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Clusters of Galaxies. Erin Ryan and Michele Benesh University of Minnesota School of Physics and Astronomy Minneapolis, MN 55455 December 6, 2006. Clusters of Galaxies. Bound by gravity – dark matter Virial equilibrium at center Scale when correlation function ~1 is 8 Mpc
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Clusters of Galaxies Erin Ryan and Michele BeneshUniversity of MinnesotaSchool of Physics and AstronomyMinneapolis, MN 55455December 6, 2006
Clusters of Galaxies • Bound by gravity – dark matter • Virial equilibrium at center • Scale when correlation function ~1 is 8 Mpc • Contain diffuse gas – intracluster medium • Dense clusters powerful emitters of X-rays • Emission is increasing with cosmic time
X-Ray Clusters • Main source of radiation is thermal bremsstrahlung • Ionized, hot intergalactic gas, T • Emission lines • attributed to highly ionized iron • yield gas temperatures • Seen in cooler clusters (< 3keV)
X-Ray Clusters • Mass of ionized gas-to-star ratio • Unity in poor clusters, up to 5 in rich clusters • Heavy elements – solar abundances • Heavily processed material likely ejected by galaxies • collisions with other galaxies • ram pressure due to hot intergalactic gas
X-Ray Clusters • Various analyses • Provide lower limit on temperature of gas • Mass and dark matter measurements • Determination of dynamical state • Interaction between cluster and intracluster gas • Emissions are proportional to
Physical Properties of clusters • Crossing times: • Virial Mass:
X-Ray properties of Clusters • Temperatures
Emission mechanism • Temperatures are high enough that gas should be fully ionized- emission dominated by thermal bremmstrahlung • Good for clusters with kT > 3 keV, for cooler systems need to include metal cooling • If integrate emissivity over X-ray range, luminosities are on the order of 1043-1045 erg s-1
Temperature-Mass Relation • For Einstein-deSitter cosmology, ∆vir is constant. For isothermal gas then T M 2/3(1+z)
Local number density of Clusters • Luminosity function normally modelled with Schechter function. If using flux limited sample with measured redshifts and luminosities, can get density of clusters in each luminosity bin:
Cluster Abundance at High Redshifts and its evolution • One major issue: for some samples redshifts aren’t available. • Another issue: Limited volume of surveys means it’s hard to find the very bright systems (as there are less of them) • In general: comoving space density of cluster population is approximately constant out to z~1 but most luminous (most massive) clusters were likely rarer at “high” redshifts (z > 0.5)
Finding the Cosmological Mass function • Using one of our favorite eqns: • Using only the number density of clusters with mass M, can constrain amplitude of density perturbations at physical scale R (M/mcrit)1/3 • Because scale depends on both M and m, mass function of nearby clusters is only able to constrain relation between 8 and m
Deriving m from cluster evolution • Link between total cluster virial mass and gas temperature: • Observationally: Mvir-T relation is consistent with T M2/3 scaling law at least for T > 3 keV clusters but with 40% lower normalization. At lower temps there is evidence for a steeper slope (possibly due to energy feedback, ie. SN and AGN and radiative cooling)
Other technique: Sunyaev-Zeldovich • Two kinds: thermal and kinetic. Mostly we see thermal
Thermal SZE • Distortion to CMB spectra cause by inverse compton scattering: CMB photon scatters off electrons, thus getting a boost of energy causing small (< 1 mK) distortion in CMB • Decreases CMB flux at < 218 GHz
Measuring thermal energy of cluster • SZE flux= temp weight mass of cluster divided by DA2 • At high z: DA(z) relatively flat • Cluster of given mass hotter and denser at high z because matter density (1+z)3
Kinetic SZE • As seen in plots it is very small: • Vpec is the line of sight velocity of the cluster
Sources of Contamination • Anisotropy: (not normally a problem as anisotropy is over larger scales than a cluster size which is normally a few arcmin). • Radio point sources • Dust
Distant Determinations, Hubble Constant • Need to use SZE and X-ray observations in combination: SZE is proportional to density to the first power, X-ray is proportional to density squared. • If you also have redshifts for clusters then one can fit the Hubble Parameter given a geometry of the universe.
Cluster Gas-Mass fractions • Know that fB = B/ M so if you can get an estimate of M if you can get a baryon fraction and know B (which you can estimate from D-H ratios in Ly- observations) • Use the gas mass fraction as a lower limit on fB • Gas mass measured directly by SZE assuming Te known (again huzzah X-ray obs): derived gas fraction proportional to ∆TSZE/Te2 • Two local samples: A2142, A2256 and Coma: fgh=0.061 +/- 0.011 @ 1-1.5h-1 Mpc A478: fgh=0.16 +/- 0.14 reported • @ high z: use temp weighting from local as no X-ray obs
Measuring Peculiar Velocities • Can measure large scale velocity fields at high redshift • Only problem is that you have to look at the thermal null at about 218 GHz, and we already know it’s a very weak signature • However- if you can do it for a number of clusters in a given redshift bin you can determine the average peculiar velocity which will trace evolution of expansion through those redshift bins
References • Calstrom, J.E., Holder, G.P., Reese, E.D., 2002, Annu. Rev. Astron. Astrophys., 40, 643. • Norman, M.L., 2005, in Proceedings of the International School of Physics CLIX, Background Microwave Radiation and Intracluster Cosmology, ed. F. Melchiorri and Y. Rephaeli (Bologna, Società Italiana di Fisica), 1. • Rees, M., 1992, in Proceedings of the NATO Advanced Study Institute on Clusters and Superclusters of Galaxies, ed. A.C. Fabian (Netherlands, Kluwer), 1. • Rosati, P., Borgani, S., Norman, C., 2002, Annu. Rev. Astron. Astrophys., 40, 539. • Schindler, S., 2003, ChJAS, 3, 97. • Uson, J.M., Wilkinson, D.T, 1988., in Galactic and Extragalacticv Astronomy, eds. G.L. Verschuur and K.I. Kellermann (Springer-Verlag), 603.
