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Andrés Balaguera-Antolínez

Publications and source records attributed to Andrés Balaguera-Antolínez.

18 recordsLinked to original sources
arXiv2026

Tracing Galaxy Bias Through the Cosmic Web: The Role of Filaments

The large-scale clustering of galaxies depends not only on their internal properties but also on their location within the cosmic web, which defines the anisotropic environments where galaxies form and evolve. Filaments serve as bridges through which galaxies and dark matter flow from low-density regions toward the highest-density nodes. In this work, we aim to map galaxy bias, which quantifies how these tracers follow the underlying dark matter density field, through the cosmic web, with a special emphasis on filaments. We look for dependencies on filament properties, such as length and density, and characterize the spatial variations of the large-scale bias along the filamentary spine. We applied the DisPerSE algorithm to identify the cosmic web in the TNG300 volume of the IllustrisTNG simulation. To measure large-scale galaxy bias, we utilized an object-by-object estimator, which provides advantages over standard estimators. We find that galaxies in node outskirts exhibit the highest large-scale bias values, reaching up to $\sim4$ times the values expected from theoretical models based on halo mass alone. Low-mass red galaxies in filaments and filament outskirts also display enhanced bias, which is strongly reduced after excluding galaxies close to nodes. Together, these results suggest that proximity to massive nodes plays a central role in shaping environmental secondary bias. Furthermore, galaxy bias decreases with filament length, from mean values of $1.4$ for short filaments to $-0.5$ for longer structures. This relation persists at fixed halo mass and galaxy color, and is not primarily driven by the average local galaxy density of the filament. Finally, short filaments exhibit an approximately uniform longitudinal bias profile, whereas long filaments show an increase in normalized bias from $\sim0.85$ near the saddle point to $\sim1.06$ close to the node.

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arXiv2026

Predicting galaxy bias using machine learning

Understanding how galaxies trace the underlying matter density field is essential for characterizing the influence of the large-scale structure on galaxy formation, being therefore a key ingredient in observational cosmology. This connection, commonly described through the galaxy bias, $b$, can be studied effectively using machine learning (ML) techniques, which offer strong predictive capabilities and can capture non-linear relationships. We aim to incorporate the linear bias parameter assigned to individual galaxies into a ML framework, quantify its dependence on various halo and environmental properties, and evaluate whether different algorithms can accurately predict this parameter and reproduce the scatter in several bias relations. We use data from the IllustrisTNG300 simulation, including the distance to different cosmic-web structures computed with DisPerSE. These data are complemented with an object-by-object estimator of the large-scale linear bias ($b_i$), providing the individual contribution of each galaxy to the bias of the entire population. Our ML framework uses three models to predict $b_i$: a Random Forest Regressor, a Neural Network and a probabilistic method (Normalizing Flows). We recover the full hierarchy of galaxy bias dependencies, showing that the most informative features are the overdensities, particularly $δ_8$, followed by the distances to cosmic-web structures and selected internal halo properties, most notably $z_{1/2}$. We also demonstrate that Normalizing Flows clearly outperform deterministic methods in predicting galaxy bias, including its joint distributions with galaxy properties, owing to their ability to capture the intrinsic variance associated with the stochastic nature of the matter-halo-galaxy connection. Our ML framework provides a foundation for future efforts to measure individual bias with upcoming spectroscopic surveys.

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arXiv2026

The Galaxy Bias Profile of Cosmic Voids:A Comparison of Void Finders

Cosmic voids, the largest underdense regions in the Universe, provide unique laboratories for studying galaxy formation and constitute powerful probes of cosmology. Recent work has shown that individual galaxy bias (b_i), which quantifies how each galaxy traces the underlying dark matter field, exhibits a characteristic radial dependence within spherical voids, defining a void bias profile in which galaxies near void centers display systematically lower bias values. We investigate how the environmental modulation of individual galaxy bias depends on the adopted void-finding algorithm by comparing measurements across five distinct void definitions: spherical voids 'sparkling', watershed-based methods ('zobov' and 'revolver' in two modes), and free-form integrated-density voids ('popcorn'). We apply these complementary void-finding algorithms to the same galaxy sample drawn from the IllustrisTNG simulation (TNG300-1 at $z=0$) and compute individual galaxy bias profiles as a function of distance from void centers. We quantify the correlation between b_i and the membership of the void catalogs and explore how this relationship varies with the integrated underdensity threshold for density-based methods. We find that the radial gradient of individual bias within voids, generally increasing from negative values at the void centers to higher values at the boundaries, is robust across most void definitions. However, density-threshold methods preferentially select galaxies with b_i<0, while watershed methods without density constraints include substantial contamination from high-bias boundary galaxies. The correlation between negative bias and void membership is systematically strengthened as the integrated underdensity threshold becomes less restrictive, with popcorn achieving the highest purity in isolating anti-biased populations.

