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-Allowed density profiles for LRG satellite galaxies within their dark matter halos. Shaded regions show the 1-σ (red), 2-σ (blue) and 3-σ (green) allowed regions for γ and f gal for the PNMCG model. Filled circles mark the locations of the NFW profile (γ = 1, f gal = 1) and the Singular Isothermal Sphere (SIS) profile (γ = 2, f gal → 0).
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We model the small-scale clustering of luminous red galaxies (LRGs) in the Sloan Digital Sky Survey. Specifically, we use the halo occupation distribution formalism to model the projected two-point correlation function of LRGs on scales well within the sizes of their host halos (0.016 h
–1 Mpc ≤ r ≤ 0.42 h
–1 Mpc). We start by varying P(N|M), the p...
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... Since the extent and spatial distribution of 'satellite' galaxies is uncertain (and empirically, for luminous galaxy samples, is not the same as that of the dark matter; e.g. Watson et al. 2010;Piscionere et al. 2015), we populate haloes with satellite galaxies according to an NFW profile (Navarro, Frenk & White 1997) with concentration and radius corrected by A conc and R rescale from the concentration and radius determined by ROCKSTAR for a given halo. ...
We describe our non-linear emulation (i.e. interpolation) framework that combines the halo occupation distribution (HOD) galaxy bias model with N-body simulations of non-linear structure formation, designed to accurately predict the projected clustering and galaxy–galaxy lensing signals from luminous red galaxies in the redshift range 0.16 < z < 0.36 on comoving scales 0.6 < rp < 30 $h^{-1} \, \text{Mpc}$. The interpolation accuracy is ≲ 1–2 per cent across the entire physically plausible range of parameters for all scales considered. We correctly recover the true value of the cosmological parameter S8 = (σ8/0.8228)(Ωm/0.3107)0.6 from mock measurements produced via subhalo abundance matching (SHAM)-based light-cones designed to approximately match the properties of the SDSS LOWZ galaxy sample. Applying our model to Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 14 (DR14) LOWZ galaxy clustering and galaxy-shear cross-correlation measurements made with Sloan Digital Sky Survey (SDSS) Data Release 8 (DR8) imaging, we perform a prototype cosmological analysis marginalizing over wCDM cosmological parameters and galaxy HOD parameters. We obtain a 4.4 per cent measurement of S8 = 0.847 ± 0.037, in 3.5σ tension with the Planck cosmological results of 1.00 ± 0.02. We discuss the possibility of underestimated systematic uncertainties or astrophysical effects that could explain this discrepancy.
... This also brackets the range of observational constraints on the radial distribution of satellite galaxies in groups and clusters (e.g. Carlberg et al. 1997;van der Marel et al. 2000;Lin, Mohr & Stanford 2004;Yang et al. 2005b;Chen 2008;More et al. 2009a;Watson et al. 2010Watson et al. , 2012Guo et al. 2012;Cacciato et al. 2013;Lange et al. 2019b). We also assume that the host haloes of satellite galaxies are spherical NFW haloes that are completely specified by their mass, i.e. we adopt the concentration-mass relation of Macciò, Dutton & van den Bosch (2008) without scatter. ...
We present a Bayesian hierarchical inference formalism (Basilisk) to constrain the galaxy–halo connection using satellite kinematics. Unlike traditional methods, Basilisk does not resort to stacking the kinematics of satellite galaxies in bins of central luminosity, and does not make use of summary statistics, such as satellite velocity dispersion. Rather, Basilisk leaves the data in its raw form and computes the corresponding likelihood. In addition, Basilisk can be applied to flux-limited, rather than volume-limited samples, greatly enhancing the quantity and dynamic range of the data. And finally, Basilisk is the only available method that simultaneously solves for halo mass and orbital anisotropy of the satellite galaxies, while properly accounting for scatter in the galaxy–halo connection. Basilisk uses the conditional luminosity function to model halo occupation statistics, and assumes that satellite galaxies are a relaxed tracer population of the host halo’s potential with kinematics that obey the spherical Jeans equation. We test and validate Basilisk using mocks of varying complexity, and demonstrate that it yields unbiased constraints on the galaxy–halo connection and at a precision that rivals galaxy–galaxy lensing. In particular, Basilisk accurately recovers the full PDF of the relation between halo mass and central galaxy luminosity, and simultaneously constrains the orbital anisotropy of the satellite galaxies. Basilisk ’s inference is not affected by potential velocity bias of the central galaxies, or by slight errors in the inferred, radial profile of satellite galaxies that arise as a consequence of interlopers and sample impurity.
