The Hubble Law

The Hubble constant H is one of the most important numbers in cosmology because it may be used to estimate the size and age of the Universe. It indicates the rate at which the universe is expanding. Although the Hubble "constant" is not really constant because it changes with time (and therefore should probably more properly be called the "Hubble parameter"). The Hubble constant is often written with a subscript "0" to denote explicitly that it is the value at the present time, but we shall not do so.

FIGURE: The image above, taken with the Advanced Camera for Surveys (ACS) of the Hubble Space Telescope shows many galaxies (most of the fuzzy patches are galaxies containing billions of stars) that are billions of light years away and are receding from us at high velocities.

The Hubble Expansion Law

In 1929, Edwin Hubble announced that almost all galaxies appeared to be moving away from us. This phenomenon was observed as a redshift of a galaxy's spectrum. This redshift appeared to have a larger displacement for faint, presumably further, galaxies. Hence, the farther a galaxy, the faster it is receding from Earth. The Hubble constant is given by

H = v/d
where v is the galaxy's radial outward velocity, d is the galaxy's distance from earth, and H is the current value of the Hubble constant.

Determining the Hubble Constant

Obtaining a true value for H is complicated. Two measurements are required. First, spectroscopic observations reveal the galaxy's redshift, indicating its radial velocity. The second measurement, the most difficult value to determine, is the galaxy's precise distance from Earth. The value of H itself must be derived from a sample of galaxies that are far enough away that motions due to local gravitational influences are negligibly small (these are called peculiar motion, and they represent deviations from the Hubble Law).

Units for Hubble's Constant

The units of the Hubble constant are "kilometers per second per megaparsec." In other words, for each megaparsec of distance, the velocity of a distant object appears to increase by some value. For example, if the Hubble constant was determined to be 50 km/s/Mpc, a galaxy at 10 Mpc would have a redshift corresponding to a radial velocity of 500 km/s.

Current Value of the Hubble Constant

The value of the Hubble constant initially obtained by Hubble was around 500 km/s/Mpc, and has since been radically revised because initial assumptions about stars yielded underestimated distances. For the past three decades, there have been two major lines of investigation into the Hubble constant. One team, associated with Allan Sandage of the Carnegie Institutions, has derived a value for H around 50 km/s/Mpc. The other team, associated with Gerard DeVaucouleurs of the University of Texas, has obtained values that indicate H to be around 100 km/s/Mpc.

This discrepency is not trivial, and has a dramatic effect on age estimates for the distance to far-off galaxies as well as the actual age of the Universe.

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