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arXiv2025

The galaxy bias profile of cosmic voids

Cosmic voids are underdense regions within the large-scale structure of the Universe, spanning a wide range of physical scales - from a few megaparsecs (Mpc) to the largest observable structures. Their distinctive properties make them valuable cosmological probes and unique laboratories for galaxy formation studies. A key aspect to investigate in this context is the galaxy bias, $b$, within voids - that is, how galaxies in these underdense regions trace the underlying dark-matter density field. We want to measure the dependence of the large-scale galaxy bias on the distance to the void center, and to evaluate whether this bias profile varies with the void properties and identification procedure. We apply a void identification scheme based on spherical overdensities to galaxy data from the IllustrisTNG magnetohydrodynamical simulation. For the clustering measurement, we use an object-by-object estimate of large-scale galaxy bias, which offers significant advantages over the standard method based on ratios of correlation functions or power spectra. We find that the average large-scale bias of galaxies inside voids tends to increase with void-centric distance when normalized by the void radius. For the entire galaxy population within voids, the average bias rises with the density of the surrounding environment and, consequently, decreases with increasing void size. Due to this environmental dependence, the average galaxy bias inside S-type voids - embedded in large-scale overdense regions - is significantly higher ($\langle b\rangle_{\rm in} > 0$) at all distances compared to R-type voids, which are surrounded by underdense regions ($\langle b\rangle_{\rm in} < 0$). The bias profile for S-type voids is also slightly steeper. Since both types of voids host halo populations of similar mass, the measured difference in bias can be interpreted as a secondary bias effect.

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arXiv2025

Power spectrum of the CODEX clusters

Aims. We analyze the clustering of galaxy clusters in a large contiguous sample, the Constrain Dark Energy with X-ray (CODEX) sample. We construct a likelihood for cosmological parameters by comparing the measured clustering signal and a theoretical prediction, and use this to obtain parameter constraints. Methods. We measured the three multipole moments (monopole, quadrupole, and hexadecapole, $\ell = 0, 2, 4$) of the power spectrum of a subset of the CODEX clusters. To fully model cluster clustering, we also determined the expected clustering bias of the sample using estimates for the cluster masses and a mass-to-bias model calibrated using N-body simulations. We estimated the covariance matrix of the measured power spectrum multipoles using a set of simulated dark-matter halo catalogs. Combining all these ingredients, we performed a Markov chain Monte Carlo sampling of cosmological parameters $Ω_m$ and $σ_8$ to obtain their posterior. Results. We found the CODEX clustering signal to be consistent with an earlier X-ray selected cluster sample, the REFLEX II sample. We also found that the measured power spectrum multipoles are compatible with the predicted, bias-scaled linear matter power spectrum when the cosmological parameters determined by the Planck satellite are assumed. Furthermore, we found the marginalized parameter constraints of $Ω_m = 0.24^{+0.06}_{-0.04}$ and $σ_8 = 1.13^{+0.43}_{-0.24}$. The full 2D posterior is consistent, for example, with the Planck cosmology within the 68% confidence region.

