arXiv subjects

Carlo Giocoli

Publications and source records attributed to Carlo Giocoli.

At least 19 recordsLinked to original sources

arXiv2026

Lambda as a Probe of Lensing Consistency

We introduce a framework to identify the radial transition in mass reconstruction reliability between strong and weak gravitational lensing in galaxy clusters. In weak lensing reconstruction, the convergence recovered from the reduced shear is subject to the mass-sheet degeneracy. We demonstrate that the degeneracy itself can serve as an indicator of the reconstruction reliability, and introduce a spatially resolved parameter $\lambda(r)$ to characterize this as a function of radius. We validate this approach on simulated clusters with realistic observational noise, and show that $\lambda(r)$ naturally quantifies the relative reliability of the two probes. Furthermore, when the global mass-sheet parameter $\lambda$ is constrained directly using strong lensing information, the tightest constraints arise where the two probes achieve comparable precision. This provides a quantitative basis for joint strong and weak lensing mass reconstruction.

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arXiv2026

CHEX-MATE: AMALGAM weak-lensing analysis of 41 Planck Sunyaev-Zel'dovich-selected galaxy clusters

We present a weak-lensing shear analysis of 41 Planck SZ-selected galaxy clusters at $0.11\le z\le 0.55$ from the CHEX-MATE sample, using wide-field Subaru/Suprime-Cam and CFHT/MegaPrime imaging from the AMALGAM project. We detect the azimuthally averaged weak-lensing signal around the X-ray peak of each cluster, achieving a median S/N of 6.5 per cluster. The $45^\circ$-rotated component has a median S/N of -0.1 and ranges from -1.8 to +1.8, consistent with zero. We model the excess surface mass density profile of each cluster with an NFW profile to infer weak-lensing mass and concentration constraints. The total systematic uncertainty in the weak-lensing mass calibration is assessed to be $8\%$. Using a hierarchical Bayesian framework, we then derive weak-lensing-calibrated scaling relations for the halo concentration, $c_{200}$, as a function of $M_{200}$ and redshift, and for the Planck SZ mass proxy, $M_{SZ}$, as a function of $M_{500}$ and redshift, while accounting for sample selection effects, weak-lensing modelling biases, and residual calibration uncertainty. At $M_{200}=10^{15}M_\odot$ and $z=0.25$, we find $c_{200}=3.53\pm0.71$ with an intrinsic scatter of $0.22\pm0.04$ dex. The inferred normalisation and scatter are consistent with recent $\Lambda$CDM predictions for massive haloes, with no significant mass or redshift dependence over the probed range. For the Planck mass proxy, our baseline regression yields $M_{SZ}/M_{500}=0.83\pm0.09$ at $M_{500}=7\times10^{14}M_\odot$ and $z=0.25$, with an intrinsic scatter of $0.10\pm0.02$ dex. A restricted model with fixed unit mass slope and no redshift evolution gives $1-b=0.72\pm0.11$. We also provide weak-lensing-calibrated posterior estimates of $M_{500}$ for the sample based on the baseline $M_{SZ}$--$M_{500}$--$z$ relation. These results provide an initial weak-lensing mass calibration for CHEX-MATE multi-probe cluster studies.

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arXiv2026

Weak lensing higher-order statistics to disentangle modified gravity and massive neutrinos

Going beyond second order in weak lensing (WL) statistics is known to break degeneracies among cosmological parameters. We take a step further here, investigating whether higher-order statistics (HOS) in weak lensing can disentangle among General Relativity (GR) and modified gravity (MG), also taking into account the presence of massive neutrinos. To this end, we rely on mock convergence maps obtained from GR and $f(R)$ gravity N - body simulations, and we look for MG signatures in a wide set of higher-order WL probes. We rely on different metrics to quantify the discriminatory power of each probe, also varying the measurement setup. We find out that WL HOS can indeed disentangle MG and GR also in the presence of massive neutrinos.

