Finding Galaxy Clusters in Simulation and Reality Martin White Department of Physics Department of Astronomy UC Berkeley Lawrence Berkeley National Lab

Using simulations to refine our methods for … Outline Using simulations to refine our methods for … Finding clusters Weak lensing Sunyaev-Zel’dovich Galaxy surveys (& our 2MASS experience) Making a mass selected sample (?!) Is this the right goal?! What do we mean by “the mass”?

Using all the mass to find clusters of galaxies … weak gravitational lensing

Weak lensing: the good news Measures (approximately) the projected mass along the line of sight, weighted by a simple kernel.

Weak lensing: the good news (contd) Can find mass concentrations, even if the cluster is dark! Independent of assumptions of the dynamical state of the cluster. The “best” way to find clusters?! Lensing is the perfect problem for N-body simulations. (Requires relatively low resolution)

Weak lensing: the bad news Measures (approximately) the projected mass along the line of sight, weighted by a simple kernel. Kernel changes by < 1% over > 100Mpc. The universe’s worst confusion problem!

Clusters are part of large-scale structure Metzler, White & Loken (2001)

Confusion leads to low efficiency Large-scale structure along the line-of-sight leads to a large scatter between mass and lensing signal. Combine Large scatter in your mass estimator and A steeply falling mass function and you get … Most of your candidates are actually low mass groups “scattered” into your sample. If nothing else, this makes follow up observations very expensive.

(Padmanabhan, Seljak & Pen, 2003; Bacon, Taylor & White, in prep) Implications … You can find clusters using weak lensing! For “standard” filters cluster finding is dramatically affected by line-of-sight projection. “Noise” from random superpositions of large-scale structure comparable to signal from a cluster of 1014 Msun at z ~ 0.5. High completeness requires high contamination. What about multiple source populations, matched filters or cross-correlation? (Padmanabhan, Seljak & Pen, 2003; Bacon, Taylor & White, in prep)

Weighting by temperature… the Sunyaev-Zel’dovich Effect(s)

The Sunyaev-Zel’dovich effect(s) Compton scattering of CMB photons by hot gas along line-of-sight. Upscattering of CMB photons leads to ~mK temperature decrements in CMB at low frequency. Like lensing, but weighting by temperature. Signal dominated by clusters of galaxies. Measures total internal energy of cluster. Independent of redshift!

New observational handles … Name Type Beam (arcmin) Cluster Yield ACBAR Bolo 4 Few Bolocam 1 10’s SZIE HEMT 100’s CBI AMI Amiba APEX 0.75 5,000 SPT 20,000 Planck 5 10,000 ALMA --

Simulation programme … with Volker Springel & Lars Hernquist The SZ effect is the “best” problem for numerical hydrodynamics. Series of simulations designed to study SZE Adiabatic hydrodynamics Box size, particle number, force softening. Artificial pre-heating Cooling only Cooling and feedback (and winds)

What have we learned? Effect is dominated by “sources”. Most of the effect comes from gas at overdensities O (102) times the mean density. Significant Y-M scatter. Cooling and feedback are small effects.

Probing massive halos … Sources found with Sextractor Typical size ~1´ 1o

What have we learned? Effect is dominated by “sources”. Most of the effect comes from gas at overdensities O (102) times the mean density. Significant Y-M scatter. Cooling and feedback are small effects.

SZ projection effects … Y~M x T ~M5/3 Effect is indep. of distance! c.f. weak lensing or richness

What have we learned? Effect is dominated by “sources”. Most of the effect comes from gas at overdensities O (102) times the mean density. Significant Y-M scatter. Cooling and feedback are small effects.

Insensitive to “extra” physics Heating or cooling alone can cause big shifts, but when combined in a self- consistent model …

Finding clusters with SZ Primary CMB anisotropies are a major contaminant for cluster searches, but smooth on the scale of clusters. Use a (hi-pass) compensated filter to suppress slowly varying background. Use a (lo-pass) smoothing filter to suppress noise. BUT … when the source density is high, want to avoid filters which are narrow in Fourier space … they “ring” in real space. Difficult optimization problem! We know the spectrum of signal and background: multi-frequency observations offer significant advantages!

Multifrequency observations turn this …. Power Angular scale Effects of 2’ beam Schulz & White (2003)

… into this!

