General Introduction to Galaxy Clusters: Scaling Relations

Brian McNamara University of Waterloo

With thanks to Helen Russell Astronomical Units & Terminology

1 " T % 2 r2500 = 500kpc$ ' # 5keV &

1 2 14 # T & M2500 = 2x10 M"% ( 5keV scaled to critical density of Universe ! $ '

21 Kiloparsec! Distance 1000 parsecs = 3x10 cm

Light year Distance 3.26 parsecs Milky Way Diameter = 100,000 ly = 30 kpc

1053 erg Energy supernova explosion/GRB keV Temperature 1 keV = 1.16 x 107 K dynes/cm2 Pressure cluster center P=10-10 dyne/cm2 10-16 Atm Why Study Galaxy Clusters?

• Cosmology - evolve by gravity: largest structures evolve slowly--dominated by dark maer, sensive to maer and energy density of the Universe - fair sample hypothesis: baryons, dark maer, baryon fracon

- observaonal goal: measuring masses; observaonal proxies for mass (Lx, T, etc.)

• Galaxy formaon & Evoluon - closed boxes: retain byproducts of stellar evoluon; history of star formaon - galaxies at same redshi: uniform sampling in space & me - merging & perturbaon: dynamical evoluon of galaxies

• Cosmic cooling problem - only few percent of baryons have condensed in clusters - cooling flows/feedback Gaussian density perturbaons 10 Mpc "# /# a

!

Ncl " a

Hierarchical clustering !

Number density of clusters: amplitude of perturbaons, a

Degree of clustering: "m

! Galaxy Cluster

Virgo Consorum, Springel et al. 05 Galaxy Cluster at X-ray & Visual wavelengths

X-ray visual

100 kpc

43 45 -1 2 7 8 Lx = 10 - 10 erg s kTgas " µmp# Tgas = 10 - 10 K

$1 $4 $3 $h% / kT "gas #10 $10 cm Bremsstrahlung emissivity: " # neni Te

2 X-ray emission ~ne! unambiguous tracer of deep potenal well ie., clusters ! ! What is a galaxy Cluster?

Abell 1689 RC =4

Richness Classes Sizes 1-3 Mpc

M3 + 2 " # 300 $1000km s$1

0 30-49 13 15 1 50-79 Mcl "10 #10 M$ 2 80-129 3 130-199! 4 200-299 5 300> !

2 15 $1 Mvir " 3# r /G "10 h M% for " #1000km s$1

! ! Gravitaonally bound systems

 Crossing time for the galaxies: R t cr , gal= 1/2 〈v2〉

t ≈ 2× 109 yr cr , gal

→ clusters are gravitationally bound Galaxy cluster mass paroning

ICM 13%

Stars 3% Credit: Abell 1689, X-ray: NASA/CXC/MIT/ E.-H Peng et al.; Optical: NASA/STScl

Dark matter 84% ? Virial Theorem

 For gravitationally bound systems:

2EK +EP = 0

〈v2 〉 R tot M tot = G

 Assuming random uncorrelated velocity vectors:

3! 2 R M = r tot tot G

15  For velocities 1000km/s and R = 1Mpc => Mtot = 10 Msun Sound crossing me

 Sound crossing time for X-ray gas: D t cr , gas= cs

 For an ideal gas the adiabatic sound speed is:

2 dP P kBT cs = =" =" d! ! µmH

 For a monatomic gas the adiabatic index is 5/3.

8 t cr , gas≈ few× 10 yr

10  Much shorter than age of cluster ~10 yrs Hydrostac Equilibrium

 Hydrostac equilibrium: compression due to gravity is balanced by a pressure gradient force.

 Assumpons:

 Sound crossing me much less than the age of the cluster

 Timescale for elasc collisions much shorter than mescale for heang or cooling Kinec Equilibrium

Timescales for electrons and ions to form a Maxwellian distribuon electrons via Coulomb collisions:

1/2 teq (p, p) ! (mp / me ) teq (e,e) ~ 43teq (e,e)

teq (p,e) ! (mp / me ) teq (e,e) ~ 1870teq (e,e)

For typical condions

Electrons & ions in equiparon, such that T = Te= Tp Detecng Clusters with X-rays Chandra XMM-Newton Suzaku

E = 0.5-10 keV E = 0.1-15 keV E = 0.4-600 keV EA = 600 cm2 @1.5 keV EA = 922 cm2 @ 1 keV EA = 900 cm2 @ 1.5 keV FOV = 16.9x16.9 arcmin FOV = 33 x 33 arcmin FOV = 20 arcmin @1keV PSF = 0.5 arcsec FWHM PSF ~ 4 arcsec FWHM PSF ~ 2 arcmin (HPD) Chandra’s mirrors

