Interpreting Hubble’s LawInterpreting Hubble’s Law

Barbara Ryden Department of

Astronomy The Ohio State University

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…

For non-science majors, a historicalhistorical overview of cosmology emphasizes how new observations lead to

new cosmological models.

Malcolm Longair (1993) QJRAS, 34, 157:

Hubble (1929) PNAS, 15, 168

Lesson: Typos happen.

Hubble (1929) PNAS, 15, 168

What are “VELOCITY” and “DISTANCE”?

Hubble (1929) PNAS, 15, 168

Humason (1931) ApJ, 74, 35

“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)

Possible interpretations of the observed redshift:

Doppler shift: z = v/c (Galaxies are moving away from the observer through space.)Gravitational redshift: z = vesc/c (More distant galaxies are more luminous, and have deeper potential wells.)

Cosmological redshift: z = aobservation/aemission - 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 = Eemission/Eobservation - 1 (Photons lose energy as they move through static space.)

Hubble (1929) PNAS, 15, 168

0

0observed

λ

λλc

Andromeda Galaxy: 2 million light-years away

Big ProblemBig Problem for Astronomers: no sense of depth looking at the sky.

Comet Hale-Bopp: 10 light-minutesminutes away

Lesson: measuring the distance to an astronomical object is damnably difficult.

Hubble used the “standard candle” method.

2r 4

L f

observed

assumed

f 4

L r

Obvious problem with standard candles: if your assumed luminosity is crap, your computed distance is

crap

Edwin Hubble fell into this trap. (Beware of “appeal to authority”: even Homer nods.)

0.0500.061

0.490.880.770.80

7.25.08.03.63.23.710.5.44.712.9.014.7.512.17.16.17.17.

Hubble (1929)

PNAS, 15, 168

Hubble (1929) PNAS, 15, 168

0

0observed

λ

λλc

observed

wrong

fπ4

L

Hubble’s law in mathematical form:

v = H0 r

v = “velocity”

r = “distance”

H0 = Hubble constant

Hubble’s value of the Hubble constant ≈ 500 km/s/Mpc

WMAP value = 71.0 ± 2.5 km/s/Mpc

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.

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.

One set of observations … many possible interpretations.

Hubble acknowledged the existence of bothboth Doppler shifts and cosmological redshifts.