Clustering Properties Of Galaxies Research Articles

Constraining Cosmological Parameters Using the Splashback Radius of Galaxy Clusters

Cosmological parameters such as ΩM and σ 8 can be measured indirectly using various methods, including galaxy cluster abundance and cosmic shear. These measurements constrain the composite parameter S 8, leading to degeneracy between ΩM and σ 8. However, some structural properties of galaxy clusters also correlate with cosmological parameters, due to their dependence on a cluster’s accretion history. In this work, we focus on the splashback radius, an observable cluster feature that represents a boundary between a cluster and the surrounding Universe. Using a suite of cosmological simulations with a range of values for ΩM and σ 8, we show that the position of the splashback radius around cluster-mass halos is greater in cosmologies with smaller values of ΩM or larger values of σ 8. This variation breaks the degeneracy between ΩM and σ 8 that comes from measurements of the S 8 parameter. We also show that this variation is, in principle, measurable in observations. As the splashback radius can be determined from the same weak lensing analysis already used to estimate S 8, this new approach can tighten low-redshift constraints on cosmological parameters, either using existing data, or using upcoming data such as that from Euclid and LSST.

Resolving high-z galaxy cluster properties through joint X-ray and millimeter analysis: Case study of SPT-CLJ0615-5746

We present a joint millimetric and X-ray analysis of hot gas properties in the distant galaxy cluster SPT-CLJ0615-5746 (z = 0.972). Combining Chandra observations with the South Pole Telescope (SPT) and Planck data, we performed radial measurements of thermodynamical quantities up to a characteristic radius of 1.2 R500. We exploited the high angular resolution of Chandra and SPT to map the innermost region of the cluster and the high sensitivity to the larger angular scales of Planck to constrain the outskirts and improve the estimation of the cosmic microwave background and the galactic thermal dust emissions. In addition to maximizing the accuracy of radial temperature measurements, our joint analysis allows us to test the consistency between X-ray and millimetric derivations of thermodynamic quantities via the introduction of a normalization parameter (ηT) between X-ray and millimetric temperature profiles. This approach reveals a substantial high value of the normalization parameter, ηT = 1.45−0.18+0.17, suggesting that the gas halo is aspherical. Assuming hot gas hydrostatic equilibrium within complementary angular sectors that intercept the major and minor elongation of the X-ray image, we infer a halo mass profile that results from an effective compensation of azimuthal variations of gas densities by variations in the ηT parameter. Consistent with earlier integrated X-ray and millimetric measurements, we infer a cluster mass of M500HE = 10.67−0.50+0.62 1014 M⊙.

Dianoga SIDM: Galaxy cluster self-interacting dark matter simulations

Context. Self-interacting dark matter (SIDM) can tackle or alleviate small-scale issues within the cosmological standard model ΛCDM, and diverse flavours of SIDM can produce unique astrophysical predictions, resulting in different possible signatures which can be used to test these models with dedicated observations of galaxy clusters. Aims. This work aims to assess the impact of dark matter 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. Methods. We re-simulated six galaxy cluster zoom-in initial conditions with a dark matter-only run and with full-physics set-up simulations that include a self-consistent treatment of baryon physics. We tested the dark matter-only setup and the full physics setup with the collisionless cold dark matter, rare self-interacting dark matter, and frequent self-interacting dark matter models. We then studied their matter density profiles as well as their subhalo population. Results. Our dark matter-only SIDM simulations 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 the dark matter-only simulations because of the cuspier baryonic potential that prevents subhalo disruption. Moreover, SIDM with small-angle scattering significantly suppresses 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.

