A'E' Evrard

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Clusters of Galaxies A Motivational Introduction
A.E. Evrard Departments of Physics and
Astronomy Michigan Center for Theoretical
Physics University of Michigan
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• - Top 10 reasons to love clusters -
• Bigger is always better!
• Cluster potentials are deep missing baryons
  are there and visible.
• Strong lensing cores make great natural
  telescopes.
• Galaxy formation is accelerated in cluster
  environments.
• The chemical debris of galaxies is observable in
  the ICM.
• Cluster statistics probe D(z), V(z) and Gaussian
  assumption for d(x).
• The biggest bubbles in the universe are found in
  clusters!
• Only a countable number of massive clusters exist
  in our Hubble Volume.
• Some galactic cosmic rays may have originated in
  cluster shocks.
• Jim Peebles thought they were interesting in
  1970.
• Fritz Zwicky!
• a bit hard to steer, though

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clustering of galaxies early large surveys
Lick catalog of 400,000 galaxies Shane
Wirtanen 1967 Seldner et al. 1977
CfA catalog 6 deg slice
1,000 galaxies deLapparent, Geller Huchra 1986
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clusters multi-component gravitational systems
estimates for Coma
Fritz Zwicky
White et al 1993
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schematic view galaxy/cluster from gravitational
instability
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modeling clusters methods
I. direct simulation - collisionless N-body
(dark matter only) - N-body gas dynamics
(darkvisible) shock heating radiative
cooling / heating heating by galaxy winds
and/or AGN conduction B-fields the kitchen
sink! II. semi-analytic methods -
approximate treatment using conservation
equations and structural assumptions
justified by direct simulations - very efficient
at parameter space exploration
Bertschinger 1998, ARAA
Cole et al 2000 Somerville et al 1999 Kauffmann
et al 1999
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starting point spherical self-similar infall
Bertschinger 1985

• collisionless (DM) infall onto point perturbation
  in an otherwise empty Einstein-deSitter
  universe
• l r/rta rta t8/9 x t2/3
• phase wrapped orbits
• hydrostatic within l1/3 boundary

• infall of g 5/3 gas
• develops shock at l1/3
• same boundary as dark matter
• hydrostatic interior
• inner gas density profile traces DM
• (except for caustics)

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evolution of dark matter - comoving view
P. Bode, Princeton U.
cosmic web emerges from linear Gaussian random
fluctuations halos form preferentially along
filaments largest halos (todays clusters)
appear at intersections of dense filaments
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evolution of dark matter - physical view
B. Moore, http//www.nbody.net
Galaxy Cluster A large knot of
quasi-equilibrium, self-gravitating matter
embedded within an evolving filamentary network
(the cosmic web) of growing density
perturbations.
typical characteristics - Ngal 10 or more
kBTX 1-15 keV R 0.3-2 h-1 Mpc M 1013 -
1015.5 h-1 Msun
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Evrard Gioia 2002
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clusters as spherical cows
Spherical model solutions and 3D simulations
point to a roughly spherical boundary that
separates an inner region of material in
hydrostatic and virial equilibrium, outer
region where matter is in infalling and out of
equilibrium.
WARNING multiple definitions in literature !
characteristic radius rD mass MDº M(ltrD)
1. critical contrast
Gunn Gott 1972 Bertschinger 1985 Evrard,
Metzler Navarro 1996
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spherical cows? wheres the hide?
M. White 2002
r200,c
r180,b
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P3MSPH dark matter phase-space structure
Evrard Gioia 2002
r200 defined by critical density threshold
r200
3D infall is complex - boundary is not sharp
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phase-space structure in concordance future
Busha et al, in prep
2563-particle Gadget model ?m 0.3, ?L 0.7
evolved to 70Gyr (a100)
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phase-space structure in concordance future
Busha et al, in prep
outer inner zero-velocity surfaces merge
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- internal structure -
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internal structure of dark matter halos
Navarro, Frenk White 1996 97
density profiles at z0 of halos spanning four
orders of magnitude in mass M200
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fit by single functional form the NFW profile
vc2 GM(ltr)/r
Navarro, Frenk White 1996
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halo structure systematic random variation
Jing Suto 2000
concentration c rD / rs
simulations show weak trend in c with mass, with
significant scatter not all profiles are well
fit due to presence of sub-structure in ongoing
mergers
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projected radial profiles of 2MASS galaxies
Lin, Mohr, Stanford 2004
radial profile fits projected NFW form with
c3.00.3
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concentration is linked to formation history
Wechsler et al 2002 Bullock et al 2001
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internal structure of dark matter halos
Wechsler et al 2002
early formation high c late formation
low c
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aspherical cows clusters are triaxial
ellipsoids
Jing Suto (2002)
2 r200
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mass redshift dependence of halo shape
Kasun Evrard (2004)
redshift dependence
z0 mass dependence
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mark correlation of halo shape
Feltenbacher et al (2000) Kasun Evrard (2004)
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- space density -
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space density (aka, mass function) takes
universal form in s(M)
Jenkins et al 2001 Sheth Tormen 1999
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critical D200 mass function calibration from
Hubble Volume sims
Evrard et al 2002
lt- rms deviations about fit at lt5 level
fit to functional form of Jenkins et al 2001
using 1.4M clusters at z0 fit parameters A,
B are now Wm dependent
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Hu Kratsov 02 - ART simulation
uses parameters fit as linear ftns of Wm
calibrated_at_ Wm0.3 applied_at_ Wm0.15
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observed space density in X-rays
Mullis et al 2004
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observed space density in X-rays
Mullis et al 2004
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observed space density in X-rays
Mullis et al 2004
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observed space density in X-rays
Mullis et al 2004
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- clustering -
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clustering massive halos are positively biased
Mo White 1996 Sheth, Mo Tormen 2000
halo 2-pt correlation function (or power
spectrum) is biased version of overall matter
2-pt ftn
for power-law P(k)kn s M-(n3)/6
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halo bias from Hubble Volume simulations
Colberg et al 2000
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halo bias from HOT simulations
Seljak Warren 2004
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observed bias in 2dFGRS groups
Yang et al 2004
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observed bias in X-ray selected REFLEX sample
Schuecker et al 2001
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- scaling relations -
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virial scaling between mass and temperature
links total mass to direct observables (gas T
galaxy velocities)
for mass defined within a critical density
threshold D, expect self-similar clusters (fixed
concentration cNFW) to follow
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ICM virial relation computational calibration
Mathiesen Evrard 01 48 P3MSPH simulations
T alone is a low-noise mass estimator 11
scatter in h(z)M500 at fixed kT
power-law fit parameters are independent of
cosmology/epoch
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ICM mass-temperature relation for X-ray
flux-limited sample
Mohr, Mathiesen Evrard 99
14 scatter in MICM at fixed TX
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X-ray luminosity-temperature relation requires
complex ICM
Mulchaey 2001
self-similar model purely gravitational heating
constant ICM gas fraction
self-similar 2
extra physics? gas cooling gas heating from
winds/AGN other ISM-like processes?
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K-band stellar mass-temperature relation
Lin, Mohr, Stanford 2004
25 scatter in L500 at fixed TX
assumes binding masses -
Finoguenov et al 2001
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halo occupation distribution
Lin, Mohr, Stanford 2004
galaxy number M0.840.04 nearly-Poisson
variations
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stellar mass-to-light ratio
Lin, Mohr, Stanford 2004 Lin Mohr 2004
galaxy formation is less efficient in higher mass
halos
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K-band galaxy populations
Lin, Mohr, Stanford 2004
composite luminosity function nearly independent
of halo mass
but brightest galaxy dominates light in smaller
halos
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baryon budget
Lin, Mohr, Stanford 2003
overall baryon fraction asymptotes to WMAP value
(sensitive to M-T reln)
stellar mass fraction decreases with mass
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- cosmological parameters? -
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clusters as cosmological tools? need correct
astrophysics!
P(cosm obs) Pprior(cosm) P(obs cosm) /
P(obs)
theoretical efforts uncertainties lie here

