1. Interpreting Hubble’s Law Barbara Ryden Department of Astronomy The Ohio State University

2. All physics & astronomy majors should take a cosmology course as a “capstone” experience. thermodynamics, statistical mechanics, quantum mechanics, classical dynamics, general relativity, nuclear physics, atomic physics, particle physics…

3. historical For non-science majors, a historical overview of cosmology emphasizes how new observations lead to new cosmological models.

5. Malcolm Longair (1993) QJRAS, 34, 157:

6. Hubble (1929) PNAS, 15, 168

7. Lesson: Typos happen. Hubble (1929) PNAS, 15, 168

8. What are “VELOCITY” and “DISTANCE”? Hubble (1929) PNAS, 15, 168

9. Humason (1931) ApJ, 74, 35

10. “VELOCITY” = c z, where c = speed of light and z = percentage shift in wavelength of light. Observation = redshift (z) Interpretation = velocity (v) (Mt. Wilson Observatory, 1931)

11. Possible interpretations of the observed redshift: Doppler shift: z = v/c (Galaxies are moving away from the observer through space.) Gravitational redshift: z = v esc /c (More distant galaxies are more luminous, and have deeper potential wells.) Cosmological redshift: z = a observation /a emission - 1 (In the limit of small redshift, z = v/c, where v is the relative speed of emitter and observer due to expansion of space.) Tired light: z = E emission /E observation - 1 (Photons lose energy as they move through static space.)

12. Hubble (1929) PNAS, 15, 168

13. Andromeda Galaxy: 2 million light-years away Big Problem Big Problem for Astronomers: no sense of depth looking at the sky. minutes Comet Hale-Bopp: 10 light-minutes away

14. Lesson: measuring the distance to an astronomical object is damnably difficult. Hubble used the “standard candle” method.

15. Obvious problem with standard candles: if your assumed luminosity is crap, your computed distance is Edwin Hubble fell into this trap. (Beware of “appeal to authority”: even Homer nods.)

16. 0.050 0.061 0.49 0.88 0.77 0.80 7.2 5.0 8.0 3.6 3.2 3.7 10. 5.4 4.7 12. 9.0 14. 7.5 12. 17. 16. 17. Hubble (1929) PNAS, 15, 168

18. Hubble’s law in mathematical form: v = H 0 r v = “velocity” r = “distance” H 0 = Hubble constant Hubble’s value of the Hubble constant ≈ 500 km/s/Mpc WMAP value = 71.0 ± 2.5 km/s/Mpc

19. Not-as-obvious problem with standard candles: our equation assumes Euclidean geometry. What if Euclid nods on large scales? Another problem with standard candles: our equation assumes photon energy is conserved. Redshifted photons lose energy.

20. But wait! These aren’t problems, they are opportunities! Deviations of Hubble’s law from a straight line at large distance/redshift tells us about the expansion history of the universe.

21. One set of observations … many possible interpretations. both Hubble acknowledged the existence of both Doppler shifts and cosmological redshifts.