Hubble Constant

The Hubble Constant (Ho) is one of the most important numbers in cosmology because it is needed to estimate the size and age of the Universe. This long-sought number indicates the rate at which the universe is expanding, from the primordial "Big Bang". The Hubble Constant can be used to determine the intrinsic brightness and masses of stars in nearby galaxies, examine those same properties in more distant galaxies and galaxy clusters, deduce the amount of dark matter present in the universe, obtain the scale size of faraway galaxy clusters, and serve as a test for theoretical cosmological models.

However, obtaining a true value for Ho is very complicated. Astronomers need two measurements. 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. Reliable "distance indicators," such as variable stars and supernovae, must be found in galaxies. The value of Ho itself must be cautiously derived from a sample of galaxies that are far enough away that motions due to local gravitational influences are negligibly small. 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. (A megaparsec is 3.26 million light-years.) 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.

Another way to find the Hubble constant is to analyze gravitational lensing of a multiply-imaged quasar. This was first done by Sjur Refsdal of Hamburg University in 1964. This technique is more elegant (and takes less steps) than most techniques.

Quasars change brightness for a variety of reasons. In a multiply-imaged quasar, the second quasar changes as well, but this is delayed. This delay is caused by lensing asymmetry, by which each image takes path of different lengths, and also by the gravitational field of the lens, which reduces parent speed of light.

Models of the lens can estimate the shape and mass distribution of the lens, and from that model and the layout of the images astronomers can estimate the time delay betwenn the events on the quasar images as fraction of light travel time. They can then divide the time delay by that fraction to find the time for the light to travel to the earth, from which they can get the distance. Traditional methods involving redshift measure receding speed of the quasar. The Hubble constant can be calculated as the constant of proportionality between distance and velocity. The resulting value for the Hubble constant obtained by employing a detailed lens model by physicists Grogin and Narayan was 67 +- 13 km/(sec*parsec)

The estimate from this method is slightly lower than other estimated values, but it is within error bars. The biggest uncertainty is in the mass distribution of lens.