arXiv subjects

Alessandro Baldi

Publications and source records attributed to Alessandro Baldi.

12 recordsLinked to original sources

arXiv2025

An alternative approach to well-posedness of McKean-Vlasov equations arising in Consensus-Based Optimization

In this work we study the mean-field description of Consensus-Based Optimization (CBO), a derivative-free particle optimization method. Such a description is provided by a non-local SDE of McKean-Vlasov type, whose fields lack of global Lipschitz continuity. We propose a novel approach to prove the well-posedness of the mean-field CBO equation based on a truncation argument. The latter is performed through the introduction of a cut-off function, defined on the space of probability measures, acting on the fields. This procedure allows us to study the well-posedness problem in the classical framework of Sznitman. Through this argument, we recover the established result on the existence of strong solutions, and we extend the class of solutions for which pathwise uniqueness holds.

math.OC↗

arXiv2025

A general perspective on CBO methods with stochastic rate of information

This paper studies a class of Consensus-Based Optimization (CBO) models featuring an additional stochastic rate of information, modeling the agents' knowledge of the environment and energy landscape. The well-posedness of the stochastic system is proved, together with its finite-particle approximation and the mean-field convergence to a kinetic PDE. Particles are shown to concentrate around the consensus point under mild assumptions on the initial spatial distribution and initial level of knowledge. In particular, the analysis unveils that a positive, however small, initial level of knowledge is enough for convergence to consensus to happen. The framework presented is general enough to include the first instances of CBO proposed in the literature.

math.OC↗

arXiv2025

Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects

A multi-agent model for individuals endowed with strategies and subject to diffusive effects is proposed. The microscopic state of each agent is described by a spatial position and a probability measure, interpreted as a mixed strategy, over a compact metric space. The evolution is governed by a non-local interaction mechanism and by stochastic effects acting on the spatial component of the state. The well-posedness of the multi-agent system and that of a certain McKean--Vlasov stochastic differential equation are proved. Eventually, a propagation of chaos result is obtained, which guarantees that the former model converges to the latter as the number of agents goes to infinity.

math.AP↗

arXiv2016

Galaxy Cluster Pressure Profiles as Determined by Sunyaev Zel'dovich Effect Observations with MUSTANG and Bolocam II: Joint Analysis of Fourteen Clusters

We present pressure profiles of galaxy clusters determined from high resolution Sunyaev-Zel'dovich (SZ) effect observations of fourteen clusters, which span the redshift range $ 0.25 < z < 0.89$. The procedure simultaneously fits spherical cluster models to MUSTANG and Bolocam data. In this analysis, we adopt the generalized NFW parameterization of pressure profiles to produce our models. Our constraints on ensemble-average pressure profile parameters, in this study $\gamma$, $C_{500}$, and $P_0$, are consistent with those in previous studies, but for individual clusters we find discrepancies with the X-ray derived pressure profiles from the ACCEPT2 database. We investigate potential sources of these discrepancies, especially cluster geometry, electron temperature of the intracluster medium, and substructure. We find that the ensemble mean profile for all clusters in our sample is described by the parameters: $[\gamma,C_{500},P_0] = [0.3_{-0.1}^{+0.1}, 1.3_{-0.1}^{+0.1}, 8.6_{-2.4}^{+2.4}]$, for cool core clusters: $[\gamma,C_{500},P_0] = [0.6_{-0.1}^{+0.1}, 0.9_{-0.1}^{+0.1}, 3.6_{-1.5}^{+1.5}]$, and for disturbed clusters: $[\gamma,C_{500},P_0] = [0.0_{-0.0}^{+0.1}, 1.5_{-0.2}^{+0.1},13.8_{-1.6}^{+1.6}]$. Four of the fourteen clusters have clear substructure in our SZ observations, while an additional two clusters exhibit potential substructure.

astro-ph.CO↗

arXiv2016

The Morphologies and Alignments of Gas, Mass, and the Central Galaxies of CLASH Clusters of Galaxies