Cosmology with galaxy cluster properties using machine learning

Context. Galaxy clusters are the largest gravitating structures in the universe, and their mass assembly is sensitive to the underlying cosmology. Their mass function, baryon fraction, and mass distribution have been used to infer cosmological parameters despite the presence of systematics. However, the complexity of the scaling relations among galaxy cluster properties has never been fully exploited, limiting their potential as a cosmological probe. Aims. We propose the first machine learning (ML) method using galaxy cluster properties from hydrodynamical simulations in different cosmologies to predict cosmological parameters combining a series of canonical cluster observables, such as gas mass, gas bolometric luminosity, gas temperature, stellar mass, cluster radius, total mass, and velocity dispersion at different redshifts. Methods. The ML model was trained on mock “measurements” of these observable quantities from Magneticum multi-cosmology simulations to derive unbiased constraints on a set of cosmological parameters. These include the mass density parameter, Ωm, the power spectrum normalization, σ8, the baryonic density parameter, Ωb, and the reduced Hubble constant, h0. Results. We tested the ML model on catalogs of a few hundred clusters taken, in turn, from each simulation and found that the ML model can correctly predict the cosmology from where they have been picked. The cumulative accuracy depends on the cosmology, ranging from 21% to 75%. We demonstrate that this is sufficient to derive unbiased constraints on the main cosmological parameters with errors on the order of ~14% for Ωm, ~8% for σ8, ~6% for Ωb, and ~3% for h0. Conclusions. This proof-of-concept analysis, though based on a limited variety of multi-cosmology simulations, shows that ML can efficiently map the correlations in the multidimensional space of the observed quantities to the cosmological parameter space and narrow down the probability that a given sample belongs to a given cosmological parameter combination. More large-volume, mid-resolution, multi-cosmology hydro-simulations need to be produced to expand the applicability to a wider cosmological parameter range. However, this first test is exceptionally promising, as it shows that these ML tools can be applied to cluster samples from multiwavelength observations from surveys such as Rubin/LSST, CSST, Euclid, and Roman in optical and near-infrared bands, and eROSITA in X-rays, to the constrain cosmology and effect of baryonic feedback.

CHEX-MATE: A LOFAR pilot X-ray – radio study on five radio halo clusters

The connection between the thermal and non-thermal properties in galaxy clusters hosting radio halos seems fairly well established. However, a comprehensive analysis of such a connection has only been done for integrated quantities (e.g. LX − Pradio relation). In recent years, new-generation radio telescopes have enabled the unprecedented possibility to study the non-thermal properties of galaxy clusters on a spatially resolved basis. In this work, we performed a pilot study to investigate the mentioned properties on five targets by combining X-ray data from the CHEX-MATE project with the second data release from the LOFAR Two meter Sky survey. We find a strong correlation (rs ∼ 0.7) with a slope less than unity between the radio and X-ray surface brightness. We also report differences in the spatially resolved properties of the radio emission in clusters that show different levels of dynamical disturbance. In particular, less perturbed clusters (according to X-ray parameters) show peaked radio profiles in the centre, with a flattening in the outer regions, while the three dynamically disturbed clusters have steeper profiles in the outer regions. We fitted a model to the radio emission in the context of turbulent re-acceleration with a constant ratio between thermal and non-thermal particles’ energy densities and a magnetic field profile linked to the thermal gas density as B(r) ∝ nth0.5. We found that this simple model cannot reproduce the behaviour of the observed radio emission.

An environment-dependent halo mass function as a driver for the early quenching of z ≥ 1.5 cluster galaxies

