Constraining Cosmology using Galaxy Clusters ============================================ Reviews ------- .. figure:: https://github.com/dr-guangtou/daily_astroph/blob/master/figure/Allen2011_1.png :alt: Allen2011 Allen2011 - `Cosmological Parameters from Observations of Galaxy Clusters - ARA&A review by Allen, Evrard & Mantz 2011 `__ - `Huterer et al. 2015 - Growth of cosmic structure: Probing dark energy beyond expansion `__ - See Section 4.2: Cluster Abundance - The primary importance of clusters in the context of dark energy is their complementarity to geometric probes, i.e. their **ability to distinguish between modified gravity and dark energy models with degenerate expansion histories**. Galaxy clusters are statistically competitive with and often better than other probes. (Fig 5, right panel, the “sweet spot” is z=0.3 - 0.8. - The basic physics behind cluster abundances as a cosmological probe are **conceptually simple**; and A cluster abundance experiment is **conceptually very simple**. - The dependence of the number of galaxy clusters on the **variance of the linear density field** that allows us to utilize galaxy clusters to constrain the growth of structure. - Future surveys will almost certainly rely on **weak lensing mass calibration** to estimate cluster masses. - Other usages of clusters as a cosmological tool: - Galaxy clusters can probe dark energy in other ways as well, most notably by **comparing cluster mass estimates from weak lensing and dynamical methods such as galaxy velocity dispersions** - Because the growth of structure is also impacted by non-zero neutrino mass, galaxy cluster abundances can provide **competitive constraints on the sum of neutrino masses**. - Difficulties and limitations: - To achieve the goal of DES Stage III (IV) requirement, we must be able to measure cluster masses with **5% (2%) precision**. See `Applegate et al. (2014) `__ (Currently can achieve 7%, but with 20% systematic differences among methods). - Systematic errors in shear measurements tend to be less critical for cluster abundance work than for cosmic shear work (only care about circular averaged tangential shear). - Key systematic is the **calibration not only of the mean relation between cluster observables (optical, X-ray, or mm signals) and cluster mass, but also the scatter (shape and amplitude) about the mean.** - **Cluster centering** remains an important systematic in optical and/or low resolution experiments (e.g. Planck). (See `Oguri & Takada 2011 about self-calibration `__). - Optical observations benefit from a lower mass detection threshold than X-ray/mm over a large redshift range, which in turn result in improved statistical constraints. - **The synergistic nature of multi-wavelength cluster cosmology will necessarily play a key role in future cluster abundance experiments.** A balanced multi-wavelength approach will be critical to the success of cluster cosmology over the next 10–20 years. - **Self-calibration**: the cluster-clustering signal is itself an observable that one can use to calibrate cluster masses, and which is insensitive to all of the above systematic effects. - `Huterer & Shafer 2018 - Dark energy two decades after: observables, probes, consistency tests `__ - See Section 5.5 Galaxy Clusters - Clusters are **versatile probes of cosmology and astrophysics** and have had an important role in the development of modern cosmology - Recent cluster observations typically do not have enough signal-to-noise to determine the cluster masses directly; instead, **forward-modeling** can be applied to the mass function to recast the theory in the space of observable quantities (e.g. see Evrard et al. 2014). - The mass function’s near-exponential dependence on the power spectrum in the high-mass limit is at the root of the power of clusters to probe the growth of density fluctuations. - (The clusters’) two-point correlation function probes the matter power spectrum as well as the growth and geometry factors sensitive to dark energy. - Clusters can also be correlated with background galaxies to probe the growth (Cluster-Galaxy lensing, see `Oguri & Takada 2011 `__ - The most important uncertainty is typically tied to parameters that describe the scaling relations