Morphology is often used to infer the state of relaxation of galaxy clusters. The regularity, symmetry, and degree to which a cluster is centrally concentrated inform quantitative measures of cluster morphology. The Cluster Lensing and Supernova survey with Hubble Space Telescope (CLASH) used weak and strong lensing to measure the distribution of matter within a sample of 25 clusters, 20 of which were deemed to be relaxed based on their X-ray morphology and alignment of the X-ray emission with the BCG. Towards a quantitative characterization of this important sample of clusters, we present uniformly estimated X-ray morphological statistics for all 25 CLASH clusters. We compare X-ray morphologies of CLASH clusters with those identically measured for a large sample of simulated clusters from the MUSIC-2 simulations, selected by mass. We confirm a threshold in X-ray surface brightness concentration of C>0.4 for cool-core clusters, where C is the ratio of X-ray emission inside 100 kpc/h70 compared to inside 500 kpc/h70. We report and compare morphologies of these clusters inferred from Sunyaev-Zeldovich Effect (SZE) maps of the hot gas and in from projected mass maps based on strong and weak lensing. We find a strong agreement in alignments of the orientation of major axes for the lensing, X-ray, and SZE maps of nearly all of the CLASH clusters at radii of 500 kpc (approximately 0.5R500 for these clusters). We also find a striking alignment of clusters shapes at the 500 kpc scale, as measured with X-ray, SZE, and lensing, with that of the near-infrared stellar light at 10 kpc scales for the 20 "relaxed" clusters. This strong alignment indicates a powerful coupling between the cluster- and galaxy-scale galaxy formation processes.

astro-ph.CO↗

arXiv2014

CLASH-X: A Comparison of Lensing and X-ray Techniques for Measuring the Mass Profiles of Galaxy Clusters

We present profiles of temperature (Tx), gas mass, and hydrostatic mass estimated from new and archival X-ray observations of CLASH clusters. We compare measurements derived from XMM and Chandra observations with one another and compare both to gravitational lensing mass profiles derived with CLASH HST and ground-based lensing data. Radial profiles of Chandra and XMM electron density and enclosed gas mass are nearly identical, indicating that differences in hydrostatic masses inferred from X-ray observations arise from differences in Tx measurements. Encouragingly, cluster Txs are consistent with one another at ~100-200 kpc radii but XMM Tx systematically decline relative to Chandra Tx at larger radii. The angular dependence of the discrepancy suggests additional investigation on systematics such as the XMM point spread function correction, vignetting and off-axis responses. We present the CLASH-X mass-profile comparisons in the form of cosmology-independent and redshift-independent circular-velocity profiles. Ratios of Chandra HSE mass profiles to CLASH lensing profiles show no obvious radial dependence in the 0.3-0.8 Mpc range. However, the mean mass biases inferred from the WL and SaWLens data are different. e.g., the weighted-mean value at 0.5 Mpc is = 0.12 for the WL comparison and = -0.11 for the SaWLens comparison. The ratios of XMM HSE mass profiles to CLASH lensing profiles show a pronounced radial dependence in the 0.3-1.0 Mpc range, with a weighted mean mass bias of value rising to ~0.3 at ~1 Mpc for the WL comparison and of 0.25 for SaWLens comparison. The enclosed gas mass profiles from both Chandra and XMM rise to a value 1/8 times the total-mass profiles inferred from lensing at 0.5 Mpc and remain constant outside of that radius, suggesting that [8xMgas] profiles may be an excellent proxy for total-mass profiles at >0.5 Mpc in massive galaxy clusters.

astro-ph.CO↗

arXiv2012

Mass, shape and thermal properties of A1689 by a multi-wavelength X-ray, lensing and Sunyaev-Zel'dovich analysis

