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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., Comment: 17 pages, 9 figures, Accepted for publication in Astronomy & Astrophysics

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)., Comment: 4 pages, 1 figure, to appear in the Proceedings of the XXXII IAU General Assembly held in Cape Town in August 2024 (Focus Meeting 9: Measures of luminous and dark matter in galaxies across time)

Star clusters stand at the crossroads between galaxies and single stars. Resolving the formation of star clusters in cosmological simulations represents an ambitious and challenging goal, since modelling their internal properties requires very high resolution. This paper is the third of a series within the SImulating the Environment where Globular clusters Emerged (SIEGE) project, where we conduct zoom-in cosmological simulations with sub-parsec resolution that include the feedback of individual stars, aimed to model the formation of star clusters in high-redshift proto-galaxies. We investigate the role of three fundamental quantities in shaping the intrinsic properties of star clusters, i. e., i) pre-supernova stellar feedback (continuous or instantaneous ejection of mass and energy through stellar winds); ii) star formation efficiency, defined as the fraction of gas converted into stars per freefall time, for which we test 2 different values (epsi_ff=0.1 and 1), and iii) stellar initial mass function (IMF, standard vs top-heavy). All our simulations are run down to z=10.5, which is sufficient for investigating some structural properties of the emerging clumps and clusters. [Abridged] The prescription for a continuous, low-intensity feedback, along with the adoption of epsi_ff=1, produces star clusters with maximum stellar density values up to 10^4 M_sun pc^(-2), in good agreement with the surface density-size relation observed in local young star clusters (YSCs). Therefore, a realistic stellar wind description and a high star formation effiency are the key ingredients that allow us to achieve realistic star clusters characterised by properties comparable to those of local YSCs. In contrast, the other models produce too diffuse clusters, in particular the one with a top-heavy IMF., Comment: 20 pages, 14 pages

Several approaches have been proposed in the literature for clustering multivariate ordinal data. These methods typically treat missing values as absent information, rather than recognizing them as valuable for profiling population characteristics. To address this gap, we introduce a Bayesian nonparametric model for co-clustering multivariate ordinal data that treats censored observations as informative, rather than merely missing. We demonstrate that this offers a significant improvement in understanding the underlying structure of the data. Our model exploits the flexibility of two independent Dirichlet processes, allowing us to infer potentially distinct subpopulations that characterize the latent structure of both subjects and variables. The ordinal nature of the data is addressed by introducing latent variables, while a matrix factorization specification is adopted to handle the high dimensionality of the data in a parsimonious way. The conjugate structure of the model enables an explicit derivation of the full conditional distributions of all the random variables in the model, which facilitates seamless posterior inference using a Gibbs sampling algorithm. We demonstrate the method's performance through simulations and by analyzing politician and movie ratings data., Comment: 25 pages, 11 figures

A dynamic treatment regime is a sequence of medical decisions that adapts to the evolving clinical status of a patient over time. To facilitate personalized care, it is crucial to assess the probability of each available treatment option being optimal for a specific patient, while also identifying the key prognostic factors that determine the optimal sequence of treatments. This task has become increasingly challenging due to the growing number of individual prognostic factors typically available. In response to these challenges, we propose a Bayesian model for optimizing dynamic treatment regimes that addresses the uncertainty in identifying optimal decision sequences and incorporates dimensionality reduction to manage high-dimensional individual covariates. The first task is achieved through a suitable augmentation of the model to handle counterfactual variables. For the second, we introduce a novel class of spike-and-slab priors for the multi-stage selection of significant factors, to favor the sharing of information across stages. The effectiveness of the proposed approach is demonstrated through extensive simulation studies and illustrated using clinical trial data on severe acute arterial hypertension.

The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this context, we propose a novel Bayesian nonparametric model that identifies clusters of networks characterized by similar connectivity patterns. Our approach relies on a location-scale Dirichlet process mixture of centered Erd\H{o}s--R\'enyi kernels, with components parametrized by a unique network representative, or mode, and a univariate measure of dispersion around the mode. We demonstrate that this model has full support in the Kullback--Leibler sense and is strongly consistent. An efficient Markov chain Monte Carlo scheme is proposed for posterior inference and clustering of multiple network data. The performance of the model is validated through extensive simulation studies, showing improvements over state-of-the-art methods. Additionally, we present an effective strategy to extend the application of the proposed model to datasets with a large number of nodes. We illustrate our approach with the analysis of human brain network data.

New, deep HST photometry allowed us to identify and study eight compact and bright (M_V< -5.8) star clusters in the outskirts of the star-forming isolated dwarf galaxy NGC5238 (M_*= 10^8 M_sun). Five of these clusters are new discoveries, and six appear projected onto, and/or aligned with the tidal tails recently discovered around this galaxy. The clusters are partially resolved into stars and their colour magnitude diagrams reveal a well developed red giant branch, implying ages older than 1-2~Gyr. Their integrated luminosity and structural parameters are typical of classical globular clusters and one of them has M_V=-10.56 +/- 0.07, as bright as Omega Cen, the brightest globular cluster of the Milky Way. Since the properties of this cluster are in the range spanned by those of nuclear star clusters we suggest that it may be the nuclear remnant of the disrupted satellite of NGC5238 that produced the observed tidal tails., Comment: Accepted for publication by A&A Letters. Latex, 10 pages, 6 figures, 5 appendices

Motivated by an increasing demand for models that can effectively describe features of complex multivariate time series, e.g. from sensor data in biomechanics, motion analysis, and sports science, we introduce a novel state-space modeling framework where the state equation encodes the evolution of latent partitions of the data over time. Building on the principles of dynamic linear models, our approach develops a random partition model capable of linking data partitions to previous ones over time, using a straightforward Markov structure that accounts for temporal persistence and facilitates changepoint detection. The selection of changepoints involves multiple dependent decisions, and we address this time-dependence by adopting a non-marginal false discovery rate control. This leads to a simple decision rule that ensures more stringent control of the false discovery rate compared to approaches that do not consider dependence. The method is efficiently implemented using a Gibbs sampling algorithm, leading to a straightforward approach compared to existing methods for dependent random partition models. Additionally, we show how the proposed method can be adapted to handle multi-view clustering scenarios. Simulation studies and the analysis of a human gesture phase dataset collected through various sensing technologies show the effectiveness of the method in clustering multivariate time series and detecting changepoints.