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arXiv2025

Individual halo bias in models of $f(R)$ gravity

Halo bias links the statistical properties of the spatial distribution of dark matter halos to those of the underlying dark matter field, providing insights into clustering properties in both general relativity (GR) and modified-gravity scenarios such as $f(R)$ models. While the primary halo mass-dependent bias has been studied in detailed, the secondary bias, which accounts for the additional dependencies on other internal halo properties, can offer a sensitive probe for testing gravity beyond the $Λ$CDM model. To quantify any potential deviations between $Λ$CDM and $f(R)$ gravity models in halo clustering, at both the primary and secondary level, as well as in the distributions of halo properties in the cosmic web. Using $N$-body simulations of $f(R)$ gravity models, we assess the scaling relations and the primary and secondary bias signals of halo populations on the basis of a halo-by-halo estimator of large-scale effective bias. Our analysis is performed using halo number density as the independent variable. The relative difference in the effective bias between the $f(R)$ models and $Λ$CDM is sensitive, albeit slightly, to the power index of modified gravity. The largest deviations from GR are measured for low-mass halos, where the average bias at fixed number density decreases by up to 5\% for fixed scaling indices. We also show that the scaling relations for some environmental properties, including neighbour statistics, Mach number and local overdensity, exhibit small but non-negligible deviations (~3-5\%) from GR for a wide range of number densities. Our results also suggests that the properties of halos in sheets and voids show the largest departures from GR (> 10\% in some cases). In terms of secondary bias, we do not find any statistically significant deviations with respect to $Λ$CDM for any of the properties explored in this work.

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arXiv2024

Field-level Lyman-alpha forest modelling in redshift space via augmented non-local Fluctuating Gunn-Peterson Approximation

We present an improved analytical model to predict the Lyman-alpha forest at the field level in redshift space from the dark matter field, expanding upon the widely-used Fluctuating Gunn-Peterson approximation (FGPA). In particular, we introduce the dependence on the cosmic web environment (knots, filaments, sheets, voids) in the model, thereby effectively accounting for non-local bias. Furthermore, we include a detailed treatment of velocity bias in the redshift space distortions modelling, allowing the velocity bias to be cosmic-web dependent. We find evidence for a significant difference of the same model parameters in different environments, suggesting that for the investigated setup the simple standard FGPA is not able to adequately predict the Lyman-alpha forest in the different cosmic web regimes. We reproduce the summary statistics of the reference cosmological hydrodynamic simulation we use for comparison, yielding accurate mean transmitted flux, probability distribution function, 3D power spectrum, and bispectrum. In particular, we achieve maximum deviation and average deviations accuracy in the Lyman-alpha forest 3D power spectrum of $\sim 3\%$ and $\sim 0.1\%$ up to $k\sim 0.4 \, h \, {\rm Mpc}^{-1}$, $\sim 5\%$ and $\sim 1.8\%$ up to $k \sim 1.4 \, h \, {\rm Mpc}^{-1}$. Our new model outperforms previous analytical efforts to predict the Lyman-alpha forest at the field level in all the probed summary statistics, and has the potential to become instrumental in the generation of fast accurate mocks for covariance matrices estimation in the context of current and forthcoming Lyman-alpha forest surveys.

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arXiv2024

Fast simulation mapping: from standard to modified gravity cosmologies using the bias assignment method

We assess the effectiveness of a non-parametric bias model in generating mock halo catalogues for modified gravity (MG) cosmologies, relying on the distribution of dark matter from either MG or $Λ$CDM. We aim to generate halo catalogues that effectively capture the distinct impact of MG, ensuring high accuracy in both two- and three-point statistics for comprehensive analysis of large-scale structures. As part of this study we aim at investigating the inclusion of MG into non-local bias to directly map the tracers onto $Λ$CDM fields, which would save many computational costs. We employ the bias assignment method (BAM) to model halo distribution statistics by leveraging seven high-resolution COLA simulations of MG cosmologies. Taking into account cosmic-web dependencies when learning the bias relations, we design two experiments to map the MG effects: one utilising the consistent MG density fields and the other employing the benchmark $Λ$CDM density field. BAM generates MG halo catalogues from both calibrations experiments excelling in summary statistics, achieving a $\sim 1\%$ accuracy in the power spectrum across a wide range of $k$-modes, with only minimal differences well below 10\% at modes subject to cosmic variance, particularly below $k<0.07$ $h$Mpc$^{-1}$. The reduced bispectrum remains consistent with the reference catalogues within 10\% for the studied configuration. Our results demonstrate that a non-linear and non-local bias description can model the effects of MG starting from a $Λ$CDM dark matter field.

