arXiv subjects

Carlo Nipoti

Publications and source records attributed to Carlo Nipoti.

At least 19 recordsLinked to original sources

arXiv2026

On the Jeans criterion for hydrostatic and infalling gas

We study the local gravitational instability of non-rotating astrophysical fluids allowing for the presence of an external gravitational potential in addition to the fluid self-gravity. We present a self-consistent linear-perturbation analysis taking into account pressure and density gradients in the background medium. We explore two different steady-state configurations for the unperturbed gas: hydrostatic equilibrium and infall into a gravitational potential well. We show that in both cases the instability criterion is the classical Jeans criterion, which, contrary to previous claims, is not modified by the presence of the external gravitational field. While in the case of hydrostatic equilibrium linear local perturbations are always gravitationally stable, the conditions for gravitational instability can be met in the case of infalling gas, also in the presence of additional non-gravitational forces such as that due to a wind. We conclude that the Jeans criterion can have a role in regulating the formation of clumps and star clusters in streams or shells of gas infalling into galactic gravitational potential wells, as well as, on smaller scales, the fragmentation of gas in collapsing molecular clouds.

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arXiv2025

Dynamical mirages: how bar-induced resonant trapping can mimic substructure clustering in dynamical parameter spaces

The complex task of unraveling the assembly history of the Milky Way is in constant evolution with new substructures identified continuously. To properly validate and characterise the family of galactic progenitors, it is important to take into account all the effects that can shape the distribution of tracers in the Galaxy. First among the often overlooked actors of galactic dynamics is the rotating bar of the Milky Way that can affect orbital tracers in multiple ways. We want to fully characterise the effect of the rotating bar of the Milky Way on the distribution of galactic tracers, provide diagnostics helpful in identifying its effect and explore the implications for the search and identification of substructures. We use the in-house Orbital Integration Tool (OrbIT), built to include the full effect of the bar and exploit its multidimensional output to perform a complete dynamical characterisation of a large sample of carefully selected Milky Way stars with very precise astrometry. We identify conspicuous overdensities in several orbital parameter spaces and verify that they are caused by the bar-induced resonances. We also show how contamination by trapped tracers provides local density enhancements that mimic the clumping usually attributed to genuine substructures. We provide a new and expedite way of identifying resonant loci and, consequently, to estimate the contribution of stars trapped into orbital resonances to phase-space overdensities previously identified as candidate relics of past merging events. Among those analysed here, we found that the detections of Cluster 3 and Shakti seem to have gained a non-negligible boost from resonance-trapped stars. Nyx is the most extreme case, with 70% of assigned member stars lying on resonant orbit, strongly suggesting that it is not the genuine relic of a merger event but an overdensity caused by bar-induced resonances

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arXiv2025

Death by Impact: Evidence for Merger-Driven Quenching in a Collisional Ring Galaxy at Cosmic Noon

The role of interactions and mergers in the rapid quenching of massive galaxies in the early Universe remains uncertain, largely due to the difficulty of directly linking mergers to quenching. Collisional ring galaxies provide a unique opportunity, as their morphology allows precise dating of the interaction, which can then be compared to quenching timescales inferred from star formation histories. We study a gravitationally bound system at $z=1.61$ in the UDS field, composed of a Host galaxy ($M_\star = 10^{11.4} M_\odot$) with a collisional ring and an X-ray AGN, and the Bullet galaxy ($M_\star = 10^{11.2} M_\odot$), located at a projected distance of $\sim 8$ kpc. Combining JWST and HST imaging with Keck/MOSFIRE spectroscopy, we find compelling evidence for an ongoing starburst in the Host concurrent with rapid quenching in the Bullet. The ring, $\sim 20$ kpc in diameter, is expanding at $127^{+72}_{-29}$ km s$^{-1}$, implying the galaxies first collided 47--96 Myr ago. This timeline is consistent with the Host's current starburst and the Bullet's sudden quenching, strongly suggesting both phenomena were triggered by the interaction. Crucially, the Bullet shows no evidence of a preceding starburst, ruling out rapid gas consumption as the primary quenching channel. Instead, we suggest that merger-driven processes -- such as enhanced turbulence and disk instabilities -- may have suppressed star formation. An additional possibility, which we term the ``Dragon Effect,'' is that AGN-driven outflows from the Host disrupted the Bullet's low-density molecular gas, thereby preventing efficient star formation and accelerating quenching.

