Todd Thompson
Department of Astronomy
The Ohio State University

Key Ideas

Hubble's Law

Galaxies are receding from us.

Recession velocity gets larger with distance.

The Hubble Parameter (H₀)

Measures the present-day rate of expansion of the Universe.

Cosmological Redshifts

Due to the expansion of space

Redshift distances

Redshift maps of the Universe

Key Ideas

V = H₀ d

Discovery of Expansion

• Measured radial velocities from spectra of 25 galaxies.

Found:

• 21 of the 25 show a redshift
• speeds of some >2000 km/sec

Most galaxies are rapidly receding from us.

Hubble's Discovery

• Used cepheids for Andromeda and Local Group
• Used brightest stars in the others
• Compared distances with recession velocities.

Discovered:

• Recession velocity gets larger with distance.

Systematic expansion of the Universe.

Edwin Hubble's 1929 expansion data (Graphic by R. Pogge)

Refined version by Hubble & Humason in 1931

[Based on the data in the original Astrophysical Journal papers.]

Hubble's Law

v = recession velocity in km/sec

d = distance in Mpc

H₀ = expansion rate today (Hubble Parameter)

In words:

The more distant a galaxy, the faster its recession velocity.

Interpretation

• The further away a galaxy is from us, the faster it appears to be moving away from us.
• Hubble Parameter: Rate of expansion of the Universe
• H₀ is the value of the Hubble Parameter today.

Comments:

• Hubble's Law is empirical - based only on data in its original form.
• Not an exact law.

Nature of the Expansion

• All observers in different galaxies see the same expansion around them.
• No center - all observers appear to be at the center.

What is the recession velocity?

• NOT motion through space...
• Expansion of spacetime: galaxies carried along.

As the Universe get 2x larger, the distances between galaxies get 2x larger.

Note:

While the distances between galaxies increase over time, the sizes of the galaxies remain the same. This is because galaxies are bound together by gravitation locally, and so do not share in the global expansion of spacetime around them.

Hubble Parameter: H₀

• H₀ = 70 +/- 7 km/sec/Mpc
• Best measurement to date is from the Hubble Key Project to measure Cepheids in nearby galaxies.

H₀ is very hard to measure

• Recession speeds are easy to measure from the shifts of spectral lines.
• But, distances are very hard to measure.
• Galaxies also have extra (non-cosmological) motions that must be taken into account.

Cosmological Redshifts

The recession is quantified in terms of the "cosmological redshift" of the galaxy, z:

As the universe expands, light waves get stretched out:

• Stretching makes the wavelength longer, hence redder
• Result is a "Cosmological Redshift"

Redshift Distances

z = cosmological redshift

c = speed of light

Limitations:

• Value of H₀ is only known to ~10%

• Random motions of galaxies affects measurements of z for nearby galaxies (random motions are comparable to recession velocity)

• At large distances, the conversion between cosmological redshift and distance is much more complicated, depending on the geometry of spacetime and the expansion history of the Universe.

Nonetheless, because cosmological redshift is a direct observable related to distance, it used as a surrogate for distance, especially for distant galaxies.

Mapping the Universe

The largest map to date is from the 2dF Galaxy Redshift Survey, which includes about 220,000 galaxies:

• Reveals sheets and filaments of galaxies surrounding great voids.
• Depth is about 500-600 Mpc
• Relative distances are good, but the absolute scale is good to only about 10%

Sloan Digital Sky Survey

Making images of 1/4 of the sky in 5 colors:

• Accurate positions and photometry for a few 100 Million stars, galaxies, & quasars.

Redshift Survey:

• 1 Million galaxy redshifts
• 100,000 quasar redshifts

One of the results will be a 3D map of a large segment of the local universe.