Grazing incidence optics

critical angle few degrees

Wolter Type 1 Hundreds of Clusters Detected with ROSAT

NRAO-VLA Sky Survey (NVSS) ROSAT X-ray Imaging J1221+4918 z = 0.7 Lx = 1.2x1045 erg s-1

19 kT = 6.5 keV

18 Declination (2000) Ma + 11

49! 17v 35s 30s 25s 20s 12h 21m 15s Right Ascension (2000) “red sequence”

Gladders & Yee 05

Optical: good for finding distant clusters poor measure of cluster properties

X-ray: good measure of cluster properties poor tracer beyond z ~ 1

Borgani & Guzzo 01 Thermal Bremsstrahlung

Primary source of X-ray emission from clusters due to diffuse intracluster plasma at 108K Power radiated by accelerang charge:

Larmor's equation 2e2a2 P = 3c3 a = acceleraon Thermal Bremsstrahlung

 Power per unit frequency and per unit volume:

See Rybicki + Lightman or Longair Thermal Bremsstrahlung Total Power

 Radiated power per unit volume:

L∝ n n T 1/2 e H

 Two body collision → power strongly dependent on density2 emitted spectrum observed spectrum

Fe L

Fe K

s "#(E,T,Z) $ R(E,%)

" # g(E,T,Z)T$1/ 2 exp($E /kT)

• ionization equilibrium ! Normalization: EM " n p nedV • temperature sensitivity # ! • metallicity sensitivity • Z ~ 1/3 solar Arnaud 05 ! Thermal Bremsstrahlung Spectrum

 Model cluster spectrum, 1/3 solar abundance

8 keV cluster 1 keV group Line Emission

Emissivity from collisionally excited line (electrons)

dE- excitaon energy of line above ground state B – branching rao (probability that excited state decays to given state) Omega – Collision strength omega_gs- stascal weight of ground state Luminosity per frequency

Emissivity:

!" = !" (z,T)nenp (erg/cm3) Significant So X-ray Lines

Peterson + 01 X-ray cooling funcon

Solar abundance !(T, Z)

1/3 solar abundance

Pure hydrogen, Helium

!" = !" (z,T)nenp Peterson & Fabian 06 X-ray cooling fluncon

!(T, Z)

!" = !" (z,T)nenp Abundances from X-ray emission

2 • Line emissivity proporonal ne and elemental abundance 2 • Thermal bremsstrahlung proporonal to ne • rao of line emission to brems connuum indep of density • Temperature sensive to brems shape and line raos (low T) • Hence, line equivalent width gives elemental abundance M87 Observed with the Reflecon Grang Spectrometer

Early metal enrichment by core collapse SN, ongoing Sn Ia

60% core collapse Werner .. Kaastra, De Plaa…06 40% Sn Ia Metallicity Distribution

SN Ia SN II

De Grandi & Molendi 01

" element enhanced (Si, S, Ne, Mg)

early enrichment z >> 0.5

top-heavy IMF? !

Wise et al. 04 X-ray surface brighness profile

#3 Ix " r

!

Isothermal Beta Model: Cavaliere & Fusco-Femiano (76) 1 ratio of energy #3$ + 2 per unit mass in surface brightness: Ix "[1+ (r /rc )] " # 2/3 galaxies to that in 2 "3# / 2 electron density: ne (r) = n0[1+ (r /rc ) ] gas I =0.35 I n = 0.5 n ! ! c 0 c 0

See Vikhlinin! + 06 for more sophiscated models Cluster Density Profiles - Vikhlinin 06

NFW profile Mass Profiles

dlnT = 0 dlnr

! " model

Gitti et al. 07 ! kTr # dln" dlnT & Mtot (< r) = % + ( Gµmp $ dlnr dlnr '

) 2,/ 30 / 2 # r & Assume "(r) = "0+1 + % ( . ! *+ $ rc ' -. - hydrostac equil. - spherical symmetry kr2 $ 3"rT dT ' - only gas pressure Mtot (< r) = & 2 2 # ) Gµmp % r + rc dr ( ! Vikhlinin + 05 ! Typcal Gas Profiles

H Clusters & Cosmology mass & luminosity function sensitivity to "m,#

!