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arXiv2025

Mass loss and dynamical friction on the Fornax dSph galaxy in the Milky Way potential

We study the interplay between mass-loss and dynamical friction (DF) on the orbital decay of the Fornax dwarf spheroidal galaxy in the potential of the Milky Way (MW). Using a simplified single particle approach combined with a mass-loss rate extrapolated by $N-$body simulations we find that the the effect of a time-dependent mass partially compensates DF, and typically produces a much less evident decay of the pergalactic distance, thus confirming that $N-$body simulations in smooth MW potentials without DF can be taken as a good model of the dynamics of dwarf satellite galaxies.

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arXiv2025

The $10~\rm{kpc}$ collar of early-type galaxies -- probing evolution by focusing on the inner stellar density profile

Aims: In this work we aim to investigate the late evolution of ETGs, both observationally and theoretically, by focusing on the stellar mass density profile inside a fixed aperture, within $10 ~\rm{kpc}$ from the galaxy center. Methods: We first studied the stellar mass and mass-weighted density slope within $10 ~\rm{kpc}$, respectively $M_{*,10}$ and $\mathit{\Gamma_{*,10}}$, of a sample of early-type galaxies from the GAMA survey. We measured the $\mathit{\Gamma_{*,10}} - M_{*,10}$ relation and its evolution over the redshift range $0.17\leq z \leq 0.37$. We then built a toy model for the merger evolution of galaxies, based on N-body simulations, to explore to what extent the observed growth in $\mathit{\Gamma_{*,10}} - M_{*,10}$ relation is consistent with a dry-merger evolution scenario. Results: From the observations, we do not detect evidence for an evolution of the $\mathit{\Gamma_{*,10}} - M_{*,10}$ relation. We put an upper limit on the redshift derivative of the normalization$~(\mu)$ and slope$~(\beta)$of the $\mathit{\Gamma_{*,10}} - M_{*,10}$ relation $|\partial \mu/\partial \log (1+z)| \leq 0.13$ and $\left|\partial \beta/\partial \log (1+z)\right| \leq 1.10$, respectively. Simulations show that most mergers induce a decrease in $\mathit{\Gamma_{*,10}}$ and an increase in $M_{*,10}$, although some show a decrease in $M_{*,10}$, particularly for the most extended galaxies and smaller merger mass ratios. By combining the observations with our merger toy model, we placed an upper limit on $f_M = 11.2 \%$ in the redshift range $0.17 \leq z \leq 0.37$. Conclusions: While our measurement is limited by systematics, the application of our approach to samples with a larger redshift baseline, particularly with a time interval $\Delta t \geq 3.2~\mathrm{Gyr}$, should enable us to detect a signal and help us better understand the late growth of ETGs.

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arXiv2025

The dynamical evolution of the stellar clumps in the Sparkler galaxy

Recent JWST observations detected stellar clumps around the z=1.4 gravitationally lensed Sparkler galaxy (of stellar mass $M_*\sim 10^9\,\mathrm{M_\odot}$), with ages and metallicities compatible with globular clusters (GCs). However, most of their masses ($>10^6\,\mathrm{M_\odot}$) and sizes (>30 pc) are about 10 times those of GCs in the local Universe. To assess whether these clumps can evolve into GCs, we performed N-body simulations of their dynamical evolution from z=1.4 to z=0 (9.23 Gyr), under the effect of dynamical friction and tidal stripping. Dynamical friction is studied performing multiple runs of a clump system in a Sparkler-like spherical halo of mass $M_{200}\simeq 5\times 10^{11}\,\mathrm{M_\odot}$ (from the stellar-to-halo mass relation). For the tidal stripping, we simulated resolved clumps, orbiting in an external, static gravitational potential including the same halo as in the dynamical friction simulations and also a Sparkler-like stellar disk. Dynamical friction causes the clumps with mass $>10^7\,\mathrm{M_\odot}$ to sink into the galaxy central regions, possibly contributing to the bulge growth. In absence of tidal stripping, the mass distribution of the surviving clumps (40%) peaks at $5\times 10^6\,\mathrm{M_\odot}$, implying the presence of uncommonly over-massive clumps at z=0. Tidal shocks by the stellar disk strip considerable mass from low-mass clumps, even though their sizes remain larger than those of present-day GCs. When the surviving clumps are corrected for tidal stripping, their mass distribution peak shifts to $2\times 10^6\,\mathrm{M_\odot}$, compatible with massive GCs. Our simulations suggest that a fraction of the Sparkler clumps is expected to fall into the central regions, where they might become bulge fossil fragments or contribute to form a nuclear star cluster. The remaining clumps are too large in size to be progenitors of GCs.

