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Galaxy Clusters and Large Scale Structure

(Also topics will touch on gravitational lensing and dark matter)

Unless noted, all figuress and equations from the textbooks Combes et al. Galaxies and Cosmology or Longair’s Galaxy Formation.

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Galaxy Clusters

• Galaxy Clusters

• Cluster Masses – – Dynamical, X-ray, and from Lensing

• Dark Matter

• Large Scale Structure

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Cluster Catalogs

• Palomar Sky Survey using 48 inch Schmidt telescope (1950s)

• Abell (1958) cataloged “rich” clusters – a famous work and worth a look

• Abell, Corwin, & Olowin (1989) did the same for the south using similar plates

• All original work was by visual inspection

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Pavo Cluster

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Cluster Selection Criteria (Abell)• Richness Criterion: 50 members brighter

than 2 magnitudes fainter than the third brightest member. Richness classes are defined by the number in this range:

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Cluster Selection Criteria (Abell)• Compactness Criterion: Only galaxies

within an angular radius of 1.7/z arcmin get counted. That corresponds to a physical radius of 1.5 h-1 Mpc. The redshifts are (were) estimated based on the apparent magnitude of the 10th brightest cluster member.

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Cluster Selection Criteria (Abell)• Distance Criteria: Lower redshift limit (z =

0.02) to force clusters onto 1 plate. Upper limit due to mag limit of POSS, which matches z of about 0.2. Distance classes based on magnitude of 10th member:

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More on Abell Clusters• Complete Northern Sample:

– 1682 Clusters of richness 1-5, distance 1-6.– Counts in Table 4.2 follow:

– This is consistent with a uniform distribution*.– Space Density of Abell Clusters richer than 1:

– For uniform distribution, cluster centers would be 50 h-1 Mpc apart, a factor of ten larger than that of mean galaxies.

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Clusters of Clusters• Based on Abell’s Northern Sample:

– Spatial 2-point correlation function (Bahcall):

– Scale at which cluster-cluster correlation function has a value of unity is 5 times greater than that for the galaxy-galaxy correlation function.

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Clusters of Clusters• Peebles (1980) schematic picture:

– Cloud of galaxies is basic unit, scale of 50 h-1 Mpc– About 25% of galaxies in these clouds– All Abell Clusters are members of clouds (with

about 2 per cloud), and contain about 25% of the galaxies in a cloud are in Abell Clusters (superclusters occur when several AC combine)

– Remaining 75% follow galaxy-galaxy function– In terms of larger structures, galaxies hug the

walls of the voids, clusters at the intersections of the cell walls.

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Galaxies within Clusters• A range of structural types (Abell)

– Regular indicates cluster is circular, centrally concentrated (cf. Globular clusters), and has mostly elliptical and S0 galaxies. Can be very rich with > 1000 galaxies. Coma is regular.

– All others are irregular (e.g., Virgo).– I don’t know why he didn’t just call them type 1

and type 2…! /sarcasm

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Galaxies within Clusters• A range of structural types (Oemler 1974)

– cD clusters have 1 or 2 central dominant cD galaxies, and no more than about 20% spirals, with a E: S0: S ratio of 3: 4: 2.

– Spiral-rich clusters have E : S0 : S ratios more like 1: 2: 3 – about half spirals.

– Remainder are spiral-poor clusters. No dominant cD galaxy and typical ratio of 1: 2: 1.

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Galaxies within Clusters• Galaxies differ in these types (Abell)

– In cD clusters galaxy distribution is very similar to star distribution in globular clusters.

– Spiral-rich clusters and irregular clusters tend not to be symmetric or concentrated.

– Spiral-poor clusters are intermediate cf. above.– In spiral rich clusters, all galaxy types similarly

distributed and no mass segregation, but in cD and spiral-poor clusters, you don’t see spirals in the central regions where the most massive galaxies reside.

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Structures of Regular Clusters• Bahcall (1977) describes distributions as

truncated isothermal distributions:

• Where f(r) is the projected distribution normalized to 1 at r=0, and C is a constant that makes N(r) = 0 at some radius. Results in steepening distribution in outer regions vs. pure isothermal soultion.

• R1/2 = 150-400 kpc (220 kpc for Coma)

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Structures of Regular Clusters• In central regions King profiles work well:

• For these distributions N0 = 2Rcρ0.• De Vaucouleur’s law can also work.• Problem is observations do not constrain

things quite tightly enough.

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Rich Cluster Summary

B-M Class I have central cD galaxy, Class III do not.

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Rich Cluster Summary

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Dark Matter in Galaxy Clusters

• How do we know it is there?– Dynamical estimates of cluster masses– X-ray emission/masses– (Sunyaev-Zeldovich Effect)– Gravitational lensing!