ABSTRACT Many z ≈1.5 galaxies with a stellar mass (M⋆) $\ge 10^{10}\, \mathrm{M}_\odot$ are already quenched in both galaxy clusters (>50 per cent) and the field (>20 per cent), with clusters having a higher quenched fraction at all stellar masses compared to the field. A puzzling issue is that these massive quenched galaxies have stellar populations of similar age in both clusters and the field. This suggests that, despite the higher quenched fraction in clusters, the dominant quenching mechanism for massive galaxies is similar in both environments. In this work, we use data from the cosmological hydrodynamic simulations Hydrangea and EAGLE to test whether the excess quenched fraction of massive galaxies in z=1.5 clusters results from fundamental differences in their halo properties compared to the field. We find that (i) at $10^{10}\le \, M_{\star }/\mathrm{M}_\odot \, \le 10^{11}$, quenched fractions at 1.5<z<3.5 are consistently higher for galaxies with higher peak maximum circular velocity of the dark matter halo (vmax, peak), and (ii) the distribution of vmax, peak is strongly biased towards higher values for cluster satellites compared to the field centrals. Due to this difference in the halo properties of cluster and field galaxies, secular processes alone may account for (most of) the environmental excess of massive quenched galaxies in high-redshift (proto-)clusters. Taken at face value, our results challenge a fundamental assumption of popular quenching models that clusters are assembled from an unbiased subset of infalling field galaxies. If confirmed, this would imply that such models must necessarily fail at high redshift, as indicated by recent observations.

Impact of filaments on galaxy cluster properties in The Three Hundred simulation

Galaxy clusters and their filamentary outskirts reveal useful laboratories to test cosmological models and investigate Universe composition and evolution. Their environment, in particular the filaments of the Cosmic Web to which they are connected, plays an important role in shaping the properties of galaxy clusters. In this project, we analyse the gas filamentary structures present in 324 regions of The Three Hundred hydrodynamical simulation extracted with the DisPerSE filament finder. We estimate the number of gas filaments globally connected to several galaxy clusters, i.e. the connectivity k, with a mass range of 1013 ≤ M200 h−1 M⊙ ≤ 1015 at redshift z = 0. We study the positive correlation between the connectivity and mass of galaxy clusters. Moreover, we explore the impact of filaments on the dynamical state of clusters, quantified by the degree of relaxation parameter χ.

Galaxy catalogs from the Sage Semi-Analytic Model calibrated on The Three Hundred hydrodynamical simulations: A method to push the limits toward lower mass galaxies in dark matter only clusters simulations

The new generation of upcoming deep photometric and spectroscopic surveys will allow us to measure the astrophysical properties of faint galaxies in massive clusters. This would demand to produce simulations of galaxy clusters with better mass resolution than the ones available today if we want to make comparisons between the upcoming observations and predictions of cosmological models. But producing full-physics hydrodynamical simulations of the most massive clusters is not an easy task. This would involve billions of computational elements to reliably resolve low mass galaxies similar to those measured in observations. On the other hand, dark matter only simulations of cluster size halos can be done with much larger mass resolution but at the cost of having to apply a model that populate galaxies within each of the subhalos in these simulations. In this paper we present the results of a new set of dark matter only simulations with different mass resolutions within the The Three Hundred project. We have generated catalogs of galaxies with stellar and luminosity properties by applying the Sage Semi-Analytical Model of galaxy formation. To obtain the catalogs consistent with the results from hydrodynamical simulations, the internal physical parameters of Sage were calibrated with the Particle Swarm Optimization method using a subset of full-physics runs with the same mass resolution than the dark matter only ones.

Multipole analysis of cluster weak lensing shear in The Three Hundred project

Weak gravitational lensing is an important tool to estimate the masses of galaxy clusters, as it allows us to directly access their projected surface mass density along the line of sight in a manner largely independent of their dynamical state. Moreover, we can extract information on the projected shape of the cluster mass distribution. In this work, we generate mock catalogs of lensed background galaxies to measure the individual lensing properties of galaxy clusters from the simulation project The Three Hundred. By repeating the analysis for different projections of the same cluster, we find that the use of shear multipoles provides constraints on the ellipticity of the cluster projected mass density but does not have a significant impact on the cluster mass reconstruction compared to the standard approach.

