variance in the number of companions is qualitatively consistent with recent results from JWST observations. Descendants of host galaxies at z=0 cover a wide range of physical properties and environments with only a small fraction of them belonging to massive galaxy clusters (M$_{\rm DM}$>10$^{14.5}$ M$_\odot$). Viceversa, GAEA predicts that only a small fraction of Bright Central Galaxies have a bright z>6 QSOs among their progenitors. Our results suggest that luminous high-z QSO loosely trace the progenitors of low-z galaxy clusters, but that additional information about their environment (like the number of active galaxy companions) are required to identify the most promising proto-cluster candidates.

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Where Giants Dwell: Probing the Environments of Early Massive Quiescent Galaxies

We investigate the environments of massive quiescent galaxies at 3 < z < 5 using the GAlaxy Evolution and Assembly (GAEA) theoretical model. We select galaxies with stellar mass ~10^10.8 Msun and specific star formation rate below 0.3x t_Hubble, yielding in a sample of about 5,000 galaxies within a simulated volume of ~685 Mpc. These galaxies have formation times that cover well the range inferred from recent observational data, including a few rare objects with very short formation time-scales and early formation epochs. Model high-z quiescent galaxies are alpha-enhanced and exhibit a wide range of stellar metallicity, in broad agreement with current observational estimates. Massive high-z quiescent galaxies in our model occupy a wide range of environments, from void-like regions to dense knots at the intersections of filaments. Quiescent galaxies in underdense regions typically reside in halos that collapsed early and grew rapidly at high redshift, though this trend becomes difficult to identify observationally due to large intrinsic scatter in star formation histories. The descendants of high-z massive quiescent galaxies display a broad distribution in mass and environment by z=0, reflecting the stochastic nature of mergers. About one-third of these systems remain permanently quenched, while most rejuvenation events are merger-driven and more common in overdense regions. Our results highlight the diversity of early quiescent galaxies and caution against assuming that all such systems trace the progenitors of present day most massive clusters.

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Simulations of the 21cm emission line for upcoming large-scale HI galaxy surveys

Upcoming galaxy surveys with the SKA Observatory will detect neutral hydrogen (HI) across unprecedented volumes, and their scientific return will crucially depend on predictive models for HI observables. In this work, we present a framework to simulate the neutral hydrogen 21cm emission line in such large-scale HI galaxy surveys. This framework is developed as a modular layer that builds on semi-analytical models. In particular we use as bases the Galaxy Evolution and Assembly (GAEA) and L-Galaxies semi-analytical models, coupled to merger trees from the Millennium Simulation suite. We validate our framework against local Universe observations, demonstrating consistency with velocity functions, and generalised Tully-Fisher relations. Predictions based on GAEA and L-Galaxies exhibit mutual consistency despite the distinct underlying physical prescriptions. We construct mock galaxy catalogues that incorporate forward-modelled selection functions, inclination effects, and redshift broadening, reproducing the statistical distributions of HI-selected galaxies in the ALFALFA survey. Finally, we present redshift distribution forecasts for future SKA Observatory HI galaxy surveys. This framework offers a flexible tool for interpreting upcoming large-scale radio surveys and studying HI line observables as cosmological probes.

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Mechanisms Affecting Galaxies Nearby and Environmental Trends (MAGNET)

[ABRIDGED] Galaxy evolution is shaped by internal and external mechanisms that regulate the baryon cycle and star formation activity. We present a theoretical framework based on the GAlaxy Evolution and Assembly (GAEA) semi-analytic model. We extracted portions of simulated volumes that include isolated galaxies, pairs, group, and filament members at z ~ 0, specifically avoiding massive clusters. Galaxies were classified using both intrinsic (halo-based) and observational (2D projected) parameterizations, reconstructing their environmental histories from z = 2 and identifying mergers, tidal interactions, ram pressure stripping (RPS), and starvation. 2D information decreases isolated and group fractions while doubles pairs. More than half of galaxies remain unaffected by the investigated processes since z = 2. Among affected galaxies, mergers dominate at high stellar masses (40-60% at log(M*/Msun) > 10.5). Tidal interactions are less frequent, and their incidence increases with stellar mass. RPS dominates in groups and filaments at intermediate masses (~50%), while starvation ranges from 20 to 30%. The incidence of the different mechanisms depends strongly on both mass and environment, though their imprints on global properties are often subtle. Distinct evolutionary pathways emerge: log(M*/Msun) < 9.5, galaxies in groups and filaments have a faster mass growth than galaxies in the other environments, especially those undergoing starvation, mergers and, to less extent, RPS. Differences are reduced moving to higher masses, where no clear dependence on physical mechanism emerge, even though at these masses a clear star formation suppression is evident in mergers and starved galaxies. This theoretical investigation provides essential context for the recently started multi-wavelength program Mechanisms Affecting Galaxies Nearby and Environmental Trends (MAGNET), which we introduce here.

