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Pietro Bergamini

Publications and source records attributed to Pietro Bergamini.

At least 37 records · Page 2Linked to original sources
arXiv2024

The powerful lens galaxy cluster PLCK G287.0+32.9 ($θ_E \sim 43''$)

We present a new high-precision strong lensing model of PLCK G287.0$+$32.9, a massive lens galaxy cluster at $z=0.383$, with the aim to get an accurate estimation of its effective Einstein radius and total mass distribution. We also present a spectroscopic catalog containing accurate redshift measurements for 490 objects, including multiply-lensed sources and cluster member galaxies. We exploit high-quality spectroscopic data from three pointings of the VLT Multi Unit Spectroscopic Explorer, covering a central $3~\rm{arcmin}^2$ region of the cluster. We complete the spectroscopic catalog by including redshift measurements from VLT-VIMOS and KECK-DEIMOS. We identify 129 spectroscopic cluster member galaxies, with redshift values $0.360 \leq z \leq 0.405$ and $m_{\rm{F160W}} \leq 21$, and 24 photometric ones identified with a Convolutional Neural Network from ancillary HST imaging. We also identify 114 multiple images from 28 background sources, of which 84 images from 16 sources are new and the remaining ones were identified in previous work. The best-fitting lens model shows a root mean square separation value between the predicted and observed positions of the multiple images of $0.75''$, corresponding to an improvement in reconstructing the observed positions of the multiple images of a factor of $2.5$ with respect to previous models. Using the predictive power of our new lens model we find 3 new multiple images and we confirm the configuration of three systems of multiple images that were not used for the optimization of the model. The derived total mass distribution confirms this cluster to be a very prominent gravitational lens with an effective Einstein $θ_{E} = 43.4'' \pm 0.1''$, that is in agreement with previous estimates and corresponds to a total mass enclosed in the critical curve of $M_E = {3.33}_{-0.07}^{+0.02} \times{ 10^{14} M_\odot}$.

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arXiv2024

An improved Magellan weak lensing analysis of the galaxy cluster Abell 2744

We present a new weak lensing analysis of the Hubble Frontier Fields galaxy cluster Abell 2744 ($z$ = 0.308) using new Magellan/MegaCam multi-band $gri$ imaging data. We carry out our study by applying brand-new PSF and shape measurement softwares that allow for the use of multi-band data simultaneously, which we first test on Subaru/Suprime-Cam $BR_cz'$ imaging data of the same cluster. The projected total mass of this system within $2.35 \, \mathrm{Mpc}$ from the south-west BCG is $(2.56 \pm 0.26) \times 10^{15} \, \mathrm{M}_\odot$, which makes Abell 2744 one of the most massive clusters known. This value is consistent, within the errors, with previous weak lensing and dynamical studies. Our analysis reveals the presence of three high-density substructures, thus supporting the picture of a complex merging scenario. This result is also confirmed by a comparison with a recent strong lensing study based on high-resolution JWST imaging. Moreover, our reconstructed total mass profile nicely agrees with an extrapolation of the strong lensing best-fit model up to several Mpc from the BCG centre.

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arXiv2023

Enhanced Sub-kpc Scale Star-formation: Results From A JWST Size Analysis of 341 Galaxies At 5<z<14

We present a comprehensive search and analysis of high-redshift galaxies in a suite of nine public JWST extragalactic fields taken in Cycle 1, covering a total effective search area of $\sim358{\rm arcmin^2}$. Through conservative ($8σ$) photometric selection, we identify 341 galaxies at $5 1.5\,σ$ below the derived size-mass slope. These compact sources exhibit a high star formation surface density $Σ_{\rm SFR}>10\,M_\odot\,{\rm yr^{-1}\,kpc^{-2}}$, a range in which only $<0.01\,\%$ of the local star-forming galaxy sample is found. For those with available NIRSpec data, no evidence of ongoing supermassive black hole accretion is observed. A potential explanation for the observed high [OIII]-to-Hbeta ratios could be high shock velocities, likely originating within intense star-forming regions characterized by high $Σ_{\rm SFR}$. Lastly, we find that the rest-frame UV and optical sizes of our sample are comparable. Our results are consistent with these early galaxies building up their structures inside-out and yet to exhibit the strong color gradient seen at lower redshift.