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arXiv2025

Chemo-dynamics of the stellar component of the Sculptor dwarf galaxy II: dynamical properties and dark matter halo density

Dwarf galaxies satellite of the Milky Way are excellent laboratories for testing dark matter (DM) models and baryonic feedback implementation in simulations. The Sculptor 'classical' dwarf spheroidal galaxy, a system with two distinct stellar populations and high-quality data, offers a remarkable opportunity to study DM distributions in these galaxies. In this work, we infer the DM halo density distribution of Sculptor, applying a method based on spherically symmetric distribution functions depending on actions to fit the stellar structural and kinematic properties of Sculptor. The galaxy is represented via four components: two distinct stellar populations based on distribution functions, tracers within a fixed and dominant DM potential, plus the contribution of a third stellar component that accounts for possible sources of contamination. The model-data comparison accounts for the kinematics and metallicities of individual stars, allowing us to assign probabilities of membership to each star. The modeling is applied on the largest available set of spectroscopic data, which have not been previously analyzed with this objective. We find the DM distribution of Sculptor to have a logarithmic inner slope of 0.39+0.23-0.26 and a scale radius of 0.79+0.38-0.17 kpc at 1 sigma confidence level. Our results show that Sculptor DM density profile deviates from predictions of DM-only simulations at a 3 sigma level over a large range of radii. Our analysis suggests that the velocity distribution of Sculptor's two main stellar components is isotropic in the center and becomes radially anisotropic in the outskirts. Additionally, we provide predictions for the projected radial and tangential velocity dispersion profiles. We also present updated DM annihilation and decay J- and D-factors, finding J = 18.15+0.11-0.12 and D = 18.07+0.10-0.10 for an angular aperture of 0.5 degrees.

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arXiv2025

TDCOSMO XXI. Accurate stellar velocity dispersions of the SL2S lens sample and the fundamental plane of the lensing mass

We reanalyzed spectra that were taken as part of the SL2S lens galaxy survey with the goal to obtain the stellar velocity dispersion with a precision and accuracy sufficient for time-delay cosmography. In order to achieve this goal, we imposed stringent cuts on the signal-to-noise ratio (S/N), and employed recently developed methods to mitigate and quantify residual systematic errors that are transferred from template libraries and fitting process. We also quantified the covariance across the sample. For galaxy spectra with S/N $>20/$\AA, our new measurements have an average random uncertainty of 3-4\%, an average systematic uncertainty of 2\%, and a covariance across the sample of 1\%. We find a negligible covariance between spectra taken with different instruments. The systematic uncertainty and covariance need to be included when the sample is used as an external dataset in time-delay cosmography. We revisited empirical scaling relations of lens galaxies based on the improved kinematics. We show that the SL2S sample, the TDCOSMO time-delay lens sample, and the lower-redshift SLACS sample follow the same correlation of the effective radius, stellar velocity dispersion, and lensing mass, known as the lensing-mass fundamental plane, as the previously derived correlation that assumed isothermal mass profiles for the deflectors. We also derived for the first time the lensing-mass fundamental plane assuming free power-law mass density profiles, and we show that the three samples also follow the same correlation. This is consistent with a scenario in which massive galaxies evolve by growing their radii and mass, but stay within the plane.

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arXiv2025

Searching for rotation in X-COP galaxy clusters

We search for evidence of rotational support by analyzing the thermodynamic profiles of the intracluster medium (ICM) in a sample of nearby, massive galaxy clusters. For each object of the XMM-Newton Cluster Outskirts Project (X-COP) sample, we present axisymmetric models of rotating ICM with composite polytropic distributions, in equilibrium in spherically symmetric dark halos, exploring cases both with and without turbulent support in the ICM. The profile of rotation velocity and the distribution of turbulent velocity dispersion are described with flexible functional forms, consistent with the properties of synthetic clusters formed in cosmological simulations. The models are tuned via a Markov Chain Monte Carlo algorithm to reproduce the radial profiles of the thermodynamic variables as resolved in the XMM-Newton and Planck maps, and to be consistent with the mass distributions estimated either from weak lensing observations (when available) or under the assumption of a "universal" value of the baryon fraction. Our models indicate that there is room for non-negligible rotation in the ICM of massive clusters, with typical peak rotation speed 300 km/s and peak rotation-velocity-to-velocity-dispersion ratio of 0.3. According to our models, the ICM in Abell 2255 can have a rotation speed as high as 500 km/s, corresponding to a rotation-velocity-to-velocity-dispersion ratio of 0.3, at a distance of 100 kpc from the center, where the X-ray emissivity is still high. This makes Abell 2255 a very promising candidate for the presence of rotation in the ICM that could be detected with the currently operating XRISM observatory, as we demonstrate computing and analyzing a mock X-ray spectrum.

