Attempts to fit/understand models: 1920-1995

•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

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At low z, N z3, 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.

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Do Galaxies Evolve? Are Galaxies created or Destroyed?

Count ObjectsAs a function ofBrightness.

Euclidean-V proportional toLuminosity DistanceCubed. Not so inOther Universes

Angular Size Distance with Compact Radio Sources

Kellerman(1993)

Stepanas & Saha 1995Result not that constraining

Excess z~2 QSOs: Loitering Universe

Petrosian, V., Saltpeter, E.E. & Szekeres, P. 1967

Brightest Cluster Galaxies

Sandage, Humason &Mayhall 1956Baum 1957Peach 1970

Deceleration q0>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 (Dn-/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 GalaxiesSandage 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 BasisDisadvantages:

•Observationally Expensive

•Limit is Z < 0.01

•Metallicity and Extinction

Fundamental PlaneElliptical 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?

7.07.2 −∝ eIL Ie surface Brightness with in

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Spiral Galaxies

Spiral Galaxies supported By Rotation, not by Random Motions. Have recent Star formation, dustAnd 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 formationNo 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.

7.07.2 −∝ eIL

Lensing Delay

input z of lensing galaxy and QSO, positions of lensing galaxy and images of source QSOGet time delay

from QSO variabilityModel galaxy to recover observables And recover distance to lensing galaxy

Advantages: Physical Method, works at 0.1>z>1Disadvantages: Observationally Very Expensive, Model of Galaxy (isothermal) is not yet agreed upon