between mass and observable properties of the cluster (e.g. Flux, temperature). - `Weinberg 2013, PhR - Observational probes of cosmic acceleration `__ - See Section 6: Clusters of galaxies Key Papers ---------- Theoretical ~~~~~~~~~~~ Predictions ^^^^^^^^^^^ - `Pillepich et al. 2018 - Forecasts on dark energy from the X-ray cluster survey with eROSITA: constraints from counts and clustering `__ - Fisher information is extracted from the number density and spatial clustering of a photon-count-limited sample of clusters of galaxies up to z ˜ 2. We consider different scenarios for the availability of (i) X-ray follow-up observations, (ii) photometric and spectroscopic redshifts, and (iii) accurate knowledge of the observable - mass relation down to the scale of galaxy groups, but no additional observation-related systematics are taken into account. Early stage ^^^^^^^^^^^ - `Wang & Steinhardt 1998 - Cluster Abundance Constraints for Cosmological Models with a Time-varying, Spatially Inhomogeneous Energy Component with Negative Pressure `__ - `Haiman, Mohr & Holder 2001, ApJ - Constraints on Cosmological Parameters from Future Galaxy Cluster Surveys `__ - **Important**: “Our results indicate a formal statistical uncertainty of ~3% (68% confidence) on both Ωm and w when the SZE survey is combined with either the CMB or SN data; a large number of clusters in the X-ray survey further suppresses the degeneracy between w and both Ωm and h.” - `Fan & Chiueh 2001 - Determining the Geometry and the Cosmological Parameters of the Universe through Sunyaev-Zeldovich Effect Cluster Counts `__ - `Holder, Haiman & Mohr 2001 - Constraints on Ωm, ΩΛ, and σ8 from Galaxy Cluster Redshift Distributions `__ - `Newman et al. 2002 - Measuring the Cosmic Equation of State with Galaxy Clusters in the DEEP2 Redshift Survey `__ - `Refregier et al. 2002 - Cosmology with galaxy clusters in the XMM large-scale structure survey `__ - `Levine et al. 2002 - Future Galaxy Cluster Surveys: The Effect of Theory Uncertainty on Constraining Cosmological Parameters `__ Systematic, (Self-)Calibration ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - `Lima & Hu 2004 - Self-calibration of cluster dark energy studies: Counts in cells `__ - **Important** Self-calibration (Using noise as signal!): **The excess variance of counts due to the clustering of clusters** provides such an opportunity and can be measured from the survey without additional observational cost. - `Lima & Hu 2005 - Self-calibration of cluster dark energy studies: Observable-mass distribution `__ - Given the shape of the actual mass function, the properties of the distribution may be internally monitored by the shape of the observable mass function. - `Hu & Cohn 2006 - Likelihood methods for cluster dark energy surveys `__ - `Lima & Hu 2007 - Photometric redshift requirements for self-calibration of cluster dark energy studies `__ - Self-calibration in combination with external mass inferences helps reduce photo-z requirements and provides important consistency checks for future cluster surveys. - `Majumdar & Mohr 2003 - Importance of Cluster Structural Evolution in Using X-Ray and Sunyaev-Zeldovich Effect Galaxy Cluster Surveys to Study Dark Energy `__ - We show that for a particular X-ray survey (Sunyaev-Zeldovich effect [SZE] survey), the constraints on w degrade by roughly a factor of 3 (factor of 2) when one accounts for the possibility of nonstandard cluster evolution. - `Majumdar & Mohr 2004 - Self-Calibration in Cluster Studies of Dark Energy: Combining the Cluster Redshift Distribution, the Power Spectrum, and Mass Measurements `__ - The best constraints are obtained when one combines both the power spectrum constraints and the mass measurements with the cluster redshift distribution; when using the survey to extract the parameters and evolution of the mass-observable relations, we estimate uncertainties on w of ~4%-6% - `Hu 2003 - Self-consistency and calibration of cluster number count surveys for dark energy `__ - “we find that the ambiguity from the normalization of the mass-observable relationships, or an extrapolation of external mass-observable determinations from higher masses, can be largely eliminated with a sufficiently deep survey, even