... This gNFW profile has sufficient flexibility to adequately describe a wide range of radial profiles, from satellites being unbiased tracers of their dark matter halo (γ = R = 1), to cored profiles that resemble the radial profile of surviving subhaloes in numerical simulations (γ = 0, R ∼ 2). This also brackets the range of observational constraints on the radial distribution of satellite galaxies in groups and clusters (e.g., Carlberg et al. 1997;van der Marel et al. 2000;Lin et al. 2004;Yang et al. 2005b;Chen 2008;More et al. 2009a;Guo et al. 2012;Cacciato et al. 2013;Watson et al. 2010Watson et al. , 2012Lange et al. 2019b). ...
We present a Bayesian hierarchical inference formalism (Basilisk) to constrain the galaxy-halo connection using satellite kinematics. Unlike traditional methods, Basilisk does not resort to stacking the kinematics of satellite galaxies in bins of central luminosity, and does not make use of summary statistics, such as satellite velocity dispersion. Rather, Basilisk leaves the data in its raw form and computes the corresponding likelihood. In addition, Basilisk can be applied to flux-limited, rather than volume-limited samples, greatly enhancing the quantity and dynamic range of the data. And finally, Basilisk is the only available method that simultaneously solves for halo mass and orbital anisotropy of the satellite galaxies, while properly accounting for scatter in the galaxy-halo connection. Basilisk uses the conditional luminosity function to model halo occupation statistics, and assumes that satellite galaxies are a relaxed tracer population of the host halo's potential with kinematics that obey the spherical Jeans equation. We test and validate Basilisk using mocks of varying complexity, and demonstrate that it yields unbiased constraints on the galaxy-halo connection and at a precision that rivals galaxy-galaxy lensing. In particular, Basilisk accurately recovers the full PDF of the relation between halo mass and central galaxy luminosity, and simultaneously constrains the orbital anisotropy of the satellite galaxies. Basilisk's inference is not affected by potential velocity bias of the central galaxies, or by slight errors in the inferred, radial profile of satellite galaxies that arise as a consequence of interlopers and sample impurity.
... However, the observed galaxy profiles of SPT and ACT are noticeably steeper in the inner regions (radii smaller than ∼0.5 h −1 Mpc) than that from simulation DM particles. While this has been previously noted by Masjedi et al. (2006) and Watson et al. (2010) for Luminous Red Galaxies, our results show that this difference also exists around massive clusters using galaxy samples down to lower mass. Models of galaxy evolution show (see e.g. ...
We present a detection of the splashback feature around galaxy clusters selected using the Sunyaev–Zel’dovich (SZ) signal. Recent measurements of the splashback feature around optically selected galaxy clusters have found that the splashback radius, rsp, is smaller than predicted by N-body simulations. A possible explanation for this discrepancy is that rsp inferred from the observed radial distribution of galaxies is affected by selection effects related to the optical cluster-finding algorithms. We test this possibility by measuring the splashback feature in clusters selected via the SZ effect in data from the South Pole Telescope SZ survey and the Atacama Cosmology Telescope Polarimeter survey. The measurement is accomplished by correlating these cluster samples with galaxies detected in the Dark Energy Survey Year 3 data. The SZ observable used to select clusters in this analysis is expected to have a tighter correlation with halo mass and to be more immune to projection effects and aperture-induced biases, potentially ameliorating causes of systematic error for optically selected clusters. We find that the measured rsp for SZ-selected clusters is consistent with the expectations from simulations, although the small number of SZ-selected clusters makes a precise comparison difficult. In agreement with previous work, when using optically selected redMaPPer clusters with similar mass and redshift distributions, rsp is ∼2σ smaller than in the simulations. These results motivate detailed investigations of selection biases in optically selected cluster catalogues and exploration of the splashback feature around larger samples of SZ-selected clusters. Additionally, we investigate trends in the galaxy profile and splashback feature as a function of galaxy colour, finding that blue galaxies have profiles close to a power law with no discernible splashback feature, which is consistent with them being on their first infall into the cluster.
... However, the observed galaxy profiles of SPT and ACT are noticeably steeper in the inner regions (radii smaller than ∼0.5 h −1 Mpc) than that from simulation DM particles. While this has been previously noted by Masjedi et al. (2006) and Watson et al. (2010) for Luminous Red Galaxies, our results show that this difference also exists around massive clusters using galaxy samples down to lower mass. Models of galaxy evolution show (see e.g. ...