• first-order treatment problem is separable
• P(obs cosm) P(M,z cosm) P(obs M,z)
• how many DM halos? n (M,z cosm)
  solved (10)
• how do halos light up? P (obs M,z)
  working on it

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constraints from a constant gas fraction
assumption
Sasaki 1996 Pen 1997 Allen et al 2004
26 luminous, dynamically relaxed clusters
observed by Chandra 0.07 lt z lt 0.9
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comparison of lensing X-ray mass estimates
Allen 1998
claim dynamically relaxed clusters have
accurate total mass estimates
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constraints from a constant gas fraction
assumption
Allen et al 2004
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constraints from a constant gas fraction
assumption
Allen et al 2004
Can we shrink the allowed region by a factor
10? And be honest about systematic
uncertainties?
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reasons for optimism -
internal structure
scaling relations
clustering
space density
(real virtual) clusters display structural
regularity many independent cluster
observables TX , LX , SX(r) y0 , y(r) Ngal ,
Lgal , Sgal(r) , sgal several independent ways
to infer mass TX , sgal , ? y , bias, large
samples (sub-mm optical X-ray) are upcoming
how entangled with astrophysical parameters?
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plenty of clusters in an LCDM universe!
Evrard et al 2002
Hubble Volume simulation calibration
mass / temperature at fixed dN/dz ( per sq deg
per unit z) solid - Jenkins MF (z-dependent
parameters) points - Hubble Volume PO(X)
sky survey (p/2 steradian, zlt1.45
1000 sq deg, z6)
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SZ surveys will find many clusters
Grego et al 2001
observations with OVRO and BIMA
interferometers cm receiver (30 Ghz) on
mm-telescopes, good u-v coverage 1-2 arcmin
effective beam resolution 18 clusters 0.17 lt z
lt 0.8 5.7 lt kTX/(keV) lt 13.2
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SZZ-ray consistent measures of Mgas
Grego et al 2001
observations with OVRO and BIMA
interferometers cm receiver (30 Ghz) on
mm-telescopes, good u-v coverage 1-2 arcmin
effective beam resolution 18 clusters 0.17 lt z
lt 0.8 5.7 lt kTX/(keV) lt 13.2
population mean gas fraction estimates agreemen
t implies that gas clumping Cltr2gt/ltrgt2
cannot be large
Mohr et al 1999, ApJ
eg, Nagai et al 2000, MNRAS
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- a related exercise -
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the LX-M relation in a LCDM universe
Stanek Evrard 2004
Exercise use REFLEX sample luminosity function
to explore the relation between LX and M
assuming a LCDM cosmology New element
introduce log-normal p(M L) characterized
by power-law median relation plus scatter DM
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the LX-M relation in a LCDM universe
Stanek Evrard 2004
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the LX-M relation in a LCDM universe
Stanek Evrard 2004
evaluate n(M,z) at median z of each LX bin small
(self-similar) z-corrections to align individual
LX values to median z LX lt 1045.3 zmed lt 0.3
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the LX-M relation in a LCDM universe
Stanek Evrard 2004
reduced c2
residuals
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the LX-M relation in a LCDM universe
Stanek Evrard 2004
large range of allowed scatter (up to factor
4) dramatically wider range in median scaling
relation (L15 , p) i.e., ICM physics!
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- The end -