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Cosmological Distances

Cosmological Distances. Intro Cosmology Short Course Lecture 3 Paul Stankus, ORNL. A. Riess American. Supernovae cosmology (1998). Two Modern Hubble Diagrams. Freedman, et al. Astrophys. J. 553 , 47 (2001). Riess, et al. (High-Z) Astron. J. 116 (1998). Generalize

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Cosmological Distances

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  1. Cosmological Distances Intro Cosmology Short Course Lecture 3 Paul Stankus, ORNL

  2. A. Riess American Supernovae cosmology (1998) Two Modern Hubble Diagrams Freedman, et al. Astrophys. J. 553, 47 (2001) Riess, et al. (High-Z) Astron. J. 116 (1998) Generalize velocity  redshift distance magnitude W. Freedman Canadian Modern Hubble constant (2001)

  3. Albert Einstein German General Theory of Relativity (1915) Minkowski Space t’ t For x’ constant “Proper time” x’ x ? t’’ t For t’’ constant Proper distance x’’ x Einstein Equivalence Principle Any small patch of GR reduces to SR General Curved Space

  4. Coordinate Distance Co-Moving Distance A B E NB: Distance along photon line What was the distance to that event? Robertson-Walker Coordinates t Us Well-defined… but is it meaningful? t= now Galaxies at rest in the Hubble flow Photons Past Event c Dc

  5. dAngular dLuminosity h Flux F Intensity I q Three definitions of distance Co-Moving/ Coordinate Angular Luminosity t a(t0)Dc t0 Observed Photons Emitted Euclidean:h=dq Define:dAngularh/q Euclidean:F=I/4pd2 Define:dLum2I/4pF c Robertson-Walker Coordinates

  6. Flat Physical Radius a(t0)Dc Physical Radius Dx t t Us Us t0 F F t1 I I c x Robertson-Walker Coordinates Newton/Minkowski Coordinates

  7. Astronomical Magnitudes Rule 1: Apparent Magnitude m ~log(FluxObserveda.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)

  8. Sun Naked eye Deneb Sirius Naked eye, daylight Full Moon Saturn Venus Pluto Ganymede Brightest Quasar Andromeda Galaxy Naked eye, urban (Source: Wikipedia) Some apparent magnitudes Jupiter Mercury Mars Uranus Neptune Vega Canopus Gamma Cassiopeiae x100 Brightness Ground-based 8m telescope 25 15 5 -5 -15 -25 20 10 -10 -20 0

  9. Magnitudes and Luminosity Distances Extended Hubble Relation dLum  z Proxy for log(dLum)

  10. Flat Generic Universe Contents: Matter t=0 Big Bang t=t0 Now Recall from Lec 2 More generally (all cosmologies): Weinberg 14.6.8

  11. Today’s big question: Slope = Hubble constant

  12. Extended Hubble dLz L0 Open Generic

  13. L0 Open Generic L0 Generic Open 2.512 in brightness

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