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., Comment: 15 pages, 12 figures. Version accepted in A&A

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 $Q_{\rm 3D}>1$., Comment: 14 pages, 9 figures, accepted for publication in A&A

From deep imaging data obtained with the Large Binocular Telescope as part of the Smallest Scale of Hierarchy Survey (SSH), we have discovered low-surface brightness tidal features around NGC 5238 and UGC 8760, two nearby and relatively isolated dwarf galaxies with stellar masses of approximately $10^8 M_\odot$ and $2\times10^7 M_\odot$, respectively. In this study, we present detailed hydrodynamical $N$-body simulations that explain the observed faint substructures as the outcome of interactions between the dwarf galaxies and smaller satellite systems. We show that the asymmetric stellar distribution of NGC 5238 and the low-luminosity substructures observed to the northeast of UGC 8760 can be well attributed to recent interactions with smaller galaxies, each with a stellar mass roughly a few $10^5 M_\odot$, 50 times less massive than their respective hosts. In the simulations, these satellites have stellar and dark-matter masses consistent with the ones predicted by $\Lambda$CDM cosmology and share properties similar to those of local dwarf galaxies with similar stellar masses. The satellite-to-main galaxy mass ratio is approximately 1:10 in both cases. This satellite population aligns closely with predictions from cosmological simulations in terms of the number and mass relative to the host galaxy mass., Comment: Accepted for publication in A&A, 15 pages, 8 figures

Local gravitational instability (LGI) is considered crucial for regulating star formation and gas turbulence in galaxy discs, especially at high redshift. Instability criteria usually assume infinitesimally thin discs or rely on approximations to include the stabilising effect of the gas disc thickness. We test a new 3D instability criterion for rotating gas discs that are vertically stratified in an external potential. This criterion reads $Q_{\rm3D}<1$, where $Q_{\rm3D}$ is the 3D analogue of the Toomre parameter $Q$. The advantage of $Q_{\rm3D}$ is that it allows us to study LGI in and above the galaxy midplane in a rigorous and self-consistent way. We apply the criterion to a sample of 44 star-forming galaxies at $0\lesssim\mathrm{z}\lesssim5$ hosting rotating discs of cold gas. The sample is representative of galaxies on the main sequence at $\mathrm{z}\approx 0$ and includes massive star-forming and starburst galaxies at $1\lesssim\mathrm{z}\lesssim5$. For each galaxy, we first apply the Toomre criterion for infinitesimally thin discs, finding 10 unstable systems. We then obtain maps of $Q_{\rm 3D}$ from a 3D model of the gas disc derived in the combined potential of dark matter, stars and the gas itself. According to the 3D criterion, two galaxies with $Q<1$ show no evidence of instability and the unstable regions that are 20% smaller than those where $Q<1$. No unstable disc is found at $0\lesssim\mathrm{z}\lesssim 1$, while $\approx 60$% of the systems at $2\lesssim\mathrm{z}\lesssim5$ are locally unstable. In these latter, a relatively small fraction of the total gas ($\approx 30$%) is potentially affected by the instability. Our results disfavour LGI as the main regulator of star formation and turbulence in moderately star-forming galaxies in the present-day Universe. LGI likely becomes important at high redshift, but the input by other mechanisms seems required [abridged], Comment: 19 pages (6 figures, 2 tables) + appendixes, accepted by Astronomy & Astrophysics

It has been recently claimed that a surprisingly massive black hole (BH) is present in the core of the dwarf spheroidal galaxy (dSph) Leo I. Based on integral field spectroscopy, this finding challenges the typical expectation of dSphs hosting BHs of intermediate-mass, since such a BH would better be classified as supermassive. Indeed, the analysis points toward Leo I harboring a BH with a lower mass limit exceeding a few $10^6M_\odot$ at $1\sigma$, and the no BH case excluded at 95\% significance. Such a value, comparable to the entire stellar mass of the galaxy, makes Leo I a unique system that warrants further investigations. Using equilibrium models based on distribution functions (DFs) depending on actions $f({\boldsymbol J})$ coupled with the same integral field spectroscopy data and an extensive exploration of a very large parameter space, we demonstrate, within a comprehensive Bayesian framework of model-data comparison, that the posterior on the BH mass is flat towards the low-mass end and, thus, that the kinematics of the central galaxy region only imposes an upper limit on the BH mass of few $10^5M_\odot$ (at $3\sigma$). Such an upper limit brings back the putative BH of Leo I under the category of intermediate-mass BHs, and it is also in line with formation scenarios and expectations from scaling relations at the mass regime of dwarf galaxies., Comment: Accepted for publication in A&A Letters

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., Comment: 18 pages, 12 figures, accepted for publication in A&A

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 $3\sigma$). 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., Comment: 10 pages, 6 figures, accepted for publication in Astronomy and Astrophysics (A&A)

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., Comment: 16 pages, 9 figures. Accepted for publication on Astronomy & Astrophysics

We use zoom-in, hydrodynamical, cosmological $N$-body simulations tracing the formation of the first stellar clumps from the SImulating the Environments where Globular clusters Emerged (SIEGE) project, to study key structural properties of dark matter haloes when the Universe was only $0.92$ Gyr old. The very high-resolution (maximum physical resolution 0.3 h$^{-1}$ pc at $z=6.14$, smallest dark-matter particle mass $164\,M_{\odot}$) allows us to reach the very low mass end of the stellar-to-halo mass relation ($M_{\rm vir}=10^{7.5-9.5}\,M_{\odot}$) to study the processes that mould dark matter haloes during the first stages of structure formation. We investigate the role of baryonic cooling and stellar feedback, modeled from individual stars, in shaping haloes, and of environmental effects as accretion of dark matter along cosmic filaments and mergers. We find that the onset of star formation (typically for $\log M_{\rm vir}/M_{\odot}\simeq7.6$) causes the inner cusp in the haloes density profile to flatten into a core with constant density and size proportionally to the halo virial mass. Even at these mass scales, we confirm that baryons make haloes that have formed stars rounder in the central regions than haloes that have not formed stars yet, with median minor-to-major $\langle q \rangle$ and intermediate-to-major $\langle s \rangle$ axes 0.66 and 0.84, respectively. Our morphological analysis shows that, at $z=6.14$, haloes are largely prolate in the outer parts, with the major axis aligned along filaments of the cosmic web or towards smaller sub-haloes, with the degree of elongation having no significant dependence on the halo mass., Comment: 20 pages, 11 figures. Accepted for publication in MNRAS