The NIKA2 Sunyaev-Zeldovich Large Program

The NIKA2 camera operating at the IRAM 30-m telescope excels in high-angular resolution mapping of the thermal Sunyaev-Zel’dovich effect towards galaxy clusters at intermediate and high-redshift. As part of the NIKA2 guaranteed-time, the SZ Large Program (LPSZ) aims at tSZ-mapping a representative sample of SZ-selected galaxy clusters in the catalogues of the Planck satellite and of the Atacama Cosmology Telescope, and also observed in X-ray with XMM-Newton or Chandra. Having completed observations in January 2023, we present tSZ maps of 38 clusters spanning the targeted mass (3 < M500/1014M⊙ < 10) and redshift (0.5 < z < 0.9) range. The first in-depth studies of individual clusters highlight the potential of combining tSZ and X-ray observations at similar angular resolution for precised mass measurements under the hydrostatic assumption MHSE. These were milestones for the development of a standard data analysis pipeline to go from NIKA2 raw data to the thermodynamic properties of galaxy clusters for the upcoming LPSZ data release. Final products will include measurements of the mean pressure profile of unprecedented quality and MHSE-observable scaling relation using a distinctive SZ-selected sample, which will be key for ultimately improving the accuracy of cluster-based cosmology.

Exploring the low-mass regime of galaxy-scale strong lensing: Insights into the mass structure of cluster galaxies

Context. Several recent studies have highlighted a discrepancy between the strong lensing (SL) properties of observed cluster galaxies and the predictions of Λ cold dark matter (CDM) cosmological hydrodynamical simulations. This discrepancy can be interpreted as the result of observed cluster members being more compact than their simulated counterparts. Aims. In this work, we aim at a direct measurement of the compactness of a few selected galaxy-scale lenses in massive clusters, testing the accuracy of the scaling laws adopted to describe the members in SL models of galaxy clusters. Methods. We selected the multiply imaged sources MACS J0416.1−2403 ID14 (z = 3.221), MACS J0416.1−2403 ID16 (z = 2.095), and MACS J1206.2−0847 ID14 (z = 3.753). Eight multiple images were observed for the first SL system, and six for the latter two. We focused on the main deflector of each galaxy-scale SL system (identified as members 8971, 8785, and 3910, respectively), and modelled its total mass distribution with a truncated isothermal sphere. To account for the lensing effects of the remaining components of the cluster, we took the most accurate SL model of its mass distribution available. To include the uncertainty and the systematics affecting the cluster-scale mass models, we explored the posterior probability distribution of its parameters and extracted 100 cluster mass distributions. For each of them, we optimised the mass parameters of the galaxy-scale lens: the bootstrapping procedure allowed us to obtain a realistic estimate of the uncertainty on their values. Results. We measured a truncation radius value of 6.1−1.1+2.3 kpc, 4.0−0.4+0.6 kpc, and 5.2−1.1+1.3 kpc for members 8971, 8785, and 3910, corresponding to total mass values of M = 1.2−0.1+0.3 × 1011 M⊙, M = 1.0−0.1+0.2 × 1010 M⊙, and M = 6.3−1.1+1.0 × 1010 M⊙, respectively. Alternative non-truncated models with a higher number of free parameters do not lead to an improved description of the SL system and show some parametric degeneracies. We measured the stellar-to-total mass fraction within the effective radius for the three cluster members, finding 0.51 ± 0.21, 1.0 ± 0.4, and 0.39 ± 0.16, respectively. Conclusions. We find that a parameterisation of the physical properties of cluster galaxies in SL models based on power-law scaling relations with respect to the observed total luminosity cannot accurately describe the compactness of the members over their full total mass range. Our results, instead, agree with recent modelling of the cluster members based on the Fundamental Plane relation. Finally, we report good agreement between our predicted values of the stellar-to-total mass fraction within the effective radius and those of early-type galaxies from the Sloan Lens ACS Survey. Our work significantly extends the regimes of the current samples of lens galaxies, towards the mass range that will be probed by the Euclid, Rubin, and James Webb Telescopes.