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arXiv2023

Exploring the low-mass regime of galaxy-scale strong lensing: Insights into the mass structure of cluster galaxies

We aim at a direct measurement of the compactness of three galaxy-scale lenses in massive clusters, testing the accuracy of the scaling laws that describe the members in strong lensing (SL) models of galaxy clusters. We selected the multiply imaged sources MACS J0416.1$-$2403 ID14 ($z=3.221$), MACS J0416.1$-$2403 ID16 ($z=2.095$), and MACS J1206.2$-$0847 ID14 ($z=3.753$). Eight images were observed for the first SL system, and six for the latter two. We focused on the main deflector of each galaxy-scale SL system (identified as members 8971, 8785, and 3910, respectively), and modelled its total mass distribution with a truncated isothermal sphere. We accounted for the lensing effects of the remaining cluster components, and included the uncertainty on the cluster-scale mass distribution through a bootstrapping procedure. We measured a truncation radius value of $6.1^{+2.3}_{-1.1} \, \mathrm{kpc}$, $4.0^{+0.6}_{-0.4} \, \mathrm{kpc}$, and $5.2^{+1.3}_{-1.1} \, \mathrm{kpc}$ for members 8971, 8785, and 3910, respectively. Alternative non-truncated models with a higher number of free parameters do not lead to an improved description of the SL system. We measured the stellar-to-total mass fraction within the effective radius $R_e$ for the three members, finding $0.51\pm0.21$, $1.0\pm0.4$, and $0.39\pm0.16$, respectively. We find that a parameterisation of the properties of cluster galaxies in SL models based on power-law scaling relations with respect to the total luminosity cannot accurately describe their compactness over their full total mass range. Our results agree with modelling of the cluster members based on the Fundamental Plane relation. Finally, we report good agreement between our values of the stellar-to-total mass fraction within $R_e$ and those of early-type galaxies from the SLACS Survey. Our work significantly extends the regime of the current samples of lens galaxies.

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arXiv2023

A persistent excess of galaxy-galaxy strong lensing observed in galaxy clusters

Previous studies have revealed that the estimated probability of galaxy-galaxy strong lensing in observed galaxy clusters exceeds the expectations from the $Λ$ Cold Dark Matter cosmological model by one order of magnitude. We aim to understand the origin of this excess by analyzing a larger set of simulated galaxy clusters and investigating how the theoretical expectations vary under different adopted prescriptions and numerical implementations of star formation and feedback in simulations. We perform a ray-tracing analysis of 324 galaxy clusters from the Three Hundred project, comparing the Gadget-X and Gizmo-Simba runs. These simulations, which start from the same initial conditions, are performed with different implementations of hydrodynamics and galaxy formation models tailored to match different observational properties of the Intra-Cluster-Medium and cluster galaxies. We find that galaxies in the Gizmo-Simba simulations develop denser stellar cores than their Gadget-X counterparts. Consequently, their probability for galaxy-galaxy strong lensing is higher by a factor of $\sim 3$. This increment is still insufficient to fill the gap with observations, as a discrepancy by a factor $\sim 4$ still persists. In addition, we find that several simulated galaxies have Einstein radii that are too large compared to observations. We conclude that a persistent excess of galaxy-galaxy strong lensing exists in observed galaxy clusters. The origin of this discrepancy with theoretical predictions is still unexplained in the framework of the cosmological hydrodynamical simulations. This might signal a hitherto unknown issue with either the simulation methods or our assumptions regarding the standard cosmological model.

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arXiv2023

Near-infrared characterization of ultra-diffuse galaxies in Abell 2744 by JWST/NIRISS imaging

We present a search and characterization of ultra-diffuse galaxies (UDGs) in the Frontier Fields cluster Abell~2744 at $z=0.308$. We use JWST/NIRISS F200W observations, acquired as part of the GLASS-JWST Early Release Science Program, aiming to characterize morphologies of cluster UDGs and their diffuse stellar components. A total number of 22 UDGs are identified by our selection criteria using morphological parameters, down to stellar mass of $\sim10^{7}M_{\odot}$. The selected UDGs are systematically larger in effective radius in F200W than in HST/ACS F814W images, which implies that some of them would not have been identified as UDGs when selected at rest-frame optical wavelengths. In fact, we find that about one third of the UDGs were not previously identified based on the F814W data. We observe a flat distribution of the UDGs in the stellar mass-size plane, similar to what is found for cluster quiescent galaxies at comparable mass. Our pilot study using the new JWST F200W filter showcases the efficiency of searching UDGs at cosmological distances, with 1/30 of the exposure time of the previous deep observing campaign with HST. Further studies with JWST focusing on spatially-resolved properties of individual sources will provide insight into their origin.

