In astronomy, absolute magnitude () is a measure of the luminosity of a celestial object on an inverse logarithmic astronomical magnitude scale; the more luminous (intrinsically bright) an object, the lower its magnitude number. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly , without extinction (or dimming) of its light due to absorption by interstellar matter and cosmic dust. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared among each other on a magnitude scale. For Solar System bodies that shine in reflected light, a different definition of absolute magnitude (H) is used, based on a standard reference distance of one astronomical unit.
Absolute magnitudes of stars generally range from approximately −10 to +20. The absolute magnitudes of galaxies can be much lower (brighter).
The more luminous an object, the smaller the numerical value of its absolute magnitude. A difference of 5 magnitudes between the absolute magnitudes of two objects corresponds to a ratio of 100 in their luminosities, and a difference of n magnitudes in absolute magnitude corresponds to a luminosity ratio of 100n/5. For example, a star of absolute magnitude MV = 3.0 would be 100 times as luminous as a star of absolute magnitude MV = 8.0 as measured in the V filter band. The Sun has absolute magnitude MV = +4.83. Highly luminous objects can have negative absolute magnitudes: for example, the Milky Way galaxy has an absolute B magnitude of about −20.8.
As with all astronomical magnitudes, the absolute magnitude can be specified for different wavelength ranges corresponding to specified filter bands or passbands; for stars a commonly quoted absolute magnitude is the absolute visual magnitude, which uses the visual (V) band of the spectrum (in the UBV photometric system). Absolute magnitudes are denoted by a capital M, with a subscript representing the filter band used for measurement, such as MV for absolute magnitude in the V band.
An object's absolute bolometric magnitude (Mbol) represents its total luminosity over all wavelengths, rather than in a single filter band, as expressed on a logarithmic magnitude scale. To convert from an absolute magnitude in a specific filter band to absolute bolometric magnitude, a bolometric correction (BC) is applied.
Stars and galaxies In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 light-years, 308.57 petameters or 308.57 trillion kilometres). A star at 10 parsecs has a parallax of 0.1″ (100 milliarcseconds). Galaxies (and other extended objects) are much larger than 10 parsecs; their light is radiated over an extended patch of sky, and their overall brightness cannot be directly observed from relatively short distances, but the same convention is used. A galaxy's magnitude is defined by measuring all the light radiated over the entire object, treating that integrated brightness as the brightness of a single point-like or star-like source, and computing the magnitude of that point-like source as it would appear if observed at the standard 10 parsecs distance. Consequently, the absolute magnitude of any object equals the apparent magnitude it would have if it were 10 parsecs away.
Some stars visible to the naked eye have such a low absolute magnitude that they would appear bright enough to outshine the planets and cast shadows if they were at 10 parsecs from the Earth. Examples include Rigel (−7.8), Deneb (−8.4), Naos (−6.2), and Betelgeuse (−5.8). For comparison, Sirius has an absolute magnitude of only 1.4, which is still brighter than the Sun, whose absolute visual magnitude is 4.83. The Sun's absolute bolometric magnitude is set arbitrarily, usually at 4.75. Absolute magnitudes of stars generally range from approximately −10 to +20. The absolute magnitudes of galaxies can be much lower (brighter). For example, the giant elliptical galaxy M87 has an absolute magnitude of −22 (i.e. as bright as about 60,000 stars of magnitude −10). Some active galactic nuclei (quasars like CTA-102) can reach absolute magnitudes in excess of −32, making them the most luminous persistent objects in the observable universe, although these objects can vary in brightness over astronomically short timescales. At the extreme end, the optical afterglow of the gamma ray burst GRB 080319B reached, according to one paper, an absolute r magnitude brighter than −38 for a few tens of seconds.
Apparent magnitude
The Greek astronomer Hipparchus established a numerical scale to describe the brightness of each star appearing in the sky. The brightest stars in the sky were assigned an apparent magnitude , and the dimmest stars visible to the naked eye are assigned . The difference between them corresponds to a factor of 100 in brightness. For objects within the immediate neighborhood of the Sun, the absolute magnitude and apparent magnitude from any distance (in parsecs, with 1 pc = 3.2616 light-years) are related by
where is the radiant flux measured at distance (in parsecs), the radiant flux measured at distance . Using the common logarithm, the equation can be written as
where it is assumed that extinction from gas and dust is negligible. Typical extinction rates within the Milky Way galaxy are 1 to 2 magnitudes per kiloparsec, when dark clouds are taken into account.
For objects at very large distances (outside the Milky Way) the luminosity distance (distance defined using luminosity measurements) must be used instead of , because the Euclidean approximation is invalid for distant objects. Instead, general relativity must be taken into account. Moreover, the cosmological redshift complicates the relationship between absolute and apparent magnitude, because the radiation observed was shifted into the red range of the spectrum. To compare the magnitudes of very distant objects with those of local objects, a K correction might have to be applied to the magnitudes of the distant objects.