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arXiv2025

Standard Sirens in 2040s: Probing the Cosmic Expansion History with Gravitational Waves and Spectroscopic Galaxy Surveys

Gravitational waves (GWs) from compact binary coalescences have matured into a robust cosmological probe, providing self-calibrated luminosity distance measurements independent of any cosmic distance ladder, hence the term "standard sirens". The binary neutron star merger GW170817 delivered the first such measurement of the Hubble constant, demonstrating that GWs offer a path to precision cosmology with systematics orthogonal to standard cosmological probes. To convert GW distances into cosmological parameters, redshift information is essential. To maximize the scientific potential, the redshift must be obtained from individual galaxies, either by identifying electromagnetic counterparts of GW events (bright sirens) or by statistically associating potential hosts within the GW localization volume (dark sirens). The precision of these redshifts sets the achievable accuracy. Forecasts show that photometric uncertainties degrade cosmological constraints by up to an order of magnitude compared to spectroscopic ones. Wide-field, high-multiplex spectroscopic facilities will therefore be an essential infrastructure for GW cosmology in the 2040s.

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arXiv2025

The AIDA-TNG project. Abundance, radial distribution, and clustering properties of halos in alternative dark matter models

Warm and self-interactive dark matter cosmologies have been proposed as nonbaryonic solutions to the tensions between the $\Lambda$ cold dark matter model and observations at the kiloparsec scale. In this paper, we used the dark matter-only runs of the \textsc{aida-tng} project, a set of cosmological simulations of different sizes and resolutions, to analyze the macroscopic impact of alternative dark matter models on the abundance, radial distribution, and clustering properties of halos. We adopted the halo occupation distribution formalism to characterize the evolution of its parameters $M_1$ and $\alpha$ with the mass and redshift selection of our sample. By dividing the halo population into centrals and satellites, we were able to study their spatial density profile. We found that a Navarro-Frenk-White model is not accurate enough to describe the radial distribution of subhalos and that a generalized Navarro-Frenk-White model is required instead. Warm dark matter models, in particular, present a cuspier distribution of satellites, whereas self-interacting dark matter exhibits a shallower density profile. Moreover, we found that the small-scale clustering of dark matter halos provides a powerful tool for distinguishing among alternative dark matter scenarios, in preparation for a more detailed study that fully incorporates baryonic effects and for a comparison with observational data from galaxy clustering.

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arXiv2025

The AIDA-TNG project: dark matter profiles and concentrations in alternative dark matter models

In the standard Cold Dark Matter (CDM) scenario, the density profiles of dark matter haloes are well described by analytical models linking their concentration to halo mass. Alternative scenarios, such as warm dark matter (WDM) and self-interacting dark matter (SIDM), modify the inner structure of haloes and predict different profile shapes and central slopes. We employ the AIDA-TNG simulations to investigate how alternative dark matter physics and baryonic processes jointly shape the internal structure of haloes. Using dark-matter-only and full-physics runs, we measure the dark matter density profiles of haloes spanning six orders of magnitude in mass, from 10^9.5 Msun to 10^14.5 Msub, and characterise them with multiple analytical models. We provide the distribution of the best-fitting parameters, as well as the concentration-mass relation in WDM and SIDM. The Einasto profile well reproduces the inner flattening produced in WDM models, both in the collisionless and in the full-physics runs. In SIDM dark-matter-only runs, haloes are better described by explicitly cored profiles, with core sizes that depend on mass and on the self-interaction model. When baryons are included, the differences between CDM and SIDM decrease, and such large dark-matter cores no longer form because adiabatic contraction in the baryon-dominated region counteracts self-interactions. Nevertheless, the coupling between baryons and self-interactions induces a broader range of inner slopes, including cases that are steeper than CDM at Milky Way masses. Alternative dark matter physics thus leaves clear signatures in the inner halo structure, even if baryons significantly reshape these differences. Our results are useful for future studies that need to predict the properties of haloes in multiple dark matter models.

