Presentation on theme: "Cosmological Distances Intro Cosmology Short Course Lecture 3 Paul Stankus, ORNL."— Presentation transcript:
Cosmological Distances Intro Cosmology Short Course Lecture 3 Paul Stankus, ORNL
Freedman, et al. Astrophys. J. 553, 47 (2001) Riess, et al. (High-Z) Astron. J. 116 (1998) W. Freedman Canadian Modern Hubble constant (2001) A. Riess American Supernovae cosmology (1998) Two Modern Hubble Diagrams Generalize velocity redshift distance magnitude
Einstein Equivalence Principle Any small patch of GR reduces to SR Albert Einstein German General Theory of Relativity (1915) x t x t General Curved SpaceMinkowski Space x’ t’ For x ’ constant “Proper time” For t’’ constant Proper distance x’’ t’’ ?
What was the distance to that event? Photons Us t t now Robertson-Walker Coordinates Past Event Coordinate Distance Co-Moving Distance A B Well-defined… but is it meaningful? E NB: Distance along photon line Galaxies at rest in the Hubble flow
Three definitions of distance Co-Moving/ Coordinate AngularLuminosity Photons t Emitted a(t0)a(t0) Observed Robertson-Walker Coordinates h d Angular Euclidean: h d Define: d Angular h/ Euclidean: F I/4 d 2 Define: d Lum 2 I/4 F t0t0 d Luminosity Intensity I Flux F
t Physical Radius a(t 0 ) Robertson-Walker Coordinates t x Physical Radius x Newton/Minkowski Coordinates I F I F t0t0 t1t1 Us Flat
Astronomical Magnitudes Rule 1: Apparent Magnitude m ~ log(Flux Observed a.k.a. Brightness ) Rule 2: More positive Dimmer Rule 3: Change 5 magnitudes 100 change in brightness Rule 4: Absolute Magnitude M = Apparent Magnitude if the source were at a standard distance (10 parsec = 32.6 light-year)