• What is the dark matter???– Baryons vs. non-Baryons

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Dynamical Masses• Virial Theorem: A relationship between

gravitational potential energy and velocities for a dynamically relaxed and bound system.

• Ellipticals not necessarily rotating.• T = ½ |U|, where T is the total kinetic

energy and U is the potential energy.• So, for a cluster of stars or a cluster of

galaxies, measuring T (by measuring velocities) can give U and therefore M.

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Galaxy Masses• Virial Theorem: T = ½ |U|

• You do need to worry about the conditions of the theorem in an astrophysical context. For instance, comparing crossing times with the relevant timescale. Text examples are the sun’s orbital period and galaxies in Coma.

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Derivation of Virial Theorem

Tensor virial theorem for a self-gravitating system of collisionless point masses. Cf. Binney & Tremaine 1987.

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Galaxy Masses• Astronomical context more complex. Cannot

in general get all the 3D velocities. In exgal context, uncertain cosmology can translate into uncertain spatial dimensions. Usually only have position on sky plus radial velocities. Must make assumptions about velocity distribution to apply virial theorem.

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Masses

• Isotropic case: <v2> = 3<vr2> (why?)

• If velocity dispersion independent of masses:– T = 3/2 M <vr

2>, where M is total mass

• More complex if the above is not true. Assuming spherical symmetry and an observed surface distribution, get a weighted mean separation Rcl:

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Dark Matter in Galaxy Clusters• Dynamical estimates of cluster masses

– Virial Theorem as we have discussed, but…• Very few clusters exist that can be well done!• E.g, which are cluster members?• Must measure many velocities

– Case of Coma• Regular rich cluster, looks like isothermal sphere• Crossing time arguments OK• Virial mass issue for Coma first by Zwicky (1937)• Surface distribution, velocities in next figure…

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Dynamic Properties of ComaKing model fit in top panel.

Projected velocities vs anglular radius.

Bottom shows three consistent velocity dipsersion profiles, vs. radius now.

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Dynamic Masses for Coma• Merritt (1987) analysis:

– Assuming constant M/L ratio, then mass is 1.79 x 1015h-1 solar masses, and M/L is 350 h-1 in solar units (think about that!).

– Typical M/L for ellipticals is 15 in solar units.– Differ by a factor of 20

• Why should the dark matter have the same distribution as the light?

• Why should the velocities even be isotropic?

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X-ray Masses for Clusters

• UHURU in 1970s:– Rich clusters very bright in X-rays!– Bremsstrahlung emission of hot intercluster gas– Very hot gas requires large potential to hold– Can use to estimate the cluster mass

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X-ray Masses for Clusters

• Fabricant, Lecar, and Gorenstein (1980, ApJ 241, 552):– Assume spherical symmetry (as usual!)– Assume hydrostatic equilibrium (yes!):

– Perfect gas law:

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X-ray Masses for Clusters

• Fabricant, Lecar, and Gorenstein:– For ionized gas, cosmic abundances, μ = 0.6– Differentiating the gas law, and inserting into

the hydrostatic equation:

– So, the mass distribution can be found if the variation of pressure and temperature with radius are known (measured).

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X-ray Masses for Clusters

• Fabricant, Lecar, and Gorenstein:– Bremsstrahlung spectral emissivity:

– Gaunt factor can be approximated:

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X-ray Masses for Clusters• Fabricant, Lecar, and Gorenstein:

– Bremsstrahlung spectrum is roughly flat up to X-ray energies, above which it cuts off exponentially. Cut-off is related to temperature. E = hν ~ kBT. The measurement is a projection onto 2D space. Integrating emissivity and converting to intensity (surface brightness at the projected radius a):

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X-ray Masses for Clusters

• Simplified procedure:– Luminosity Density = total energy per second per

unit volume integrating over all frequencies, for a fully ionized hydrogen plasma:

– Lvol = 1.42 x 10-27ne2T1/2 ergs/s/cm3

– Sometimes it can be assumed that you have an isothermal sphere (which is the case when the dark matter and the gas have the same radial dependence).

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X-ray Masses for Clusters

• So, from the spectrum we can get the temperature as a function of radius, and from the intensity we can get the emissivity and hence the particle density.

• Chandra is great for this type of observation:

• http://chandra.harvard.edu/photo/2002/0146/

• http://chandra.harvard.edu/photo/0087/

• http://www1.msfc.nasa.gov/NEWSROOM/news/photos/2002/photos02-037.html

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Chandra Images of Clusters

Abell 1689, Optical + X-rays Abell 2125, X-rays only

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X-ray Masses for Clusters

• ROSAT pictures: old and busted.

• Chandra images: The New Hotness.

• Important result is that the dark matter does follow the galaxies.