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arXiv2023

Early Results from GLASS-JWST. XXI: Rapid assembly of a galaxy at z=6.23 revealed by its C/O abundance

The abundance of carbon relative to oxygen (C/O) is a promising probe of star formation history in the early universe, as the ratio changes with time due to production of these elements by different nucleosynthesis pathways. We present a measurement of $\log{\mathrm{(C/O)}} = -1.01\pm0.12$ (stat) $\pm0.15$ (sys) in a $z=6.23$ galaxy observed as part of the GLASS-JWST Early Release Science Program. Notably, we achieve good precision thanks to the detection of the rest-frame ultraviolet O III], C III], and C IV emission lines delivered by JWST/NIRSpec. The C/O abundance is $\sim$0.8 dex lower than the solar value and is consistent with the expected yield from core-collapse supernovae, indicating that longer-lived intermediate mass stars have not fully contributed to carbon enrichment. This in turn implies rapid buildup of a young stellar population with age $\lesssim100$ Myr in a galaxy seen $\sim$900 million years after the Big Bang. Our chemical abundance analysis is consistent with spectral energy distribution modeling of JWST/NIRCam photometric data, which indicates a current stellar mass $\log\,\mathrm{M}_* / \mathrm{M_{sun}} = 8.4^{+0.4}_{-0.2}$ and specific star formation rate sSFR $\simeq 20$ Gyr$^{-1}$. These results showcase the value of chemical abundances and C/O in particular to study the earliest stages of galaxy assembly.

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arXiv2023

The nature of an ultra-faint galaxy in the cosmic Dark Ages seen with JWST

In the first billion years after the Big Bang, sources of ultraviolet (UV) photons are believed to have ionized intergalactic hydrogen, rendering the Universe transparent to UV radiation. Galaxies brighter than the characteristic luminosity $L^{*}$ do not provide enough ionizing photons to drive this cosmic reionization. Fainter galaxies are thought to dominate the photon budget; however they are surrounded by neutral gas that prevents the escape of the Lyman-$α$ photons, which has been the dominant way to identify them so far. JD1 was previously identified as a triply-imaged galaxy with a magnification factor of 13 provided by the foreground cluster Abell 2744, and a photometric redshift of $z\sim10$. Here we report the spectroscopic confirmation of this very low luminosity ($\sim0.05 L^{*}$) galaxy at $z=9.79$, observed 480 Myr after the Big Bang, by means of the identification of the Lyman break and redward continuum, as well as multiple $\gtrsim4σ$ emission lines, with the Near-InfraRed Spectrograph (NIRSpec) and Near-InfraRed Camera (NIRCam) instruments. The combination of the James Webb Space Telescope (JWST) and gravitational lensing shows that this ultra-faint galaxy ($M_{\rm UV}=-17.35$) -- with a luminosity typical of the sources responsible for cosmic reionization -- has a compact ($\sim$150 pc) and complex morphology, low stellar mass (10$^{7.19}$ M$_\odot$), and subsolar ($\sim$0.6 $Z_{\odot}$) gas-phase metallicity.

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arXiv2023

Early results from GLASS-JWST. XIV: A spectroscopically confirmed protocluster 650 million years after the Big Bang

We present the spectroscopic confirmation of a protocluster at $z=7.88$ behind the galaxy cluster Abell2744 (hereafter A2744-z7p9OD). Using JWST NIRSpec, we find seven galaxies within a projected radius of 60kpc. Although the galaxies reside in an overdensity around $>20\times$ greater than a random volume, they do not show strong Lyman-alpha emission. We place 2-$σ$ upper limits on the rest-frame equivalent width $<16$-$28$AA. Based on the tight upper limits to the Lyman-alpha emission, we constrain the volume-averaged neutral fraction of hydrogen in the intergalactic medium to be $x_{\rm HI} > 0.45$ (68% CI). Using an empirical $M_{\rm UV}$-$M_{\rm halo}$ relation for individual galaxies, we estimate that the total halo mass of the system is $\gtrsim 4\times10^{11}\,M_\odot$. Likewise, the line of sight velocity dispersion is estimated to be $1100 \pm 200$km/s. Using an empirical relation, we estimate the present-day halo mass of A2744-z7p9OD to be $\sim2\times10^{15}\,M_\odot$, comparable to the Coma cluster. A2744-z7p9OD is the highest redshift spectroscopically confirmed protocluster to date, demonstrating the power of JWST to investigate the connection between dark-matter halo assembly and galaxy formation at very early times with medium-deep observations at $<20$hrs total exposure time. Follow-up spectroscopy of the remaining photometric candidates of the overdensity will further refine the features of this system and help characterize the role of such overdensities in cosmic reionization.