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Dust evolution across cosmic times as seen through DUSTY-GAEA

For many decades, dust has been recognised as an important ingredient in galaxy formation and evolution. This paper presents a novel self-consistent implementation of dust formation by stars, destruction by supernova shocks and hot gas, and growth within the dense interstellar medium (ISM) in the GAEA state-of-the-art galaxy formation model. Our new model, DUSTY-GAEA, reproduces well the dust buildup as a function of stellar mass out to z $\sim$ 6, the scaling relations between the dust-to-gas/dust-to-metal ratios and stellar mass/metallicty in the local Universe, and the dust mass function in the local Universe and out to z $\sim$ 1. In the framework of our model, dust growth dominates the cosmic dust budget out to z $\sim$ 8, and we find that observational constraints beyond the local Universe can be reproduced only assuming such efficient dust growth in the dense ISM. Yet, reproducing the estimated number densities of dust-rich galaxies at higher redshifts remains challenging, as found also in independent theoretical work. We discuss our model predictions in comparison with both observational data and independent theoretical efforts, and highlight how further observational constraints at high redshifts would help constrain dust models.

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A semi-analytical mock galaxy catalog for the CSST extragalactic surveys from the Jiutian simulations

We introduce a mock galaxy catalog built for the CSST extragalactic surveys using the primary runs of the Jiutian $N$-body simulation suites. The catalogs are built by coupling the GAlaxy Evolution and Assembly (GAEA) semi-analytical model of galaxy formation with merger trees extracted from the simulations using the Hierarchical Bound-Tracing (HBT+) algorithm. The spectral energy distributions (SEDs) and broadband magnitudes are computed using the neural-network-based stellar population synthesizer StarDuster, which is trained on radiative transfer simulations to account for detailed galaxy geometry in modeling dust obscuration. Galaxy light-cones up to $z=5$ are subsequently generated with the BLiC light-cone builder which interpolates the properties of galaxies over time using an optimized interpolation scheme. The resulting catalogs exhibit good convergence in many statistical properties of the galaxy population produced from two different resolution simulations. The catalogs reproduce a number of observed galaxy properties across a range of galaxy mass and redshift, including the stellar mass functions, the luminosity function, gas mass fraction, galaxy size-mass relation and galaxy clustering. We also present the photometric and redshift distributions of galaxies expected to be observed in the CSST surveys.

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Probing the dawn of galaxies: star formation and feedback in the JWST era through the GAEA model

The James Webb Space Telecope (JWST) opened a new window for the study of the highest redshift ($z>7$) Universe. This work presents a theoretical investigation of the very-high redshift Universe using the state-of-the-art GALaxy Evolution and Assembly (GAEA) model, run on merger trees from the Planck-Millennium $N$-body simulation. We show that GAEA successfully reproduces a wide range of high-$z$ observational estimates including: the galaxy stellar mass function up to $z\sim13$ and the total (galaxies and AGN) UV luminosity function (LF) up to $z\sim10$. We find that the AGN UV emission represents an important contribution at the bright end of the UVLF up to $z\sim8$, but it is negligible at higher redshift. Our model reproduces well the observed mass-metallicity relation at $z\leq4$, while it slightly overestimates the normalization of the relation at earlier cosmic epochs. At $z\geq11$, current UVLF estimates are at least one order of magnitude larger than model predictions. We investigate the impact of different physical mechanisms, such as an enhanced star formation efficiency coupled with a reduced stellar feedback or a negligible stellar feedback at $z>10$. In the framework of our model, both the galaxy stellar mass and UV luminosity functions at $z\geq10$ can be explained by assuming feedback-free starbursts in high-density molecular clouds. However, we show that this model variant leads to a slight increase of the normalization of the $z\geq10$ mass-metallicity relation, strengthening the tension with available data. A model with negligible stellar feedback at $z>10$ also predicts larger numbers of massive and bright galaxies aligning well with observations, but it also overestimates the metallicity of the interstellar medium. We show that these model variants can in principle be discriminated using the relation between the star formation rate and galaxy stellar mass.