We developed self-consistent dynamical models of stellar systems in the framework of quasi-linear modified Newtonian dynamics (QUMOND). The models are constructed from the anisotropic distribution function of Gunn & Griffin (1979), combined with the modified Poisson equation defining this gravitation theory and take into account the external field effect. We have used these models, and their Newtonian analogues, to fit the projected density and the velocity dispersion profiles of a sample of 18 Galactic globular clusters, using the most updated datasets of radial velocities and Gaia proper motions. We have thus obtained, for each cluster, estimates of the dynamical mass-to-light ratio ($M/L$) for each theory of gravity. The selected clusters have accurate proper motions and a well sampled mass function down to the very low mass regime. This allows us to constrain the degree of anisotropy and to provide, from comparison with stellar evolution isochrones, a dynamics-independent estimate of the minimum mass-to-light ratio $(M/L)_{min}$. Comparing the best-fitting dynamical $M/L$ with $(M/L)_{min}$, we find that for none of the analyzed clusters the two gravity theories are significantly incompatible with the observational data, although for one of them (NGC 5024) the dynamical $M/L$ predicted by QUMOND lies at $2.8\sigma$ below $(M/L)_{min}$. Though the proposed approach suffers from some limitations (in particular the lack of a treatment of mass segregation), the obtained results suggest that the kinematics of globular clusters in a relatively weak external field can be a powerful tool to prove alternative theories of gravitation., Comment: Accepted for publication in MNRAS. Dedicated to the memory of Antonio Sollima, who conceived, developed and carried out most of this work

An anti-correlation between the central density of the dark matter halo ($\rho_{150,\ {\rm DM}}$) 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 $\rho_{150}$ 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 $3\sigma$ level only in $\sim$12$\%$ of the combinations of $\rho_{150}$ 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., Comment: 10 pages, 3 figures. Accepted for publication in MNRAS

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse structures. Sparsity, in addition, is beneficial in terms of regularization and, thus, to avoid over-fitting. By exploiting Bayesian shrinkage priors, we devise a computationally convenient approach for high-dimensional matrix factorization. The dependence between row and column entities is modeled by inducing flexible sparse patterns within factors. The availability of external information is accounted for in such a way that structures are allowed while not imposed. Inspired by boosting algorithms, we pair the the proposed approach with a numerical strategy relying on a sequential inclusion and estimation of low-rank contributions, with data-driven stopping rule. Practical advantages of the proposed approach are demonstrated by means of a simulation study and the analysis of soccer heatmaps obtained from new generation tracking data.

HI and CO observations indicate that the cold gas in galaxies is very turbulent. However, the turbulent energy is expected to be quickly dissipated, implying that some energy source is needed to explain the observations. The nature of such turbulence was long unclear, as even the main candidate, supernova (SN) feedback, seemed insufficient. Other mechanisms have been proposed, but without reaching a general consensus. The key novelty of our work is considering that the gas disc thickness and flaring increase the dissipation timescale of turbulence, thus reducing the energy injection rate required to sustain it. In excellent agreement with the theoretical expectations, we found that the fraction of the SN energy (a.k.a. SN coupling efficiency) needed to maintain the cold gas turbulence is $\sim 1$%, solving a long-standing conundrum., Comment: 3 pages, 1 figure, Proceedings IAU Symposium 373, accepted

Star formation laws are empirical relations between the cold gas (HI+H$_2$) content of a galaxy and its star formation rate (SFR), being crucial for any model of galaxy formation and evolution. A well known example of such laws is the Schmidt-Kennicutt law, which is based on the projected surface densities. However, it has been long unclear whether a more fundamental relation exists between the intrinsic volume densities. By assuming the vertical hydrostatic equilibrium, we infer radial profiles for the thickness of gaseous discs in a sample of 23 local galaxies, and use these measurements to convert the observed surface densities of the gas and the SFR into the de-projected volume densities. We find a tight correlation linking these quantities, that we call the volumetric star formation law. This relation and its properties have crucial implications for our understanding of the physics of star formation., Comment: 3 pages, 1 figure, Proceedings IAU Symposium 373, accepted

Fragmentation of rotating gaseous systems via gravitational instability is believed to be a crucial mechanism in several astrophysical processes, such as formation of planets in protostellar discs, of molecular clouds in galactic discs, and of stars in molecular clouds. Gravitational instability is fairly well understood for infinitesimally thin discs. However, the thin-disc approximation is not justified in many cases, and it is of general interest to study the gravitational instability of rotating fluids with different degrees of rotation support and stratification. We derive dispersion relations for axisymmetric perturbations, which can be used to study the local gravitational stability at any point of a rotating axisymmetric gaseous system with either barotropic or baroclinic distribution. 3D stability criteria are obtained, which generalize previous results and can be used to determine whether and where a rotating system of given 3D structure is prone to clump formation. For a vertically stratified gaseous disc of thickness $h_z$ (defined as containing $\approx$70% of the mass per unit surface), a sufficient condition for local gravitational instability is $Q_{\rm 3D}\equiv\left(\sqrt{\kappa^2+\nu^2}+c_s h_z^{-1}\right)/{\sqrt{4\pi G\rho}}<1$, where $\rho$ is the gas volume density, $\kappa$ the epicycle frequency, $c_s$ the sound speed, and $\nu^2\equiv\rho_z p_z/\rho^2$, where $\rho_z$ and $p_z$ are the vertical gradients of, respectively, gas density and pressure. The combined stabilizing effects of rotation ($\kappa^2$) and stratification ($\nu^2$) are apparent. In unstable discs, the conditions for instability are typically met close to the midplane, where the perturbations that are expected to grow have characteristic radial extent of a few $h_z$., Comment: 11 pages, 2 figures, accepted for publication in MNRAS