The absolute magnitude can also be written in terms of the apparent magnitude and stellar parallax :
or using apparent magnitude and distance modulus :
Examples Rigel has a visual magnitude of 0.12 and distance of about 860 light-years:
Vega has a parallax of 0.129″, and an apparent magnitude of 0.03:
The Black Eye Galaxy has a visual magnitude of 9.36 and a distance modulus of 31.06:
Bolometric magnitude
The absolute bolometric magnitude () takes into account electromagnetic radiation at all wavelengths. It includes those unobserved due to instrumental passband, the Earth's atmospheric absorption, and extinction by interstellar dust. It is defined based on the luminosity of the stars. In the case of stars with few observations, it must be computed assuming an effective temperature.
Classically, the difference in bolometric magnitude is related to the luminosity ratio according to:
which makes by inversion:
where is the Sun's luminosity (bolometric luminosity) is the star's luminosity (bolometric luminosity) is the bolometric magnitude of the Sun is the bolometric magnitude of the star.
In August 2015, the International Astronomical Union passed Resolution B2 defining the zero points of the absolute and apparent bolometric magnitude scales in SI units for power (watts) and irradiance (W/m2), respectively. Although bolometric magnitudes had been used by astronomers for many decades, there had been systematic differences in the absolute magnitude-luminosity scales presented in various astronomical references, and no international standardization. This led to systematic differences in bolometric corrections scales. Combined with incorrect assumed absolute bolometric magnitudes for the Sun, this could lead to systematic errors in estimated stellar luminosities (and other stellar properties, such as radii or ages, which rely on stellar luminosity to be calculated).
Resolution B2 defines an absolute bolometric magnitude scale where corresponds to luminosity , with the zero point luminosity set such that the Sun (with nominal luminosity ) corresponds to absolute bolometric magnitude . Placing a radiation source (e.g. star) at the standard distance of 10 parsecs, it follows that the zero point of the apparent bolometric magnitude scale corresponds to irradiance . Using the IAU 2015 scale, the nominal total solar irradiance ("solar constant") measured at 1 astronomical unit () corresponds to an apparent bolometric magnitude of the Sun of .
Following Resolution B2, the relation between a star's absolute bolometric magnitude and its luminosity is no longer directly tied to the Sun's (variable) luminosity:
where is the star's luminosity (bolometric luminosity) in watts is the zero point luminosity is the bolometric magnitude of the star
The new IAU absolute magnitude scale permanently disconnects the scale from the variable Sun. However, on this SI power scale, the nominal solar luminosity corresponds closely to , a value that was commonly adopted by astronomers before the 2015 IAU resolution.
The luminosity of the star in watts can be calculated as a function of its absolute bolometric magnitude as:
using the variables as defined previously.
Solar System bodies ()
+ Abs Mag (H)and Diameterfor asteroids(albedo=0.14)CNEOS Asteroid Size Estimator H Diameter 10 36 km 12.7 10 km 15 3.6 km 17.7 1 km 19.2 510 m 20 360 m 22 140 m 22.7 100 m 24.2 51 m 25 36 m 26.6 17 m 27.7 10 m 30 3.6 m 32.7 1 m
For planets and asteroids, a definition of absolute magnitude that is more meaningful for non-stellar objects is used. The absolute magnitude, commonly called , is defined as the apparent magnitude that the object would have if it were one astronomical unit (AU) from both the Sun and the observer, and in conditions of ideal solar opposition (an arrangement that is impossible in practice). Because Solar System bodies are illuminated by the Sun, their brightness varies as a function of illumination conditions, described by the phase angle. This relationship is referred to as the phase curve. The absolute magnitude is the brightness at phase angle zero, an arrangement known as opposition, from a distance of one AU. Newly discovered comets with a weakly active coma can masquerade as an asteroid resulting in unrealistic size estimates as a comet's absolute magnitude (M1) can not be directly compared to an asteroid's absolute magnitude (H).
Apparent magnitude
The absolute magnitude can be used to calculate the apparent magnitude of a body. For an object reflecting sunlight, and are connected by the relation
where is the phase angle, the angle between the body-Sun and body–observer lines. is the phase integral (the integration of reflected light; a number in the 0 to 1 range).
By the law of cosines, we have:
Distances: is the distance between the body and the observer is the distance between the body and the Sun is the distance between the observer and the Sun , a unit conversion factor, is the constant 1 AU, the average distance between the Earth and the Sun
Approximations for phase integral The value of depends on the properties of the reflecting surface, in particular on its roughness. In practice, different approximations are used based on the known or assumed properties of the surface. The surfaces of terrestrial planets are generally more difficult to model than those of gaseous planets, the latter of which have smoother visible surfaces.
Planets as diffuse spheres
Planetary bodies can be approximated reasonably well as ideal diffuse reflecting spheres. Let be the phase angle in degrees, then
A full-phase diffuse sphere reflects two-thirds as much light as a diffuse flat disk of the same diameter. A quarter phase () has as much light as full phase ().