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The formation of supermassive black holes from Population III.1 seeds. III. Galaxy evolution and black hole growth from semi-analytic modelling

We present an implementation of Pop III.1 seeding of supermassive black holes (SMBHs) in a theoretical model of galaxy formation and evolution to assess the growth the SMBH population and the properties of the host galaxies. The model of Pop III.1 seeding involves SMBH formation at redshifts $z\gtrsim 20$ in dark matter minihalos that are isolated from external radiative feedback, parameterized by isolation distance $d_{\rm iso}$. Within a standard $Λ$CDM cosmology, we generate dark matter halos using the code PINOCCHIO and seed them according to the Pop III.1 scenario, exploring values of $d_{\rm iso}$ from 50 to 100~kpc (proper distance). We consider two alternative cases of SMBH seeding: a Halo Mass Threshold (HMT) model in which all halos $>7\times10^{10}\:M_\odot$ are seeded with $\sim 10^5\:M_\odot$ black holes; an All Light Seed (ALS) model in which all halos are seeded with low, stellar-mass black holes. We follow the redshift evolution of the halos, populating them with galaxies using the GAlaxy Evolution and Assembly theoretical model of galaxy formation, including accretion on SMBHs and related feedback processes. Here we present predictions for the properties of galaxy populations, focusing on stellar masses, star formation rates, and black hole masses. The local, $z\sim0$ metrics of occupation fraction as a function of the galaxy stellar mass, galaxy stellar mass function (GSMF), and black hole mass function (BHMF) all suggest a constraint of $d_{\rm iso}<75\:$kpc. We discuss the implications of this result for the Pop III.1 seeding mechanism.

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Virgo Filaments V: Disrupting the Baryon Cycle in the NGC 5364 Galaxy Group

The Virgo Filament Survey (VFS) is a comprehensive study of galaxies that reside in the extended filamentary structures surrounding the Virgo Cluster, out to 12 virial radii. The primary goal is to characterize all of the dominant baryonic components within galaxies and to understand whether and how they are affected by the filament environment. A key constituent of VFS is a narrowband H$α$ imaging survey of over 600 galaxies, VFS-H$α$. The H$α$ images reveal detailed, resolved maps of the ionized gas and massive star-formation. This imaging is particularly powerful as a probe of environmentally-induced quenching because different physical processes affect the spatial distribution of star formation in different ways. In this paper, we present the first results from the VFS-H$α$ for the NGC~5364 group, a low-mass ($\log_{10}(M_{dyn}/M_\odot) < 13)$ system located at the western edge of the Virgo~III filament. We combine H$α$ imaging with resolved H~I observations from MeerKAT for eight group members. These galaxies exhibit peculiar morphologies, including strong distortions in the stars and the gas, truncated H~I and H$α$ disks, H~I tails, extraplanar H$α$ emission, and off-center H$α$ emission. These signatures are suggestive of environmental processing such as tidal interactions, ram pressure stripping, and starvation. We quantify the role of ram pressure stripping expected in this group, and find that it can explain the cases of H~I tails and truncated H-alpha for all but one of the disk-dominated galaxies. Our observations indicate that multiple physical mechanisms are disrupting the baryon cycle in these group galaxies.