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arXiv2024

Secondary halo bias through cosmic time I: Scaling relations and the connection with the cosmic web

We measure the signal of secondary halo bias as a function of a variety of intrinsic and environmental halo properties, and characterize its statistical significance as a function of cosmological redshift. Using fixed and paired $N$-body simulations of dark-matter halos -- the UNIT simulation -- with masses above $10^{11}M_{\odot}h^{-1}$ identified over a wide range of cosmological redshifts (0<z<5), we explore the behavior of the scaling relations among different halo properties. We include novel environmental properties based on the halo distribution as well as the underlying dark-matter field. We implement an object-by-object estimator of large-scale effective bias and test its validity against standard approaches. With a bias assigned to each tracer, we perform a statistical analysis aiming at characterizing the distribution of bias and the signal of secondary halo bias. We show how the halo scaling relations linking direct probes of the halo potential well do not depend on the environment. On the contrary, links between halo mass and the so called set of secondary halo properties are sensitive to the cosmological environment. We show that the signal of secondary bias derives statistically from secondary correlations beyond the standard link to halo mass. We also show that the secondary bias arise through non-local and/or environmental properties related either to the halo distribution or to the properties of the underlying dark-matter field. Properties such as the tidal field and the local Mach number generates the signals of secondary bias with the highest significance. We propose applications of the assignment of individual bias for the generation of mock catalogs containing the signal of secondary bias, as well as a series of cosmological analyses aiming at mining large galaxy data sets.

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arXiv2023

DESI Mock Challenge: Halo and galaxy catalogs with the bias assignment method

We present a novel approach to the construction of mock galaxy catalogues for large-scale structure analysis based on the distribution of dark matter halos obtained with effective bias models at the field level. We aim to produce mock galaxy catalogues capable of generating accurate covariance matrices for a number of cosmological probes that are expected to be measured in current and forthcoming galaxy redshift surveys (e.g. two- and three-point statistics). We use the bias assignment method (BAM) to model the statistics of halo distribution through a learning algorithm using a few detailed $N$-body simulations, and approximated gravity solvers based on Lagrangian perturbation theory. Using specific models of halo occupation distributions, we generate galaxy mocks with the expected number density and central-satellite fraction of emission-line galaxies, which are a key target of the DESI experiment. BAM generates mock catalogues with per cent accuracy in a number of summary statistics, such as the abundance, the two- and three-point statistics of halo distributions, both in real and redshift space. In particular, the mock galaxy catalogues display $\sim 3\%-10\%$ accuracy in the multipoles of the power spectrum up to scales of $k\sim 0.4\,h^{-1}{\rm Mpc}$. We show that covariance matrices of two- and three-point statistics obtained with BAM display a similar structure to the reference simulation. BAM offers an efficient way to produce mock halo catalogues with accurate two- and three-point statistics, and is able to generate a variety of multi-tracer catalogues with precise covariance matrices of several cosmological probes. We discuss future developments of the algorithm towards mock production in DESI and other galaxy-redshift surveys. (Abridged)

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arXiv2022

The cosmic web connection to the dark matter halo distribution through gravity

This work investigates the connection between the cosmic web and the halo distribution through the gravitational potential at the field level. We combine three fields of research, cosmic web classification, perturbation theory expansions of the halo bias, and halo (galaxy) mock catalogue making methods. In particular, we use the invariants of the tidal field and the velocity shear tensor as generating functions to reproduce the halo number counts of a reference catalogue from full gravity calculations, populating the dark matter field on a mesh well into the non-linear regime ($3\,h^{-1}\,{\rm Mpc}$ scales). Our results show an unprecedented agreement with the reference power spectrum within 1% up to $k=0.72\,h\,{\rm Mpc}^{-1}$. By analysing the three-point statistics on large scales (configurations of up to $k=0.2\,h\,{\rm Mpc}^{-1}$), we find evidence for non-local bias at the 4.8 $σ$ confidence level, being compatible with the reference catalogue. In particular, we find that a detailed description of tidal anisotropic clustering on large scales is crucial to achieve this accuracy at the field level. These findings can be particularly important for the analysis of the next generation of galaxy surveys in mock galaxy production.

