Measuring the Brightness of Stars

Photometry dates back more than 2,000 years to when the Greek astronomer Hipparchos divided the naked-eye stars into six brightness classes. The brightest visible stars he called stars of the first magnitude and the faintest visible he called stars of the sixth magnitude. Pogson in 1856 defined the magnitude scale so that a difference of 5 magnitudes was exactly a factor of 100 in brightness, which had earlier been shown by Herschel to be roughly the intensity ratio of first to sixth magnitude stars. Pogson defined his scale to be a logarithmic one where the difference in magnitude of two stars (m₁ and m₂) is directly linked to the ratio of their intensities (I₁ and I₂) by

m₁ - m₂='-2.5' log (I₁ / I₂)

The human eye can detect differences of brightness of about 20% or 0.2 magnitudes and with training and use of special techniques this can be reduced to 10%.

The apparent brightness of any object in the sky is due to its intrinsic brightness and to its distance. For instance, the brightest known object in the Universe is a very faint quasar as seen from the Earth, and can only be seen with a large telescope. If it were as close as the nearest galaxy, it would be easily visible to the naked-eye.

After 1850, photography was used to determine the brightnesses of stars as the density and size of the image is directly related to the brightness of the star. It was soon apparent, however, that the photographic magnitudes did not agree very well with those obtained visually. The reason for this is that early photographs responded mainly to blue light whereas the eye responds best to greenish-yellow. Stars have different ratios in the amount of light they emit in these different colours; some stars appear reddish, others bluish and this difference causes the determined brightnesses to be different. With modern photographic plates, which have been developed specially for astronomy, and filters to isolate different regions of the spectrum astronomers can use large field telescopes to obtain plates covering several square degrees of the sky. Such plates can contain a million images of stars and galaxies which can be measured by computer-controlled automatic measuring machines, such as the APM at Cambridge.

During this century photoconductive cells and later, and more importantly, photoelectric devices were developed. These, used with sensitive amplifiers, now detect each individual photon received by the telescope and by counting these, astronomers can directly compare the light intensities received from individual stars. The modern successor to the photographic plate, the Charge Coupled Device (CCD), is capable of measuring individual photons from stars and galaxies in fields of a few square arcminutes. For many applications it is supplanting the photoelectric photometer.

Other devices are available which can measure the brightness of an astronomical object in X-rays, the ultraviolet, the infrared and in radio-waves. Some of these have to be used outside the Earth's atmosphere, in rockets or satellites, because the radiation does not pass through the atmosphere.

By using filters to isolate particular parts of the spectrum, astronomers can make photometric measurements which enable them to determine the intrinsic brightness, the distance, chemical composition and age of individual stars and galaxies and discover quasars near the limit of the observable universe.

Stellar Evolution

A composite H-R diagram. The magnitudes and temperatures (measured by photometry) of stars in several star clusters are plotted. The position of a group of points in the diagram can tell us how old that particular star cluster is. Much of our knowledge of how stars change as they grow older has been derived from photometry of stars grouped in clusters. These stars are believed to have been formed at almost the same time from one gas cloud. They all, therefore, have almost identical distances, ages and compositions. The observation of all the members of a cluster gives us an instant picture of what a large number of stars are like at one particular age. By combining pictures for different clusters of different ages we can deduce how a star's properties change with age. The classical diagram of this kind is shown above. It is known that even the very fastest phases of the evolution of the stars take thousands of years and it is likely that the Sun will remain essentially the same for more than 5 thousand million years.

Variable Stars

At this stage, the total brightness of the binary system is at a maximum because neither star is eclipsing the other. When the dim star revolves in front of the bright one, the brightness dims to a minimum. When the bright star revolves in front of the dim one, a smaller dip in brightness is observed. Image credit: Duncan Kopernicki. Our Sun is believed to be of constant brightness (although it may vary very slightly). Many other stars, however, change their brightness quite markedly. By studying the manner in which they change, astronomers can learn more about the details of stellar evolution and the internal structure of stars.

Many stars are not single stars, like the Sun, but double. The two component stars circle one another and if the plane of their mutual orbit is near the line of sight, one star will pass in front of the other thus eclipsing it and giving a reduction in the observed total brightness. Due to the very large distances to stars, the two stars cannot be separated even in the biggest telescopes but by an analysis of the shape of the light variation the masses and sizes of the two individual stars may be found.

Some stars are intrinsically variable; that is, the variability is due to internal causes rather than external ones. The cepheid variables are members of a very important class of variables. These are stars that brighten and fade because of a cyclic expansion and contraction of the whole star.

The Cepheid period-luminosity relationship. Cepheid stars with long pulsation periods are intrinsically brighter than stars with short periods. Measurement of the period allows us to measure the star's brightness and, hence, its distance from the Earth. Image credit: Royal Observatory Greenwich/National Maritime Museum. In 1908 Miss Leavitt noted that in one of the Magellanic clouds (which are satellite galaxies to the Milky Way), there was a strong relationship between the brightness of the cepheids and their period of pulsation. This period-luminosity relation, as it is called, has been studied in great detail and is now one of the most important methods used for determining the distances to other galaxies.