Clusters and cluster galaxies

• Many galaxies reside in groups or clusters of galaxies, systems that are a few Mpc across. Clusters contain dozens to hundreds of galaxies; typical masses are $10^{14}$ to $10^{15}$ solar masses.

• Probably best known catalog of local galaxy clusters is Abell cluster, with richness classes 1 to 5.

• Galaxies in galaxy clusters (see e.g.Boselli and Gavazzi, PASP 118, 517 (2006)
  • morphology-density relation. Note applies to both high and low luminosity galaxies.
  • S0 galaxies
  • Anemic spirals: spirals with significantly lower gas fractions ($\sim$ 50%) than comparable field spirals. Gas deficiency appears largely in HI (not molecular), and preferentially in outer regions of galaxies. However, SFR is also notably lower than in field.

• galaxy clusters contain distributed hot gas, with total mass comparable to that found in galaxies.
  • observed with X-ray observations;
  • typical temperatures are $10^7-10^8$ K,
  • intracluster gas is enriched in heavy elements.
  • X-ray observations useful for probing cluster masses, under assumption of hydrostatic equilibrium
    • Mass functions of clusters useful for probing/constraining cosmology
    • Most accurate determination requires measurement of density and temperature profiles of X-ray gas
    • Mass estimates can be made from X-ray luminosity and/or temperature (better): the $M-kT$ relation. Has been suggested that $Y_X = M_{gas} T_X$ is an even better mass estimate.
  • Cooling flows: observed central densities from X-ray observations suggest relatively short cooling times. Possible resolution by energy input from AGN.
  • Shapes of clusters, inhomogeneities: not all clusters are in equilibrium

• Physical mechanisms affecting galaxy morphology in clusters: ram pressure stripping, tidal stripping, harassment, mergers, thermal evaporation.
  • Note mergers actually less common in clusters because of large velocity dispersion, e.g. Boselli and Galazzi Fig 14 ($\sim$ 1000 km/s) within cluster

  • tidal stripping happens when tidal force (change of gravitational force) from an neighboring object overcomes the gravitational force holding the object together. Tidal force is symmetric around center of object towards and away from neighboring object. This results in tails of material (gas and/or stars) to be stipped off in both directions - tidal tails.

    Tidal stripping will occur when tidal force exceed gravitational force:
    

    $$\left(2 G M / R^3\right) r > G m / r^2$$
    
    
    where $M$ is mass of perturber, $R$ is distance of perturber, $m$ is mass of perturbed object, $r$ is distance from center of perturbed object.

    As with mergers, tidal interactions may have relatively short timescales in clusters; potentially more likely in cluster outskirts.

    In cluster environment, can have galaxy-galaxy tidal forces and galaxy-cluster tidal forces, but latter are expected only to be significant near cluster center.

  • Harrassment refers to the accumulated effect of multiple gravitational interactions, both galaxy-galaxy, and galaxy-cluster. Can significantly effect lower mass/luminosity galaxies.

  • Tides and harrassment can act to channel gas towards galaxy centers

  • Ram pressure is the pressure exerted by a moving gas, depends on the density and the velocity of the gas. Can be observed in some galaxies (e.g. CGCG97-073

    The expression for ram pressure is:
    

    $$P_{ram} = \rho v^2$$
    
    
    This can be derived from the definition of pressure as a force per unit area, and force as the change of momentum. Consider a cylinder of gas moving at velocity v:
    
    $$M =\rho A v \Delta t$$
    
    
    This gives mass crossing a plane, where $A$ is cross-sectional area. Momentum crossing plane is:
    
    $$\Delta p = M v$$
    
    
    and pressure is change of momenum per unit time per unit area:
    
    $$P = {\Delta p \over \Delta t A} = \rho v^2$$
    
    

    Ram pressure expected to be more significant in higher gas density environments, e.g. centers of clusters. Timescale for gas removal are relatively short, e.g. compared to tidal removal.

  • Thermal evaporation can occur in clusters with hot ICM

  • Note that many of these processes may also operate in group environment, sometimes at higher efficiency, and that ``preprocessing'' in groups may be responsible for some fraction of differences between cluster and field environments, if clusters form from groups

• Unlikely that gas removal processes alone can account for morphology-density relation: S0 galaxies do not appear only to be stripped spirals (although possible for low luminosity S0s).