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arXiv2023

Early Results from GLASS-JWST. XIX: A High Density of Bright Galaxies at $z\approx10$ in the Abell 2744 Region

We report the detection of a high density of redshift $z\approx 10$ galaxies behind the foreground cluster Abell 2744, selected from imaging data obtained recently with NIRCam onboard {\it JWST} by three programs -- GLASS-JWST, UNCOVER, and DDT\#2756. To ensure robust estimates of the lensing magnification $μ$, we use an improved version of our model that exploits the first epoch of NIRCam images and newly obtained MUSE spectra, and avoids regions with $μ>5$ where the uncertainty may be higher. We detect seven bright $z\approx 10$ galaxies with demagnified rest-frame $-22 \lesssim M_{\rm UV}\lesssim -19$ mag, over an area of $\sim37$ sq. arcmin. Taking into account photometric incompleteness and the effects of lensing on luminosity and cosmological volume, we find that the density of $z\approx 10$ galaxies in the field is about $10\times$ ($3\times$) larger than the average at $M_{UV}\approx -21~ (-20)$ mag reported so far. The density is even higher when considering only the GLASS-JWST data, which are the deepest and the least affected by magnification and incompleteness. The GLASS-JWST field contains 5 out of 7 galaxies, distributed along an apparent filamentary structure of 2 Mpc in projected length, and includes a close pair of candidates with $M_{\rm UV}< -20$ mag having a projected separation of only 16 kpc. These findings suggest the presence of a $z\approx 10$ overdensity in the field. In addition to providing excellent targets for efficient spectroscopic follow-up observations, our study confirms the high density of bright galaxies observed in early {\it JWST} observations, but calls for multiple surveys along independent lines of sight to achieve an unbiased estimate of their average density and a first estimate of their clustering.

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arXiv2023

Early results from GLASS-JWST. XX: Unveiling a population of "red-excess'' galaxies in Abell2744 and in the coeval field

We combine JWST/NIRCam imaging and MUSE data to characterize the properties of galaxies in different environmental conditions in the cluster Abell2744 ($z=0.3064$) and in its immediate surroundings. We investigate how galaxy colors, morphology and star forming fractions depend on wavelength and on different parameterizations of environment. Our most striking result is the discovery of a ``red-excess'' population in F200W$-$F444W colors both in the cluster regions and the field. These galaxies have normal F115W$-$F150W colors, but are up to 0.8 mag redder than red sequence galaxies in F200W$-$F444W. They also have rather blue rest frame B$-$V colors. {Galaxies in the field and at the cluster virial radius are overall characterized by redder colors, but galaxies with the largest color deviations are found in the field and in the cluster core. Several results} suggest that mechanisms taking place in these regions might be more effective in producing these colors. Looking at their morphology, many cluster galaxies show signatures consistent with ram pressure stripping, while field galaxies have features resembling interactions and mergers. Our hypothesis is that these galaxies are characterized by dust enshrouded star formation: a JWST/NIRSpec spectrum for one of the galaxies is dominated by a strong PAH at 3.3$μm$, suggestive of dust obscured star formation. Larger spectroscopic samples are needed to understand if the color excess is due exclusively to dust-obscured star formation, and the role of environment in triggering it.

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arXiv2023

The GLASS-JWST Early Release Science Program. III. Strong lensing model of Abell 2744 and its infalling regions

We present a new high-precision, JWST-based, strong lensing model for the galaxy cluster Abell 2744 at $z=0.3072$. By combining the deep, high-resolution JWST imaging from the GLASS-JWST and UNCOVER programs and a Director's Discretionary Time program, with newly obtained VLT/MUSE data, we identify 32 multiple images from 11 background sources lensed by two external sub-clusters at distances of ~160" from the main cluster. The new MUSE observations enable the first spectroscopic confirmation of a multiple image system in the external clumps. Moreover, the re-analysis of the spectro-photometric archival and JWST data yields 27 additional multiple images in the main cluster. The new lens model is constrained by 149 multiple images ($\sim66\%$ more than in our previous Bergamini et al. 2023 model) covering an extended redshift range between 1.03 and 9.76. The subhalo mass component of the cluster includes 177 member galaxies down to $m_{\rm F160W}=21$, 163 of which are spectroscopically confirmed. Internal velocity dispersions are measured for 85 members. The new lens model is characterized by a remarkably low scatter between predicted and observed positions of the multiple images (0.43"). This precision is unprecedented given the large multiple image sample, the complexity of the cluster mass distribution, and the large modeled area. The improved accuracy and resolution of the cluster total mass distribution provides a robust magnification map over a $\sim\!45$ arcmin$^2$ area, which is critical for inferring the intrinsic physical properties of the highly magnified, high-$z$ sources. The lens model and the new MUSE redshift catalog are released with this publication.

