Cluster-galaxy Cross-correlation Research Articles

Self-calibrating optical galaxy cluster selection bias using cluster, galaxy, and shear cross-correlations

ABSTRACT The clustering signals of galaxy clusters are powerful tools for self-calibrating the mass–observable relation and are complementary to cluster abundance and lensing. In this work, we explore the possibility of combining three correlation functions – cluster lensing, the cluster–galaxy cross-correlation function, and the galaxy autocorrelation function – to self-calibrate optical cluster selection bias, the boosted clustering and lensing signals in a richness-selected sample mainly caused by projection effects. We develop mock catalogues of redMaGiC-like galaxies and redMaPPer-like clusters by applying halo occupation distribution models to N-body simulations and using counts-in-cylinders around massive haloes as a richness proxy. In addition to the previously known small-scale boost in projected correlation functions, we find that the projection effects also significantly boost three-dimensional correlation functions to scales of 100 $h^{-1} \, \rm Mpc$. We perform a likelihood analysis assuming survey conditions similar to the Dark Energy Survey and show that the selection bias can be self-consistently constrained at the 10 per cent level. We discuss strategies for applying this approach to real data. We expect that expanding the analysis to smaller scales and using deeper lensing data would further improve the constraints on cluster selection bias.

Is the Large-scale Structure Traced by the BOSS LOWZ Galaxies Consistent with Planck?

Recently, several studies reported a significant discrepancy between the clustering and lensing of the Baryon Oscillation Spectroscopic Survey (BOSS) galaxies in the Planck cosmology. We construct a simple yet powerful model based on the linear theory to assess whether this discrepancy points toward deviations from Planck. Focusing on scales 10 < R < 30 h −1Mpc, we model the amplitudes of clustering and lensing of BOSS LOWZ galaxies using three parameters: galaxy bias b g; galaxy-matter cross-correlation coefficient r gm; and A, defined as the ratio between the true and Planck values of σ 8. Using the cross-correlation matrix as a diagnostic, we detect systematic uncertainties that drive spurious correlations among the low-mass galaxies. After building a clean LOWZ sample with r gm ∼ 1, we derive a joint constraint of b g and A from clustering+lensing, yielding and , i.e., a 2σ tension with Planck. However, due to the strong degeneracy between b g and A, systematic uncertainties in b g could masquerade as a tension with A = 1. To ascertain this possibility, we develop a new method to measure b g from the cluster-galaxy cross correlation and cluster weak lensing using an overlapping cluster sample. By applying the independent bias measurement (b g = 1.76 ± 0.22) as a prior, we successfully break the degeneracy and derive stringent constraints of and A = 0.96 ± 0.07. Therefore, our result suggests that the large-scale clustering and lensing of LOWZ galaxies are consistent with Planck, while the different bias estimates may be related to some observational systematics that need to be mitigated in future surveys.

Observational constraints of an anisotropic boost due to the projection effects using redMaPPer clusters

ABSTRACT Optical clusters identified from red-sequence galaxies suffer from projection effects, where interloper galaxies along the line of sight to a cluster are mistaken as genuine members of the cluster. In the previous study, we found that the projection effects cause the boost on the amplitudes of clustering and lensing on large scale compared to the expected amplitudes in the absence of any projection effects. These boosts are caused by preferential selections of filamentary structure aligned to the line of sight due to distance uncertainties in photometric surveys. We model the projection effects with two simple assumptions and develop a novel method to quantify the size of the boost using cluster-galaxy cross-correlation functions. We validate our method using mock cluster catalogues built from cosmological N-body simulations and find that we can obtain unbiased constraints on the boost parameter with our model. We then apply our analysis on the SDSS redMaPPer clusters and find that the size of the boost is roughly 20 per cent for all the richness bins except the cluster sample with the richness bin λ ∈ [30, 40]. This is the first study to constrain the boost parameter independent from cluster cosmology studies and provides a self-consistency test for the projection effects.

