Precision Cosmology with X-ray and SZE Galaxy Cluster Surveys?

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1 Precision Cosmology with X-ray and SZE Galaxy Cluster Surveys? Joe Mohr University of Illinois Outline SZE and X-ray Observations of Clusters Cluster survey yields and cosmology Precision cosmology and systematics?

2 I. SZE Observations as a Probe of Structure Formation SZE versus X-ray as High Redshift Probe T( R) σ = 2 T dl ne(, l R) kbte(, l R) T cmb mc 2 e Ix ( R) = 1 µ e 2 dlne ( l, R) ( Te) 4π( 1+ z) 4 H µ Λ Data from SZE Imaging Collaboration and ROSAT Archive Credit: Mohr & Carlstrom SZE contours every 75µK. Same range of X-ray surface brightness in all three insets. Total SZE flux from Cluster k T f M T S T cmb ICM vir e n tot = 4 ν 2 σ 1 mc 4 d 2 µ m e A e p Sufficiently sensitive SZE surveys will detect low mass clusters at any redshift, allowing observation of clusters at the epoch where they first appear. Planck will not allow studies of the high redshift cluster population.

3 II. Galaxy Cluster Surveys and Survey Yields Cluster surveys probe (1) volume-redshift relation, (2) abundance evolution, (3) structural evolution SZ-Array Survey Surveys Constrain: Cluster surface density LogN-LogS Angular distribution Redshift distribution (Mass) function

4 Cluster Survey Yields and Cosmology! Cluster redshift distribution dn(z)/dz/dω abundance of detectable clusters cluster mass function ( ) dn( z) dv dzd dz d nz c Hz d z dm dn M, z Ω = Ω ()= 2 A + ( 1 2 ) ( ) dm m z lim ( ) volume element Minimum mass of detectable cluster (typically function of redshift) Critical components: Volume element Mass function Limiting mass

5 1: The Volume-redshift Relation! Classic Volume-Redshift Test» Count non-evolving tracers measure volume Volume Element» Cluster abundance does evolve Evolution well understood dv c d z dzdω = 2 H z A ( + ) 2 1 ( ) da ( 1 + z) is proper distance Hz ()= HoEz () is the Hubble parameter

6 2: Cluster Abundance and Cosmology! Cluster mass function dn(m,z)/dm depends on mean matter density and amplitude of density fluctuations ( ) ( ) (, ) σ 2 M d 3 k P k W k M 2 where WkM (, ) is the Fourier transform of the spherical tophat» Vintage Press-Schechter formalism dn dm M z b d M, z c (, ) = 2 ρ σ ( ) δ π M dm σ ( M, z) δ 2 exp c 2 2σ 2 Mz, ( )» Modern numerical simulations: Jenkins et al 2000 dn dm M z ρb dσ ( M, z) 1 (, ) = exp 061. log M dm σ ( D σ ) z M 38. ( ) δ()= z Dzδ z= 0 1 Dz = ( 1+ z) if Ωm = 1 Growth function sensitive to expansion history of Universe. a δ + 2 δ = 4πGρoδ a δρ where δ and H = ρ o a a

7 Figures taken from Jenkins et al. 2001, MNRAS 321, 372 dn( M, z) dm ρ = b M ( ) dσ M, z 1 exp 061. log D dm σ ( σ ) z M 38. Fitting function good to better than 20% over entire range, corresponding to to solar masses at z=0 in standard cosmologies.

8 Abundance Evolution and Cosmology Normalize locally» Tricky because of volume dependence of survey yield» Using local survey removes all but Hubble parameter H o dependence» Large solid angle survey minimizes sample variance Comoving Abundance High redshift abundance requires knowledge of growth function a δ + 2 δ = 4πGρoδ a δρ where δ and H = ρ o a a δ z D δ z D ()= ( = 0) z z 1 if m ( ) = = 1+ z Ω 1

9 3: Importance of the Survey Detection Limit Cluster redshift distribution dn(z)/dz/dω dn() z c dn M, z d z dm dzdω = 2 Hz A ( + ) 2 ( ) 1 () dm mlim Minimum mass of detectable cluster Limiting mass M lim (z)» Connecting cluster virial mass to observables is critically important X-ray luminosity or emission weighted temperature SZE luminosity Weak lensing shear amplitude Galaxy light / dynamical estimators Limiting Mass Sensitivity Total SZE flux from Cluster k T S tot = 4 ν 2 σt cmb 1 mc 4 e d 2 A ficmmvir Te n µ emp

