# Presentation: 951191

## Clusters of Galaxies:

- A.E. Evrard
- Departments of Physics and Astronomy
- Michigan Center for Theoretical Physics
- University of Michigan

**Clusters of Galaxies:**
**A Motivational Introduction**

## - 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 (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...

## 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

## clusters: multi-component gravitational systems

- White et al 1993

- estimates for Coma

- Fritz Zwicky

## schematic view: galaxy/cluster from gravitational instability

## modeling clusters: methods

- I. direct simulation
- 	- collisionless N-body (dark matter only)
- 	- N-body + gas dynamics (dark+visible)
- 		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

## starting point: spherical self-similar infall

- collisionless (DM) infall onto point perturbation in an otherwise `empty’ Einstein-deSitter universe
- 	 = r/rta       rta ~ t8/9         ~ t2/3
-  phase wrapped orbits
-  hydrostatic within ~1/3 `boundary’

- infall of  = 5/3 gas
-  develops shock at ~1/3
-   same `boundary’ as dark matter
-  hydrostatic interior
-  inner gas density profile traces DM
-    (except for caustics)

- Bertschinger 1985

## evolution of dark matter - comoving view  

- halos form preferentially along filaments
- largest halos (today’s clusters) appear at   intersections of dense filaments

- P. Bode, Princeton U.

- evolution of dark matter - comoving view

## evolution of dark matter - physical view

- “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

- B. Moore, http://www.nbody.net

## Evrard & Gioia 2002 

- Evrard & Gioia 2002

## Slide 11

## clusters as spherical cows...

- Evrard, Metzler & Navarro 1996

- 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*_.

- 1. _critical_ contrast

*WARNING:*
*multiple*
*definitions in *
*literature !*

**characteristic radius**** *****r*********& mass**** *****M**************M**********r*********)**

## spherical cows?  where’s the hide? 

- spherical cows?  where’s the hide?

- M. White 2002

- r200,c

- r180,b

## P3MSPH dark matter phase-space structure

- Evrard & Gioia 2002

- 3D infall is complex - boundary is not sharp...

- r200 defined by* critical* density threshold

- r200

## phase-space structure in concordance future

- 2563-particle Gadget model ; Ωm= 0.3,  Ω= 0.7 ;  evolved to 70Gyr (a=100)

## phase-space structure in concordance future

- Busha et al, in prep

- outer & inner zero-velocity surfaces merge

## - internal structure -

## internal structure of dark matter halos

- density profiles at z=0 of
- halos spanning four orders of magnitude in mass M200

## fit by single functional form:  the `NFW profile’

- vc2 = GM(<r)/r

- Navarro, Frenk & White 1996

## halo structure: systematic + random variation

- concentration
-         c = r/ 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

- Jing & Suto 2000

## projected radial profiles of 2MASS galaxies 

- projected radial profiles of 2MASS galaxies

- radial profile fits projected NFW form with c=3.0±0.3

## concentration is linked to formation history

- Wechsler et al  2002
- Bullock et al 2001

## internal structure of dark matter halos

- Wechsler et al  2002

- early formation        high c
- late formation         low c

## aspherical cows: clusters are ~ triaxial ellipsoids

- Jing & Suto (2002)

- 2 r200

## mass & redshift dependence of halo shape 

- Kasun & Evrard (2004)

- z=0 mass dependence:

- redshift dependence:

## mark correlation of  halo shape 

- Feltenbacher et al (2000)
- Kasun & Evrard (2004)

## - space density -

## space density (aka, mass function) takes `universal’ form in (M)

- Jenkins et al 2001
- Sheth & Tormen 1999

- space density (aka, ***mass function***) takes `universal’ form in (M)

## critical =200 mass function calibration from Hubble Volume sims

- <date/time>

-  <- rms deviations about
-       fit  at <~5% level

- fit to functional form of Jenkins et al 2001 using
- ~1.4M clusters  at z=0
- fit parameters A, B are now m dependent

- Evrard et al 2002

- _critical_ =200 mass function calibration from Hubble Volume sims

## Hu & Kratsov `02 - ART simulation

- uses parameters fit as linear ftn’s of  m
-    calibrated@ m=0.3
-    applied@ m=0.15

## observed space density in X-rays

- Mullis et al 2004

## observed space density in X-rays

- Mullis et al 2004

## observed space density in X-rays

- Mullis et al 2004

## observed space density in X-rays

- Mullis et al 2004

## - clustering -

## 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

| Model | m |  | 8 |
| --- | --- | --- | --- |
| CDM | 0.3 | 0.7 | 0.90 |
| CDM | 1.0 | 0 | 0.60 |