• Typical masses then are 5x1014-15 solar masses, only 5% visible light, 10-30% hot gas, rest is DM.

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Forms of Dark Matter???

• We’re certain it is present (Bullet Cluster and newer observations nail it): A Direct Empirical Proof of the Existence of Dark Matter. Clowe, D., Bradac, M., Gonzalez, A. H., Markevitch, M, Randall, S., Jones, C., & Zaritsky, D. 2006, ApJ Letters, 648, 109

• Some is baryonic (1/6).

• Most is non-baryonic (5/6), WIMPs

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Large Scale Structure

• Galaxy structure – how is the mass in the universe distributed (and recall gas can be important, too!)? Homogeneous? On what scale?

• Current best work is the SDSS

• Background radiation also of interest (discrete sources vs. true diffuse background).

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Background “SED”

• CMBR of special interest (as we will get to) and X-ray is a recent development (CXO).

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The “Third Dimension”• Galaxy distributions seen in images are 2-d

projections on the sky.

• Need distances…easiest way is to use the Hubble flow and redshifts, either photometric or spectra (best).

• Reminder – SDSS and 2dF rule here now.

• Huchra and Gellar’s “Z-machine” for the CfA survey as recounted in “Lonely Hearts of the Cosmos” by Dennis Overbye – Great!

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The “Third Dimension”

• Look at distance “slices” here.

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The “Third Dimension”

• The famous “man” in the distribution. Shows walls, voids, etc.

• Why elongations, “finger of god” distributions pointing at “us?”

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Statistical Methods

• Correlation functions– How do you measure, quantitatively, the

tendency of galaxies to cluster?– Following is specifically from Longair, but also

present in Combes et al. with a different presentation.

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Large-scale Distribution of Galaxies

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Large-scale Distribution of Galaxies• On small scales, the universe is very

inhomogeneous (stars, galaxies). What about larger scales?

• Angular two-point correlation function w(θ):

Where w(θ) represents the excess probability of finding a galaxy at an angular distance θ from another galaxy. dΩ is a solid angle element. ng is the average galaxy surface density.

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Large-scale Distribution of Galaxies• This function w(θ) describes apparent clustering

on the sky down to some magnitude limit.• More physically meaningful is the spatial two-

point correlation function ξ(r) which describes clustering in 3-D about a galaxy:

• Now N(r) dV describes the number of galaxies in the volume element dV at a distance r from any galaxy. No is another normalization factorv (ave.).

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Large-scale Distribution of Galaxies

• w(θ) isn’t so hard to measure from various surveys – just need positions.

• ξ(r) is harder – must have redshifts to do properly. Can make some assumptions however.

• Observationally verified parameterization works for scales of 100 h-1 kpc to 10 h-1 Mpc, and you get r0 = 5 h-1 Mpc and γ = 1.8. Note use of “h”.

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Large-scale Distribution of Galaxies

• Maddox et al. (1990)

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Large-scale Distribution of Galaxies

•Points to consider with regard to the two-point correlation studies:

•Galaxies appear to be sampled from a homogeneous but clustered distribution.

•Clustering appears over a wide range of scales.

•No clearly preferred scales.

•Clustering drops off more rapidly on largest scales (smooths out, essentially isotropic).

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Large-scale Distribution of Galaxies

3D distribution from Geller and Huchra 1989 (using the “z-machine”). Some 14000 galaxies.

Holes up to about 50/h Mpc in size.

“Spongelike”

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Large-scale Distribution of GalaxiesLas Campanas Redshift Survey, 4 times greater distances than Harvard. Over 26,000 galaxies. Similar results, with same scales for clumping, etc.

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Large-scale Distribution of Galaxies

Brightest galaxies in the sky. Note local supercluster.

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Large-scale Distribution of Galaxies

Slices through the 3-dimensional map of the distribution of galaxies from the Sloan Digital Sky Survey (SDSS). The earth is at the center, and each point represents a galaxy, typically containing about 100 billion stars. Galaxies are colored according to the ages of their stars, with the redder, more strongly clustered points showing galaxies that are made of older stars. The outer circle is at a distance of two billion light years. The region between the wedges was not mapped by the SDSS because dust in our own Galaxy obscures the view of the distant universe in these directions. The lower slice is thinner than the upper slice, so it contains fewer galaxies. Credit: M. Blanton and the SDSS.

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Large-scale Distribution of Galaxies

Distribution of 31000 brightest radio sources (6 cm).

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Large Scale Motions• Milky Way motion vs. CMBR, a “dipole”

with velocity of about 1000 km/s (from COBE)

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Large Scale Motions• “The Great Attractor”

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Large-scale Distribution of Galaxies

Simulations were performed at National Center for Supercomputer Applicationsby Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University).