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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.

 
 

Related Topics


Further Reading

  • Star and Their Spectra - James Kaler

Related Pages

Other Web Sites

  • 333
 
 

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

m = const - 2.5 log ls (1)
where ls is the luminosity (total light energy received) within the wavelength range under consideration, and the constant is adjusted to provide the "zero" value of the scale. In practice, the zero point is set at the value of the star Alpha Lyrae (Vega) although, technically, it is actually defined by a number of stars measured accurately by Johnson and Morgan (1953).

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

M = m - 5 log (d/10) (2)
d in parsecs.

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 mv and Mv for apparent and absolute magnitudes). However, magnitudes may be integrated over all wavelengths, when they are known as bolometric magnitudes, denoted mbol and Mbol respectively. These values express the total energy output of the star.

Mbol may be calculated from Mv 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.

Class Main Sequence Giants Supergiants
O3 -4.3 -4.2 -4.0
B0 -3.00 -2.9 -2.7
A0 -0.15 -0.24 -0.3
F0 -0.01 0.01 0.14
G0 -0.10 -0.13 -0.1
K0 -0.24 -0.42 -0.38
M0 -1.21 -1.28 -1.3
M8 -4.0    
Table 1: Table of bolometric corrections for some stars. After 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.


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