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