We present a detection of the splashback feature around galaxy clusters selected using the Sunyaev–Zel’dovich (SZ) signal. Recent measurements of the splashback feature around optically selected galaxy clusters have found that the splashback radius, rsp, is smaller than predicted by N-body simulations. A possible explanation for this discrepancy is that rsp inferred from the observed radial distribution of galaxies is affected by selection effects related to the optical cluster-finding algorithms. We test this possibility by measuring the splashback feature in clusters selected via the SZ effect in data from the South Pole Telescope SZ survey and the Atacama Cosmology Telescope Polarimeter survey. The measurement is accomplished by correlating these cluster samples with galaxies detected in the Dark Energy Survey Year 3 data. The SZ observable used to select clusters in this analysis is expected to have a tighter correlation with halo mass and to be more immune to projection effects and aperture-induced biases, potentially ameliorating causes of systematic error for optically selected clusters. We find that the measured rsp for SZ-selected clusters is consistent with the expectations from simulations, although the small number of SZ-selected clusters makes a precise comparison difficult. In agreement with previous work, when using optically selected redMaPPer clusters with similar mass and redshift distributions, rsp is ∼2σ smaller than in the simulations. These results motivate detailed investigations of selection biases in optically selected cluster catalogues and exploration of the splashback feature around larger samples of SZ-selected clusters. Additionally, we investigate trends in the galaxy profile and splashback feature as a function of galaxy colour, finding that blue galaxies have profiles close to a power law with no discernible splashback feature, which is consistent with them being on their first infall into the cluster.
... While we only have halo catalogs for spherical overdensity halos determined by the virial overdensity criterion of Bryan & Norman (1998), and thus cannot marginalize over halo definition, marginalizing over the R rescale parameter allows us to take into account the main effect of varying halo definitions, namely the dependence of halo radii on halo definition. Since the extent and spatial distribution of 'satellite' galaxies is uncertain (and empirically, for luminous galaxy samples, is not the same as that of the dark matter; e.g., Watson et al. 2010;Piscionere et al. 2015), we populate halos with satellite galaxies according to an NFW profile (Navarro et al. 1997) with concentration and radius corrected by A conc and R rescale from the concentration and radius determined by Rockstar for a given halo. ...
We describe our nonlinear emulation (i.e., interpolation) framework that combines the halo occupation distribution (HOD) galaxy bias model with $N$-body simulations of nonlinear structure formation, designed to accurately predict the projected clustering and galaxy-galaxy lensing signals from luminous red galaxies (LRGs) in the redshift range $0.16 < z < 0.36$ on comoving scales $0.6 < r_p < 30$ $h^{-1}$ Mpc. The interpolation accuracy is $\lesssim 1-2$ per cent across the entire physically plausible range of parameters for all scales considered. We correctly recover the true value of the cosmological parameter $S_8 = (\frac{\sigma_8}{0.8228}) (\frac{\Omega_{\text{m}}}{0.3107})^{0.6}$ from mock measurements produced via subhalo abundance matching (SHAM)-based lightcones designed to approximately match the properties of the SDSS LOWZ galaxy sample. Applying our model to the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 14 (DR14) LOWZ galaxy clustering and the galaxy-shear cross-correlation measurements of Singh et al. (2018), made with Sloan Digital Sky Survey (SDSS) Data Release 8 (DR8) imaging, we perform a prototype cosmological analysis marginalizing over $w$CDM cosmological parameters and galaxy HOD parameters. We obtain a 4.4 per cent measurement of $S_8 = 0.847 \pm 0.037$, in $3.5\sigma$ tension with the Planck cosmological results of $1.00 \pm 0.02$. We discuss the possibility of underestimated systematic uncertainties or astrophysical effects that could explain this discrepancy.
... As one of the most powerful probes of the growth rate of the matter density field, it can put strong constraints on the many fundamental quantities, including the cosmological parameters (Jing et al. 2002Tegmark et al. 2004Tegmark et al. , 2006Wang & Tegmark 2004;Yang et al. 2004;Seljak et al. 2005;Anderson et al. 2012;Sánchez et al. 2012Sánchez et al. , 2017Cacciato et al. 2013;Samushia et al. 2014;Shi et al. 2018), neutrino masses, the nature of gravity, and the properties of dark energy (Kaiser 1987;Peacock et al. 2001;Eisenstein et al. 2005;Guzzo et al. 2008;Reid et al. 2012;Contreras et al. 2013;Beutler et al. 2017;Wang et al. 2018a). At the same time, galaxy clustering studies also provide crucial insights into the physics of galaxy formation and their connections to dark matter halos on small and intermediate scales (e.g., Springel et al. 2005;Croton et al. 2007;Dalal et al. 2008;Mo et al. 2010;Watson et al. 2010;Wang et al. 2013Wang et al. , 2018bZentner et al. 2014;Piscionere et al. 2015;Yang et al. 2017). ...
