Attempts to fit/understand models: Number counts of Galaxies – Hubble,Yoshii/Peterson Angular Size Distances - distant radio cores Kellerman Loitering Universes with z=2 Quasars Luminosity Distance with Brightest Cluster Galaxies

Volume Effects At low z, N  z 3, for any non-diverging luminosity function, Hubble observed this to be true, demonstrating that Galaxies uniformly fill the local Universe. He and Humason were unable to reach conclusions on Geometry.

Do Galaxies Evolve? Are Galaxies created or Destroyed? Count Objects As a function of Brightness. Euclidean- V proportional to Luminosity Distance Cubed. Not so in Other Universes

Angular Size Distance with Compact Radio Sources Kellerman (1993)

Stepanas & Saha 1995 Result not that constraining

Excess z~2 QSOs: Loitering Universe Petrosian, V., Saltpeter, E.E. & Szekeres, P. 1967

Brightest Cluster Galaxies Sandage, Humason & Mayhall 1956 Baum 1957 Peach 1970 Deceleration q 0 >1 But Tinsley 1976 showed Evolution dominates Cosmology

cz=1350km/s

cz=6200km/s

Methods for Measuring Extra- Galactic Distances Brightest Cluster Galaxies Cepheids Fundamental Plane (D n -  /Faber Jackson) Lensing Delay Planetary Nebulae Tully-Fisher Sunyaev-Zeldovich Surface Brightness Fluctuations Supernovae Ia Supernovae II

Relative versus Absolute Distances Most Astronomical Distance methods are relative. Object A is X times further than object B. They need to be calibrated with a different method in the nearby Universe – A process we call the Astronomical Distance Ladder. A few distance methods provide Absolute physical distances, independent of the Distance Ladder.

The Distance Ladder Parallax Distance to nearest Stars Spectroscopic Parallax of these stars to clusters of stars Main Sequence Fitting of Clusters to Other Clusters which contain Cepheid Variable Stars Comparison Cepheid Variable Stars to Cepheids in the Large Magellanic Cloud. Large Magellanic Cloud is the Anchor of the Extra Galactic Distance Scale

Freedman et al 2001 Eclipsing Binaries (Fitzpatrick et al.) Recently Published Values of the Distance to the LMC.

Brightest Cluster Galaxies Sandage et al. (1956) Lauer & Postman 1992 Concentration Advantages: Easy, high-Z possible; Disadvantages: Poor Physical Basis, unexplained results, Evolution

Cepheids Advantages: Can be calibrated within Galaxy Precise (0.1 mag) Good Physical Basis Disadvantages: Observationally Expensive Limit is Z < 0.01 Metallicity and Extinction

Fundamental Plane Elliptical Galaxies, Surface Brightess (I) within ½ light radius (R), and velocity dispersion (  ) are correlated L related to R and I Advantages: Observationally cheap. Works to z>0.5 Disadvantages: Imprecise Evolution Physical Understanding not great Environmental Effects? I e surface Brightness with in ½ light radius

Spiral Galaxies Spiral Galaxies supported By Rotation, not by Random Motions. Have recent Star formation, dust And tend to be less massive than elliptical Galaxies

Elliptical Galaxies Supported by random motions of stars, Biggest Galaxies in the Universe. No Dust, No Star formation No Gas, Old Stars

Fundamental Plane Prescription: Measure Flux within an ellipse which contains ½ the light – I=Flux/Area Take Spectrum to measure the velocity dispersion (  ) of the stars.

Lensing Delay input z of lensing galaxy and QSO, positions of lensing galaxy and images of source QSO Get time delay from QSO variability Model galaxy to recover observables And recover distance to lensing galaxy Advantages: Physical Method, works at 0.1>z>1 Disadvantages: Observationally Very Expensive, Model of Galaxy (isothermal) is not yet agreed upon