Absolute magnitude

Definition

By definition of the international astronomical Union, “the absolute magnitude of an object is the magnitude which would see an observer located at a distance from exactly 10 Parsec S: 32,6 [[light-year|light-years]] of this object”.

The absolute magnitude is thus a logarithmic scale directly related to the luminosity of the star. The definition absolute magnitude is written in mathematical terms:

M = -2,5 \, \ log L + C

where L is the luminosity of star and C a constant. Being a reversed logarithmic scale, plus a star is luminous, plus its magnitude is weak .

According to whether the luminosity is calculated on a spectral Bande blue B (around 436 Nm) or visible V (in the neighborhoods of 545 Nm), the absolute magnitude is noted M_B or M_V . The constant is today selected such as the absolute magnitudes of the Sun in the bands B and V are M_B = 5,48 and M_V = 4,83.

When one considers the totality of the electromagnetic Specter, about the waves radio with the Gamma rays S, and not only a given spectral band, one speaks about bolometric luminosity, and thus about bolometric Magnitude.

The absolute magnitudes of stars generally extend from -10 to +17 according to their spectral Type: a blue supergéante has an absolute magnitude going down up to -10 while that of a Naine red can go up to +17. The Sun, with an absolute magnitude of +4,8 is about halfway located these two extremes.

Apparent magnitude and distance

The comparison between the absolute magnitude and the Magnitude connects (which is the magnitude observed indeed on Earth) allows an estimate of the distance from the object. According to the decrease of the luminosity with the square of the distance, one obtains:

$m - M = 5 \, \ log (D) - 5$

where $m$ is the apparent real magnitude, $M$ the absolute magnitude and $D$ the distance expressed in Parsec driven S. the value $\ = m - M$ is also called Module of distance, this last being more often used for the extragalactic objects.

To have the absolute magnitude, one needs stellar models, and to know the temperature of the star (which can be obtained starting from the Indice of color, which is not other than the difference the apparent magnitudes of an object in two different spectral bands).

In practice, the only easily accessible quantity is obviously the magnitude observed, which is in fact the combination apparent magnitude and the interstellar Absorption: $m = m_ {R} = m_ {obs} - A$ , where $A$ is the absorption.

The knowledge of absorption is often critical. Absorption modifies the real luminosity of the object, because of the diffusion of the light by the grains of interstellar Poussière. The chaotic distribution of the grains in space makes extremely difficult the estimate of the absorption interstellar, since that which is valid in a direction given for a given object, can be significantly different for star from at side (by making the assumption that the two stars are at the same distance). Moreover, because of the effect of diffusion, absorption depends on the Wavelength, and is thus a chromatic effect (see detailed article).

Therefore, in practice, the equation is written as follows:

$m_ {obs} - M - has = 5 \, \ log (D) - 5$

and only the value of $m_ {obs}$ is easy to measure.

Absolute magnitude of the objects of the Solar system

In this particular case, the distance from reference is not 10 parsec, but a astronomical Unité.

The objects of the Solar system like the Planet S, the Comet S or the Astéroïde S do nothing but think the light that they receive sun and their apparent magnitude thus depends, not only of their distance of the Earth, but also of their distance to the Sun. The absolute magnitude of these objects is thus defined as their apparent magnitude if they were located at a astronomical Unité sun and a astronomical Unité of the ground, while being with a phase of zero degree (“full moon”, all visible surface since the ground is enlightened).

For a body located at a distance $r$ of the Earth and $a$ of the sun, the relation between its magnitude (relative) $m$ and its absolute magnitude, noted $H$ , is given by the formula:

$m = H + 5 \, \ log (R) + 5 \, \ log (a) - 2,5 \, \ log \ chi$

where $\ chi$ represents the phase of the object ( $\ chi = 1$ for full moon, 0,5 for a district and 0 for the new moon); $r$ and $a$ must be expressed in astronomical units.

The situation described by the definition absolute magnitude is physically impossible: the phase is of 30 degrees for a spherical star with an astronomical unit of the Earth and sun. It must be regarded as a reference - and it is to give the good order of magnitude for the result observed.

Very luminous celestial objects

Many stars visible with the naked eye have an absolute magnitude such as these stars, if they were indeed distant from only 10 parsec, would be more brilliant than planets. It is the case of the supergéantes Rigel (- 7,0), Deneb (- 7,2), Naos (- 7,3) and Bételgeuse (- 5,6). As comparison, the object more the brilliance of the sky after the Sun (which has an apparent magnitude of -26.73) is Venus with an apparent magnitude of -4,3; full the the Moon is apparent magnitude -12.

The last Celestial object of which the magnitude connects was comparable with the absolute magnitude of the three objects above was a Supernova which occurred in 1054 (and named SN 1054) and of which today there remains only a Nébuleuse planet gear, the Nébuleuse of the Crab, and a Pulsar. The astronomers of the time reported that the luminosity of this object was so large that they could read in middle of the night, to see the shadows of its light and to observe it in full day.

See too

Magnitude connects
bolometric Magnitude
Indice of color
Excès of interstellar color
Absorption
Diagramme of Hertzsprung-Russell, showing the distribution of stars according to their absolute magnitude and their spectral characteristics.
Module of distance

Simple: Absolute magnitude

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