Fiber collision is a persistent problem faced by modern spectroscopic galaxy surveys. In this work, we propose a new method to correct for this undesired effect, focusing on the clustering from the fiber-collision scale up to ?10 Mpc h-1. We assume that the fiber-collided galaxies are in association with their nearest three angular neighbors. Compared with the conventional nearest-neighbor method, we have properly accounted for the foreground (background) galaxies that are associated with the foreground (background) cosmic webs relative to the nearest neighbor. We have tested the new method with mock catalogs of the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). The test demonstrates that our new method can recover the projected two-point correlation functions at an accuracy better than 1% on small (below the fiber-collision scale) to intermediate (i.e., 10 Mpc h-1) scales, where the fiber collision takes effect and the SDSS main sample can probe. The new method also gives a better recovery of the redshift-space correlation functions almost on all scales that we are interested in. © 2019. The American Astronomical Society. All rights reserved.
... As one of the most powerful probes of the growth rate of the matter density field, it can put strong constraints on the many fundamental quantities, including the cosmological parameters (Jing et al. 2002Tegmark et al. 2006Tegmark et al. , 2004Wang & Tegmark 2004;Yang et al. 2004;Seljak et al. 2005;Anderson et al. 2012;Sánchez et al. 2012Sánchez et al. , 2017Cacciato et al. 2013;van den Bosch et al. 2013;Samushia et al. 2014;Shi et al. 2018), neutrino masses, the nature of gravity, and the properties of dark energy (Kaiser 1987;Peacock et al. 2001;Eisenstein et al. 2005;Guzzo et al. 2008;Reid et al. 2012;Contreras et al. 2013;Beutler et al. 2017;Wang et al. 2017). At the same time, galaxy clustering studies also provide crucial insights into the physics of galaxy formation and their connections to dark matter halos on small and intermediate scales (e.g., Springel et al. 2005;Croton et al. 2007;Dalal et al. 2008;Mo et al. 2010;Watson et al. 2010;Wang et al. 2013Wang et al. , 2018Zentner et al. 2014;Piscionere et al. 2015;Yang et al. 2017). ...
The widely used fiber-fed spectrograph in galaxy surveys is the most efficient tool to productively obtain accurate redshifts for millions of galaxies. However, there is a defect in this technique known as the fiber-collision problem that cannot be easily overcome. In this work, we propose a new method to correct this undesired effect. First, we assume that the fiber-collided galaxies are in association with their nearest a few, here up to three, angular neighbors. Then we reconstruct the redshifts of fiber-collided galaxies by sampling the line-of-sight comoving separations of galaxy pairs within a coherence length of 20 Mpc$/h$. We test this new method with mock catalogs and compare the results with other previous methods. The comparisons demonstrate that our new method can reliably reduce the bias to $1\%$ level below the fiber-collision scale with a better error constraining for the projected two-point correlation functions. It also gives a better recovery of the redshift-space correlation functions almost on all scale that we are interested in. Finally, we discuss the limits of this new method and summarize the advantages of using this method to measure galaxy clustering.
... The halo model has since been used by a large number of studies to model galaxy clustering data in several galaxy redshift surveys: the 2dF Galaxy Redshift Survey (2dFGRS; Colless et al. 2001), the Sloan Digital Sky Survey (SDSS; York et al. 2000), the 6dF Galaxy Redshift Survey (6dFGRS; Jones et al. 2004), and the SDSS III Baryon Os-cillation Spectroscopic Survey (BOSS; Dawson et al. 2013). Some studies investigated the two-point correlation function of low redshift galaxies (Magliocchetti & Porciani 2003;Zehavi et al. 2004;Collister & Lahav 2005;Zehavi et al. 2005;Tinker et al. 2005;Zehavi et al. 2011;Watson et al. 2012;Beutler et al. 2013;Piscionere et al. 2015), others investigated the same for red galaxies (Blake et al. 2008;Brown et al. 2008;Zheng et al. 2009;Watson et al. 2010;White et al. 2011;Parejko et al. 2013;Nikoloudakis et al. 2013;Guo et al. 2014;Reid et al. 2015;Guo et al. 2015a), or other special classes of galaxies such as AGN or radio galaxies (Wake et al. 2008;Mandelbaum et al. 2009;Richardson et al. 2013). Many studies modelled the two-point correlation function of Lyman Break and other types of high redshift galaxies (Bullock et al. 2002;Moustakas & Somerville 2002;Hamana et al. 2004;Zheng 2004;Lee et al. 2006;Jose et al. 2013;Kim et al. 2014), while others combined modelling of galaxies at different redshifts in order to learn about the co-evolution of galaxies and halos (Yan et al. 2003;Cooray 2006;Tinker & Wetzel 2010;Abbas et al. 2010;Wake et al. 2011;Tinker et al. 2013). ...