1015 N(L) N(M)

Eke et al. 92 Mullis et al. 04 M Lx

44 -1 Evolution: Lx > 5x10 erg s z > 0.5 "m =1

"m = 0.3,"# = 0.7 Problem: Lx to M ? Need L-T, M-T, relaons L-T – baryon physics ! ! Cluster Cosmology requires: Simulations + Observations

Is cluster maer distribuon only a funcon of Mass and Redshi?

Compare observations to scaling relations

Deviations: models deal primarily with DM mass observations deal with luminous baryons simulated & observed parameters (eg. L,T) do not always probe same quantity

mean matter density Mass Function constrains in units of critial density, "m,# 8 amplitude of primordial density fluctuations

strategy: find observational proxies for mass ! Lx - easy to measure, sensitive to non-gravitational processes

Tx - difficult to measure except for brightest objects M - even tougher Clusters Grow by Mergers Cold Fronts – mildly transonic mergers/sloshing

Contact disconity

Markevich & Vikhlinin 06 Contact Disconnuity: Abell 2142

Markevich & Vikhlinin 06 Cluster Scaling Relations Simple assumptions: gravity, adiabatic compression, shocks self similarity: scale free, cluster defined by its mass and redshift 3 / 2 #1 M "Tx (1+ z) 2 3 / 2 Lx "Tx (1+ z) 4 / 3 7 / 2 Lx " M (1+ z) Implications:! Same internal structure, but distant clusters denser, smaller, more luminous ! Observables in reverse order of difficulty: Lx, Tx, M !Departures from scaling relations: additional physics (cooling, feedback, etc.) Evolution of scaling laws: Ettori et al. 04

Are clusters self-similar ? Do they scale as expected? Do they evolve as expected? Relaonship between Mass, Temperature, Luminosity

examples:

2 M "TR Lx " # V$ cooling 1/ 2 R "T M " #V " Mgas

1/ 2 (T > 2 keV) 3 / 2 " #T M "T ! ! 1/ 2 Lx " M#T ! ! M "T1.5 ! 4/3 ! L ~ M L T 2 ! x ! ! Gas Temperature is related to velocity dispersion, Mass

! !T 0.59

1/2 Mushotzky 2004 Scaling relaons ! !T Gas temperature => GM/R Cluster Mass Profiles closely follow Universal NFW Profile Good News for Cluster Cosmology

M/M200

R/R200 Mass-Temperature Relation: Temperature good Mass proxy Problem: Hard to measure in abundance

Scaling relation: M ~ T3/2

r500

M "T1.5

r Vikhlinin et al. 06 2500! Ettori et al. 04 Arnaud 05 Issues: • Beta model fits • inner core • small deviations from self similarity for cool clusters • reference radius • normalization varies by ~30% between studies • redshift range • least affected by non-gravitational physics • consistent with self-similar evolution -Ettori et al. 04

Mass-luminosity Relation: clusters too luminous for their masses

scaling relation: L~M4/3

L " M1.59±0.05

!

Stanek et al. 06

L " M p P = 1.59 +/- 0.05 Stanek et al. 06 too steep! = 1.88 +/- 0.43 Ettori et al. 04

! Luminosity-Temperature Relation: too steep

10 ) 2.6 -1 L ~ T 5 EM ~ T1/2 SS 1. preheating 2. feedback EM ~ T1.38 observed 3. cooling (erg s 2 X L ~ T

L steepens L-T gravity

1

3 5 10 T (keV) Markevitch 1998

Evolution see Branchesi, Gioia et al. 07 Baryon fraction as cosmological probe

)

500 -r gas f 2500 (r gas f

T(keV) T(keV)

Vikhlinin et al. 06 assumption: universal fb Ettori & Fabian 99 f / f 10 Ettori et al. 03 fb = "b /"m fgal ~ 0.016 " gas gal # f f f #2 b = gas + gal "b = 0.045h70 (from BBN & WMAP) " = " / f = 0.30+0.04 ! m ! b b #0.03 ! !

! Constraints on from f "m,"# gas

"m = 0.25 " = 0.96 ! #

)

2500 ! (r gas f

! Z Z Allen et al. Allen et al.

assume fgas = constant geometrical test 2 3 / 2 • fgas "(1+ z) d(h(z))A • precise mass estimates over z • biases in aperture size, f constancy 3 2 h(z) = "m (1+ z) + "# • priors: H , 0 " b h !

! ! Summary

Clusters are a rich area of studies at all wavelengths • Clusters close to self-similar population (M-T) • Dark matter profile universal: theory solid • Gas scaling steeper than predicted: problem: baryon physics: cooling, heating