1	Astr 5460 Fri., Feb. 28, 2003 Today: Reminders/Assignments Longair, Chapter 4, Clusters Unless noted, all figs and eqs from Longair.
2	Reminders/Preliminaries Astro-ph preprints: http://xxx.lanl.gov/ Galaxy Spectra/Modeling Assignment Reading Bennett et al. 2003 (MAP) paper WIRO possible on Saturday? (WEBDA)
3	Galaxy Spectra assignment 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.
4	King Profiles More complex version based on Fokker-Planck equation by King (1966). Assumes no particles present with escape velocity+.
5	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. R_1/2 = 150-400 kpc (220 kpc for Coma)
6	Structures of Regular Clusters In central regions King profiles work well: For these distributions N₀ = 2R_cρ₀. De Vaucouleur’s law can also work. Problem is observations do not constrain things quite tightly enough.
7	Rich Cluster Summary
8	Rich Cluster Summary
9	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
10	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…
11	Dynamic Properties of Coma
12	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?
13	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
14	X-ray Masses for Clusters Fabricant, Lecar, and Gorenstein: Assume spherical symmetry (as usual!) Assume hydrostatic equilibrium (again!): Perfect gas law:
15	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).
16	X-ray Masses for Clusters Fabricant, Lecar, and Gorenstein: Bremsstrahlung spectral emissivity: Gaunt factor can be approximated:
17	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. The measurement is a projection onto 2D space. Integrating emissivity and converting to intensity:
18	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 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 Cooling flows are one possible complication.
19	X-ray Masses for Clusters Textbook shows old ROSAT picture, which sucks compared to new Chandra images. Important result is that the dark matter does follow the galaxies. Typical masses then are 5x10^14-15 solar masses, only 5% visible light, 10-30% hot gas, rest is DM.
20	Sunyaev-Zeldovich Effect Hot gas can also be studied by looking for decrements in the Cosmic Background radiation, resulting from Compton scattering by hot electrons. Net energy is slightly increased. Not a symmetric effect – in Rayleigh-Jeans region there is decrement but in Wein region there is an excess. First predicted by Sunyaev and Zeldovich in 1969, and has been observed.
21	Sunyaev-Zeldovich Effect Compton scattering optical depth: Resulting decrement in R-J spectral region is: Predicted to be on order of 1 part in 10000 given observed hot intercluster gas.
22	S-Z Effect for Clusters
23	Sunyaev-Zeldovich Effect Note that the S-Z effect + X-ray observations over-constrain the physical conditions. With some assumptions then, the physical sizes of the clouds can be determined. Comparison of angular sizes then can give distances measured independent of redshift, and thus used to make estimates of Hubble’s constant.
24	Gravitational Lensing by Clusters Mass bends space and hence light paths (Einstein 1915; General relativity). Angular deflection by point mass is: Where p is the “collision parameter.” What happens when p goes to zero?
25	Gravitational Lensing by Clusters
26	Gravitational Lensing by Clusters Previous derivation assumes Euclidean geometry (which WMAP says is OK!). Still OK if the distances are angular diameter distances (chapter 5). Expressing the result in physical terms: So, what is the typical size for clusters?
27	Gravitational Lensing by Clusters
28	Gravitational Lensing by Clusters OK, but clusters are not point sources. See discussion on P. 96-97. For our isothermal gas sphere can derive the result that:
29	Gravitational Lensing by Clusters
30	Forms of Dark Matter??? We’re certain it is present. Some is baryonic. More is non-baryonic.
31	Baryonic Dark Matter Protons, Neutrons, electrons (include black holes here too). Text example of bricks (yes bricks!). Brown dwarfs and the like. BB nucleosynthesis constrains baryons to less than 0.036 h^-2 of closure density.
32	Baryonic Dark Matter Black holes constrained by lensing effects (or lack thereof). MACHOs (Alcock et al. 1993):
33	Baryonic Dark Matter MACHOs: http://www.owlnet.rice.edu/~spac250/coco/spac.html MACHOs are rather massive, around half a solar mass, and can contribute up to half of the dark halo mass. White dwarfs???
34	Non-Baryonic Dark Matter I’m no expert on this stuff (and in some sense NO ONE is). Particle physicists play in this area more than astronomers. Leading candidates include Axions. Cold, low mass, avoid strong CP violation. Neutrinos. Hot, low mass (getting better constrained), lots of them. SN helps. WIMPs. Gravitino, photino, etc. Mirror Matter. May use in my next novel.