We compare stellar mass surface density, metallicity, age, and line-of-sight velocity dispersion profiles in massive ($M_*\geq10^{10.5}\,\mathrm{M_\odot}$) present-day early-type galaxies (ETGs) from the MaNGA survey with simulated galaxies from the TNG100 simulation of the IllustrisTNG suite. We find an excellent agreement between the stellar mass surface density profiles of MaNGA and TNG100 ETGs, both in shape and normalisation. Moreover, TNG100 reproduces the shapes of the profiles of stellar metallicity and age, as well as the normalisation of velocity dispersion distributions of MaNGA ETGs. We generally also find good agreement when comparing the stellar profiles of central and satellite galaxies between MaNGA and TNG100. An exception is the velocity dispersion profiles of very massive ($M_*\gtrsim10^{11.5}\,\mathrm{M_\odot}$) central galaxies, which, on average, are significantly higher in TNG100 than in MaNGA ($\approx50\,\mathrm{km\,s^{-1}}$). We study the radial profiles of $\mathit{in}$-$\mathit{situ}$ and $\mathit{ex}$-$\mathit{situ}$ stars in TNG100 and discuss the extent to which each population contributes to the observed MaNGA profiles. Our analysis lends significant support to the idea that high-mass ($M_*\gtrsim10^{11}\,\mathrm{M_\odot}$) ETGs in the present-day Universe are the result of a merger-driven evolution marked by major mergers that tend to homogenise the stellar populations of the progenitors in the merger remnant., Comment: 22 pages, 9 figures, accepted for publication in MNRAS

When interpreted within the standard framework of Newtonian gravity and dynamics, the kinematics of stars and gas in dwarf galaxies reveals that most of these systems are completely dominated by their dark matter halos. These dwarf galaxies are thus among the best astrophysical laboratories to study the structure of dark halos and the nature of dark matter. We review the properties of the dwarf galaxies of the Local Group from the point of view of stellar dynamics. After describing the observed kinematics of their stellar components and providing an overview of the dynamical modelling techniques, we look into the dark matter content and distribution of these galaxies, as inferred from the combination of observed data and dynamical models. We also briefly touch upon the prospects of using nearby dwarf galaxies as targets for indirect detection of dark matter via annihilation or decay emission., Comment: Invited Review published on May 16, 2022 in Nature Astronomy. The Version of Record is available online at http://dx.doi.org/10.1038/s41550-022-01638-7

At fixed stellar mass $M_*$, the effective radius $R_{\rm e}$ of massive satellite early-type galaxies (ETGs) in galaxy clusters is, on average, larger at lower redshift. We study theoretically this size evolution using the state-of-the-art cosmological simulation IllustrisTNG100: we sampled $75$ simulated satellite ETGs at redshift $z=0$ with $M_* \ge 10^{10.4} M_{\odot}$ belonging to the two most massive ($\approx 10^{14.6} M_{\odot} $) haloes of the simulation. We traced back in time the two clusters' main progenitors and we selected their satellite ETGs at $z>0$ with the same criterion adopted at $z=0$. The $R_{\rm e}-M_*$ relation of the simulated cluster satellite ETGs, which is robustly measured out to $z=0.85$, evolves similarly to the observed relation over the redshift range $0\lesssim z \lesssim 0.85$. In the simulation the main drivers of this evolution are the acquisition of new galaxies ("newcomers") by the clusters and the transformation of member galaxies located at large clustercentric distance ("suburbanites") at $z=0.85$, which end up being massive satellite ETGs at $z=0$. Though several physical processes contribute to change the population of satellite ETGs in the considered redshift interval, the shape of the stellar mass function of the simulated cluster ETGs is not significantly different at $z=0.85$ and at $z=0$, consistent with observations., Comment: 14 pages, 11 figures, resubmitted to MNRAS

Using Large Binocular Telescope deep imaging data from the Smallest Scale of Hierarchy Survey (SSH) and archival Hubble Space Telescope data, we reveal the presence of two elongated stellar features contiguous to a bar-like stellar structure in the inner regions of the dwarf irregular galaxy NGC 3741. These structures are dominated by stars younger than a few hundred Myr and collectively are about twice as extended as the old stellar component. These properties are very unusual for dwarf galaxies in the nearby Universe and difficult to explain by hydro-dynamical simulations. From the analysis of archival 21-cm observations, we find that the young stellar "bar" coincides with an HI high-density region proposed by previous studies to be a purely gaseous bar; we furthermore confirm radial motions of a few km/s, compatible with an inflow/outflow, and derive a steeply-rising rotation curve and high HI surface density at the center, indicating a very concentrated mass distribution. We propose that the peculiar properties of the stellar and gaseous components of NGC 3741 may be explained by a recent merger or ongoing gas accretion from the intergalactic medium, which caused gas inflows towards the galaxy center and triggered star formation a few hundred Myr ago. This event may explain the young and extended stellar features, the bar-like structure, the very extended HI disc and the central HI spiral arms. The high central HI density and the steeply rising rotation curve suggest that NGC 3741 may be the progenitor or the descendant of a starburst dwarf., Comment: Accepted for publication in MNRAS. Corrected typo in the list of authors

Using hydrodynamical $N$-body simulations, we show that the observed structure and kinematics of the extremely metal-poor, dwarf irregular galaxy DDO 68 is compatible with a merger event with at least two smaller satellite galaxies. We were able to obtain a self-consistent model that simultaneously reproduces several of its observed features, including: the very asymmetric and disturbed shape of the stellar component, the overall HI distribution and its velocity field, the arc-like stellar structure to the west, the low-surface brightness stellar stream to the north. The model implies the interaction of the main progenitor of DDO 68 with two systems with dynamical masses $7\times10^8\,M_{\odot}$ and almost $10^8\,M_{\odot}$ -- 1/20 and 1/150 times the dynamical mass of DDO 68, respectively. We show that the merger between DDO 68 and the most massive of its satellites offers a route to explain the large offset of DDO 68 from the mass-metallicity relation. Assuming that the interacting galaxies have metallicities prior to the merger compatible with those of galaxies with similar stellar masses, we provide quantitative evidence that gas mixing alone does not suffice at diluting the gas of the two components; according to our simulations, the HII regions observed along the Cometary Tail trace the low metallicity of the accreted satellite rather than that of DDO 68's main body. In this case, the mass corresponding to the low metallicity is that of the secondary body and DDO 68 becomes consistent with the mass-metallicity relation., Comment: Accepted for publication in MNRAS. 17 pages, 10 figures