Cosmology with stacked cluster weak lensing and cluster–galaxy cross-correlations

ABSTRACT Cluster weak lensing is a sensitive probe of cosmology, particularly the amplitude of matter clustering σ8 and matter density parameter Ωm. The main nuisance parameter in a cluster weak lensing cosmological analysis is the scatter between the true halo mass and the relevant cluster observable, denoted $\sigma _{\ln M_\mathrm{ c}}$. We show that combining the cluster weak lensing observable ΔΣ with the projected cluster–galaxy cross-correlation function wp,cg and galaxy autocorrelation function wp,gg can break the degeneracy between σ8 and $\sigma _{\ln M_\mathrm{ c}}$ to achieve tight, per cent-level constraints on σ8. Using a grid of cosmological N-body simulations, we compute derivatives of ΔΣ, wp,cg, and wp,gg with respect to σ8, Ωm, $\sigma _{\ln M_\mathrm{ c}}$, and halo occupation distribution (HOD) parameters describing the galaxy population. We also compute covariance matrices motivated by the properties of the Dark Energy Survey cluster and weak lensing survey and the BOSS CMASS galaxy redshift survey. For our fiducial scenario combining ΔΣ, wp,cg, and wp,gg measured over 0.3−30.0 h−1 Mpc, for clusters at z = 0.35−0.55 above a mass threshold Mc ≈ 2 × 1014 h−1 M⊙, we forecast a $1.4{{\ \rm per\ cent}}$ constraint on σ8 while marginalizing over $\sigma _{\ln M_\mathrm{ c}}$ and all HOD parameters. Reducing the mass threshold to 1 × 1014 h−1 M⊙ and adding a z = 0.15−0.35 redshift bin sharpens this constraint to $0.8{{\ \rm per\ cent}}$. The small-scale (rp &amp;lt; 3.0 h−1 Mpc) ‘mass function’ and large-scale (rp &amp;gt; 3.0 h−1 Mpc) ‘halo-mass cross-correlation’ regimes of ΔΣ have comparable constraining power, allowing internal consistency tests from such an analysis.

Gravitational redshift and asymmetric redshift-space distortions for stacked clusters

We derive the expression for the observed redshift in the weak field limit in the observer's past light cone, including all relativistic terms up to second order in velocity. We then apply it to compute the cluster–galaxy cross-correlation functions (CGCF) using N-body simulations. The CGCF is asymmetric along the line of sight owing to the presence of the small second-order terms such as the gravitational redshift (GRedshift). We identify two systematics in the modelling of the GRedshift signal in stacked clusters. First, it is affected by the morphology of dark matter haloes and the large-scale cosmic-web. The non-spherical distribution of galaxies around the central halo and the presence of neighbouring clusters systematically reduce the GRedshift signal. This bias is approximately 20 per cent for Mmin ≃ 1014 M⊙ h−1, and is more than 50 per cent for haloes with Mmin ≃ 2 × 1013 M⊙ h−1 at r > 4 Mpc h−1. Secondly, the best-fitting GRedshift profiles as well as the profiles of all other relativistic terms are found to be significantly different in velocity space compared to their real space versions. We find that the relativistic Doppler redshift effect, like other second-order effects, is subdominant to the GRedshift signal. We discuss some subtleties relating to these effects in velocity space. We also find that the S/N of the GRedshift signal increases with decreasing halo mass.

Testing the Large-scale Environments of Cool-core and Non-cool-core Clusters with Clustering Bias

Abstract There are well-observed differences between cool-core (CC) and non-cool-core (NCC) clusters, but the origin of this distinction is still largely unknown. Competing theories can be divided into internal (inside-out), in which internal physical processes transform or maintain the NCC phase, and external (outside-in), in which the cluster type is determined by its initial conditions, which in turn leads to different formation histories (i.e., assembly bias). We propose a new method that uses the relative assembly bias of CC to NCC clusters, as determined via the two-point cluster-galaxy cross-correlation function (CCF), to test whether formation history plays a role in determining their nature. We apply our method to 48 ACCEPT clusters, which have well resolved central entropies, and cross-correlate with the SDSS-III/BOSS LOWZ galaxy catalog. We find that the relative bias of NCC over CC clusters is b = 1.42 ± 0.35 (1.6σ different from unity). Our measurement is limited by the small number of clusters with core entropy information within the BOSS footprint, 14 CC and 34 NCC clusters. Future compilations of X-ray cluster samples, combined with deep all-sky redshift surveys, will be able to better constrain the relative assembly bias of CC and NCC clusters and determine the origin of the bimodality.

