Apparent Magnitude

Contents

Introduction

Apparent magnitude is a measure of how much energy from a star reaches Earth. The term "magnitude" could be misleading, since it is a star's brightness that is being measured, not its size. All stars are points of light to the unaided eye. Each star is assigned a numerical magnitude based on its brightness, with smaller numbers indicating brighter stars.

Magnitudes were invented by classical Greek astronomers, who noticed that all the visible stars could be divided into six classes, such that the stars within each class appeared about equally bright, but stars in neighboring classes differed noticeably in brightness. The brightest stars were classified as "first magnitude", the next brightest "second magnitude", and down to the faintest, which were classed as "sixth magnitude."

With the development of modern light measurement techniques, it became evident that not all stars in the same magnitude class are equally bright. In addition, some stars are much brighter than the average first-magnitude star. And, of course, with the invention of the telescope, it became possible to see stars much fainter than sixth magnitude. These problems were addressed by including decimal numbers, zero, negative numbers, and magnitudes larger than six and, most importantly, by developing a mathematical formula for magnitudes.

The modern definition of magnitude involves a comparison between two stars, of which one can be a star defined to have a magnitude of zero. If the stars are numberd 1 and 2, their magnitudes are m₁ and m₂, and the radiative fluxes (power per unit area) from them are f₁ and f₂, then the magnitude difference between them is given by:

m₁ - m₂ = -2.5 log (f₁/f₂)

(the logarithm is to the base 10). Thus, the magnitude scale is logarithmic, just as is the decibel scale for describing the intensity of sound, because of the logarithmic response of human senses. Each difference of 5 magnitudes corresponds to a factor of 100, or each difference of one magnitude corresponds to a factor of the fifth root of 100 (100^0.2), which is 2.512. On the other hand, the number in the defining equation above is exactly 2.5. The negative sign in the definition reflects the fact that smaller numbers refer to brighter stars.

Magnitudes have to refer to the region of the spectrum that is actually measured, usually a region that is selected by a filter. In that case, the central wavelength of the region used is indicated by a subscript on the symbols for the magnitudes and fluxes, and the units of flux become power received per unit area and per unit wavelength interval in the spectrum, for example erg/s/cm²/Å.

A set of magnitudes defined by a partciular set of filters is called a photometric system. (Photometric systems can also be defined by the magnitudes of a set of standard stars, but that is another topic.) The system in most common use is called UBV, after the letters designating its three filters: U for ultraviolet, B for blue, and V for visual, or yellow (the color to which the human eye is most sensitive). It was first developed by H. L. Johnson and W. W. Morgan (1953, The Astrophysical Journal, vol. 117, p. 313), and their system is still used, but modified and extended versions of their systems have also been developed since then. Apparent magnitudes in the UBV system are also symbolized by U, B, and V, and colors of stars are described by color indices, or magnitude differences (which correspond to flux ratios) U-B and B-V.

A magnitude including all the energy in a star's emitted spectrum is called a bolometric magnitude after an older type of radiation detector called a bolometer, which undergoes a measurable temperature rise when any radiation within a broad range of wavelengths falls on it. An apparent bolomeric magnitude is symbolized by m_bol. Because some parts of the radiation of most stars are blocked by the Earth's atmosphere or by the interstellar medium, bolometric magnitudes cannot usually be directly measured, but must be calculated. The exceptions are the Sun and a few of the nearest stars.

Magnitudes are used not only for stars but also for other point sources, such as asteroids, and for the total brightness of extended sources such as galaxies. Catalogued magnitudes refer to the amount of energy that would be measured above the Earth's atmosphere.