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arXiv2025

Galaxy cluster virial quantities from extrapolating strong lensing mass profiles

We study the radial total mass profiles of nine massive galaxy clusters ($M_\mathrm{200c}>5\times10^{14}$ M$_\odot$) in the redshift range $0.2 < z < 0.9$. These clusters were observed as part of the CLASH, HFF, BUFFALO, and CLASH-VLT programs, that provided high-quality photometric and spectroscopic data. Additional high-resolution spectroscopic data were obtained with MUSE at the VLT. Our research is based on strong lensing analyses that rely on these measurements. From these data, we measure the projected total mass profiles of each galaxy cluster in our sample. We fit these mass profiles with one-component, spherically symmetric mass models including the Navarro-Frenk-White (NFW), non-singular isothermal sphere, beta model, and Hernquist profiles. We perform a Bayesian analysis to sample the posterior probability distributions of the free parameters of the models. We find that the NFW, Hernquist, and beta models are the most suitable profiles to fit the measured projected cluster total mass profiles. Moreover, we test the robustness of our results in a twofold way: we slightly modify the center of the projected mass profiles and the radial range of the considered region. We employ the results obtained with the Hernquist profile to compare our total mass estimates ($M_\mathrm{H}^\mathrm{tot} = M_\mathrm{H} (r\rightarrow + \infty)$), with the $M_\mathrm{200c}$ values from weak lensing studies. Through this analysis, we find scaling relations between $M_\mathrm{H}^\mathrm{tot}$ and $M_\mathrm{200c}$ and the value of the scale radius, $r_\mathrm{S}$, and $R_\mathrm{200c}$. Interestingly, we also find that the $M_\mathrm{200c}$ values, obtained by extrapolating the fitted total mass profiles, are very close to the weak lensing results. This feature can be exploited in future studies on clusters and cosmology, as it provides an easy way to infer galaxy cluster virial masses.

astro-ph.CO↗

arXiv2025

Weak-lensing tunnel voids in simulated light cones: A new pipeline to investigate modified gravity and massive neutrinos signatures

Cosmic voids offer a unique opportunity to explore modified gravity (MG) models. Their low-density nature and vast extent make them especially sensitive to cosmological scenarios of the class $f(R)$, which incorporate screening mechanisms in dense, compact regions. Weak lensing (WL) by voids, in particular, provides a direct probe for testing MG scenarios. While traditional voids are identified from 3D galaxy positions, 2D voids detected in WL maps trace underdense regions along the line of sight and are sensitive to unbiased matter distribution. To investigate this, we developed an efficient pipeline for identifying and analyzing tunnel voids, i.e., underdensities detected in WL maps, specifically in the signal-to-noise ratio (SNR) of the convergence. In this work, we used this pipeline to generate realistic SNR maps from cosmological simulations featuring different $f(R)$ scenarios and massive neutrinos, comparing their effects against the standard $\Lambda$CDM model. Using the convergence maps and the 2D void catalogs, we analyzed various statistics, including the probability density function, angular power spectrum, and void size function. We then focused on the tangential shear profile around 2D voids, demonstrating how the proposed void-finding algorithm maximizes the signal. We showed that MG leads to deeper void shear profiles due to the enhanced evolution of cosmic structures, while massive neutrinos have the opposite effect. Furthermore, we found that parametric functions typically applied to 3D void density profiles are not suitable for deriving the shear profiles of tunnel voids. We, therefore, proposed a new parametric formula that provides an excellent fit to the void shear profiles across different void sizes and cosmological models. Finally, we tested the sensitivity of the free parameters of this new formula to the cosmological model.

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arXiv2025

The fifth data release of the Kilo Degree Survey: Multi-epoch optical/NIR imaging covering wide and legacy-calibration fields

We present the final data release of the Kilo-Degree Survey (KiDS-DR5), a public European Southern Observatory (ESO) wide-field imaging survey optimised for weak gravitational lensing studies. We combined matched-depth multi-wavelength observations from the VLT Survey Telescope and the VISTA Kilo-degree INfrared Galaxy (VIKING) survey to create a nine-band optical-to-near-infrared survey spanning $1347$ deg$^2$. The median $r$-band $5\sigma$ limiting magnitude is 24.8 with median seeing $0.7^{\prime\prime}$. The main survey footprint includes $4$ deg$^2$ of overlap with existing deep spectroscopic surveys. We complemented these data in DR5 with a targeted campaign to secure an additional $23$ deg$^2$ of KiDS- and VIKING-like imaging over a range of additional deep spectroscopic survey fields. From these fields, we extracted a catalogue of $126\,085$ sources with both spectroscopic and photometric redshift information, which enables the robust calibration of photometric redshifts across the full survey footprint. In comparison to previous releases, DR5 represents a $34\%$ areal extension and includes an $i$-band re-observation of the full footprint, thereby increasing the effective $i$-band depth by $0.4$ magnitudes and enabling multi-epoch science. Our processed nine-band imaging, single- and multi-band catalogues with masks, and homogenised photometry and photometric redshifts can be accessed through the ESO Archive Science Portal.