10 III. Precision Cosmology with Cluster Surveys? Cluster survey yields are sensitive to the expansion history of the Universe: H(z)» through volume» through growth of density perturbations» through the dependence of the limiting mass on the distance Expansion history depends on the nature and density of matter and energy Hz HoEz where w E ()= z Ωm( 1+ z) + ( 1 Ωm ΩE) ( 1+ z) + ΩE( 1+ z) w p 31+ w and a a ( ) and z aa o 1 + ρ, ρ( ), ()= () ( ) Surveys provide a measure of» the matter density parameter Ω m» the dark energy density parameter Ω E» the equation of state parameter of the dark energy w(z)» Normalization of P(k): σ 8 Precision measurements are possible with high yield surveys Precision of such surveys will be limited by systematics.

11 Sensitivity and Systematic Errors in Mass Estimates! DUET: Large solid angle X-ray survey» F x >5e-14 erg/s/cm 2 over 10 4 deg 2» ~20,000 clusters detected! Precise constraints on w and Ω E Ω E to 0.01» <w> to 0.07! Systematic Errors in Mass Estimates» What is the effect of a constant fractional mass error with redshift? Parameter Biases logm Ω E <w> σ 8 Minimizing systematic errors in estimates of Cluster Mass derived from Observables (i.e. X-ray or SZE flux, weak lensing shear) is the primary challenge in using cluster redshift distributions to do precision cosmology. +25% % % % % % %

12 Sensitivity: Cluster Surveys vs SNe Ia Cluster surveys are generally many times more sensitive to cosmological parameters than are SNe Ia distance measurements.

13 Importance of Cluster Redshifts Redshifts unknown! South Pole 8m Survey: Large solid angle SZE survey» M>2.5e+14h-1 Mo over 4x10 3 deg 2» ~20,000 clusters detected! Precise constraints on w and Ω E Ω M to 0.01» <w> to ~0.1! Redshifts extremely important» Photometric redshifts preferred» Large solid angle surveys available PRIME survey VST VISTA SNAP

14 IV. Survey Systematics: How Important?! Realizing the full statistical power of these high yield surveys requires» Precise understanding of biases in mapping from observables to virial masses» Good understanding of the nature of the scatter/uncertainty in this mapping (correct for Malmquist like bias)! A full answer requires significant effort analyzing ensembles of clusters observationally and theoretically» Studies of preheating and cooling to reproduce observed scaling relations» Calibration of the mass- X-ray luminosity, mass-temperature and mass-sze luminosity relations! Can we appeal to existing analyses of clusters for an indication of where we stand?» Implications of exciting new Chandra and XMM results Higher resolution reveals sharp density discontinuities The cooling instabilities in clusters cores are much weaker than previously expected» Substructure and regularity Let s take a look at some data.

15 Substructure and Merging Contour plots of Einstein IPC Cluster X-ray Images! Evidence for merging at present epoch is widespread» Multipeaked galaxy distributions Geller & Beers 1982, PASP» Velocity structure Dressler & Shectman 1988, ApJ» X-ray morphologies Forman et al 1981, ApJ Mohr et al 1993, ApJ! Substructure useful as cosmological diagnostic Richstone, Loeb & Turner ApJ, 1992 Evrard et al, ApJ, 1993 Mohr et al 1995, ApJ Buote & Tsai 1995, ApJ Thomas et al 1998, MNRAS

16 X-ray Emission from Abell 3667 Res ~ 90 Res ~30 Pt. source 37 arcmin = 3.3 Mpc Res ~1 Chandra ACIS Einstein IPC ROSAT PSPC Sharp surface Brightness feature From Chandra Archive; CIAO Firstlook Cluster X-ray morphologies reflect the underlying distribution of the intracluster medium.