- for power-law P(k)~kn
- ~ M-(n+3)/6

## halo bias from Hubble Volume simulations

- Colberg et al 2000

## halo bias from HOT simulations

- Seljak & Warren 2004

## observed bias in 2dFGRS groups

- Yang et al 2004

## observed bias in X-ray selected REFLEX sample

- Schuecker et al 2001

## - scaling relations -

## virial scaling between mass and temperature

- for mass defined within a *critical* density threshold , expect self-similar clusters (fixed concentration cNFW) to follow

## ICM virial relation: computational calibration

- 48 P3MSPH simulations

- power-law fit parameters are  independent of
- cosmology/epoch

*T*  _alone_ is a low-noise mass estimator:
- ~11 % scatter in
*h(z)M*500*  *at fixed *kT*

## ICM mass-temperature relation for X-ray flux-limited sample

- Mohr, Mathiesen & Evrard 99

## X-ray luminosity-temperature relation requires complex ICM

- purely gravitational heating + constant ICM gas fraction

- Mulchaey 2001

- self-similar –2

- _extra physics_?
- – gas cooling
- – gas heating from
-     winds/AGN
- – other `ISM-like’
-     processes?

## K-band stellar mass-temperature relation

- Lin, Mohr, & Stanford 2004

- ~25% scatter in L500 at fixed TX

- assumes binding masses -

- Finoguenov et al 2001

## halo occupation distribution

- galaxy number ~  M0.84±0.04
- nearly-Poisson variations

## stellar mass-to-light ratio

- Lin & Mohr 2004

- galaxy formation is less efficient in higher mass halos

## K-band galaxy populations

- but brightest galaxy dominates light in smaller halos

- composite luminosity function nearly independent of halo mass

## baryon budget

- stellar mass fraction decreases with mass

- overall baryon fraction asymptotes to WMAP value (sensitive to M-T rel’n)

## - cosmological parameters? -

## clusters as cosmological tools?  need correct astrophysics! 

- 	 *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**_** ... **

*P*(cosm | obs)  =   *P*prior(cosm) *P*(obs | cosm) / *P*(obs)

- theoretical efforts & uncertainties lie here

- clusters as cosmological tools?  need correct astrophysics!

## constraints from a constant gas fraction assumption  

- Pen 1997
- Allen et al 2004

- constraints from a constant gas fraction assumption

- 26 luminous, `dynamically relaxed’ clusters observed by Chandra
-   0.07 < z < 0.9

## comparison of lensing & X-ray mass estimates 

- comparison of lensing & X-ray mass estimates

- _claim:_
- `dynamically relaxed’ clusters have accurate total mass estimates

## constraints from a constant gas fraction assumption  

- constraints from a constant gas fraction assumption

## constraints from a constant gas fraction assumption  

- constraints from a constant gas fraction assumption

- Can we shrink the allowed region by a factor 10?
- _And_ be honest about systematic uncertainties?

## reasons for optimism -

- <date/time>

- – (real + virtual) clusters display structural regularity
- – many independent cluster observables:
- 	TX , LX , X(r)
- 	y0 , y(r)
- 	Ngal , Lgal , gal(r) , gal
- – several independent ways to infer mass:
- 	TX , gal , ∫ y , bias, ...
- – large samples (sub-mm + optical + X-ray) are upcoming
- – how `entangled’ with astrophysical parameters?

- space
- density

- scaling
- relations

- clustering

- internal structure

## plenty of clusters in an CDM universe!

- Evrard et al 2002

- 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
-     (/2 steradian, z<1.45
-       + 1000 sq deg, z=6)

- plenty of clusters in an CDM universe!

- Hubble Volume simulation
- calibration

## 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 < z < 0.8  ;  5.7 < kTX/(keV) < 13.2

## SZ+Z-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 < z < 0.8  ;  5.7 < kTX/(keV) < 13.2

- population mean gas   fraction estimates
- agreement implies that gas clumping
-          C=<2>/<>2
- cannot be large

- Mohr et al 1999, ApJ

- eg, Nagai et al 2000, MNRAS

## - a related exercise -

## the LX-M relation in a CDM universe

- the LX-M relation in a CDM universe

- _Exercise_: use REFLEX sample luminosity function to explore the
- 	relation between LX and M assuming a CDM cosmology
- _New element_: introduce log-normal p(M | L) characterized by
- 	power-law median relation plus scatter M

## the LX-M relation in a CDM universe

- the LX-M relation in a CDM universe

## the LX-M relation in a CDM universe

- the LX-M relation in a CDM universe

- 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 < 1045.3
- zmed < 0.3

## the LX-M relation in a CDM universe

- Stanek & Evrard 2004

- the LX-M relation in a CDM universe

- reduced 2

- residuals

## the LX-M relation in a CDM universe

- the LX-M relation in a CDM universe

- large range of allowed scatter
- (up to factor ~4)
- dramatically wider range in median scaling relation (L15 , p) :
- i.e., ICM physics!

## - The end -