The gravitational potentials of realistic galaxy models are in general non-integrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic orbits are a small minority in a stellar system, it is expected that they have negligible impact on the main dynamical properties of the system. In this paper we address the question of quantifying the importance of chaotic orbits in a stellar system, focusing, for simplicity, on axisymmetric systems. Chaotic orbits have been found in essentially all (non-St\"ackel) axisymmetric gravitational potentials in which they have been looked for. Based on the analysis of the surfaces of section, we add new examples to those in the literature, finding chaotic orbits, as well as resonantly trapped orbits among regular orbits, in Miyamoto-Nagai, flattened logarithmic and shifted Plummer axisymmetric potentials. We define the fractional contributions in mass of chaotic ($\xi_{\rm c}$) and resonantly trapped ($\xi_{\rm t}$) orbits to a stellar system of given distribution function, which are very useful quantities, for instance in the study of the dispersal of stellar streams of galaxy satellites. As a case study, we measure $\xi_{\rm c}$ and $\xi_{\rm t}$ in two axisymmetric stellar systems obtained by populating flattened logarithmic potentials with the Evans ergodic distribution function, finding $\xi_{\rm c}\sim 10^{-4}-10^{-3}$ and $\xi_{\rm t}\sim 10^{-2}-10^{-1}$., Comment: Accepted for publication in MNRAS. 15 pages, 11 figures

Discrete Bayesian nonparametric models whose expectation is a convex linear combination of a point mass at some point of the support and a diffuse probability distribution allow to incorporate strong prior information, while still being extremely flexible. Recent contributions in the statistical literature have successfully implemented such a modelling strategy in a variety of applications, including density estimation, nonparametric regression and model-based clustering. We provide a thorough study of a large class of nonparametric models we call inner spike and slab hNRMI models, which are obtained by considering homogeneous normalized random measures with independent increments (hNRMI) with base measure given by a convex linear combination of a point mass and a diffuse probability distribution. In this paper we investigate the distributional properties of these models and our results include: i) the exchangeable partition probability function they induce, ii) the distribution of the number of distinct values in an exchangeable sample, iii) the posterior predictive distribution, and iv) the distribution of the number of elements that coincide with the only point of the support with positive probability. Our findings are the main building block for an actual implementation of Bayesian inner spike and slab hNRMI models by means of a generalized P\'olya urn scheme., Comment: 19 pages, 3 figures

Thermal annealing plays a crucial role for healing the defectiveness in the ion implanted regions of DIMOSFETs (Double Implanted MOSFETs) devices. In this work, we have studied the effect of a double step annealing on the body (Al implanted) and the source (P implanted) regions of such devices. We found that a high temperature annealing (1750{\deg}C, 1h) followed by a lower temperature one (1500{\deg}C, 4h) is mandatory to achieve low defects concentration and good crystal quality in both the n- and p- type zones of the device.

The stratified proportional hazards model represents a simple solution to account for heterogeneity within the data while keeping the multiplicative effect on the hazard function. Strata are typically defined a priori by resorting to the values taken by a categorical covariate. A general framework is proposed, which allows for the stratification of a generic accelerated life time model, including as a special case the Weibull proportional hazard model. The stratification is determined a posteriori by taking into account that strata might be characterized by different baseline survivals as well as different effects of the predictors. This is achieved by considering a Bayesian nonparametric mixture model and the posterior distribution it induces on the space of data partitions. The optimal stratification is then identified by means of the variation of information criterion and, in turn, stratum-specific inference is carried out. The performance of the proposed method and its robustness to the presence of right-censored observations are investigated by means of an extensive simulation study. A further illustration is provided by the analysis of a data set extracted from the University of Massachusetts AIDS Research Unit IMPACT Study., Comment: 33 pages, 13 figures

Gas-poor galaxies can be modelled as composite collisionless stellar systems, with a dark matter halo and one or more stellar components, representing different stellar populations. The dynamical evolution of such composite systems is often studied with numerical N-body simulations, whose initial conditions typically require realizations with particles of stationary galaxy models. We present a novel method to conceive these N-body realizations, which allows one to exploit at best a collisionless N-body simulation that follows their evolution. The method is based on the use of an effective N-body model of a composite system, which is in fact realized as a one-component system of particles that is interpreted a posteriori as a multi-component system, by assigning in post-processing fractions of each particle's mass to different components. Examples of astrophysical applications are N-body simulations that aim to reproduce the observed properties of interacting galaxies, satellite galaxies and stellar streams. As a case study we apply our method to an N-body simulation of tidal stripping of a two-component (dark matter and stars) satellite dwarf galaxy orbiting in the gravitational potential of the Milky Way., Comment: 10 pages, 9 figures, accepted for publication in MNRAS. Figures 3, 7 and 9 illustrate the method applied to tidal streams

A scintillating bolometer based on a large cubic Li$_{2}$$^{100}$MoO$_4$ crystal (45 mm side) and a Ge wafer (scintillation detector) has been operated in the CROSS cryogenic facility at the Canfranc underground laboratory in Spain. The dual-readout detector is a prototype of the technology that will be used in the next-generation $0\nu2\beta$ experiment CUPID. The measurements were performed at 18 and 12 mK temperature in a pulse tube dilution refrigerator. This setup utilizes the same technology as the CUORE cryostat that will host CUPID and so represents an accurate estimation of the expected performance. The Li$_{2}$$^{100}$MoO$_4$ bolometer shows a high energy resolution of 6 keV FWHM at the 2615 keV $\gamma$ line. The detection of scintillation light for each event triggered by the Li$_{2}$$^{100}$MoO$_4$ bolometer allowed for a full separation ($\sim$8$\sigma$) between $\gamma$($\beta$) and $\alpha$ events above 2 MeV. The Li$_{2}$$^{100}$MoO$_4$ crystal also shows a high internal radiopurity with $^{228}$Th and $^{226}$Ra activities of less than 3 and 8 $\mu$Bq/kg, respectively. Taking also into account the advantage of a more compact and massive detector array, which can be made of cubic-shaped crystals (compared to the cylindrical ones), this test demonstrates the great potential of cubic Li$_{2}$$^{100}$MoO$_4$ scintillating bolometers for high-sensitivity searches for the $^{100}$Mo $0\nu2\beta$ decay in CROSS and CUPID projects., Comment: 19 pages, 7 figures, 1 table

