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Today: Reminders/Assignments
- Longair, Chapter 4, Clusters
- Unless noted, all figs and
eqs from Longair.
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- Astro-ph preprints on Friday:
- Galaxy Spectra/Modeling Assignment – deadline extended to
Friday. L
- Reading Bennett et al. 2003 (MAP) paper
- WIRO possible on Saturday (WEBDA)
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- The textbook is rather weak when it comes to observational properties
like spectra – as budding young observers you need to know more!
- Find and download the galaxy spectra templates of Kinney et al. (1996)
– and read the paper!
- Find and download the spectral synthesis population models of Bruzual
and Charlot.
- “Fit” the elliptical template and one spiral galaxy.
- Show some plots indicating how broad-band colors change with redshift
assuming not evolution (up to z=2).
- Write up your results like you would for publication with clarity,
citations, etc.
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4
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- Large Scale Distribution of Clusters
- Galaxy Distribution in Clusters
- Dark Matter in Clusters
- Forms of Dark Matter
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- 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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- 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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- 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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- 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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- 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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- 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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- 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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- 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…!
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- 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 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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- Kormendy (1982) distinguishes these from being merely giant ellipticals.
- Extensive stellar envelope up to 100 kpc
- Only in regions of enhanced galaxy density (a factor of 100 denser than
the average)
- Mutiple nuclei in 25-50% of cDs (a very rare thing)
- Regular cD clusters are systems that have relaxed into dynamical
equilibirum.
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- Clusters appear to have relaxed to stationary dynamical states similar
to that seen in globular clusters, which can be represented by the mass
distribution of so-called isothermal gas spheres.
- Mean kinetic energy constant throughout a cluster – that is,
velocity distribution is Maxwellian everywhere.
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- Starting point is the Lane-Emden equation, which assumes spherical
symmetry and hydrostatic equilibrium:
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- Simple case, for which ideal gas law holds at all radii, p = ρkT/mass. In thermal equilibrium, 3/2 kT =
½ mass <v2>, therefore:
- Non-linear, only has an analytical solution for large r using a
power-series expansion and applying some reasonable boundary conditions.
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- Boundary conditions:
- Smoluchowski’s Envelope at large radii where density, timescales
go to extremes.
- In astrophysical systems, outmost radii are subject to interactions
with other clusters, hence a tidal radius.
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- Then recast our equation as:
- Where we have the dimensionless quantities x=r/α and ρ = ρ0y,
& A, structural length α:
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- As usual in real astronomy things are complicated because we only see a
projection rather than a 3D distribution. The projection surface density
distribution onto a plane is:
- Where now q is the projected distance from the center.
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- Fit the function to an observed distribution.
- N(q) = ½ at q=3, or core radius R1/2 =3 α.
- To get a central mass density then also need to measure the velocity
distribution. From
equipartition ½ m<v2>=3/2 kT. So:
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- More complex version based on Fokker-Planck equation by King
(1966). Assumes no particles
present with escape velocity+.
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- 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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- 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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Notes