allowing for an arbitrary evolution” - `Wu, Rozo & Wechsler 2008 - The Effects of Halo Assembly Bias on Self-Calibration in Galaxy Cluster Surveys `__ - **Halo assembly bias**: the clustering amplitude of halos depends not only on the halo mass, but also on various secondary variables. - The impact of the secondary dependence is determined by (1) the scatter in the observable-mass relation and (2) the correlation between observable and secondary variables. **Could be important to DES and LSST like survey** - `Cunha 2009 - Cross-calibration of cluster mass observables `__ - We use a **Fisher matrix analysis** to study the improvements in the joint dark energy and cluster mass-observables constraints resulting from combining cluster counts and clustering abundances measured with different techniques. - The **cross-calibrated constraints** are less sensitive to variations in the mass threshold or maximum redshift range. - `Cunha, Huterer & Frieman 2009 - Constraining dark energy with clusters: Complementarity with other probes `__ - We find that optimally combined optical and Sunyaev-Zeldovich effect cluster surveys should improve the Dark Energy Task Force figure of merit - `Wu, Rozo & Wechsler 2010 - Annealing a Follow-up Program: Improvement of the Dark Energy Figure of Merit for Optical Galaxy Cluster Surveys `__ - Considering clusters selected from optical imaging in the Dark Energy Survey, we find that approximately 200 low-redshift X-ray clusters or massive Sunyaev-Zel’dovich clusters can improve the dark energy figure of merit by 50%, provided that the follow-up mass measurements involve no systematic error. - The scatter in the optical richness–mass distribution, which needs to be made as tight as possible to improve the efficacy of follow-up observations - `Oguri & Takada 2011, PhRvD - Combining cluster observables and stacked weak lensing to probe dark energy: Self-calibration of systematic uncertainties `__ - `Rozo et al. 2011, ApJ - Stacked Weak Lensing Mass Calibration: Estimators, Systematics, and Impact on Cosmological Parameter Constraints `__ - `Evrard, Arnault, Huterer & Farahi 2014 - A model for multiproperty galaxy cluster statistics `__ - We derive closed-form expressions for the space density of haloes as a function of multiple observables as well as forms for the low-order moments of properties of observable-selected samples. Other issues ^^^^^^^^^^^^ - `Takada & Bridle 2007, NJPh - Probing dark energy with cluster counts and cosmic shear power spectra: including the full covariance `__ - `Ichiki & Takada 2012, PhRvD - Impact of massive neutrinos on the abundance of massive clusters `__ - `Takada & Spergel 2014, MNRAS - Joint analysis of cluster number counts and weak lensing power spectrum to correct for the super-sample covariance `__ Observational ~~~~~~~~~~~~~ - **Chandra Cluster Cosmology Project** - `Vilhlinin et al. 2009a - Chandra Cluster Cosmology Project. II. Samples and X-Ray Data Reduction `__ - `Vilhlinin et al. 2009b - Chandra Cluster Cosmology Project III: Cosmological Parameter Constraints `__ - **37** Chandra clusters at = 0.55 from ROSAT and **49** brightest z=0.05 clusters - **The observed growth of massive galaxy clusters using ROSAT/Chandra** - `Mantz, Allen, Rapetti & Ebeling 2010a - I. Statistical methods and cosmological constraints `__ - **238** clusters from RASS; **94** Chandra follow-up. - `Mantz, Allen, Ebeling, Rapetti & Drlica-Wagner 2010 - II. X-ray scaling relations `__ - `Rapetti, Allen, Mantz & Ebeling 2010 - III. Testing general relativity on cosmological scales `__ - `Mantz, Allen & Rapetti 2010 - IV. Robust constraints on neutrino properties `__ - **maxBCG clusters** - `Rozo et al. 2010 - Cosmological Constraints from the Sloan Digital Sky Survey maxBCG Cluster Catalog `__ - **SDSS-maxBCG**: fully consistent with the WMAP five-year data, and in a joint analysis we find σ8 = 0.807 ± 0.020 and Ωm = 0.265 ± 0.016 - `Zu et al. 2014, MNRAS - Cosmological constraints from the large-scale weak lensing of SDSS MaxBCG clusters `__ - `Tinker et al. 2012 - Cosmological Constraints from Galaxy Clustering and the Mass-to-number Ratio of Galaxy Clusters `__ - **SDSS 2PCF + mass-to-galaxy number ratio within cluster** - **Cosmology and astrophysics