Galaxy infall kinematics as a test of modified gravity

Infrared modifications of General Relativity (GR) can be revealed by comparing the mass of galaxy clusters estimated from weak lensing to that from infall kinematics. We measure the 2D galaxy velocity distribution in the cluster infall region by applying the galaxy infall kinematics (GIK) model developed by Zu and Weinberg (2013) to two suites of f(R) and Galileon modified gravity simulations. Despite having distinct screening mechanisms, namely, the Chameleon and the Vainshtein effects, the f(R) and Galileon clusters exhibit very similar deviations in their GIK profiles from GR, with ~ 100-200 k/s enhancement in the characteristic infall velocity at r=5 Mpc/h and 50-100 km/s broadening in the radial and tangential velocity dispersions across the entire infall region, for clusters with mass ~ 10^{14} Msol/h at z=0.25. These deviations are detectable via the GIK reconstruction of the redshift--space cluster-galaxy cross-correlation function, xi_cg^s(r_p,r_\pi), which shows ~ 1-2 Mpc/h increase in the characteristic line-of-sight distance r_\pi^c at r_p<6 Mpc/h from GR predictions. With overlapping deep imaging and large redshift surveys in the future, we expect that the GIK modelling of xi_cg^s, in combination with the stacked weak lensing measurements, will provide powerful diagnostics of modified gravity theories and the origin of cosmic acceleration.

The redshift-space cluster–galaxy cross-correlation function – I. Modelling galaxy infall on to Millennium simulation clusters and SDSS groups

The large scale infall of galaxies around massive clusters provides a potentially powerful diagnostic of structure growth, dark energy, and cosmological deviations from General Relativity. We develop and test a method to recover galaxy infall kinematics (GIK) from measurements of the redshift-space cluster-galaxy cross-correlation function \xi_{cg}(r_p,r_\pi). Using galaxy and halo samples from the Millennium simulation, we calibrate an analytic model of the galaxy kinematic profiles comprised of a virialized component with an isotropic Gaussian velocity distribution and an infall component described by a skewed 2D t-distribution with a characteristic infall velocity v_r and separate radial and tangential dispersions. We show that convolving the real-space cross-correlation function with this velocity distribution accurately predicts the redshift-space \xi_{cg}, and we show that measurements of \xi_{cg} can be inverted to recover the four distinct elements of the GIK profiles. These in turn provide diagnostics of cluster mass profiles, and we expect the characteristic infall velocity v_r(r) in particular to be insensitive to galaxy formation physics that can affect velocity dispersions within halos. As a proof of concept we measure \xi_{cg} for rich galaxy groups in the Sloan Digital Sky Survey and recover GIK profiles for groups in two bins of central galaxy stellar mass. The higher mass bin has a v_r(r) curve very similar to that of 10^{14} Msun halos in the Millennium simulation, and the recovered kinematics follow the expected trends with mass. GIK modeling of cluster-galaxy cross-correlations can be a valuable complement to stacked weak lensing analyses, allowing novel tests of modified gravity theories that seek to explain cosmic acceleration.