astro-ph.CO↗

arXiv2025

Evolution of massive quiescent galaxies via envelope accretion

Massive quiescent galaxies at high redshift are significantly more compact than their present-day counterparts. We investigate the roles, in determining this evolution, of major and minor mergers, and of the accretion of diffuse envelopes of stars and dark matter. We model the evolution in stellar mass ($M_\star$), effective radius ($R_{\rm e}$), and effective stellar velocity dispersion ($\sigma_{\rm e}$) of a representative massive quiescent galaxy from $z\approx 3$ to $z\approx 0$, and compare the model with the observed redshift-dependent $R_{\rm e}$-$M_\star$ and $\sigma_{\rm e}$-$M_\star$ relations. In the model we account for the effects of collisionless (dry) major (satellite-to-main galaxy mass ratio $\xi>1/4$) and minor ($1/10<\xi<1/4$) mergers, using analytic recipes consistent with the results of $N$-body simulations of binary mergers. For the poorly constrained mini mergers ($\xi<1/10$) we explore both a 'standard' model (based on the same assumptions used in the case of higher-$\xi$ mergers), and a heuristic 'envelope accretion' model, aimed at describing the case in which diffuse satellites are completely disrupted in the galaxy outskirts. Major and minor dry mergers, at rates estimated observationally from galaxy-pair counts, induce relatively small variations in $R_{\rm e}$ and $\sigma_{\rm e}$, accounting only for $\approx 6\% $ of the size evolution and $\approx 40\%$ of the velocity-dispersion evolution observed from $z\approx 3$ to $z\approx 0$. As an addition to major and minor dry mergers, envelope accretion performs better than standard mini mergers at reproducing the redshift-dependence of the $R_{\rm e}$-$M_\star$ and $\sigma_{\rm e}$-$M_\star$ relations, being also consistent with plausible evolutionary scenarios of scaling relations involving the mass of the central supermassive black hole.

astro-ph.GA↗

arXiv2024

Chemo-dynamics of the stellar component of the Sculptor dwarf galaxy I: observed properties

Aims. Recently, both the presence of multiple stellar chemo-kinematic components and rotation in the Sculptor dwarf spheroidal galaxy have been put into question. Therefore, we re-examine the chemo-kinematic properties of this galaxy making use of the best spectroscopic data-set available containing both line-of-sight velocities and metallicities of individual stars. Methods. We carry out a detailed, quantitative analysis on the recent spectroscopic data-set from Tolstoy et al. (2023) that contains high precision velocities and metallicities for 1339 members of Sculptor. In particular, we assess whether Sculptor is best represented by a single stellar population with a negative metallicity gradient or by the super-position of two or more components with different mean metallicity, spatial distribution and kinematic properties. For this analysis, we also include the incompleteness of the spectroscopic data-set. Results. We find that Sculptor is better described by a two-populations model than by a single-population model with a metallicity gradient. Moreover, given the assumptions of the current modeling, we find evidence of a third population, composed of few stars, that is more extended and metal-poor than the two other populations. This very metal-poor group of stars shows a shift of around 15 km/s in its average l.o.s. velocity (vlos) with respect to the rest of the galaxy. We discuss several possible origins for this new population, finding a minor merger as the most likely one. We also find a vlos gradient of 4.0 +1.5 -1.5 km s-1 deg-1 but its statistical evidence is inconclusive and, moreover, its detection is partially driven by the group of stars with off-set velocities.