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arXiv2023

The production of ionizing photons in UV-faint z~3-7 galaxies

The demographics of the production and escape of ionizing photons from UV-faint early galaxies is a key unknown in discovering the primary drivers of reionization. With the advent of JWST it is finally possible to observe the rest-frame optical nebular emission from individual sub-L$^*$ z>3 galaxies to measure the production of ionizing photons, $ξ_\mathrm{ion}$. Here we study a sample of 370 z~3-7 galaxies spanning -23 0.5) in our sample, based on their photometric properties, even amongst the Lyman-alpha selected galaxies. This work demonstrates that considering the full distribution of $ξ_\mathrm{ion}$ across galaxy properties is important for assessing the primary drivers of reionization.

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arXiv2022

Early Results from GLASS-JWST. I: Confirmation of Lensed $z\geqslant7$ Lyman-Break Galaxies Behind the Abell 2744 Cluster With NIRISS

We present the first search for $z\geqslant7$, continuum-confirmed sources with NIRISS/WFS spectroscopy over the Abell 2744 Frontier Fields cluster, as part of the GLASS-JWST ERS survey. With $\sim15$ hrs of pre-imaging and multi-angle grism exposures in the F115W, F150W, and F200W filters, we describe the general data handling (i.e., reduction, cleaning, modeling, and extraction processes) and analysis for the GLASS-JWST survey. We showcase the power of JWST to peer deep into reionization, when most intergalactic hydrogen is neutral, by confirming two galaxies at $z=8.04\pm0.15$ and $z=7.90\pm0.13$ by means of their Lyman breaks. Fainter continuum spectra are observed in both the F150W and F200W bands, indicative of blue ($-1.69$ and $-1.33$) UV slopes and moderately-bright absolute magnitudes ($-20.37$ and $-19.68$ mag). We do not detect strong Ly$α$ in either galaxy, but do observe tentative ($\sim2.7-3.8σ$) HeII$λ$1640 A, OIII]$λλ$1661,1666 A, and NIII]$λλ$1747,1749 A line emission in one, suggestive of low metallicity, star-forming systems with possible non-thermal contributions. These novel observations provide a first look at the extraordinary potential of JWST/NIRISS for confirming representative samples of bright $z\geqslant7$ sources in the absence of strong emission lines, and gain unprecedented insight into their contributions towards cosmic reionization.

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arXiv2022

Early results from GLASS-JWST. IX: First spectroscopic confirmation of low-mass quiescent galaxies at $z>2$ with NIRISS

How passive galaxies form, and the physical mechanisms which prevent star formation over long timescales, are some of the most outstanding questions in understanding galaxy evolution. The properties of quiescent galaxies over cosmic time provide crucial information to identify the quenching mechanisms. Passive galaxies have been confirmed and studied out to $z\sim4$, but all of these studies have been limited to massive systems (mostly with $\log{(M_{\rm star}/M_{\odot})}>10.8$). Using James Webb Space Telescope (JWST) NIRISS grism slitless spectroscopic data from the GLASS JWST ERS program, we present spectroscopic confirmation of two quiescent galaxies at $z_{\rm spec}=2.650^{+0.004}_{-0.006}$ and $z_{\rm spec}=2.433^{+0.032}_{-0.016}$ (3$σ$ errors) with stellar masses of $\log{(M_{\rm star}/M_{\odot})}=10.53^{+0.18}_{-0.06}$ and $\log{(M_{\rm star}/M_{\odot})}=9.93^{+0.06}_{-0.07}$ (corrected for magnification factors of $μ=2.0$ and $μ=2.1$, respectively). The latter represents the first spectroscopic confirmation of the existence of low-mass quiescent galaxies at cosmic noon, showcasing the power of JWST to identify and characterize this enigmatic population.

