## Hubble constant

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## Hubble Constant

# HUBBLE CONSTANT

The Hubble constant (*H*_{0}) is a measure of the rate at which the universe is currently expanding. Together with the total energy and matter content of the universe, it sets the size of the observable universe and its age. The Hubble constant is one of the most important parameters in Big Bang cosmology: the square of the Hubble constant relates the total energy plus the matter density of the universe to its overall geometry. In addition, a comparison of the age derived from the Hubble constant and the age of the oldest stars in our galaxy provides constraints on the cosmological model that describes the dynamics of the expansion of the universe. The density of light elements (hydrogen, deuterium, helium, and lithum) synthesized after the Big Bang also depends on the expansion rate. Finally, the determination of numerous physical properties of all the galaxies and quasars (mass, luminosity, and energy density) requires knowledge of the Hubble constant.

The expansion of the universe was first established by the Carnegie Institute's astronomer, Edwin Hubble, in 1929. Determination of the Hubble constant requires the measurement of distances to galaxies *d* as well as their velocities of recession *υ* : *H*_{0} = υ/*d* . Velocities are simply measured from the observed shift of lines in the spectra of galaxies. (For sound, a similar phenomenon is the Doppler effect, in which, for example, the pitch of an oncoming police siren changes as the police car first passes and then recedes.) In the case of galaxies that are moving away from Earth, their light is shifted (and stretched) to redder wavelengths, a phenomenon referred to as redshift. The shift in wavelength is proportional to velocity.

Measuring distances presents a greater challenge. Distances to the nearest stars can be measured using a method called parallax, which uses the Earth's orbit as a basis for triangulation, permitting the distance to be calculated using simple, high-school geometry. Moving out to the nearest galaxies is accomplished using a type of star known as a Cepheid. There is a well-established relationship between these stars' luminosities and period of variation, discovered by astronomer Henrietta Leavitt in1908. This unique property allows the distance to be obtained using the inverse square law of radiation. This law states that the brightness of an object decreases in proportion to the square of its distance from the Earth. (One also experiences this effect in everyday life. This is the reason, for example, that car headlights in the distance appear fainter than those nearby.)

Using the Hubble Space Telescope, distances to galaxies with Cepheids can be measured out to the nearest massive cluster of galaxies—the Virgo cluster, located about 50 million light years away. Beyond this distance, other methods—for example, bright supernovae—are used to extend the extragalactic distance scale and measure the Hubble constant. These supernovae are believed to result from the explosion of a star near the end of its lifetime. The brightnesses of these objects are so great that for brief periods, they may be as luminous as an entire galaxy. Hence, they may be seen to enormous distances, about half the radius of the observable universe. A key project of the Hubble Space Telescope was the measurement of the Hubble constant to an accuracy of 10 percent. A number of different groups and methods have converged on a value of the Hubble constant in the range of about 60 to 70 km/sec/Mpc.

## Implications for Cosmology

The dynamics of the evolution of the universe are described within Einstein's general theory of relativity by what is referred to as the Friedmann equation. The Friedmann equation relates the Hubble parameter (*H,* where *H*_{0} is the value of this parameter at the current epoch), the average density of matter, the curvature of the universe, and the amount of energy associated with the vacuum of space (or dark energy). Einstein's original equation contained a term that he called the cosmological constant, a term that forced the universe to be static. When Edwin Hubble discovered the expansion of the universe, Einstein later referred to the cosmological constant as his greatest blunder. However, a discovery of a component of dark energy in the universe, based on observations of very distant supernovae, suggests that Einstein may have been correct after all.

One of the classical tests of cosmology is the comparison of timescales as given by the age of the oldest stars and the amount of time the universe has been expanding. The best estimates of the oldest stars in the universe are obtained from systems of stars within our galaxy known as globular clusters. Stars spend most of their lifetime undergoing nuclear burning of hydrogen into helium in their central cores. Detailed computer models of the evolution compared to observations of globular cluster stars yield ages of about 12 or 13 billion years. Integration of the Friedmann equation yields the expansion age of the universe. An accurate determination of the expansion age requires knowledge of the Hubble constant, as well as the average density of matter and the contribution of dark energy. Calculating the expansion age of the universe for a Hubble constant of 70, for a flat universe with no dark energy, yields an expansion age of only 9 billion years, younger than the oldest observed stars in the galaxy. This led to an earlier paradox with a universe that appeared to be younger than its oldest stars.