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arXiv2024

Dark-matter central density, annihilation J-factor and decay D-factor of the Fornax, Sculptor and Leo I dwarf spheroidal galaxies

The dwarf spheroidal galaxies (dSphs) satellites of the Milky Way (MW) are nearby astrophysical laboratories to study the nature of dark matter (DM). We present some properties of the DM halos of the three classical dSphs Fornax, Sculptor and Leo I, obtained using dynamical models based on distribution functions depending on the action integrals. In particular, we report accurate estimates of their central DM density rho150 (measured at a distance of 150 pc from the galaxy centre), which is relevant for galaxy formation studies and for models of self-interacting DM, and their DM annihilation J-factor and decay D-factor, which are key tools for indirect DM detection experiments. Among these three galaxies, Fornax has the highest J- and D- factors (but the lowest rho150), while Leo I has the highest rho150 (but the lowest J- and D- factors).

astro-ph.GA↗

arXiv2024

Tidal mass loss in the Fornax dwarf spheroidal galaxy through N-body simulations with Gaia DR3-based orbits

The Fornax dwarf spheroidal galaxy (dSph) represents a challenge for some globular cluster (GC) formation models, because an exceptionally high fraction of its stellar mass is locked in its GC system. In order to shed light on our understanding of GC formation, we aim to constrain the amount of stellar mass that Fornax has lost via tidal interaction with the Milky Way (MW). Exploiting the flexibility of effective multi-component $N$-body simulations and relying on state-of-the-art estimates of Fornax's orbital parameters, we study the evolution of the mass distribution of the Fornax dSph in observationally justified orbits in the gravitational potential of the MW over 12 Gyr. We find that, though the dark-matter mass loss can be substantial, the fraction of stellar mass lost by Fornax to the MW is always negligible, even in the most eccentric orbit considered. We conclude that stellar-mass loss due to tidal stripping is not a plausible explanation for the unexpectedly high stellar mass of the GC system of the Fornax dSph and we discuss quantitatively the implications for GC formation scenarios.

astro-ph.GA↗

arXiv2024

Local gravitational instability of two-component thick discs in three dimensions

The local gravitational instability of rotating discs is believed to be an important mechanism in different astrophysical processes, including the formation of gas and stellar clumps in galaxies. We aim to study in three dimensions the local gravitational instability of two-component thick discs. We take as starting point a recently proposed analytic three-dimensional (3D) instability criterion for discs with non-negligible thickness which takes the form $Q_{\rm 3D}<1$, where $Q_{\rm 3D}$ is a 3D version of the classical 2D Toomre $Q$ parameter for razor-thin discs. Here we extend the 3D stability analysis to two-component discs, considering first the influence on $Q_{\rm 3D}$ of a second unresponsive component, and then the case in which both components are responsive. We present the application to two-component discs with isothermal vertical distributions, which can represent, for instance, galactic discs with both stellar and gaseous components. Finally, we relax the assumption of vertical isothermal distribution, by studying one-component self-gravitating discs with polytropic vertical distributions for a range of values of the polytropic index corresponding to convectively stable configurations. We find that $Q_{\rm 3D}<1$, where $Q_{\rm 3D}$ can be computed from observationally inferred quantities, is a robust indicator of local gravitational instability, depending only weakly on the presence of a second component and on the vertical gradient of temperature or velocity dispersion. We derive a sufficient condition for local gravitational instability in the midplane of two-component discs, which can be employed when both components have $Q_{\rm 3D}>1$.

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arXiv2023

Gas rotation and dark matter halo shape in cool-core clusters of galaxies

Aims. We study the possibility that the gas in cool-core clusters of galaxies has non-negligible rotation support, the impact of gas rotation on mass estimates from current X-ray observations, and the ability of forthcoming X-ray observatories to detect such rotation. Methods. We present three representative models of massive cool-core clusters with rotating intracluster medium (ICM) in equilibrium in cosmologically motivated spherical, oblate or prolate dark matter halos. In the models, the gas follows a composite-polytropic distribution, and has rotation velocity profiles consistent with current observational constraints. We show that the models are consistent with the available measurements of the ICM properties of the massive cluster population: thermodynamic profiles, shape of surface-brightness distribution, hydrostatic mass bias and broadening of X-ray emitting lines. Using the configuration for the microcalorimeter onboard the XRISM satellite, we generate a set of mock X-ray spectra of our cluster models, which we then analyze to make predictions on the estimates of the rotation speed that will be obtained with such an instrument. We then assess what fraction of the hydrostatic mass bias of our models could be accounted for by detecting rotation speed with XRISM spectroscopy over the range (0.1-1)r500. Results. Current data leave room for rotating ICM in cool-core clusters with peaks of rotation speed as high as 600 km/s. We have shown that such rotation, if present, will be detected with upcoming X-ray facilities such as XRISM and that 60-70% of the hydrostatic mass bias due to rotation can be accounted for using the line-of-sight velocity measured from X-ray spectroscopy with XRISM, with a residual bias smaller than 3% at an overdensity of 500. In this way, XRISM will allow us to pin down any mass bias of origin different from rotation.