Cluster finding 101 The optimal way to find and characterize sources in the next generation of SZ experiments is an open question. This is much easier with 2 frequencies than 1! Source confusion is likely. Proposed experiments are tremendously powerful and will return huge numbers of cluster candidates. How do we select a subset for follow up? How do we estimate mass and redshift? Diego, Mohr, Silk & Bryan (2003)

Finding clusters of galaxies using … galaxies! … with Chris Kochanek

Matched filter algorithm New implementation of the matched filter algorithm of Postman et al. (1996) Several technical improvements over existing methods. Combines matched filter with “CLEAN” to build a global likelihood. Can understand results “analytically”. Tested on simulations, applied to 2MASS data – an iterative sequence.

Mock galaxy surveys Use a strategy borrowed from semi-analytic galaxy formation, but don’t follow mergers so can keep full N-body resolution. Start with a high resolution N-body simulation in which we can identify the halos which will host the galaxies of interest. [Actually harder than it sounds …] Each halo gets an integer number of galaxies, drawn from a distribution N(M). Poisson at high mass. Sub-poisson at low mass. First galaxy lies at halo center. Satellites trace the mass. Luminosities follow Φ(L|M) Typical luminosity decreases at low M. Faint-end slope decreases at low M.

Suitable for testing algorithms By construction, the luminosity function and number counts match observations. Colors can be added in a number of ways. It is relatively easy to adjust N(M) to get the right clustering (2-point function). Clusters and redshift space distortions look “okay”. All the ‘galaxy formation’ physics is put in by hand to match observations - little predictive power!

Results from 2MASS … Test with galaxies in the 2MASS catalog. Galaxies selected in K band K<12.25 (extinction corrected) |b|>5o 91,670 galaxies over 91% sky. Redshifts 86% complete for K<11.25 and 35% complete for K<12.25. Deeper photometric catalogue really helps in finding clusters.

2MASS clusters Find ~700 cluster candidates. Redshifts and dispersions agree with literature. [Can use prob. weighting.] Scaling relations well measured. Can use counting to estimate N(M): N(M)~M [2MASS galaxies trace mass?!] Scatter consistent with Poisson.

Completeness …

Scaling relations …

Conclusions Optical, SZ and lensing all “work” for finding clusters but all suffer from projection effects. Photo-z or “true”-z information can mitigate this for optical surveys. Future SZ surveys have awesome power to find large numbers of clusters to very high redshift. Any scatter in the M-observable relation leads to low “efficiency” for constructing complete, mass limited samples. Is a mass limited sample the right goal?

STOP

Weak lensing maps: simulations 50 Raw convergence map – roughly projected mass. + noise from shear reconstruction Filtered White, van Waerbeke & Mackey (2002)

Lensing mass is not “The Mass” WvW&M

Lensing mass is not “The Mass” WvW&M

Another view … MW&L

Lensing: Completeness & Efficiency White, van Waerbeke & Mackey (2002)

Lensing scatterplots M>1014Msun Large scatter means low completeness At fixed mass the threshold is distance dependent!

SZ Observations In contrast to X-ray emission, SZ surface brightness is independent of cluster redshift, clusters can be seen at any distance!

ALMA pathfinder experiment (APEX) MPIfR/ESO/Onsala/Berkeley Telescope Specifications: 12 m on-axis ALMA prototype. 45’’ at 150 GHz/ 30’ field of view. Use in drift scanning mode. Located at 16,500 ft in the Andes. Telescope and receiver fully funded. Receiver Specifications: 300 element bolometer array 300 mK s ½ 1 pixel @ 10mK in 3 sec!! On line, late 2004 25% of telescope time will be dedicated to SZ survey

Results from simulations … Works with mix of photo- and spectro- data. Deeper photo catalog helps cluster hunting! Efficient and reliable method for finding clusters, even with “crude” redshifts. Get membership probability for each galaxy Allows estimate of <z> or s. Robustly finds clusters to well past survey median, usually out to 90th percentile. The most common failure modes easily eliminated by follow-up.

G-Series: L=100Mpc/h Name Np MDM Mgas Softening (kpc/h) G-3 2x1443 18 G-4 2x2163 7.2x109 1.1x109 12 G-5 2x3243 2.1x109 3.3x108 8