2PIGG group masses via 2dF galaxyz-space distortion

Prompted by indications from QSO lensing that there may be more mass associated with galaxy groups than expected, we have made new dynamical infall estimates of the masses associated with 2PIGG groups and clusters. We have analysed the redshift distortions in the cluster-galaxy cross-correlation function as a function of cluster membership, cross-correlating z<0.12 2PIGG clusters and groups with the full 2dF galaxy catalogue. We have made estimates of the dynamical infall parameter beta and new estimates of the group velocity dispersions. We first find that the amplitude of the full 3-D redshift space cross-correlation function, xi_{cg}, rises monotonically with group membership. We use a simple linear-theory infall model to fit xi(sigma, pi) in the range 5<s<40h^{-1}Mpc. We find that the beta versus membership relation for the data shows a minimum at intermediate group membership n~20 or L~2x10^11h^-2Lsun, implying that the bias and hence M/L ratios rise by a significant factor (~5x) both for small groups and rich clusters. However, the mocks show a systematic shift between the location of the beta minimum and the M/L minimum at L~10^10h^-2Lsun given by direct calculation using the known DM distribution. Our overall conclusion is that bias estimates from dynamical infall appear to support the minimum in star-formation efficiency at intermediate halo masses. Nevertheless, there may still be significant systematic problems arising from measuring beta~1/b using large-scale infall rather than M/L using small-scale velocity dispersions.

Spatial clustering of Ultra Steep Spectrum sources and galaxies

We present measurements of the clustering properties of galaxies in the field of redshift range 0.5 ≤ z ≤ 1.5 Ultra Steep Spectrum radio sources selected from the Sydney University Molonglo Sky Survey and the National Radio Astronomy Observatories Very Large Array Sky Survey. Galaxies in these USS fields were identified in deep near-infrared observations, complete down to K s = 20, using the IRIS2 instrument at the Anglo-Australian Telescope. We used the redshift distribution of K s < 20 galaxies taken from Cimatti et al. (2002) to constrain the correlation length r 0 . We find a strong correlation signal of galaxies with K s < 20 around our USS sample. A comoving correlation length r 0 = 14.0 ± 2.8 h -1 Mpc and y = 1.98 ± 0.15 are derived in a flat cosmological model universe. We compare our findings with those obtained in a cosmological N-body simulation populated with GALFORM semi-analytic galaxies. We find that clusters of galaxies with masses in the range M = 10 13.4-14.2 2 h -1 M ⊙ have a cluster-galaxy cross-correlation amplitude comparable to those found between the USS hosts and galaxies. These results suggest that distant radio galaxies are excellent tracers of galaxy overdensities and pinpoint the progenitors of present day rich clusters of galaxies.

Cross-correlations of X-ray and optically selected clusters with near-infrared and optical galaxies

We compute the real-space cluster-galaxy cross-correlation ξ cg (r) using the ROSAT-ESO Flux Limited X-ray (REFLEX) cluster survey, a group catalogue (2dFGGC) constructed from the final version of the Two-degree Field Galaxy Redshift Survey (2dFGRS), and galaxies extracted from the Two Micron All Sky Survey (2MASS) and Automated Plate Measurement (APM) surveys. This first detailed calculation of the cross-correlation for X-ray clusters and groups is consistent with previous works and shows that ξ eg (r) cannot be described by a single power law. We analyse the clustering dependence on the cluster X-ray luminosity L x and virial mass M vir thresholds as well as on the galaxy limiting magnitude. We also make a comparison of our results with those obtained for the halo-mass cross-correlation function in a ACDM N-body simulation to infer the scale dependence of galaxy bias around clusters. Our results indicate that the distribution of galaxies shows a significant anti-hias at highly non-linear small cluster-centric distances, b eg (r) ≃ 0.7, irrespective of the group/cluster virial mass or X-ray luminosity and galaxy characteristics. This shows that a generic process controls the efficiency of galaxy formation and evolution in high-density regions. On larger scales, b eg (r) rises to a nearly constant value of the order of unity, the transition occurring at approximately 2 h -1 Mpc for 2dF groups and 5 h -1 Mpc for REFLEX clusters.

The APM cluster--galaxy cross-correlation function: constraints on and galaxy bias

