Magnitude is a unitless measure of the brightness of a star in a defined passband, often in the visible or infrared spectrum, but sometimes across all wavelengths.
Magnitude Scale
The magnitude scale is logarithmic and defined such that each step of one magnitude changes the brightness by a factor of the fifth root of 100, ~2.512. (1st magnitude star is 100 times brighter than a 6th magnitude star).
Types of Magnitude
Astronomers use two different definitions of magnitude: apparent magnitude and absolute magnitude.
Apparent Magnitude
Apparent magnitude is a measure of the brightness of a star or other astronomical object observed from the Earth. An object’s apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object’s light caused by interstellar dust along the line of sight to the observer.
The brightest astronomical objects have negative apparent magnitudes: for example, Venus at -4.2 and Sirius at -1.46.
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The faintest stars visible with the naked eye on the darkest night have apparent magnitudes of about +6.5. The apparent magnitudes of known objects range from the Sun at -26.7 to objects in deep Hubble Space Telescope images of around magnitude +30.
Apparent magnitude is usually denoted by ‘m’.
Let the brightness of the first magnitude star be B1, the second magnitude star be B2,………….., 6th magnitude star be B6.
Then
Consider two stars with brightness Bm and Bn, with m and n being their apparent magnitudes with n>m.
Apparent magnitude is inversely proportional to the square of the distance of the object from the Earth.
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Absolute Magnitude
Absolute magnitude is another measure of the brightness of a star/astronomical object. It is defined as the object’s apparent magnitude as seen from a specific distance, conventionally 10 parsecs (32.6 ly).
Absolute magnitude is usually denoted by ‘M’.
The more luminous an object, the smaller the numerical value of its absolute magnitude.
The Sun has an absolute magnitude of +4.83 in the visual band, whereas Milky Way has an absolute magnitude of -20.8.
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Let the apparent magnitude of a star be m and its absolute magnitude is M.
Where m is the apparent magnitude, M is the absolute magnitude and D is the distance in parsecs. Apparent or absolute bolometric magnitude mbol is a measure of an object’s apparent or absolute brightness integrated over all wavelengths of the electromagnetic spectrum. The zero-point of the apparent bolometric magnitude of 0 mag is equivalent to a received irradiance of 2.518×10-8watts/meter square.
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