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arXiv2022

Mapping Lyman-alpha forest three-dimensional large scale structure in real and redshift space

This work presents a new physically-motivated supervised machine learning method, Hydro-BAM, to reproduce the three-dimensional Lyman-$α$ forest field in real and in redshift space learning from a reference hydrodynamic simulation, thereby saving about 7 orders of magnitude in computing time. We show that our method is accurate up to $k\sim1\,h\,\rm{Mpc}^{-1}$ in the one- (PDF), two- (power-spectra) and three-point (bi-spectra) statistics of the reconstructed fields. When compared to the reference simulation including redshift space distortions, our method achieves deviations of $\lesssim2\%$ up to $k=0.6\,h\,\rm{Mpc}^{-1}$ in the monopole, $\lesssim5\%$ up to $k=0.9\,h\,\rm{Mpc}^{-1}$ in the quadrupole. The bi-spectrum is well reproduced for triangle configurations with sides up to $k=0.8\,h\,\rm{Mpc}^{-1}$. In contrast, the commonly-adopted Fluctuating Gunn-Peterson approximation shows significant deviations already neglecting peculiar motions at configurations with sides of $k=0.2-0.4\,h\,\rm{Mpc}^{-1}$ in the bi-spectrum, being also significantly less accurate in the power-spectrum (within 5$\%$ up to $k=0.7\,h\,\rm{Mpc}^{-1}$). We conclude that an accurate analysis of the Lyman-$α$ forest requires considering the complex baryonic thermodynamical large-scale structure relations. Our hierarchical domain specific machine learning method can efficiently exploit this and is ready to generate accurate Lyman-$α$ forest mock catalogues covering large volumes required by surveys such as DESI and WEAVE.

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arXiv2021

The bias from hydrodynamic simulations: mapping baryon physics onto dark matter fields

This paper investigates the hierarchy of baryon physics assembly bias relations obtained from state-of-the-art hydrodynamic simulations with respect to the underlying cosmic web spanned by the dark matter field. Using the Bias Assignment Method (BAM) we find that non-local bias plays a central role. We classify the cosmic web based on the invariants of the curvature tensor defined not only by the gravitational potential, but especially by the over-density, as small scale clustering becomes important in this context. First, the gas density bias relation can be directly mapped onto the dark matter density field to high precision exploiting the strong correlation between them. In a second step, the neutral hydrogen is mapped based on the dark matter and the gas density fields. Finally, the temperature is mapped based on the previous quantities. This permits us to statistically reconstruct the baryon properties within the same simulated volume finding percent-precision in the two-point statistics and compatible results in the three-point statistics, in general within 1-$σ$, with respect to the reference simulation (with 5 to 6 orders of magnitude less computing time). This paves the path to establish the best set-up for the construction of mocks probing the intergalactic medium for the generation of such key ingredients in the statistical analysis of large forthcoming missions such as DESI, Euclid, J-PAS and WEAVE.

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arXiv2019

One simulation to have them all: performance of the Bias Assignment Method against N-body simulations

In this paper we demonstrate that the information encoded in \emph{one} single (sufficiently large) $N$-body simulation can be used to reproduce arbitrary numbers of halo catalogues, using approximated realisations of dark matter density fields with different initial conditions. To this end we use as a reference one realisation (from an ensemble of $300$) of the Minerva $N$-body simulations and the recently published Bias Assignment Method to extract the local and non-local bias linking the halo to the dark matter distribution. We use an approximate (and fast) gravity solver to generate $300$ dark matter density fields from the down-sampled initial conditions of the reference simulation and sample each of these fields using the halo-bias and a kernel, both calibrated from the arbitrarily chosen realisation of the reference simulation. We show that the power spectrum, its variance and the three-point statistics are reproduced within $\sim 2\%$ (up to $k\sim1.0\,h\,{\rm Mpc}^{-1}$), $\sim 5-10\%$ and $\sim 10\%$, respectively. Using a model for the real space power spectrum (with three free bias parameters), we show that the covariance matrices obtained from our procedure lead to parameter uncertainties that are compatible within $\sim 10\%$ with respect to those derived from the reference covariance matrix, and motivate approaches that can help to reduce these differences to $\sim 1\%$. Our method has the potential to learn from one simulation with moderate volumes and high-mass resolution and extrapolate the information of the bias and the kernel to larger volumes, making it ideal for the construction of mock catalogues for present and forthcoming observational campaigns such as Euclid or DESI.