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arXiv2025

AMICO-WL: an optimal filtering algorithm for galaxy cluster detections with weak lensing

The detection of galaxy clusters, the most massive bounded structures in the universe, is crucial for cosmological analysis. Weak lensing signals allow us to track the distribution of all (dark and baryonic) matter regardless of its observable electromagnetic properties. Upcoming wide-field surveys like Euclid and LSST-Rubin will provide enhanced shape measurements of billions of background galaxies, presenting an unparalleled opportunity to detect galaxy clusters on a vast cosmic scale. The immense data volume generated by these surveys will require efficient and accurate analysis techniques. In this work, we introduce AMICO-WL, an extension of the optimal filtering algorithm implemented in AMICO, a well-tested code developed for optical cluster detection. AMICO-WL implements a specific linear optimal matched filter for weak lensing data in the AMICO infrastructure, using parallelisation and adding an efficient signal-to-noise ratio thresholding approach to set a desired sample purity and a cleaning procedure to deal with blended detections. The algorithm has been tested on a 25 deg$^2$ field of Euclid-like mock galaxy catalogue with the simulated shear signal produced using DUSTGRAIN-$pathfinder$ past-light-cones. We implemented a foreground removal procedure based on different cuts of low redshift galaxies from the input catalogue. To evaluate the performance of the method, we used an efficient matching procedure based on the 'blinking' of the simulation's individual redshift lensing planes. Cross-matching the AMICO-WL detections with the dark matter halo sample in the simulation having $M_{200} > 5 \times 10^{13}$ $M_{\odot}/h$ and considering a purity level of $\sim70\%$, the application of the foreground removal doubles the completeness from $6.5\%$ to $13.0\%$ and at the same time produces a significant decrease of spurious detections.

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arXiv2025

The Three Hundred Project hydrodynamical simulations: Hydrodynamical weak-lensing cluster mass biases and richnesses using different hydro models

The mass of galaxy clusters estimated from weak-lensing observations is affected by projection effects, leading to a systematic underestimation compared to the true cluster mass, varying with both mass and redshift. The magnitude depends on the criteria used to select clusters and the spatial scale over which their mass is measured. We leverage hydrodynamical simulations of galaxy clusters carried out with GadgetX and GIZMO-SIMBA as part of the Three Hundred project. We used them to quantify weak-lensing mass biases with respect also to the results from dark matter-only simulations. We also investigate how the biases propagate into the richness-mass relation. We aim to shed light on the effect of the presence of baryons on the weak-lensing mass bias and also whether this bias depends on the galaxy formation recipe; we seek to model the richness-mass relation that can be used as guidelines for observational experiments for cluster cosmology. We produced weak-lensing simulations of random projections to model the expected excess surface mass density profile of clusters up to redshift $z=1$. We then estimated the observed richness by counting the number of galaxies in a cylinder and correcting by projected contaminants. We derived the weak-lensing mass-richness relation and found consistency across hydrodynamical simulations. The intercept parameter of the relation is independent of redshift but varies with the minimum of the stellar mass to define the richness. At the same time, the slope is relatively constant up to $z=0.55$. The scatter in observed richness at a fixed weak-lensing mass increases linearly with redshift at a fixed stellar mass cut. As expected, we observed that the scatter in richness at a given true mass is smaller than at a given weak-lensing mass. Our results for the weak-lensing mass-richness relation align well with SDSS redMaPPer cluster analyses. [Abridged]

