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)

Some apparent magnitudes SunFull MoonVenusSaturn Ganymed e Uranus Neptune Pluto Mercury Mars Jupiter Sirius Canopus Veg a Deneb Gamma Cassiopeiae Andromeda Galaxy Brightest Quasar Naked eye, daylightNaked eye, urbanNaked eye Ground-based 8m telescope x100 Brightness (Source: Wikipedia)

Extended Hubble Relation d Lum  z Proxy for log(d Lum ) Magnitudes and Luminosity Distances

t  0  Big Bang t  t 0  Now Flat Recall from Lec 2 More generally (all cosmologies): Weinberg

Today’s big question: Slope = Hubble constant

Generic 00 Extended Hubble d L  z Open

 in brightness Generic 00 Open Generic 00 Open