astro-ph.CO↗

arXiv2023

The most stringent upper limit from dynamical models on the mass of a central black hole in 47 Tucanae

Globular clusters (GCs) were proposed as promising sites for discovering intermediate-mass black holes (IMBHs), possibly providing crucial insights into the formation and evolution of these elusive objects. The Galactic GC 47 Tucanae (also known as NGC 104) has been suggested as a potential IMBH host, but, previous studies have yielded conflicting results. We, therefore, present self-consistent dynamical models based on distribution functions (DFs) that depend on action integrals to assess the presence (or absence) of an IMBH in 47 Tucanae. Leveraging state-of-the-art Multi Unit Spectroscopic Explorer and Hubble Space Telescope data, we analyzed the three-dimensional (3D) kinematics of the cluster's central regions, fitting individual star velocities down to the sub-arcsec scale (approximately $10^{-2}$ pc). According to our analysis, the inner kinematics of 47 Tucanae is incompatible with a central BH more massive than 578 M$_\odot$ (at $3σ$). This is the most stringent upper limit on the mass of a putative IMBH in 47 Tucanae that has been put by any dynamical study.

astro-ph.GA↗

arXiv2023

Multiple stellar population mass loss in massive Galactic globular clusters

The degree of mass loss, i.e. the fraction of stars lost by globular clusters, and specifically by their different populations, is still poorly understood. Many scenarios of the formation of multiple stellar populations, especially the ones involving self-enrichment, assume that the first generation (FG) was more massive at birth than now to reproduce the current mass of the second generation (SG). This assumption implies that, during their long-term evolution, clusters lose around $90\%$ of the FG. We have tested whether such strong mass loss could take place in a massive globular cluster orbiting the Milky Way at $4\ {\rm kpc}$ from the centre and composed of two generations. We perform a series of $N$-body simulations for ${12\ \rm Gyr}$ to probe the parameter space of internal cluster properties. We have derived that, for an extended FG and a low-mass second one, the cluster loses almost $98\%$ of its initial FG mass and the cluster mass can be as much as 20 times lower after a Hubble time. Furthermore, under these conditions, the derived fraction of SG stars, $f_{\rm enriched}$, falls in the range occupied by observed clusters of similar mass ($\sim 0.6-0.8$). In general, the parameters that affect the most the degree of mass loss are the presence or not of primordial segregation, the depth of the central potential, $W_{0,FG}$, the initial mass of the SG, $M^{ini}_{SG}$, and the initial half-mass radius of the SG, $r_{h,SG}$. Higher $M^{ini}_{SG}$ have not been found to imply higher final $f_{\rm enriched}$ due to the deeper cluster potential well which slows down mass loss.

astro-ph.GA↗

arXiv2023

On the anti-correlation between pericentric distance and inner dark matter density of Milky Way's dwarf spheroidal galaxies

An anti-correlation between the central density of the dark matter halo ($ρ_{150,\ {\rm DM}}$) and the pericentric distances ($r_{p}$) of the Milky Way's (MW's) dwarf spheroidal galaxies (dSphs) has been reported in the literature. The existence and origin of such anti-correlation is however controversial, one possibility being that only the densest dSphs can survive the tidal field towards the centre of our Galaxy. In this work, we place particular emphasis on quantifying the statistical significance of such anti-correlation, by using available literature data in order to explore its robustness under different assumptions on the MW gravitational potential, and for various derivations of $ρ_{150}$ and $r_{p}$. We consider models in which the MW is isolated and has a low ($8.8\times10^{11}\,M_{\odot}$) and high ($1.6\times10^{12}\, M_{\odot}$) halo mass, respectively, as well as configurations in which the MW's potential is perturbed by a Large Magellanic Cloud (LMC) infall. We find that, while data generally support models in which the dSphs' central DM density decreases as a function of their pericentric radius, this anti-correlation is statistically significant at $3σ$ level only in $\sim$12$\%$ of the combinations of $ρ_{150}$ and $r_{p}$ explored. Moreover, including the impact of the LMC's infall onto the MW weakens or even washes away this anti-correlation, with respect to models in which the MW is isolated. Our results suggest that the strength and existence of such anti-correlation is still debatable: exploring it with high-resolution simulations including baryonic physics and different DM flavours will help us to understand its emergence.

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