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arXiv2019

Comparing approximate methods for mock catalogues and covariance matrices I: correlation function

This paper is the first in a set that analyses the covariance matrices of clustering statistics obtained from several approximate methods for gravitational structure formation. We focus here on the covariance matrices of anisotropic two-point correlation function measurements. Our comparison includes seven approximate methods, which can be divided into three categories: predictive methods that follow the evolution of the linear density field deterministically (ICE-COLA, Peak Patch, and Pinocchio), methods that require a calibration with N-body simulations (Patchy and Halogen), and simpler recipes based on assumptions regarding the shape of the probability distribution function (PDF) of density fluctuations (log-normal and Gaussian density fields). We analyse the impact of using covariance estimates obtained from these approximate methods on cosmological analyses of galaxy clustering measurements, using as a reference the covariances inferred from a set of full N-body simulations. We find that all approximate methods can accurately recover the mean parameter values inferred using the N-body covariances. The obtained parameter uncertainties typically agree with the corresponding N-body results within 5% for our lower mass threshold, and 10% for our higher mass threshold. Furthermore, we find that the constraints for some methods can differ by up to 20% depending on whether the halo samples used to define the covariance matrices are defined by matching the mass, number density, or clustering amplitude of the parent N-body samples. The results of our configuration-space analysis indicate that most approximate methods provide similar results, with no single method clearly outperforming the others.

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arXiv2019

Comparing approximate methods for mock catalogues and covariance matrices II: Power spectrum multipoles

We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constrains related to growth rate of structure, Alcock-Paczynski distortions and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE-COLA, Pinocchio and PeakPatch), methods that rely on halo assignment schemes onto dark-matter overdensities calibrated with a target N-body run (Halogen, Patchy) and two standard assumptions about the full density PDF (Gaussian and Lognormal). We benchmark their performance against a set of three hundred N-body simulations, running similar sets of approximate simulations with matched initial conditions, for each method. We find that most methods reproduce the monopole to within $5\%$, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within $10\%$. Overall, we find that covariances built from approximate simulations yield errors on model parameters within $10\%$ of those from the N-body based covariance.

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arXiv2018

Comparing approximate methods for mock catalogues and covariance matrices III: Bispectrum

We compare the measurements of the bispectrum and the estimate of its covariance obtained from a set of different methods for the efficient generation of approximate dark matter halo catalogs to the same quantities obtained from full N-body simulations. To this purpose we employ a large set of three-hundred realisations of the same cosmology for each method, run with matching initial conditions in order to reduce the contribution of cosmic variance to the comparison. In addition, we compare how the error on cosmological parameters such as linear and nonlinear bias parameters depends on the approximate method used for the determination of the bispectrum variance. As general result, most methods provide errors within 10% of the errors estimated from N-body simulations. Exceptions are those methods requiring calibration of the clustering amplitude but restrict this to two-point statistics. Finally we test how our results are affected by being limited to a few hundreds measurements from N-body simulation, and therefore to the bispectrum variance, by comparing with a larger set of several thousands realisations performed with one approximate method.

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arXiv2014

What can the spatial distribution of galaxy clusters tell about their scaling relations?

We aim to quantify the capability of the inhomogeneous distribution of galaxy clusters, represented by the two-point statistics in Fourier space, to retrieve information on the underlying scaling relations. We make a case study using the mass X-ray luminosity scaling relation for galaxy clusters and study its impact on the clustering pattern of these objects. We define the luminosity-weighted power spectrum and introduce the luminosity power spectrum as direct assessment of the clustering of the property of interest, in our case, the cluster X-ray luminosity. Using a suite of halo catalogs extracted from N-body simulations and realistic estimates of the mass X-ray luminosity relation, we measured these statistics with their corresponding covariance matrices. By carrying out a Fisher matrix analysis, we quantified the content of information (by means of a figure-of merit) encoded in the amplitude, shape, and full shape of our probes for two-point statistics. The full shape of the luminosity power spectrum, when analyzed up to scales of k~0.2 h/Mpc, yields a figure of merit which is two orders of magnitude above the figure obtained from the unweighted power spectrum, and only one order of magnitude below the value encoded in X-ray luminosity function estimated from the same sample. This is a significant improvement over the analysis developed with the standard (i.e., unweighted) clustering probes. The measurements of the clustering of galaxy clusters and its explicit dependence on the cluster intrinsic properties can contribute to improving the degree of knowledge regarding the underlying links between cluster observables and the cluster masses (Abridged).

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