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arXiv2024

A deconstruction of methods to derive one-point lensing statistics

Gravitational lensing is a crucial tool for exploring cosmic phenomena, providing insights into galaxy clustering, dark matter, and dark energy. Given the substantial computational demands of $N$-body simulations, approximate methods like $\texttt{PINOCCHIO}$ and $\texttt{turboGL}$ have been proposed as viable alternatives for simulating lensing probability density functions (PDFs). This paper evaluates these methods and their effectiveness across both weak and strong lensing regimes, with a focus in the context where baryonic effects are negligible. Our comparative analysis reveals that these methods are effective for applications where lensing is mild, such as the majority of sources of electromagnetic and gravitational waves. However, both $\texttt{PINOCCHIO}$ and $\texttt{turboGL}$ break down for large values of convergence and magnification due to their loss of accuracy in capturing small-scale nonlinear matter fields, owing to oversimplified assumptions about internal halo structures and reliance on perturbation theory. $\texttt{PINOCCHIO}$ yields second-to-fourth moments of the lensing PDFs, which are 6-10% smaller than those resulting from $N$-body simulations in regimes where baryonic effects are minimal. These findings aim to inform future studies on gravitational lensing of point sources, which are increasingly relevant with upcoming supernova and gravitational wave datasets.

astro-ph.CO↗

arXiv2024

On the tomographic cluster clustering as a cosmological probe

The spatial distribution of galaxy clusters is a valuable probe for inferring fundamental cosmological parameters. We measured the clustering properties of dark matter haloes from the \textsc{Pinocchio} simulations, in the redshift range $0.2 < z < 1.0$ and with virial masses $M_\mathrm{vir} > 10^{14} M_\odot \, h^{-1}$, which reproduce the expected mass selection of galaxy cluster samples. The past-light cones we analysed have an angular size of 60 degrees, which approximately corresponds to a quarter of the sky. We adopted a linear power spectrum model, accounting for nonlinear corrections at the baryon acoustic oscillations scale, to perform a comparative study between 3D and 2D tomographic clustering. For this purpose, we modelled the multipoles of the 3D two-point correlation function, $ξ(r)$, the angular correlation function, $w(θ)$, and the angular power spectrum, $C_\ell$. We considered observational effects such as redshift-space distortions, produced by the peculiar velocities of tracers, and redshift errors. We found that photometric redshift errors have a more severe consequence on the 3D than on the 2D clustering, as they affect only the radial separation between haloes and not the angular one, with a relevant impact on the 3D multipoles. Using a Bayesian analysis, we explored the posterior distributions of the considered probes with different tomographic strategies, in the $Ω_m-σ_8$ plane, focusing on the summary parameter $S_8\equiv σ_8\sqrt{Ω_m/0.3}$. Our results show that in the presence of large photometric errors the 2D clustering can provide competitive cosmological constraints with respect to the full 3D clustering statistics, and can be successfully applied to analyse the galaxy cluster catalogues from the ongoing and forthcoming Stage-III and Stage-IV photometric redshift surveys.

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arXiv2024

AMICO galaxy clusters in KiDS-DR3: measuring the splashback radius from weak gravitational lensing

Context. Weak gravitational lensing offers a powerful method to investigate the projected matter density distribution within galaxy clusters, granting crucial insights into the broader landscape of dark matter on cluster scales. Aims. In this study, we make use of the large photometric galaxy cluster data set derived from the publicly available Third Data Release of the Kilo-Degree Survey, along with the associated shear signal. Our primary objective is to model the peculiar sharp transition in the cluster profile slope, that is what is commonly referred to as the splashback radius. The data set under scrutiny includes 6962 galaxy clusters, selected by AMICO - an optimised detection algorithm of galaxy clusters - on the KiDS-DR3 data, in the redshift range of 0.1 < z < 0.6, all observed at a signal-to-noise ratio greater than 3.5. Methods. Employing a comprehensive Bayesian analysis, we model the stacked excess surface mass density distribution of the clusters. We adopt a model from recent results on numerical simulations that capture the dynamics of both orbiting and infalling materials, separated by the region where the density profile slope undergoes a pronounced deepening. Results. We find that the adopted profile successfully characterizes the cluster masses, consistent with previous works, and models the deepening of the slope of the density profiles measured with weak-lensing data up to the outskirts. Moreover, we measure the splashback radius of galaxy clusters and show that its value is close to the radius within which the enclosed overdensity is 200 times the mean matter density of the Universe, while theoretical models predict a larger value consistent with a low accretion rate. This points to a potential bias of optically selected clusters preferentially characterized by a high density at small scales compared to a pure mass-selected cluster sample.