The CUPID Collaboration is designing a tonne-scale, background-free detector to search for double beta decay with sufficient sensitivity to fully explore the parameter space corresponding to the inverted neutrino mass hierarchy scenario. One of the CUPID demonstrators, CUPID-Mo, has proved the potential of enriched Li$_{2}$$^{100}$MoO$_4$ crystals as suitable detectors for neutrinoless double beta decay search. In this work, we characterised cubic crystals that, compared to the cylindrical crystals used by CUPID-Mo, are more appealing for the construction of tightly packed arrays. We measured an average energy resolution of (6.7$\pm$0.6) keV FWHM in the region of interest, approaching the CUPID target of 5 keV FWHM. We assessed the identification of $\alpha$ particles with and without a reflecting foil that enhances the scintillation light collection efficiency, proving that the baseline design of CUPID already ensures a complete suppression of this $\alpha$-induced background contribution. We also used the collected data to validate a Monte Carlo simulation modelling the light collection efficiency, which will enable further optimisations of the detector.

We present dynamical models of the star-forming galaxy NGC 5474 based on $N$-body hydrodynamical numerical simulations. We investigate the possible origin of the compact round stellar structure, generally interpreted as the bulge of the galaxy, but unusually off-set by $\simeq1$ kpc in projection from the visual and the kinematic centres of both the star and the gas discs. We argue that it is very unlikely that the putative bulge is in a co-planar orbit in the disc plane, showing that such a configuration would be hardly compatible with its smooth and regular spatial distribution, and, in case its mass is above $10^8\,M_{\odot}$, also with the regular HI velocity field of NGC 5474. Instead, if the putative bulge is in fact an early-type satellite galaxy orbiting around NGC 5474, not only the off-set can be easily produced by projection effects, but our simulations suggest that the gravitational interaction between the two systems can explain also the warped HI distribution of NGC 5474 and the formation of its loose spiral arms. As a by-product of the simulations, we find that the peculiar over-density of old stars detected in the south-west region of NGC 5474 may be explained with the interaction between NGC 5474 and a smaller stellar system, unrelated to the putative bulge, accreted in the disc plane., Comment: Accepted for publication on MNRAS. 22 pages, 19 figures. Comments are welcome

Precise characterization of detector time resolution is of crucial importance for next-generation cryogenic-bolometer experiments searching for neutrinoless double-beta decay, such as CUPID, in order to reject background due to pile-up of two-neutrino double-beta decay events. In this paper, we describe a technique developed to study the pile-up rejection capability of cryogenic bolometers. Our approach, which consists of producing controlled pile-up events with a programmable waveform generator, has the benefit that we can reliably and reproducibly control the time separation and relative energy of the individual components of the generated pile-up events. The resulting data allow us to optimize and benchmark analysis strategies to discriminate between individual and pile-up pulses. We describe a test of this technique performed with a small array of detectors at the Laboratori Nazionali del Gran Sasso, in Italy; we obtain a 90% rejection efficiency against pulser-generated pile-up events with rise time of ~15ms down to time separation between the individual events of about 2ms.

The stellar initial mass function (IMF) is believed to be non-universal among early-type galaxies (ETGs). Parameterizing the IMF with the so-called IMF mismatch parameter $\alpha_{\rm IMF}$, which is a measure of the stellar mass-to-light ratio of an ensemble of stars and thus of the 'heaviness' of its IMF, one finds that for ETGs $\alpha_{\rm e}$ (i.e. $\alpha_{\rm IMF}$ integrated within the effective radius $R_{\rm e}$) increases with $\sigma_{\rm e}$ (the line-of-sight velocity dispersion $\sigma_{\rm los}$ integrated within $R_{\rm e}$) and that, within the same ETG, $\alpha_{\rm IMF}$ tends to decrease outwards. We study the effect of dissipationless (dry) mergers on the distribution of the IMF mismatch parameter $\alpha_{\rm IMF}$ in ETGs using the results of binary major and minor merging simulations. We find that dry mergers tend to make the $\alpha_{\rm IMF}$ profiles of ETGs shallower, but do not alter significantly the shape of the distributions in the spatially resolved $\sigma_{\rm los}\alpha_{\rm IMF}$ space. Individual galaxies undergoing dry mergers tend to decrease their $\alpha_{\rm e}$, due to erosion of $\alpha_{\rm IMF}$ gradients and mixing with stellar populations with lighter IMF. Their $\sigma_{\rm e}$ can either decrease or increase, depending on the merging orbital parameters and mass ratio, but tends to decrease for cosmologically motivated merging histories. The $\alpha_{\rm e}$-$\sigma_{\rm e}$ relation can vary with redshift as a consequence of the evolution of individual ETGs: based on a simple dry-merging model, ETGs of given $\sigma_{\rm e}$ are expected to have higher $\alpha_{\rm e}$ at higher redshift, unless the accreted satellites are so diffuse that they contribute negligibly to the inner stellar distribution of the merger remnant., Comment: 15 pages, 13 figures, accepted for publication in MNRAS