Galaxy cluster optical mass proxies from probabilistic memberships

ABSTRACT Robust galaxy cluster mass estimates are fundamental for constraining cosmological parameters from counts. For this reason, it is essential to search for tracers that, independent of the cluster’s dynamical state, have a small intrinsic scatter and can be easily inferred from observations. This work uses a simulated data set to focus on photometric properties and explores different optical mass proxies including richness, optical luminosity, and total stellar mass. We have developed a probabilistic membership assignment that makes minimal assumptions about the galaxy cluster properties, limited to a characteristic radius, velocity dispersion, and spatial distribution. Applying the estimator to over 919 galaxy clusters with zphot < 0.45 within a mass range of 1012.8–1015 M⊙, we obtain robust richness estimates that deviate from the median true value (from simulations) by −0.01 ± 0.12. The scatter in the mass–observable relations is $\sigma _{log_{10}(M|\mathcal {R})}=0.181 \pm 0.009$ dex for richness, $\sigma _{log_{10}(M|L_\lambda)}=0.151 \pm 0.007$ dex for optical luminosity, and $\sigma _{log_{10}(M|M_\lambda ^{*})}=0.097 \pm 0.005$ dex for stellar mass. We also discuss membership assignment, completeness and purity, and the consequences of small centre and redshift offsets. We conclude that the application of our method for photometric surveys delivers competitive cluster mass proxies.

ALMA Lensing Cluster Survey: average dust, gas, and star-formation properties of cluster and field galaxies from stacking analysis

ABSTRACT We develop new tools for continuum and spectral stacking of Atacama Large Millimeter/submillimeter Array (ALMA) data, and apply these to the ALMA Lensing Cluster Survey. We derive average dust masses, gas masses, and star-formation rates (SFRs) from the stacked observed 260-GHz continuum of 3402 individually undetected star-forming galaxies, of which 1450 are cluster galaxies and 1952 field galaxies, over three redshift and stellar mass bins (over z = 0–1.6 and log$M_{*} \, [{\rm M}_{\odot }] = 8$–11.7), and derive the average molecular gas content by stacking the emission line spectra in a SFR-selected subsample. The average SFRs and specific SFRs of both cluster and field galaxies are lower than those expected for main-sequence (MS) star-forming galaxies, and only galaxies with stellar mass of log$M_{*} \, [{\rm M}_{\odot }] = 9.35$–10.6 show dust and gas fractions comparable with those in the MS. The ALMA-traced average ‘highly obscured’ SFRs are typically lower than the SFRs observed from optical to near-infrared spectral analysis. Cluster and field galaxies show similar trends in their contents of dust and gas, even when field galaxies were brighter in the stacked maps. From spectral stacking we find a potential CO (J = 4 → 3) line emission (signal-to-noise ratio being ∼4) when stacking cluster and field galaxies with the highest SFRs.

Accelerated Structural Evolution of Galaxies in a Starbursting Cluster at z = 2.51

Structural properties of cluster galaxies during their peak formation epoch, z ∼ 2–4 provide key information on whether and how the environment affects galaxy formation and evolution. Based on deep Hubble Space Telescope (HST)/Wide Field Camera 3 (WFC3) imaging toward the z = 2.51 cluster, J1001, we explore environmental effects on the structure, color gradients, and stellar populations of a statistical sample of cluster star-forming galaxies (SFGs). We find that the cluster SFGs are on average smaller than their field counterparts. This difference is most pronounced at the high-mass end (M ⋆ > 1010.5 M ⊙), with nearly all of them lying below the mass–size relation of field galaxies. The high-mass cluster SFGs are also generally old, with a steep negative color gradient, indicating an early formation time likely associated with strong dissipative collapse. For low-mass cluster SFGs, we unveil a population of compact galaxies with steep positive color gradients that are not seen in the field. This suggests that the low-mass compact cluster SFGs may have already experienced strong environmental effects, e.g., tidal/ram pressure stripping, in this young cluster. These results provide evidence on the environmental effects at work in the earliest formed clusters with different roles in the formation of low- and high-mass galaxies.