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arXiv2024

Imaging dark matter at the smallest scales with $z\approx1$ lensed stars

Observations of caustic-crossing galaxies at redshift $0.7 2$ and the number density of events is greater around substructureand the number density of events is greater around substructures, and (ii) negative imaging regime where $β<2$. We study the particular case of seven microlensing events found by HST in the Dragon arc (at z=0.725). We find that a population of supergiant stars with a steep LF with $β=2.55$ fits the distribution of these events. We identify a small region of high density of microlensing events, and interpret it as evidence of a possible invisible substructure, for which we derive a mass of $\sim 1.3 \times 10^8\,\Msun$ (within its Einstein radius).

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arXiv2024

Dianoga SIDM: galaxy cluster self-interacting dark matter simulations

This work aims at assessing the impact of DM self-interactions on the properties of galaxy clusters. In particular, the goal is to study the angular dependence of the cross section by testing rare (large angle scattering) and frequent (small angle scattering) SIDM models with velocity-dependent cross sections. We re-simulate six galaxy cluster zoom-in initial conditions with a dark matter only run and with a full-physics setup simulations that includes a self-consistent treatment of baryon physics. We test the dark matter only setup and the full physics setup with either collisionless cold dark matter, rare self-interacting dark matter, and frequent self-interacting dark matter models. We then study their matter density profiles as well as their subhalo population. Our dark matter only SIDM simlations agree with theoretical models, and when baryons are included in simulations, our SIDM models substantially increase the central density of galaxy cluster cores compared to full-physics simulations using collisionless dark matter. SIDM subhalo suppression in full-physics simulations is milder compared to the one found in dark matter only simulations, because of the cuspier baryionic potential that prevent subhalo disruption. Moreover SIDM with small-angle scattering significantly suppress a larger number of subhaloes compared to large angle scattering SIDM models. Additionally, SIDM models generate a broader range of subhalo concentration values, including a tail of more diffuse subhaloes in the outskirts of galaxy clusters and a population of more compact subhaloes in the cluster cores.

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arXiv2023

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

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

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arXiv2023

The Three Hundred: $M_{sub}-V_{circ}$ relation

In this study, we investigate a recent finding based on strong lensing observations, which suggests that the sub-halos observed in clusters exhibit greater compactness compared to those predicted by $Λ$CDM simulations. To address this discrepancy, we performed a comparative analysis by comparing the cumulative mass function of sub-halos and the $M_{\text{sub}}$-$V_{\text{circ}}$ relation between observed clusters and 324 simulated clusters from The Three Hundred project, focusing on re-simulations using GADGET-X and GIZMO-SIMBA baryonic models. The sub-halos' cumulative mass function of the GIZMO-SIMBA simulated clusters agrees with observations, while the GADGET-X simulations exhibit discrepancies in the lower sub-halo mass range possibly due to its strong SuperNova feedback. Both GADGET-X and GIZMO-SIMBA simulations demonstrate a redshift evolution of the sub-halo mass function and the $V_{max}$ function, with slightly fewer sub-halos observed at lower redshifts. Neither the GADGET-X nor GIZMO-SIMBA(albeit a little closer) simulated clusters' predictions for the $M_{\text{sub}}$-$V_{\text{circ}}$ relation align with the observational result. Further investigations on the correlation between sub-halo/halo properties and the discrepancy in the $M_{\text{sub}}$-$V_{\text{circ}}$ relation reveals that the sub-halo's half mass radius and galaxy stellar age, the baryon fraction and sub-halo distance from the cluster's centre, as well as the halo relaxation state play important roles on this relation. Nevertheless, we think it is still challenging in accurately reproducing the observed $M_{\text{sub}}$-$V_{\text{circ}}$ relation in our current hydrodynamic cluster simulation under the standard $Λ$CDM cosmology.

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