Stellar Magnitude

Abstract

The "brightness" of a star is usually expressed as a magnitude. This page outlines the main measures of stellar brightness, introduces the magnitude scale, and explains the difference between apparent and absolute magnitudes.

Keywords: stellar birghtness, magnitude, apparent magnitude, absolute magnitude, bolometric magnitude

Introduction

The "brightness" of a star is usually expressed as a magnitude. The magnitude scale, like the sensitivity of the naked eye, is logarithmic and, by convention, defined so that brighter stars have smaller magnitude values. Thus a first magnitude star is very bright, a sixth magnitude star is at the limit of normal vision.

The brightness of a star is diminished by distance. By including corrections for the distances to stars, where known, absolute magnitudes provide a means to compare the "real" brightness of stars at difference distances.

The human eye is sensitive to only a narrow band of radiation wavelengths. Some wavelengths are filtered out by the earth's atmosphere, though others are available and detectable by instruments at the earth's surface. Still others can be measured from high altitude instruments carried by balloons or satellites. Knowing a small proportion of the wavelengths radiated from a star, it is possible to reconstruct the entire continuum, providing an estimate of the bolometric magnitude.

Apparent Magnitude

The brightness perceived at the surface of the Earth (corrected for atmospheric effects) is known as the apparent magnitude and is given by

Absolute Magnitude

The apparent magnitude of a star is diminished if its distance is great. Absolute magnitude is the apparent magnitude that a star would have if it were located at a standard distance of 10 parsecs from the Earth. The absolute magnitude, M, is related to the apparent magnitude, m, and true distance to the star, d, by

Bolometric Magnitude

Apparent and absolute magnitudes are measured by instruments sensitive to a small wavelength interval of the radiation continuum, such as the visual band: approximately 400 nm/7 ´ 10¹⁴ Hz to 700 nm/4 ´ 10¹⁴ Hz (hence m_v and M_v for apparent and absolute magnitudes). However, magnitudes may be integrated over all wavelengths, when they are known as bolometric magnitudes, denoted m_bol and M_bol respectively. These values express the total energy output of the star.

M_bol may be calculated from M_v for a given star by adding the appropriate bolometric correction characteristic for the type of star. Table 1 provides an abbreviated list of such corrections; for a more complete table showing additional classes, refer to Kaler 1997, p. 263.

References

Johnson, H.L.; Morgan, W.W. 1953: Astrophysical Journal, 117: 313.

Kaler, James B. 1997: Stars and Their Spectra. Cambridge. (Corrected paperback ed.) 300 pp.