from relaxed galaxy clusters in Chandra & ROSAT** - `Mantz et al. 2015 - I. Sample selection `__ - `Mantz et al. 2014 - II. Cosmological constraints `__ - `Mantz et al. 2016 - III. Thermodynamic profiles and scaling relations `__ - `Applegate et al. 2016 - IV. Robustly calibrating hydrostatic masses with weak lensing `__ - `Mantz et al. 2016 - V. Consistency with cold dark matter structure formation `__ - `de Haan et al. 2016 - Cosmological Constraints from Galaxy Clusters in the 2500 Square-degree SPT-SZ Survey `__ - **377** clusters at z>0.2 from 2500 square-degree South Pole Telescope SZ survey Cluster mass calibration and scaling relations ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - `Becker & Kravtsov 2011 - On the Accuracy of Weak-lensing Cluster Mass Reconstructions `__ - **Important**: We find that correlated large-scale structure within several virial radii of clusters contributes a smaller, but nevertheless significant, amount to the scatter. The intrinsic scatter due to these physical sources is ≈20% for massive clusters and can be as high as ≈30% for group-sized systems. - We find that WL mass measurements can have a small, ≈5%-10%, but non-negligible amount of bias. - `Rasia et al. 2012 - Lensing and x-ray mass estimates of clusters (simulations) `__ - We confirm previous results showing that lensing masses obtained from the fit of the cluster tangential shear profiles with Navarro-Frenk-White functionals are **biased low by ˜5-10% with a large scatter (˜10-25%)** - `Rozo, Bartlett, Evrard & Rykoff 2014 - Closing the loop: a self-consistent model of optical, X-ray and Sunyaev-Zel’dovich scaling relations for clusters of Galaxies `__ - We find that scaling relations derived from optical and X-ray selected cluster samples are consistent with one another. These cluster scaling relations satisfy several non- trivial spatial abundance constraints and closure relations. Using Velocity Distribution Function ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - `The Velocity Distribution Function of Galaxy Clusters as a Cosmological Probe `__ - `Cluster Cosmology with the Velocity Distribution Function of the HeCS-SZ Sample `__ - **On the Cluster Physics of Sunyaev-Zeldovich and X-Ray Surveys** - `Battaglia, Bond, Pfommer & Sievers 2012a - I. The Influence of Feedback, Non-thermal Pressure, and Cluster Shapes on Y-M Scaling Relations `__ - `Battaglia, Bond, Pfommer & Sievers 2012b - II. Deconstructing the Thermal SZ Power Spectrum `__ - `Battaglia, Bond, Pfommer & Sievers 2013 - III. Measurement Biases and Cosmological Evolution of Gas and Stellar Mass Fractions `__ - `Penna-Lima et al. 2017 - Calibrating the Planck cluster mass scale with CLASH `__ - **1 - b_sz = 0.73 +/- 0.10** Lectures and Conferences ------------------------ - `Ushering in DES Cluster Cosmology with redMaPPer by Eduardo Rozo `__ - Galaxy clusters are the most massive gravitationally bound structures in the Universe. - Number of galaxy clusters as a function of halo mass measures the amount of structure in the Universe (sigma_8). - Optical selection allows detection of low mass systems; more abundant == better weak lensing halo mass == Better cosmology. Finding clusters in the optical maximizes the cosmological information that can be drawn from clusters. - Centering cluster is hard! - `SLAC-2017 Conference on Cluster Cosmology `__ - `Cosmology with Clusters of Galaxies by Ben Maughan (Undergraduate Level) `__ - `KITP Conference: Astrophysics and Cosmology with Galaxy Clusters `__ Important References -------------------- - Galaxy clusters have been recognized as powerful cosmological probes - Henry et al. 2009; Vikhlinin et al. 2009; Mantz et al. 2010; Rozo et al. 2010; Clerc et al. 2012; Benson et al. 2013; Hasselfield et al. 2013). - Early optical cluster finders can be divided into roughly two classes 1. Those based on photometric redshifts - Kepner et al. 1999; van Breukelen & Clewley 2009; Milkeraitis et al. 2010; Durret et al. 2011; Szabo et al. 2011; Soares-Santos et al. 2011; Wen et al. 2012 2. Those utilizing the cluster red sequence - Annis et al. 1999; Gladders & Yee 2000; Koester et al. 2007a; Gladders et al. 2007; Gal et al. 2009; Thanjavur et al. 2009; Hao et al. 2010; Murphy et al. 2012