17 The Observed X-ray Size-Temperature (ST) Relation» For an X-ray flux limited sample of 45 galaxy clusters:» log(r I )= 0.93 log(t/6 kev) » Raw Scatter in R I : 15% (Intrinsic: 10%)» Galaxy Cluster Regularity» Cluster scatter around ST relation is similar to elliptical/s0 galaxy scatter around the Fundamental Plane» Observed regularity in X-ray properties reflects underlying regularity in the dark matter Mohr & Evrard, 1997, ApJ 491, 38

18 The Observed ICM Mass-Temperature Relation» For an X-ray flux limited sample of 45 galaxy clusters:» Raw Scatter in M ICM : 18% (Intrinsic: 10%)» These two axes are independent» X-ray count rate of parcel of gas is very insensitive to temperature for T>1.5keV! Virial mass-temperature relation?» Similar or smaller scatter because of small variations in ICM mass fraction Micm M ficm σ σ + σ Note: constant metric radius Mohr Mathiesen & Evrard, 1999, ApJ

19 Other Galaxy Cluster Scaling Relations! Luminosity-Temperature relation» Large scatter- irregularity? Yes, but in core region where cooling instabilities can begin Luminosity-Temperature Relation Mass-Temperature Relation Horner, Mushotzky, & Scharf 1999, ApJ! Binding mass-temperature relation» Masses estimated from galaxy dynamics» Slope consistent with self-similar expectation

20 The Size-Temperature Relation at Intermediate Redshift! Evolution of the ST Relation» Evolution of the dark matter properties r T δ 12 Ez ( ) Hz ()= Ho Ez () Local ST M T δ 32 Ez ( )» Evolution of X-ray isophotal size η 4 RI( T, z)= RI( T, 0) E ( z), = 6β where η 6β 1 HRI Observations of 11 CNOC Clusters Best Fit ST Local ST Best Fit ST Mohr, Reese, Ellingson, Lewis & Evrard, ApJ, submitted

21 Cluster Scaling Relations and Regularity Cluster population is young, undergoing accretion even at the present epoch Tight scaling relations in cluster properties exist both in observations and in hydro simulations of structure formation- clusters can be well modeled theoretically These scaling relations appear to persist at intermediate redshift in observations and in simulations (even at high z) Precision cosmology requires mass-observable relationships and models for their evolution that have systematic biases at the 5% - 10% level (or smaller). Existence of tight scaling relations (10%-20% scatter) means halo mass can be predicted with reasonably good accuracy from simple observables. Calibrating mass-observable relationships likely requires multiple mass estimators (i.e. weak lensing, hydrostatic, dynamical. Small scatter simplifies mass calibrations at the 5%-10% level.

22 V. An Evolution - Cosmology Degeneracy? Consider the number of clusters in a redshift bin dz=0.1 centered at z=0.5 in the DUET sample: ~2000 clusters in fiducial model ~200 will have measured Tx The number of clusters can be altered (1) by changing cosmological parameters (i.e. Ω m ) or (2) by altering the X-ray luminosity for a cluster of a given mass. Thus, evolution of the mass-observable relationship is potentially degenerate with cosmological parameters.

23 Scaling Relations and Evolution Introducing a non-standard evolution model to offset a change of δω m =0.03 leads to a 20% offset in the X-ray flux- temperature (fx-tx) relationship for the clusters in this z=0.5 redshift bin. Assuming scatter in Lx-T of 50%, the 200 clusters with measured Tx in this redshift bin would provide enough information to discern this shift with great confidence (~6σ significance). Surveys constrain the cluster redshift distribution and the evolution of scaling relations

24 Overview High sensitivity SZE cluster surveys provide a generic test of structure formation models: they probe for massive, collapsed structures at all redshifts Within the context of the standard model for structure formation, cluster surveys are a precision cosmological probe» Complementary to CMB anisotropy studies, because the parameter degeneracies differ and because cluster surveys probe the z<3 universe» Complementary to SNe Ia studies (any standard rod/candle) because parameter degeneracies are different. Cluster surveys are potentially far more powerful than distance indicators. The properties of clusters on the scale of the virial region are (very) likely easier to understand than SNe Ia.» Clusters exhibit regularity and complexity. Exciting new results from Chandra showing inner core structure with exquisite detail must be considered within the context of what we know about cluster regularity from Einstein, ROSAT and ASCA studies. Large solid angle SZE and X-ray surveys especially important» Shallow surveys like Planck (i.e. low cluster sensitivity- due to 5-10 beamso that only the most massive systems are detected) are ideal for normalizing the power spectrum of density fluctuations» Higher sensitivity surveys with photometric redshift followup would be ideal for measuring the equation of state of the dark energy