Some issues in cluster cosmology Tim McKay University of Michigan Department of Physics 12/7/2018 CFCP Dark Energy Workshop

CFCP Dark Energy Workshop An outline Cluster counting in theory Cluster counting in practice General considerations Optical cluster selection Weak lensing cluster surveys Imagining the future 12/7/2018 CFCP Dark Energy Workshop

Cluster counting constraints on the expansion history Probing growth of linear perturbations by measuring the space density of the largest peaks Theorist’s cluster = mass peak to R200 Counts, mass spectrum of halos Analytic theory and N-body simulations predict dn/dM as a function of z Cosmology comes from comparison of observed dn/dM vs. z to theory 12/7/2018 CFCP Dark Energy Workshop

Cluster detection methods How do we measure mass peaks in 3D? We don’t 12/7/2018 CFCP Dark Energy Workshop

What’s a ‘cluster’ made of? Large peak in matter density Dark matter clump (~75% of mass) Many luminous galaxies (~2.5%: 10% of baryons) BCG and red sequence Additional galaxies Diffuse light Hot gas (~22.5%: 90% of baryons) Emits X-rays Causes SZ decrement in microwave background 12/7/2018 CFCP Dark Energy Workshop

What’s are the cluster observables? Cluster detection measures something other than mass: some observables like SZe, X-ray flux, X-ray temperature, galaxy richness, galaxy v, shear….. To approach dn/dM vs. z we need to know: M(observables,z) Efficiency(observables, z) The mass function is very steep! 12/7/2018 CFCP Dark Energy Workshop

Relating cluster counts to the predicted dn/dM Usually this relation is written: In reality this should be something like: 12/7/2018 CFCP Dark Energy Workshop

Cluster detection methods: observer’s clusters Clusters of galaxies: 2D, 2.5D, 3D Clusters of hot gas: X-ray, Sunyaev-Zeldovitch Clusters of projected mass: 2D, 2.1D? In every case we must learn the astrophysics to constrain M=f(observable) 12/7/2018 CFCP Dark Energy Workshop

CFCP Dark Energy Workshop Analogy to SNe For SNe, we want to know luminosity: measure spectrum, stretch, rise time, extinction, peak to tail ratio etc…. For clusters, we want to know mass: measure SZe, Fx, Tx, gal, lensing, Ngal, etc. We need to count all clusters: absolute efficiency required fundamentally a Poisson limited process (cosmic variance) 12/7/2018 CFCP Dark Energy Workshop

How will we learn what we need to know? Study clusters through all these methods Add extensions of structure formation modeling Couple both through observations of scaling relations Once we constrain clusters, we still need to understand observational effects K-corrections, angular resolution effects, projection, sensitivity vs. z, noise correlations 12/7/2018 CFCP Dark Energy Workshop

Finding clusters of galaxies in 2D optical data In the common wisdom this is plagued by projection New methods rely on uniform colors of cluster ellipticals (they are all old) Color <=> redshift: find clusters of objects with tightly clustered colors Provides good redshifts and projection is not an issue 12/7/2018 CFCP Dark Energy Workshop

CFCP Dark Energy Workshop 12/7/2018 CFCP Dark Energy Workshop

SDSS ‘maxBCG’ cluster catalog Jim Annis (FNAL) An example cluster at z=0.15 E/S0 ridgeline 12/7/2018 CFCP Dark Energy Workshop

SDSS ‘maxBCG’ cluster catalog Jim Annis (FNAL) Redshift estimates tested by > 104 spectra 12/7/2018 CFCP Dark Energy Workshop

How do we compare maxBCG to clusters of mass? Do all clusters of mass have red sequence ellipticals? => Galaxy evolution vs. environment The observables are ‘Ngals’, z, and a luminosity. How do these relate to mass? Uncertainties here affect both efficiency and mass estimation 12/7/2018 CFCP Dark Energy Workshop

Mass calibration for maxBCG clusters Calibration of mass (v) from weak lensing vs. Ngals Distribution of Ngals(M)? 12/7/2018 CFCP Dark Energy Workshop

Finding clusters in the projected mass distribution The weak lensing observable is shear, related to projected mass by a geometric filter Weak lensing signal is independent of evolution in the baryons 12/7/2018 CFCP Dark Energy Workshop