It is well known that gas in galaxy discs is highly turbulent, but there is much debate on which mechanism can energetically maintain this turbulence. Among the possible candidates, supernova (SN) explosions are likely the primary drivers but doubts remain on whether they can be sufficient in regions of moderate star formation activity, in particular in the outer parts of discs. In this paper, we measure the SN efficiency $\eta$, namely the fraction of the total SN energy needed to sustain turbulence in galaxies, and verify that SNe can indeed be the sole driving mechanism. The key novelty of our approach is that we take into account the increased turbulence dissipation timescale associated to the flaring in outer regions of gaseous discs. We analyse the distribution and kinematics of HI and CO in 10 nearby star-forming galaxies to obtain the radial profiles of the kinetic energy per unit area, for both the atomic gas and the molecular gas. We use a theoretical model to reproduce the observed energy with the sum of turbulent energy from SNe, as inferred from the observed star formation rate (SFR) surface density, and the gas thermal energy. We find that the observed kinetic energy is remarkably well reproduced by our model across the whole extent of the galactic discs, assuming $\eta$ constant with the galactocentric radius. Taking into account the uncertainties on the SFR surface density and on the atomic gas phase, we obtain that the median SN efficiencies for our sample of galaxies are $\langle \eta_\mathrm{atom} \rangle=0.015_{-0.008}^{+0.018}$ for the atomic gas and $\langle \eta_\mathrm{mol} \rangle = 0.003_{-0.002}^{+0.006}$ for the molecular gas. We conclude that SNe alone can sustain gas turbulence in nearby galaxies with only few percent of their energy and that there is essentially no need for any further source of energy., Comment: 18 pages, 6 figures, and 2 appendices; accepted by Astronomy & Astrophysics; abridged abstract

The evolution of the structural and kinematic properties of early-type galaxies (ETGs), their scaling relations, as well as their stellar metallicity and age contain precious information on the assembly history of these systems. We present results on the evolution of the stellar mass-velocity dispersion relation of ETGs, focusing in particular on the effects of some selection criteria used to define ETGs. We also try to shed light on the role that in-situ and ex-situ stellar populations have in massive ETGs, providing a possible explanation of the observed metallicity distributions., Comment: 5 pages, 2 figures. To appear in Proceedings of IAU Symposium 359 (T. Storchi-Bergmann, R. Overzier, W. Forman & R. Riffel, eds.)

We present the first analysis of the stellar content of the structures and substructures identified in the peculiar star-forming galaxy NGC5474, based on Hubble Space Telescope resolved photometry from the LEGUS survey. NGC5474 is a satellite of the giant spiral M101, and is known to have a prominent bulge that is significantly off-set from the kinematic center of the underlying HI and stellar disc. The youngest stars (age~ 100 Myr) trace a flocculent spiral pattern extending out to ~8 kpc from the center of the galaxy. On the other hand intermediate-age (age > 500 Myr) and old (age > 2 Gyr) stars dominate the off-centred bulge and a large substructure residing in the South Western part of the disc and not correlated with the spiral arms (SW over-density). The old age of the stars in the SW over-density suggests that this may be another signature of the dynamical interaction/s that have shaped this anomalous galaxy. We suggest that a fly by with M101, generally invoked as the origin of the anomalies, may not be sufficient to explain all the observations. A more local and more recent interaction may help to put all the pieces of this galactic puzzle together., Comment: Accepted for publication on Astronomy & Astrophysics. Latex, 10 pages, 12 figures (colors)

Present-day elliptical, spiral and irregular galaxies are large systems made of stars, gas and dark matter. Their properties result from a variety of physical processes that have occurred during the nearly fourteen billion years since the Big Bang. This comprehensive textbook, which bridges the gap between introductory and specialized texts, explains the key physical processes of galaxy formation, from the cosmological recombination of primordial gas to the evolution of the different galaxies that we observe in the Universe today. In a logical sequence, the book introduces cosmology, illustrates the properties of galaxies in the present-day Universe, then explains the physical processes behind galaxy formation in the cosmological context, taking into account the most recent developments in this field. The text ends on how to find distant galaxies with multi-wavelength observations, and how to extract the physical and evolutionary properties based on imaging and spectroscopic data., Comment: 17 pages, 3 figures, first introductory chapter of the textbook published by Cambridge University Press. For more information https://decdb4ae-c884-4971-9114-5f11b6929fd9.filesusr.com/ugd/f44359_26d2207ea96e4f359636feb5b7473336.pdf

The Smallest Scale of Hierarchy (SSH) survey is an ongoing strategic large program at the Large Binocular Telescope, aimed at the detection of faint stellar streams and satellites around 45 late-type dwarf galaxies located in the Local Universe within $\simeq$10 Mpc. SSH exploits the wide-field, deep photometry provided by the Large Binocular Cameras in the two wide filters $g$ and $r$. This paper describes the survey, its goals, and the observational and data reduction strategies. We present preliminary scientific results for five representative cases (UGC 12613, NGC 2366, UGC 685, NGC 5477 and UGC 4426) covering the whole distance range spanned by the SSH targets. We reach a surface brightness limit as faint as $\mu(r)\sim$ 31 mag arcsec$^{-2}$ both for targets closer than 4$-$5 Mpc, which are resolved into individual stars, and for more distant targets through the diffuse light. Our analysis reveals the presence of extended low surface brightness stellar envelopes around the dwarfs, reaching farther out than what traced by the integrated light, and as far out as, or even beyond, the observed HI disk. Stellar streams, arcs, and peculiar features are detected in some cases, indicating possible perturbation, accretion, or merging events. We also report on the discovery of an extreme case of Ultra Diffuse Galaxy ($\mu_g(0)=27.9$~mag/arcsec$^2$) in the background of one of our targets, to illustrate the power of the survey in revealing extremely low surface brightness systems., Comment: Accepted for publication in MNRAS

Several open questions on galaxy formation and evolution have their roots in the lack of a universal star formation law, that could univocally link the gas properties, e.g. its density, to the star formation rate (SFR) density. In a recent paper, we used a sample of nearby disc galaxies to infer the volumetric star formation (VSF) law, a tight correlation between the gas and the SFR volume densities derived under the assumption of hydrostatic equilibrium for the gas disc. However, due to the dearth of information about the vertical distribution of the SFR in these galaxies, we could not find a unique slope for the VSF law, but two alternative values. In this paper, we use the scale height of the SFR density distribution in our Galaxy adopting classical Cepheids (age$\lesssim 200$ Myr) as tracers of star formation. We show that this latter is fully compatible with the flaring scale height expected from gas in hydrostatic equilibrium. These scale heights allowed us to convert the observed surface densities of gas and SFR into the corresponding volume densities. Our results indicate that the VSF law $\rho_\mathrm{SFR} \propto \rho_\mathrm{gas}^\alpha$ with $\alpha \approx 2$ is valid in the Milky Way as well as in nearby disc galaxies., Comment: 9 pages, 4 figures, + 4 pages of Appendix, accepted by A&A