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The impact of ram pressure on cluster galaxies, insights from GAEA and TNG

Ram pressure stripping (RPS) has a non-negligible impact on the gas content of cluster galaxies. We use the semi-analytic model GAEA and the hydro-simulation TNG to investigate whether cluster galaxies suffer a strong RPS that is sufficient to remove a significant fraction of their gas during the first pericentric passage. We estimate that a ram pressure of $10^{-10.5}$, $10^{-12} $, $10^{-13.5} $ $g cm^{-1} s^{-2}$ can remove at most $90\%$, $50\%$, and $20\%$ of the cold gas reservoir from low-mass galaxies with $9<\log M_{\star}/{\rm M}_{\odot} <9.5$, assuming the gas can be stripped instantaneously. We then use this information to divide the phase space diagram into `strong', `moderate', `weak', and `no' RPS zones. By tracing the orbit of galaxies since $2.5R_{vir}$, we find in both GAEA and TNG that about half of the galaxies in Virgo-like halos ($\log M_h / M_{\odot} \sim 14 $) did not suffer strong RPS during the first pericentric passage. In Coma-like halos ($\log M_h / M_{\odot} \sim 15$), almost all galaxies have suffered strong RPS during the first pericentric passage, which can remove all gas from low-mass galaxies but is insufficient to significantly reduce the gas content of more massive galaxies. In general, results from TNG and GAEA are consistent, with the RPS being only slightly stronger in TNG than in GAEA. Our findings suggest that most cluster galaxies will maintain a notable fraction of their gas and continue forming stars after the first pericentric passage, except for those with low stellar mass ($\log M_{\star}/{\rm M}_{\odot} <9.5$) in very massive halos ($\log M_{h}/{\rm M}_{\odot} > 15$).

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Galaxy Assembly and Evolution in the P-Millennium simulation: galaxy clustering

[abridged] We present results from the latest version of the GAEA theoretical model of galaxy formation coupled with merger trees extracted from the Planck Millennium Simulation (PMS). With respect to the Millennium Simulation, the PMS provides a better mass resolution, a larger volume and assumes cosmological parameters consistent with latest results from the Planck mission. The model includes a treatment for the partition of cold gas into atomic and molecular (H$_2$) components; a better treatment for environmental processes; an updated modelling of cold gas accretion on Super-Massive Black Holes. We compare GAEA predictions based on the PMS, with model realizations based on other simulations in the Millennium Suite, showing that the new model provides a remarkable consistency for most statistical properties of galaxy populations. We interpret this as due to the interplay between AGN feedback and H$_2$-based SFR, as model versions considering only one of the two mechanisms do not show the same level of consistency. We then compare model predictions with available data for the galaxy 2-point correlation function (2pCF) in the redshift range 0<z$\lesssim$3. We show that GAEA runs correctly recover the main dependencies of the 2pCF as a function of stellar mass, star formation activity, HI-content and redshift for galaxies more massive than 10$^{9}$ M$_\odot$. These results suggest that our model correctly captures both the distribution of galaxy populations in the Large Scale Structure and the interplay between the main physical processes regulating their baryonic content, both for central and satellite galaxies. The model predicts a small redshift evolution of the clustering amplitude, that results in an overprediction of z$\sim$3 clustering strength with respect to the available estimates, but is still consistent with data within 1-$σ$ uncertainties.

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Discovering Large-Scale Structure at $2<z<5$ in the C3VO Survey

The Charting Cluster Construction with VUDS and ORELSE (C3VO) survey is an ongoing imaging and spectroscopic campaign aiming to map out the growth of structure up to $z\sim5$ and was born from the combination of the Visible Multi-Object Spectrograph Ultra Deep Survey and the Observations of Redshift Evolution in Large-Scale Environments (ORELSE) survey. As we previously accomplished with the ORELSE survey, we apply our technique known as Voronoi tessellation Monte Carlo (VMC) mapping to search for serendipitous galaxy overdensities at $2 14$ and $2 14.5$. In the C3VO fields, we were able to recover many of the previously known structures in the literature as well as find hundreds of new overdensity candidates, once again demonstrating the powerful capabilities of VMC mapping when applied to wide-field optical and infrared galaxy evolution surveys at ever higher redshifts.