Knowledge of mass and concentration of galaxy clusters is crucial to understand their formation and evolution. Unbiased estimates require the understanding of the shape and orientation of the halo as well as its equilibrium status. We propose a novel method to determine the intrinsic properties of galaxy clusters from a multi-wavelength data set spanning from X-ray spectroscopic and photometric data to gravitational lensing to the Sunyaev-Zel'dovich effect (SZe). The method relies on two quite non informative geometrical assumptions: the distributions of total matter or gas are approximately ellipsoidal and co-aligned; they have different, constant axial ratios but share the same degree of triaxiality. Weak and strong lensing probe the features of the total mass distribution in the plane of the sky. X-ray data measure size and orientation of the gas in the plane of the sky. Comparison with the SZ amplitude fixes the elongation of the gas along the line of sight. These constraints are deprojected thanks to Bayesian inference. The mass distribution is described as a Navarro-Frenk-White halo with arbitrary orientation, gas density and temperature are modelled with parametric profiles. We applied the method to Abell 1689. Independently of the priors, the cluster is massive, M_{200}=(1.3+-0.2)*10^{15}M_sun, and over-concentrated, c_{200}=8+-1, but still consistent with theoretical predictions. The total matter is triaxial (minor to major axis ratio ~0.5+-0.1 exploiting priors from N-body simulations) with the major axis nearly orientated along the line of sight. The gas is rounder (minor to major axis ratio ~0.6+-0.1) and deviates from hydrostatic equilibrium. The contribution of non-thermal pressure is ~20-50 per cent in inner regions, <~ 300 kpc, and ~25+-5 per cent at ~1.5 Mpc.

astro-ph.CO↗

arXiv2012

Self-similarity of temperature profiles in distant galaxy clusters: the quest for a Universal law

We present the XMM-Newton temperature profiles of 12 bright clusters of galaxies at 0.4 =0.6 as NCC clusters. The profiles of CC and NCC clusters differ mainly in the central regions, with the latters exhibiting a marginally flatter central profile. A significant dependence of the temperature profiles on the pseudo-entropy ratio sigma is detected by fitting a function of both r and sigma, showing an indication that the outer part of the profiles becomes steeper for higher values of sigma (i.e. transitioning towards the NCC clusters). No significant evidence of redshift evolution could be found within the redshift range sampled by our clusters (0.4 0.4 has been attempted, as we were able to define the closest possible relation to a Universal law for the temperature profiles of galaxy clusters at 0.1<z<0.9, showing a dependence on both the state of relaxation of the clusters and the redshift.

astro-ph.CO↗

arXiv2011

An XMM-Newton spatially-resolved study of metal abundance evolution in distant galaxy clusters

We present an XMM-Newton analysis of the X-ray spectra of 39 clusters of galaxies at 0.4 2sigma) abundance evolution with redshift. The most significant deviation from no evolution (90% c.l.) is observed in the emission from the whole cluster (r<0.6r500), that could be parametrized as Z=A*(1+z)^(-0.8+/-0.5). Dividing the emission in 3 radial bins, no significant evidence of abundance evolution could be observed fitting the data with a power-law. A substantial agreement with measures presented in previous works is found. The error-weighted mean of the spatially resolved abundances in 3 redshift bins is consistent to be constant with z. Although the large error bars in the measure of the weighted-mean abundance prevent us from claiming any significant spatially resolved evolution, the trend with z in the 0.15-0.4r500 radial bin complements nicely the measures of Maughan et al., and broadly agrees with theoretical predictions. We also found that the data points derived from the spatially resolved analysis are well fitted by the relation Z(r,z)=Z0*(1+(r/0.15r500)^2)^(-a)*((1+z)/1.6)^(-gamma), showing a significant negative trend of Z with the radius and no significant evolution with the redshift. The present study is the first attempt made to spatially resolve the evolution of abundance with redshift. However, the sample size and the low statistics associated with most of the clusters in the sample prevents us to draw any statistically significant conclusion on the different evolutionary path that the different regions of the clusters may have traversed.

astro-ph.CO↗

arXiv2005

Accretion and nuclear activity of quiescent supermassive black holes. II: optical study and interpretation