... For the most part, the constraints are focused on the relation between the luminosity or stellar mass of galaxies and the mass of their halos (e.g., Zehavi et al. 2011). However, some studies focused on other aspects of the HOD, such as the radial distribution of galaxies within halos (e.g., Watson et al. 2010Watson et al. , 2012Piscionere et al. 2015), the velocity distribution of galaxies within halos (Guo et al. 2015a,b,c), or galaxy assembly bias (Zentner et al. 2016). These results have been quite illuminating and have helped to explain many observed features of the galaxy population, such as the morphology-density relation and the different clustering strengths of different galaxy types. ...
Interpreting the small-scale clustering of galaxies with halo models can elucidate the connection between galaxies and dark matter halos. Unfortunately, the modelling is typically not sufficiently accurate for ruling out models in a statistical sense. It is thus difficult to use the information encoded in small scales to test cosmological models or probe subtle features of the galaxy-halo connection. In this paper, we attempt to push halo modelling into the "accurate" regime with a fully numerical mock-based methodology and careful treatment of statistical and systematic errors. An advantage of this approach is that it can easily incorporate clustering statistics beyond the traditional two-point statistics. We use this modelling methodology to test the standard $\Lambda\mathrm{CDM}$ + halo model against the clustering of SDSS DR7 galaxies. Specifically, we use the projected correlation function, group multiplicity function and galaxy number density as constraints. We find that while the model provides a good match to each statistic separately, it struggles to fit them jointly. Adding group statistics leads to a more stringent test of the model and significantly tighter constraints on model parameters. We explore the impact of varying the adopted halo definition and cosmological model and find that changing the cosmology makes a significant difference. The most successful model we tried (Planck cosmology with Mvir halos) matches the clustering of low luminosity galaxies, but exhibits a $2.3 \sigma$ tension with the clustering of luminous galaxies, thus providing evidence that the "standard" halo model needs to be extended. This work represents the most accurate modelling of small-scale clustering to-date and opens the door to adding interesting freedom to the halo model and including additional clustering statistics as constraints.
... Chen et al. (2006) used the SDSS spectroscopic sample to study the projected radial distribution of satellites around isolated L * galaxies, constraining the power-law slope to be −1.7. Watson et al. (2010) modeled the clustering of luminous red galaxies in SDSS in the framework of halo occupation distribution. They found that on projected scales 0.016 h −1 Mpc r p 0.42 h −1 Mpc, the radial density profile of luminous red galaxies is close to an isothermal distribution. ...
We investigate the radial number density profile and the abundance distribution of faint satellites around central galaxies in the low-redshift universe using the Canada-France-Hawaii Telescope (CFHT) Legacy Survey. We consider three samples of central galaxies with magnitudes of M
r = –21, –22, and –23 selected from the Sloan Digital Sky Survey group catalog of Yang et al. The satellite distribution around these central galaxies is obtained by cross-correlating these galaxies with the photometric catalog of the CFHT Legacy Survey. The projected radial number density of the satellites obeys a power-law form with the best-fit logarithmic slope of –1.05, independent of both the central galaxy luminosity and the satellite luminosity. The projected cross-correlation function between central and satellite galaxies exhibits a non-monotonic trend with satellite luminosity. It is most pronounced for central galaxies with M
r = –21, where the decreasing trend of clustering amplitude with satellite luminosity is reversed when satellites are fainter than central galaxies by more than 2 mag. A comparison with the satellite luminosity functions in the Milky Way (MW) and M31 shows that the MW/M31 system has about twice as many satellites as around a typical central galaxy of similar luminosity. The implications for theoretical models are briefly discussed.