Fraction of stars in clusters for the LEGUS dwarf galaxies

ABSTRACT We study the young star cluster populations in 23 dwarf and irregular galaxies observed by the Hubble Space Telescope (HST) Legacy ExtraGalactic Ultraviolet Survey (LEGUS), and examine relationships between the ensemble properties of the cluster populations and those of their host galaxies: star formation rate (SFR) density (ΣSFR). A strength of this analysis is the availability of SFRs measured from temporally resolved star formation histories that provide the means to match cluster and host galaxy properties on several time-scales (1–10, 1–100, and 10–100 Myr). Nevertheless, studies of this kind are challenging for dwarf galaxies due to the small numbers of clusters in each system. We mitigate these issues by combining the clusters across different galaxies with similar ΣSFR properties. We find good agreement with a well-established relationship ($M_{V}^{\mathrm{ brightest}}$–SFR), but find no significant correlations between ΣSFR and the slopes of the cluster luminosity function, mass function, nor the age distribution. We also find no significant trend between the fraction of stars in bound clusters at different age ranges (Γ1–10, Γ10–100, and Γ1–100) and ΣSFR of the host galaxy. Our data show a decrease in Γ over time (from 1–10 to 10–100 Myr) suggesting early cluster dissolution, though the presence of unbound clusters in the youngest time bin makes it difficult to quantify the degree of dissolution. While our data do not exhibit strong correlations between ΣSFR and ensemble cluster properties, we cannot rule out that a weak trend might exist given the relatively large uncertainties due to low number statistics and the limited ΣSFR range probed.

Machine learning methods to estimate observational properties of galaxy clusters in large volume cosmological N-body simulations

ABSTRACT In this paper, we study the applicability of a set of supervised machine learning (ML) models specifically trained to infer observed related properties of the baryonic component (stars and gas) from a set of features of dark matter (DM)-only cluster-size haloes. The training set is built from the three hundred project that consists of a series of zoomed hydrodynamical simulations of cluster-size regions extracted from the 1 Gpc volume MultiDark DM-only simulation (MDPL2). We use as target variables a set of baryonic properties for the intracluster gas and stars derived from the hydrodynamical simulations and correlate them with the properties of the DM haloes from the MDPL2 N-body simulation. The different ML models are trained from this data base and subsequently used to infer the same baryonic properties for the whole range of cluster-size haloes identified in the MDPL2. We also test the robustness of the predictions of the models against mass resolution of the DM haloes and conclude that their inferred baryonic properties are rather insensitive to their DM properties that are resolved with almost an order of magnitude smaller number of particles. We conclude that the ML models presented in this paper can be used as an accurate and computationally efficient tool for populating cluster-size haloes with observational related baryonic properties in large volume N-body simulations making them more valuable for comparison with full sky galaxy cluster surveys at different wavelengths. We make the best ML trained model publicly available.

A pair of early- and late-forming galaxy cluster samples: A novel way of studying halo assembly bias assisted by a constrained simulation

The halo assembly bias, a phenomenon referring to dependencies of the large-scale bias of a dark matter halo other than its mass, is a fundamental property of the standard cosmological model. First discovered in 2005 from the Millennium Run simulation, it has been proven very difficult to be detected observationally, with only a few convincing claims of detection so far. The main obstacle lies in finding an accurate proxy of the halo formation time. In this study, by utilizing a constrained simulation that can faithfully reproduce the observed structures larger than 2 Mpc in the local universe, for a sample of 634 massive clusters at z ≤ 0.12, we found their counterpart halos in the simulation and used the mass growth history of the matched halos to estimate the formation time of the observed clusters. This allowed us to construct a pair of early- and late-forming clusters, with a similar mass as measured via weak gravitational lensing, and large-scale biases differing at the ≈3σ level, suggestive of the signature of assembly bias, which is further corroborated by the properties of cluster galaxies, including the brightest cluster galaxy and the spatial distribution and number of member galaxies. Our study paves a way to further detect assembly bias based on cluster samples constructed purely on observed quantities.