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Molecular gas and dust properties in $z>7$ quasar hosts

Observational campaigns hunting the elusive reservoirs of cold gas in the host galaxies of quasars at the epoch of reionization (EoR) are crucial for studying the formation and evolution of the first massive systems at early epochs. We present new Northern Extended Millimeter Array (NOEMA) observations tracing CO(6--5) and CO(7--6) emission lines as well as the underlying continuum in five of the eight quasars at redshift $z>7$ known to date, thus completing the survey of the cold molecular gas reservoir in the host galaxies of the first quasars. Combining NOEMA observations with archival Atacama Large Millimeter/submillimeter Array (ALMA) data, we modeled the far-infrared spectral energy distribution with a modified blackbody function to measure dust properties and star formation rates. We used CO and [CII] lines to derive molecular gas masses, which we compared with results from semi-analytic models and observations of galaxies at different epochs. No statistically significant detection of CO emission lines was reported for the five quasars in this sample, resulting in a relatively low amount of cold molecular gas in the host when compared with galaxies at later epochs. Nonetheless, gas-to-dust ratios are consistent with the local value, suggesting that the scaling relation between dust and cold gas holds up to $z>7$. Quasars at the EoR show star formation efficiencies that are among the highest observed so far and comparable with those observed in luminous quasars at Cosmic Noon and those predicted for the brightest ($L_{bol}>3\times10^{46}$ erg s$^-1$) quasar objects drawn from the semi-analytic model GAEA. Quasar host galaxies at the EoR are undergoing an intense phase of star formation, which suggests a strong coupling between the luminous phase of the quasar and the rapid growth of the host.

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Cosmic quenching

The quenching of star formation activity represents a critical phase for a non-negligible fraction of the observed galaxy population at all cosmic epochs, marking a transition from an epoch of intense mass growth to an extended period of passive evolution. Over the past years, we have collected a detailed characterization of how the fraction of quenched galaxies evolves as a function of cosmic time (it grows at later cosmic epochs), and correlates with the physical properties of galaxies (more massive galaxies, that also tend to be bulge-dominated, are more likely to be quenched) and with their environment (denser environments host larger fractions of quiescent galaxies). Different physical processes can lead to a suppression of star formation. These include internal processes (processes that do not depend on the environment in which galaxies live, e.g. stellar and AGN feedback mechanisms) and processes that instead depend on the environment (e.g. mergers, gas stripping processes). In this chapter, we summarize the observational and theoretical status of the field, highlighting the most recent results and the questions that are yet to be answered. We also summarize our view on the expected developments in the next few years.

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The diverse star formation histories of early massive, quenched galaxies in modern galaxy formation simulations

We present a comprehensive study of the star formation histories of massive-quenched galaxies at $z=3$ in 3 semi-analytic models (SHARK, GAEA, GALFORM) and 3 cosmological hydrodynamical simulations (EAGLE, IllustrisTNG, Simba). We study the predicted number density and stellar mass function of massive-quenched galaxies, their formation and quenching timescales and star-formation properties of their progenitors. Predictions are disparate in all these diagnostics, for instance: (i) some simulations reproduce the observed number density of very massive-quenched galaxies ($>10^{11}\rm M_{\odot}$) but underpredict the high density of intermediate-mass ones, while others fit well the lower masses but underpredict the higher ones; (ii) In most simulations, except for GAEA and EAGLE, most massive-quenched galaxies had starburst periods, with the most intense ones happening at $4 300\rm M_{\odot}\,yr^{-1}$; (iii) quenching timescales are in the range $\approx 20-150$~Myr depending on the simulation; among other differences. These disparate predictions can be tied to the adopted Active Galactic Nuclei (AGN) feedback model. For instance, the explicit black-hole (BH) mass dependence to trigger the "radio mode" in IllustrisTNG and Simba makes it difficult to produce quenched galaxies with intermediate stellar masses, also leading to higher baryon collapse efficiencies ($\approx 15-30$%); while the strong bolometric luminosity dependence of the AGN outflow rate in GAEA leads to BHs of modest mass quenching galaxies. Current observations are unable to distinguish between these different predictions due to the small sample sizes. However, these predictions are testable with current facilities and upcoming observations, allowing a "true physics experiment" to be carried out.