We estimate the cluster-galaxy cross-correlation function (ξcg), from the APM galaxy and galaxy cluster surveys. We obtain estimates both in real space from the inversion of projected statistics and in redshift space using the galaxy and cluster redshift samples. The amplitude of ξcg is found to be almost independent of cluster richness. At large separations, r ≥ 5 h−1Mpc (h=H0/100 km s−1 Mpc−1, where H0 is the Hubble constant), ξcg has a similar shape to the galaxy-galaxy and cluster-cluster autocorrelation functions. ξcg in redshift space can be related to the real-space ξcg by convolution with an appropriate velocity field model. Here we apply a spherical collapse model, which we have tested against N-body simulations, finding that it provides an accurate description of the averaged infall velocity of matter into galaxy clusters. We use this model to estimate β (β =Ω0.6/b, where b is the linear bias parameter), and find that it tends to overestimate the true result in simulations by only ∼ 10–30 per cent. Application to the APM results yields β =0.46 with β < 0.73 at 95 per cent confidence. This measure is complementary to the estimates made of the density parameter from larger scale bulk flows and from the virialized regions of clusters on smaller scales. We also compare the APM ξcg and galaxy autocorrelations directly with the mass correlation and cluster-mass correlations in COBE-normalized simulations of popular cosmological models, and derive two independent estimates of the galaxy biasing expected as a function of scale. This analysis reveals that both low-density and critical-density COBE-normalized cold dark matter (CDM) models require anti-biasing by a factor ∼ 2 on scales r ≤ 2 h−1 Mpc, and that the mixed dark matter (MDM) model is consistent with a constant biasing factor on all scales. The critical-density CDM model also suffers from the usual deficit of power on large scales (r ≥ 20 h−1 Mpc). We use the velocity fields predicted from the different models to distort the APM real-space cross-correlation function. Comparison with the APM redshift-space ξcg yields an estimate of the value of Ω0.6 needed in each model. We find that only the low-Ω model is fully consistent with observations, with MDM marginally excluded at the ∼ 2 σ level.

The cluster-galaxy cross-correlation and the average infall velocity around cluster in the modified CDM models

The cluster-galaxy cross-correlation and the average infall velocity around cluster for the tilted CDM models, the hot-cold mixed dark matter models (MDM) and theA CDM models are calculated. And it is found that the prediction of the cluster-galaxy cross-correlation of theA CDM models with ΩA=0.9, ΩC=0.1,h=1,b = 1 or 2 is much higher than that of observation for the radius larger than 10 h−1 Mpc (H0 = 100 h.kms−1Mpc−1), and the other models are compatible with the observation on the scale of (3–20) h− Mpc. The results can be used to compare with new observations to restrict the nature of the dark matter and the biasing factor.

Evolution of velocity and density fields around clusters of galaxies

The evolution of the averaged density and infall velocity profiles around clusters of galaxies is explored in several cosmological scenarios based on gravitational instability. The analysis is based on the statistics of peaks in random Gaussian fields and the spherical infall model. This method is shown to give accurate predictions of the cluster-galaxy cross-correlation function when compared with N-body simulations. The predictions for the average infall velocity as function of radius are not as accurate but are still useful. The predictions for the cluster-galaxy cross-correlation function on large scales are very different for models with little power on large scales (such as the cold dark matter and the hot dark matter models) and models with much power on large scales (such as primordial isocurvature baryon models). The ensemble average infall velocity as a function of radius provides a useful method for distinguishing between models with different levels of biasing of the galaxy number density fluctuations relative to mass fluctuations. 45 refs.

Clustering due to cluster galaxies

This paper presents a calculation of the contribution that galaxies in clusters make toward the clustering exhibited by all galaxies. It is shown that, within observational uncertainties, cluster galaxies may be responsible for all the clustering measured by the galaxy–galaxy correlatioan function, |$\xi_\text{gg}(r)$|⁠. This extends Peebles’s result that cluster galaxies make a significant contribution to the two-point function on a scale of 1 h−1 Mpc.(h is the value of Hubble’s constant in units of |$100\enspace \text {km s}^{-1}\enspace \text {Mpc}^{-1}$|⁠.) This then accounts for the apparent paradox that the two-point correlation function in redshift space is elongated along the line-of-sight on scales where |$\xi_ \text {gg}(r)$| is significantly less than unity. It has previously been argued that the elongation is a direct indication of non-linear dynamical effects. This result also suggests that n-point correlation functions do little more than probe cluster structure on scales up to 10 h−1 Mpc. The variance of the galaxy density field is also considered and used to place constraints on the amplitude of the cluster–galaxy cross-correlation function.