1	Astr 5460 Wed., Nov. 3, 2004 This week: Large Scale Structure (Ch. 11, Combes et al., parts) Unless noted, all figs from Combes et al. Already talked about galaxy clusters a lot, and some distance ladder topics will be covered in more detail in Mike Pierce’s class next semester.
2	Some other issues Discuss homework Not as great as expected – just busier now? Can turn in problem 6 next week for extra credit – please write up the process! Discuss Observing Project (briefly!) Mid-term exam: 2 hours, take-home, on your honor, only calculator and constants/conversions Some “basic knowledge” questions in addition to more analytic problems. Know terms, definitions, other intangible issues.
3	Large Scale Structure Galaxy structure – how is the mass in the universe distributed (and recall gas can be important, too!)? Homogeneous? On what scale? Text is a bit old (fine for history), but the best newest information will come from SDSS and 2dF. CHECK IT OUT! Background radiation also of interest (discrete sources vs. true diffuse background).
4	Background “SED” CMBR of special interest (as we will get to) and X-ray is a recent development (CXO).
5	Distance Scales Parallax and Trigonometric Methods:
6	Distance Scales Parallax and Trigonometric Methods
7	Distance Scales Parallax and Trigonometric Methods tan λ = Vt/Vr = μd/Vr So then d = Vr tanλ/4.74μ [pc] Where velocities are in km/s and proper motion μ is in arcseconds per year. Should be something you can derive (it would be a good problem to work in your free time)
8	Distance Scales Parallax and Trigonometric Methods – once Hyades distance known, can use main-sequence cluster fitting.
9	Distance Scales Parallax and Trigonometric Methods – once Hyades distance known, can use main-sequence cluster fitting. Then employ the distance modulus, basically a vertical shift on the CMD diagram, (m-M = 5 logd(pc) -5)
10	Distance Scales Cepheids and Standard Candles Various stars in the instability strip of the H-R diagram with Period-luminosity relations.
11	Distance Scales Cepheids and Standard Candles Various stars in the instability strip of the H-R diagram with Period-luminosity relations. Figures for Cepheids from Horizons (Michael Seeds)
12	Distance Scales The Tully-Fischer Relation L = kΔV^α – where the index is ~ 4. Better in the near-IR, as we discussed before, less star formation visible at H-band, so less distortion. The velocity dispersion comes from either 21 cm or stellar optical absorption lines.
13	Distance Scales This is where Combes et al. discusses the Hubble Law: Vr = H_od where Ho is in km/s/Mpc Hubble constant Ho is independent of direction in the sky (that’s important, think about it!) Also recall Ho = h 100 km/s/Mpc
14	Distance Scales The Tully-Fischer Relation
15	Distance Scales Malmquist Bias:
16	Distance Scales The Sunyaev-Zeldovich Effect: Look toward hot intercluster medium in galaxy clusters…Thomson scattering can affect the CMBR seen through such a medium Optical thickness is τ_T = ∫σ_Tn_e dl Cluster properties can indeed “hamper” the CMBR The CMBR is heated by the ICM, altering the frequency: Δν/ν = 4kT_e/m_ec², leading to: ΔT/T = - ∫ 2kT_e/m_ec²dτ_T (hν << kT_e) At low frequencies, REDUCES the temperature of the CMBR. Can get distance estimates from S-Z effect.
17	Distance Scales The Sunyaev-Zeldovich Effect Measure the X-ray flux, the temperature fluctuations, and the temperature, and can get distance, and hence Ho. Compton effect here
18	Distance Scales Surface-Brightness Fluctuations Surface brightness does not vary with distance – why? How about, say, the number of stars per pixel as a function of distance? That does change, and the statistical uncertainty does vary with distance.
19	Distance Scales Surface-Brightness Fluctuations
20	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!
21	The “Third Dimension” Look at distance “slices” here.
22	The “Third Dimension” The famous “man” in the distribution. Shows walls, voids, etc. Why elongations, “finger of god” distributions pointing at “us?”
23	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.
24	Large-scale Distribution of Galaxies
25	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):
26	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:
27	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.
28	Large-scale Distribution of Galaxies
29	Large-scale Distribution of Galaxies
30	Large-scale Distribution of Galaxies
31	Large-scale Distribution of Galaxies
32	Large-scale Distribution of Galaxies
33	Large-scale Distribution of Galaxies
34	Large Scale Motions Milky Way motion vs. CMBR, a “dipole” with velocity of about 1000 km/s (from COBE)
35	Large Scale Motions “The Great Attractor”