How to find masses from lensing: ‘Tangential shear’ is related to density contrast crit is the surface mass density for multiple lensing Measure T and crit and you have the surface mass density contrast. Deriving a mass from this still requires model fitting. 12/7/2018 CFCP Dark Energy Workshop

CFCP Dark Energy Workshop How to measure shear? Intrinsic shapes are elliptical and unknown (mean0.3) => how to determine distortion? Strong lensing: distortions larger than intrinsic ellipticity Weak lensing: distortions smaller than intrinsic ellipticity Statistical measurement: many source galaxies required Must be able to measure the shape of each galaxy to use it Shear measurement requires correction of instrumental PSF and distortion effects. For stable PSFs new methods will allow this to arbitrary precision (Gary Bernstein later…) 12/7/2018 CFCP Dark Energy Workshop

Size magnitude relation 25th magnitude Ground: >0.3” half light radius Space: >0.05” half light radius Gardner & Satyapal: Sizes from STIS HDF south images 12/7/2018 CFCP Dark Energy Workshop

critical: Important geometry dependence    ’  Observer Source Lens Ds Dds Dd 12/7/2018 CFCP Dark Energy Workshop

Some model lensing data sets Ground based R=25 (size limited) Space based R=28 Space based R=30 Apply these ‘observations’ to the Virgo simulation cluster catalogs from Evrard et al. 12/7/2018 CFCP Dark Energy Workshop

Basics for three surveys: why go so faint? Basic geometry is similar for the three surveys. Sensitivity changes due to source density. Lensing S/N is much higher for a deeper space based survey. Sensitivity tilted to low-z. 12/7/2018 CFCP Dark Energy Workshop

CFCP Dark Energy Workshop Survey to 25th magnitude Dotted lines: Detected Dashed lines: Detected with an incorrect source z distribution! Virgo ‘truth’ M>5x1013Msun M>1x1014Msun 12/7/2018 CFCP Dark Energy Workshop

CFCP Dark Energy Workshop Survey to 28th magnitude Dotted lines: Detected Dashed lines: Detected with an incorrect source z distribution! M>5x1013Msun M>1x1014Msun 12/7/2018 CFCP Dark Energy Workshop

CFCP Dark Energy Workshop Survey to 30th magnitude Dotted lines: Detected Dashed lines: Detected with an incorrect source z distribution! M>5x1013Msun M>1x1014Msun 12/7/2018 CFCP Dark Energy Workshop

What goes into formulating mass? Cluster redshift Source distribution (variance?) Other mass projected along line of sight Random Associated (filaments etc.) (X-ray and SZ are better….) 12/7/2018 CFCP Dark Energy Workshop

Cluster detection: peaks in the projected mass Projection effects and ‘dark clusters’: White, van Waerbeke and Mackey astro-ph/0111490 Combined methods: find in optical, measure with lensing, understand projection? Very bad on a steeply falling spectrum! 12/7/2018 CFCP Dark Energy Workshop

Combined Foreground lens Background lens Example of projection effects from White, van Waerbeke, and Mackey 12/7/2018 CFCP Dark Energy Workshop

An additional concern: cosmic variance in cluster normalization Virgo simulations of Evrard et al. astro-ph/011024 Shows dn/dM for 16 independent ‘local’ universes (5000 square degrees to z<0.15) 12/7/2018 CFCP Dark Energy Workshop

CFCP Dark Energy Workshop Cosmic variance and 8 Interpreting dn/dM for cosmology requires 8 constraints from local universe. Cosmic variance is about 0.06 Local counts to 6x1014M 12/7/2018 CFCP Dark Energy Workshop

Clusters for cosmology Clusters make great cosmological probes Very detectable Evolution is approachable Sensitive (exponential) dependence on cosmology Clusters are complex: we must understand them better to use them for cosmology Observing clusters is complex: measurements are projected 12/7/2018 CFCP Dark Energy Workshop

Clusters for cosmology Imagine having: SZe, z, Fx, Tx, gal, lensing, Ngal, etc. This will allow systematic control analogous to Sne Still need to know absolute number (cosmic variance, dark clusters?) 12/7/2018 CFCP Dark Energy Workshop