Our X-ray study of the nuclear activity in a new sample of six quiescent early-type galaxies, and in a larger sample from the literature, confirmed (Soria et al., Paper I) that the Bondi accretion rate of diffuse hot gas is not a good indicator of the supermassive black hole (SMBH) X-ray luminosity. Here we suggest that a more reliable estimate of the accretion rate must include the gas released by the stellar population inside the sphere of influence of the SMBH, in addition to the Bondi inflow of hot gas across that surface. We use optical surface-brightness profiles to estimate the mass-loss rate from stars in the nuclear region: we show that for our sample of galaxies it is an order of magnitude higher (~ 10^{-4} - 10^{-3} M_sun/yr) than the Bondi inflow rate of hot gas, as estimated from Chandra (Paper I). Only by taking into account both sources of fuel can we constrain the true accretion rate, the accretion efficiency, and the power budget. Radiatively efficient accretion is ruled out, for quiescent SMBHs. For typical radiatively inefficient flows, the observed X-ray luminosities of the SMBHs imply accretion fractions ~ 1 - 10% (ie, ~ 90 - 99% of the available gas does not reach the SMBH) for at least five of our six target galaxies, and most of the other galaxies with known SMBH masses. We discuss the conditions for mass conservation inside the sphere of influence, so that the total gas injection is balanced by accretion plus outflows. We show that a fraction of the total accretion power (mechanical plus radiative) would be sufficient to sustain a self-regulating, slow outflow which removes from the nuclear region all the gas that does not sink into the BH (``BH feedback''). The rest of the accretion power may be carried out in a jet, or advected. We also discuss scenarios that would lead to an intermittent nuclear activity.

astro-ph↗

arXiv2005

Accretion and nuclear activity of quiescent supermassive black holes. I: X-ray study

We have studied the nuclear activity in a sample of six quiescent early-type galaxies, with new Chandra data and archival HST optical images. Their nuclear sources have X-ray luminosities ~ 10^{38} - 10^{39} erg/s (L_X/L_Edd ~ 10^{-8} - 10^{-7}), and colors or spectra consistent with accreting supermassive black holes (SMBHs)--except for the nucleus of NGC 4486B, which is softer than typical AGN spectra. In a few cases, the X-ray morphology of the nuclear sources shows hints of marginally extended structures, in addition to the surrounding diffuse thermal emission from hot gas, which is detectable on scales >~ 1 kpc. In one case (NGC 5845), a dusty disk may partially obstruct our direct view of the SMBH. We have estimated the temperature and density of the hot interstellar medium, which is one major source of fuel for the accreting SMBH; typical central densities are n_e ~ (0.02 +/- 0.01) cm^{-3}. Assuming that the hot gas is captured by the SMBH at the Bondi rate, we show that the observed X-ray luminosities are too faint to be consistent with standard disk accretion, but brighter than predicted by radiatively-inefficient solutions (eg, ADAF). In total, there are ~ 20 galaxies for which SMBH mass, hot gas density, and nuclear X-ray luminosity are simultaneously known. In some cases, the nuclear sources are brighter than predicted by the ADAF model; in other cases, they are consistent or fainter. We discuss the apparent lack of correlations between Bondi rate and X-ray luminosity, and suggest that, in order to understand the observed distribution, we need to know two additional parameters: the amount of gas supplied by the stellar population inside the accretion radius, and the fraction (possibly << 1) of the total gas available that is accreted by the SMBH. We shall discuss these issues in our Paper II.

astro-ph↗

arXiv2001

A study of the core of the Shapley Concentration: VI. Spectral properties of galaxies

We present the results of a study of the spectral properties of galaxies in the central part of the Shapley Concentration, covering an extremely wide range of densities, from the rich cluster cores to the underlying supercluster environment. Our sample is homogeneous, in a well defined magnitude range (17=<b_J=<18.8) and contains ~1300 spectra of galaxies at the same distance, covering an area of ~26 sq.deg. These characteristics allowed an accurate spectral classification, that we performed using a Principal Components Analysis technique. This spectral classification, together with the [OII] equivalent widths and the star formation rates, has been used to study the properties of galaxies at different densities: cluster, intercluster (i.e. galaxies in the supercluster but outside clusters) and field environment. No significant differences are present between samples at low density regimes (i.e. intercluster and field galaxies). Cluster galaxies, instead, not only have values significantly different from the field ones, but also show a dependence on the local density. Moreover, a well defined morphology-density relation is present in the cluster complexes, although these structures are known to be involved in major merging events. Also the mean equivalent width of [OII] shows a trend with the local environment, decreasing at increasing densities, even if it is probably induced by the morphology-density relation. Finally we analyzed the mean star formation rate as a function of the density, finding again a decreasing trend (at ~ 3sigma significance level). Our analysis is consistent with the claim of Balogh et al. (1998) that the star formation in clusters is depressed.

astro-ph↗