Much progress has been made toward measuring these individual cosmological parameters, yielding a Standard Model with a Hubble constant of 70, with matter contributing one-third and dark energy approximately two-thirds of the overall mass-energy density. The resulting age for the universe is then calculated to be 13 billion years, in very good agreement with the ages of the oldest stars. Taken together, the results from globular cluster ages and a value for a Hubble constant of 70 favor a model for the universe dominated by dark energy, consistent with the results from distant supernovae.

*See also:*Astrophysics; Big Bang; Cosmological Constant and Dark Energy; Cosmology

## Bibliography

Croswell, K. *The Universe at Midnight: Observations Illuminating the Cosmos* (Free Press, New York, 2001).

Ferguson, K. *Measuring the Universe* (Walker & Co., New York,
1999).

Freedman, W. "The Expansion Rate of the Universe." *Scientific American Quarterly***1** , 92–97 (1988).

*Wendy L. Freedman*

## Hubble Constant

# Hubble Constant

In the standard **Big Bang** model, the universe expands according to the Hubble law, a simple relation expressed as v=H_{o}d, where v is the velocity of a galaxy at a distance d, and H_{o} is the Hubble constant. The Hubble constant characterizes both the scale and age of the universe. A measurement of the Hubble constant, together with the ages of the oldest objects in the universe, and the average density of the universe, are all separately required to describe the universe's evolution. Measuring an accurate value of H_{o} was one of the motivating reasons for building the Hubble Space Telescope (HST).

The measurement of most distances in astronomy cannot be done directly because the size scales are simply too big. In general, the basis for estimating distances in astronomy is the inverse square radiation law, which states that the brightness of an object falls off in proportion to the square of its distance from us. (We all experience this effect in our own lives. A street light in the distance appears fainter than the one beside us.) Astronomers identify objects that exhibit a constant brightness (so-called "standard candles"), or those where the brightness is perhaps related to a quantity
that is independent of distance (for example, period of **oscillation** , rotation rate, or color). The standard candles must then be independently calibrated (to absolute physical units) so that true distances (in meters or megaparsecs, where 1 megaparsec = 3.08 × 10^{22} meters) can be determined using the inverse square law.

## Cepheid Variables

The most precise method for measuring distances is based on the observations of **Cepheid variables** , stars whose atmospheres pulsate regularly for periods ranging from 2 to about 100 days. Experimentally it has been established that the period of pulsation is correlated with the brightness of the star. High resolution is the key to discovering Cepheids in other galaxies—in other words, the telescope must have enough resolving power to distinguish Cepheids from other stars that contribute to the overall light of the galaxy. The resolution of the Hubble Space Telescope is about ten times better than can be generally obtained through Earth's turbulent atmosphere.

The reach of Cepheid variables as distance indicators is limited, however, even with the HST. For distances beyond 20 megaparsecs or so, brighter objects than ordinary stars are required; for example, bright supernovae or the brightnesses of entire galaxies. The absolute calibration for all of these methods is presently established using the Cepheid distance scale. A Key Project of the HST has provided Cepheid distances for a sample of galaxies useful for setting the absolute distance scale using these and other methods.

Until recently, a controversy has existed about the value of the Hubble constant, with published distances disagreeing by a factor of two. However the new Cepheid distances from the HST have provided a means of calibrating several distance methods. For the first time, to within an uncertainty of 10 percent, all of these methods are consistent with a value of the Hubble constant in the range of about 60 to 70 kilometers (37.28 to 43.5 miles) per second per megaparsec. This implies an age of the universe of between 13,000 and 15,000 million years.

see also Hubble, Edwin P. (volume 2); Hubble Space Telescope (volume 2); Age of the Universe (volume 2).

*Wendy L.* *Freedman*

### Bibliography

Barrow, John. D. *The Origin of the Universe.* New York: Basic Books, 1994.

Ferguson, Kitty. *Measuring the Universe.* New York: Walker & Co., 1999.

Freedman, Wendy L. "The Expansion Rate of the Universe." *Scientific American* 1(1988):92-97.