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Virgo Filaments IV: Using WISE to Measure the Modification of Star-Forming Disks in the Extended Regions Around the Virgo Cluster

Recent theoretical work and targeted observational studies suggest that filaments are sites of galaxy preprocessing. The aim of the WISESize project is to directly probe galaxies over the full range of environments to quantify and characterize extrinsic galaxy quenching in the local Universe. In this paper, we use GALFIT to measure the infrared 12$μ$m ($R_{12}$) and 3.4$μ$m ($R_{3.4}$) effective radii of 603 late-type galaxies in and surrounding the Virgo cluster. We find that Virgo cluster galaxies show smaller star-forming disks relative to their field counterparts at the $2.5σ$ level, while filament galaxies show smaller star-forming disks to almost $1.5σ$. Our data, therefore, show that cluster galaxies experience significant effects on their star-forming disks prior to their final quenching period. There is also tentative support for the hypothesis that galaxies are preprocessed in filamentary regions surrounding clusters. On the other hand, galaxies belonging to rich groups and poor groups do not differ significantly from those in the field. We additionally find hints of a positive correlation between stellar mass and size ratio for both rich group and filament galaxies, though the uncertainties on these data are consistent with no correlation. We compare our size measurements with the predictions from two variants of a state-of-the-art semi-analytic model (SAM), one which includes starvation and the other incorporating both starvation and ram-pressure stripping (RPS). Our data appear to disfavor the SAM, which includes RPS for the rich group, filament, and cluster samples, which contributes to improved constraints for general models of galaxy quenching.

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NeutralUniverseMachine: Predictions of HI gas in Different Theoretical Models

We investigate the distribution and evolution of HI gas in different theoretical models, including hydro-dynamical simulations (Illustris-TNG and SIMBA), semi-analytic models (GAEA), and the empirical models ( NeutralUniverseMachine; NUM). By comparing model predictions for the HI mass function (HIMF), HI-halo and HI-stellar mass relations, conditional HI mass function (CHIMF) and the halo occupation distribution (HOD) of HI-selected galaxies, we find that all models show reasonable agreement with the observed HIMF at $z\sim0$, but the differences become much larger at higher redshifts of $z=1$ and $z=2$. The HIMF of NUM shows remarkable agreement with the observation at $z=1$, whereas other models predict much lower amplitudes of HIMF at the high-mass end. Comparisons of CHIMF distributions indicate that the HIMF is dominated by halos of $10< \log(M_{\rm vir}/M_\odot) <11$ and $11< \log(M_{\rm vir}/M_\odot)<12$ at the low- and high-mass ends, respectively. From the HI HODs of central galaxies, we find that TNG100 overpredicts the number of central galaxies with high $M_{\rm HI}$ in massive halos and GAEA shows a very strong depletion of HI gas in quenched centrals of massive halos. The main cause of the differences is the AGN feedback mechanisms implemented in different models.

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Efficient formation of a massive quiescent galaxy at redshift 4.9

Within the established framework of structure formation, galaxies start as systems of low stellar mass and gradually grow into far more massive galaxies. The existence of massive galaxies in the first billion years of the Universe, suggested by recent observations, appears to challenge this model, as such galaxies would require highly efficient conversion of baryons into stars. An even greater challenge in this epoch is the existence of massive galaxies that have already ceased forming stars. However, robust detections of early massive quiescent galaxies have been challenging due to the coarse wavelength sampling of photometric surveys. Here we report the spectroscopic confirmation with the James Webb Space Telescope of the quiescent galaxy RUBIES-EGS-QG-1 at redshift $z=4.90$, 1.2 billion years after the Big Bang. Deep stellar absorption features in the spectrum reveal that the galaxy's stellar mass of $10^{11}\,M_\odot$, corroborated by the mass implied by its gas kinematics, formed in a short $200\,$Myr burst of star formation, after which star formation activity dropped rapidly and persistently. According to current galaxy formation models, systems with such rapid stellar mass growth and early quenching are too rare to plausibly occur in the small area probed spectroscopically with JWST. Instead, the discovery of RUBIES-EGS-QG-1 implies that early massive quiescent galaxies can be quenched earlier or exhaust gas available for star formation more efficiently than currently assumed.

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