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arXiv2022

Galaxies in the central regions of simulated galaxy clusters

In this paper, we assess the impact of numerical resolution and of the implementation of energy input from AGN feedback models on the inner structure of cluster sub-haloes in hydrodynamic simulations. We compare several zoom-in re-simulations of a sub-sample of the cluster-sized haloes studied in Meneghetti et al. (2020), obtained by varying mass resolution, softening length and AGN energy feedback scheme. We study the impact of these different setups on the subhalo abundances, their radial distribution, their density and mass profiles and the relation between the maximum circular velocity, which is a proxy for subhalo compactness. Regardless of the adopted numerical resolution and feedback model, subhaloes with masses Msub < 1e11Msun/h, the most relevant mass-range for galaxy-galaxy strong lensing, have maximum circular velocities ~30% smaller than those measured from strong lensing observations of Bergamini et al. (2019). We also find that simulations with less effective AGN energy feedback produce massive subhaloes (Msub> 1e11 Msun/h ) with higher maximum circular velocity and that their Vmax - Msub relation approaches the observed one. However the stellar-mass number count of these objects exceeds the one found in observations and we find that the compactness of these simulated subhaloes is the result of an extremely over-efficient star formation in their cores, also leading to larger-than-observed subhalo stellar mass. We conclude that simulations are unable to simultaneously reproduce the observed stellar masses and compactness (or maximum circular velocities) of cluster galaxies. Thus, the discrepancy between theory and observations that emerged from the analysis of Meneghetti et al. (2020) persists. It remains an open question as to whether such a discrepancy reflects limitations of the current implementation of galaxy formation models or the LCDM paradigm.

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arXiv2022

The probability of galaxy-galaxy strong lensing events in hydrodynamical simulations of galaxy clusters

Meneghetti et al. (2020) recently reported an excess of galaxy-galaxy strong lensing (GGSL) in galaxy clusters compared to expectations from the LCDM cosmological model. Theoretical estimates of the GGSL probability are based on the analysis of numerical hydrodynamical simulations in the LCDM cosmology. We quantify the impact of the numerical resolution and AGN feedback scheme adopted in cosmological simulations on the predicted GGSL probability and determine if varying these simulation properties can alleviate the gap with observations. We repeat the analysis of Meneghetti et al. (2020) on cluster-size halos simulated with different mass and force resolutions and implementing several independent AGN feedback schemes. We find that improving the mass resolution by a factor of ten and twenty-five, while using the same galaxy formation model that includes AGN feedback, does not affect the GGSL probability. We find similar results regarding the choice of gravitational softening. On the contrary, adopting an AGN feedback scheme that is less efficient at suppressing gas cooling and star formation leads to an increase in the GGSL probability by a factor between three and six. However, we notice that such simulations form overly massive subhalos whose contribution to the lensing cross-section would be significant while their Einstein radii are too large to be consistent with the observations. The primary contributors to the observed GGSL cross-sections are subhalos with smaller masses, that are compact enough to become critical for lensing. The population with these required characteristics appears to be absent in simulations.

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arXiv2022

Improved strong lensing modelling of galaxy clusters using the Fundamental Plane: Detailed mapping of the baryonic and dark matter mass distribution of Abell S1063

From Hubble Frontier Fields photometry, and data from the Multi Unit Spectroscopic Explorer on the Very Large Telescope, we build the Fundamental Plane (FP) relation for the early-type galaxies of the cluster Abell S1063. We use this relation to develop an improved strong lensing model of the total mass distribution of the cluster, determining the velocity dispersions of all 222 cluster members included in the model from their measured structural parameters. Fixing the hot gas component from X-ray data, the mass density distributions of the diffuse dark matter haloes are optimised by comparing the observed and model-predicted positions of 55 multiple images of 20 background sources, distributed over the redshift range $0.73-6.11$. We determine the uncertainties on the model parameters with Monte Carlo Markov chains. Compared to previous works, our model allows for the inclusion of a scatter on the relation between the total mass and the velocity dispersion of cluster members, which also shows a shallower slope. We notice a lower statistical uncertainty on the value of some parameters, such as the core radius, of the diffuse mass component of the cluster. Thanks to a new estimate of the stellar mass of all members, we measure the cumulative projected mass profiles out to a radius of 350 kpc, for all baryonic and dark matter components of the cluster. At the outermost radius, we find a baryon fraction of $0.147 \pm 0.002$. We compare the sub-haloes as described by our model with recent hydrodynamical cosmological simulations. We find good agreement in terms of the stellar over total mass fraction. On the other hand, we report some discrepancies in terms of the maximum circular velocity, which is an indication of their compactness, and the sub-halo mass function in the central cluster regions.

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