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, sensiWve to maer and energy density of the Universe - fair sample hypothesis: baryons, dark maer, baryon fracWon - observaonal goal: measuring masses; observaonal proxies for mass (Lx, T, etc.) • Galaxy formaon & Evoluon - closed boxes: retain byproducts of stellar evoluWon; history of star formaon - galaxies at same redshi^: uniform sampling in space & Wme - merging & perturbaon: dynamical evoluWon 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 potenWal 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 parWWoning 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 M = tot 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. AssumpWons: Sound crossing Wme much less than the age of the cluster Timescale for elasWc collisions much shorter than Wmescale for heang or cooling Kinec Equilibrium Timescales for electrons and ions to form a Maxwellian distribuWon 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 condiWons Electrons & ions in equiparWWon, such that T = Te= Tp DetecWng 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- stasWcal weight of ground state Luminosity per frequency Emissivity: !" = !" (z,T)nenp (erg/cm3) Significant So^ X-ray Lines Peterson + 01 X-ray cooling funcWon 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 proporWonal ne and elemental abundance 2 • Thermal bremsstrahlung proporWonal to ne • rao of line emission to brems connuum indep of density • Temperature sensiWve to brems shape and line raos (low T) • Hence, line equivalent width gives elemental abundance M87 Observed with the ReflecWon 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 sophisWcated 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 distribuWon only a funcWon 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 DisconWnuity: 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.