We study the evolution of the observed correlation between central stellar velocity dispersion $\sigma_\mathrm{e}$ and stellar mass $M_*$ of massive ($M_*\gtrsim 3\times 10^{10}\,\mathrm{M_\odot}$) early-type galaxies (ETGs) out to redshift $z\approx 2.5$, exploiting a Bayesian hierarchical inference formalism. Collecting ETGs from state-of-the-art literature samples, we build a $fiducial$ sample ($0\lesssim z\lesssim 1$), which is obtained with homogeneous selection criteria, but also a less homogeneous $extended$ sample ($0\lesssim z\lesssim 2.5$). Based on the fiducial sample, we find that the $M_*$-$\sigma_\mathrm{e}$ relation is well represented by $\sigma_\mathrm{e}\propto M_*^{\beta}(1+z)^{\zeta}$, with $\beta\simeq 0.18$ independent of redshift and $\zeta\simeq 0.4$ (at given $M_*$, $\sigma_\mathrm{e}$ decreases for decreasing $z$, for instance by a factor of $\approx1.3$ from $z=1$ to $z=0$). When the slope $\beta$ is allowed to evolve, we find it increasing with redshift: $\beta(z)\simeq 0.16+0.26\log(1+z)$ describes the data as well as constant $\beta\simeq 0.18$. The intrinsic scatter of the $M_*$-$\sigma_\mathrm{e}$ relation is $\simeq0.08$ dex in $\sigma_\mathrm{e}$ at given $M_*$, independent of redshift. Our results suggest that, on average, the velocity dispersion of $individual$ massive ($M_*\gtrsim 3\times 10^{11}\,M_\odot$) ETGs decreases with time while they evolve from $z\approx 1$ to $z\approx 0$. The analysis of the extended sample leads to results similar to that of the fiducial sample, with slightly stronger redshift dependence of the normalisation ($\zeta\simeq 0.5$) and weaker redshift dependence of the slope (${\rm d} \beta/{\rm d} \log (1+z)\simeq 0.18$) when $\beta$ varies with time. At $z=2$ ETGs with $M_*\approx 10^{11}\,M_\odot$ have, on average, $\approx1.7$ higher $\sigma_\mathrm{e}$ than ETGs of similar stellar mass at $z=0$., Comment: 26 pages, 15 figures, accepted for publication in MNRAS

We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a connection between Hurwitz zeta function and the cumulants of the beta-exponential distribution., Comment: 8 pages, 1 figure

We investigate the dynamics of supermassive black holes (SMBHs) in galactic cores by means of a semi-analytic model based on the Langevin equation, including dynamical friction and stochastic noise accounting for the gravitational interactions with stars. The model is validated against direct $N$-body simulations of intermediate-mass black holes in stellar clusters where a realistic number of particles is accessible. For the galactic case, we find that the SMBH experiences a Brownian-like motion with a typical displacement from the geometric center of the Galaxy of a few parsecs, for system parameters compatible with M87. \keywords{stellar dynamics, black hole physics, methods: n-body simulations, methods: statistical., Comment: 4 pages 2 figures. To appear in the Proceedings of the 351 IAU Symposium "Star Clusters: From the Milky Way to the Early Universe"

We address an issue that arises when self-consistently flattened dynamical stellar systems are constructed by adopting a distribution function (DF) that depends on the action integrals. The velocity distribution at points on the symmetry axis is controlled by the the dependence of the DF on just one action, while at points off the symmetry axis two actions are involved. Consequently, the physical requirement that the velocity distribution evolves continuously in the neighbourhood of the symmetry axis restricts the functional forms of acceptable DFs. An algorithm for conforming to this restriction is presented and used to construct a variety of flattened models., Comment: 9 pages, 7 figures. Submitted to MNRAS. Comments welcome

Nonparametric mixture models based on the Pitman-Yor process represent a flexible tool for density estimation and clustering. Natural generalization of the popular class of Dirichlet process mixture models, they allow for more robust inference on the number of components characterizing the distribution of the data. We propose a new sampling strategy for such models, named importance conditional sampling (ICS), which combines appealing properties of existing methods, including easy interpretability and a within-iteration parallelizable structure. An extensive simulation study highlights the efficiency of the proposed method which, unlike other conditional samplers, shows stable performances for different specifications of the parameters characterizing the Pitman-Yor process. We further show that the ICS approach can be naturally extended to other classes of computationally demanding models, such as nonparametric mixture models for partially exchangeable data., Comment: 39 pages, 10 figures

Dwarf spheroidal galaxies (dSphs) appear to be some of the most dark matter dominated objects in the Universe. Their dynamical masses are commonly derived using the kinematics of stars under the assumption of equilibrium. However, these objects are satellites of massive galaxies (e.g.\ the Milky Way) and thus can be influenced by their tidal fields. We investigate the implication of the assumption of equilibrium focusing on the Sculptor dSph by means of ad-hoc $N$-body simulations tuned to reproduce the observed properties of Sculptor following the evolution along some observationally motivated orbits in the Milky Way gravitational field. For this purpose, we used state-of-the-art spectroscopic and photometric samples of Sculptor's stars. We found that the stellar component of the simulated object is not directly influenced by the tidal field, while $\approx 30\%-60\%$ the mass of the more diffuse DM halo is stripped. We conclude that, considering the most recent estimate of the Sculptor proper motion, the system is not affected by the tides and the stellar kinematics represents a robust tracer of the internal dynamics. In the simulations that match the observed properties of Sculptor, the present-day dark-to-luminous mass ratio is $\approx 6$ within the stellar half-light radius ($\approx0.3$ kpc) and $>50$ within the maximum radius of the analysed dataset ($\approx1.5^\circ\approx2$ kpc)., Comment: 19 pages, 10 figures, accepted for publication in MNRAS. V3: updated after editor comments See our playlist for simulation videos: https://av.tib.eu/series/633/supplemental+videos+of+the+paper+the+effect+of+tides+on+the+sculptor+dwarf+spheroidal+galaxy