A general framework to test gravity using galaxy clusters – VI. Realistic galaxy formation simulations to study clusters in modified gravity

ABSTRACT We present a retuning of the IllustrisTNG baryonic physics model which can be used to run large-box realistic cosmological simulations with a lower resolution. This new model employs a lowered gas density threshold for star formation and reduced energy releases by stellar and black hole feedback. These changes ensure that our simulations can produce sufficient star formation to closely match the observed stellar and gas properties of galaxies and galaxy clusters, despite having ∼160 times lower mass resolution than the simulations used to tune the fiducial IllustrisTNG model. Using the retuned model, we have simulated Hu–Sawicki f(R) gravity within a 301.75 h−1 Mpc box. This is, to date, the largest simulation that incorporates both screened modified gravity and full baryonic physics, offering a large sample (∼500) of galaxy clusters and ∼8000 galaxy groups. We have reanalysed the effects of the f(R) fifth force on the scaling relations between the cluster mass and four observable proxies: the mass-weighted gas temperature, the Compton Y-parameter of the thermal Sunyaev–Zel’dovich effect, the X-ray analogue of the Y-parameter, and the X-ray luminosity. We show that a set of mappings between the f(R) scaling relations and their Lambda cold dark matter counterpart, which have been tested in a previous work using a much smaller cosmological volume, are accurate to within a few per cent for the Y-parameters and $\lesssim 7{{\ \rm per\ cent}}$ for the gas temperature for cluster-sized haloes ($10^{14}\, {\rm M}_{\odot }\lesssim M_{500}\lesssim 10^{15}\, {\rm M}_{\odot }$). These mappings will be important for unbiased constraints of gravity using the data from ongoing and upcoming cluster surveys.

The environmental dependence of the stellar velocity dispresion of active galactic nucleus (AGN) host galaxies and dependence of the clustering properties of AGN host galaxies on the stellar velocity dispersion

We use two volume-limited active galactic nucleus (AGN) host galaxy samples constructed by Deng & Wen [47], and explore the environmental dependence of the stellar velocity dispersion in these two volume-limited AGN host galaxy samples. In the luminous volume-limited AGN host galaxy sample, the stellar velocity dispersion of AGN host galaxies apparently depends on local environments: AGN host galaxies with large stellar velocity dispersion exist preferentially in high density regime, while AGN host galaxies with small stellar velocity dispersion are located preferentially in low density regions. But in the faint volume-limited AGN host galaxy sample, this dependence is fairly weak. We also examine the dependence of the clustering properties of AGN host galaxies on the stellar velocity dispersion by cluster analysis, and find that in the luminous volume-limited AGN host galaxy sample, AGN host galaxies with small stellar velocity dispersion preferentially form isolated galaxies, close pairs and small groups, while AGN host galaxies with large stellar velocity dispersion preferentially inhabit the dense groups and clusters. In the faint volume-limited AGN host galaxy sample, although the fraction of isolated galaxies with small stellar velocity dispersion is apparently higher than the one with large stellar velocity dispersion, the trend in the luminous volume-limited sample is very difficultly observed. This likely is due to the galaxy number of the faint volume-limited AGN host galaxy sample being too small to ensure an ideal statistical analysis.

The Environmental Dependence of the Stellar Velocity Dispersion of Active Galactic Nucleus (AGN) Host Galaxies and Dependence of the Clustering Properties of AGN Host Galaxies on the Stellar Velocity Dispersion

The Environmental Dependence of the Stellar Velocity Dispersion of Active Galactic Nucleus (AGN) Host Galaxies and Dependence of the Clustering Properties of AGN Host Galaxies on the Stellar Velocity Dispersion