absolute magnitude

In astronomy , absolute magnitude ( M ) is the apparent magnitude , m , that an object would have if it were at a distance of 10 parsecs (about 32,616 light years , or 3 × 10 14 kilometers ) in completely empty space with no interstellar absorption.

To define the absolute magnitude, it is necessary to specify the type of electromagnetic radiation that is being measured. The absolute magnitude is generally deduced from the visual magnitude measured with a filter V, expressed as M v . If it is defined for other wavelengths, it will have different subscripts, and if the radiation at all wavelengths is considered, it is called the bolometric absolute magnitude (M bol ).

The absolute magnitude can be found, if the apparent magnitude ( ) and the distance ( \$ d \$ ) in parsec are known by means of: md

M = m + 5 – 5 × log d [1]

or if the parallax (π) is known from

M = m + 5 + 5 × log π   [2]

It should be noted that in formula [2] logarithms with negative characteristic and positive mantissa should be used, but negative logarithms. For example, for Vega (α Lyr) it is m = +0.03 and π = 0 ”123; When the logarithm of π has the negative characteristic and the positive mantissa, we will write —1 + 0.08991 = —0.91009 and find

M = 0.03 + 5 + (5 × (—0.91009)) = 0.48

unique in its class, it is the Sun ; its visual magnitude is m = —26.75, but the solar parallax is the one corresponding to the astronomical unit of distance, which is contained 206264,806248 times in the parsec, so we will put this number of seconds, that is, π = 206264 ”806248, whereupon

M = —26.75 + 5 + 5 × log 206264,806248 = —21.75 + 5 × 5.31443 = —21.75 + 26.57 = + 4.81

The absolute magnitude   is the conventional magnitude the star would have if its distance were brought to 10pc.
For this, the apparent brightness of the star and its distance   from Earth are related. In this way, the luminosity   of the star that measures the total radiated power is obtained:

The flux of a star varies with the inverse of the square of the distance, therefore in a given magnitude system, the relationship between the absolute and apparent magnitudes is written :

Apparent and absolute magnitudes

 Object (pc) Sun -26.7 4.9 Sirius -1.45 1.4 2.7 Vega 0.00 0.5 8.1 Antares 1.00 -4.8 130 Mimosa 1.26 -4.7 150 Adhara 1.50 -5.0 200

The distance module

The quantity   is called the distance module . The module links the distance to a difference in magnitude. Indicates the distance on a logarithmic scale.

Distance module

 Object distance module distance to the Sun (pc) reference 0 10 Hyades cluster 3.3 48 The Magellanic Clouds 18.5 50,000 The Andromeda Galaxy 24.1 890,000

The distance module is null, by definition, for a distance of 10 pc; It is worth 5 for a distance of 100 pc, 10 for a distance of 1000 pc.

Absorption correction

To go from apparent magnitude to absolute magnitude, one must correct, in addition to distance, the effects due to interstellar absorption. This absorption is caused by various elements (dust, gas) present in the line of sight. The absolute magnitude is expressed as a function of the apparent magnitude by:

The absorption term   must be positive; not taking it into account leads to overestimating the absolute magnitude, that is, to underestimating the luminosity of the object.

Bolometric magnitude

Contrary to monochromatic magnitude, bolometric magnitude measures radiated energy across the electromagnetic spectrum. Measuring such magnitude is not easy. It is generally obtained by extrapolation of the absolute magnitude measured in various spectral bands.