Absolute magnitude
Logarithmic measure of the luminosity of a celestial object
Top 10 Absolute magnitude related articles

Contents
Absolute magnitude (M) is a measure of the luminosity of a celestial object, on an inverse logarithmic astronomical magnitude scale. 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 10 parsecs (32.6 lightyears), 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.
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 M_{V} for absolute magnitude in the V band.
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 100^{n/5}. For example, a star of absolute magnitude M_{V}=3.0 would be 100 times as luminous as a star of absolute magnitude M_{V}=8.0 as measured in the V filter band. The Sun has absolute magnitude M_{V}=+4.83.^{[1]} Highly luminous objects can have negative absolute magnitudes: for example, the Milky Way galaxy has an absolute B magnitude of about −20.8.^{[2]}
An object's absolute bolometric magnitude (M_{bol}) 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.^{[3]}
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 magnitude Intro articles: 10
Stars and galaxies
In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 lightyears, 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 pointlike or starlike source, and computing the magnitude of that pointlike 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.
The measurement of absolute magnitude is made with an instrument called a bolometer. When using an absolute magnitude, one must specify the type of electromagnetic radiation being measured. When referring to total energy output, the proper term is bolometric magnitude. The bolometric magnitude usually is computed from the visual magnitude plus a bolometric correction, M_{bol} = M_{V} + BC. This correction is needed because very hot stars radiate mostly ultraviolet radiation, whereas very cool stars radiate mostly infrared radiation (see Planck's law).
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 (−7.0), Deneb (−7.2), Naos (−6.0), and Betelgeuse (−5.6). 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.^{[4]}^{[5]} Absolute magnitudes of stars generally range from −10 to +17. 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 CTA102) can reach absolute magnitudes in excess of −32, making them the most luminous objects in the observable universe.
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 m = 1, and the dimmest stars visible to the naked eye are assigned m = 6.^{[6]} The difference between them corresponds to a factor of 100 in brightness. For objects within the immediate neighborhood of the Sun, the absolute magnitude M and apparent magnitude m from any distance d (in parsecs, with 1 pc = 3.2616 lightyears) are related by
 $100^{\frac {mM}{5}}={\frac {F_{10}}{F}}=\left({\frac {d}{10\;\mathrm {pc} }}\right)^{2},$
where F is the radiant flux measured at distance d (in parsecs), F_{10} the radiant flux measured at distance 10 pc. Using the common logarithm, the equation can be written as
 $M=m5\log _{10}(d_{\text{pc}})+5=m5\left(\log _{10}d_{\text{pc}}1\right),$
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.^{[7]}
For objects at very large distances (outside the Milky Way) the luminosity distance d_{L} (distance defined using luminosity measurements) must be used instead of d, 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 M can also be written in terms of the apparent magnitude m and stellar parallax p:
 $M=m+5\left(\log _{10}p+1\right),$
or using apparent magnitude m and distance modulus μ:
 $M=m\mu$
.
Examples
Rigel has a visual magnitude m_{V} of 0.12 and distance of about 860 lightyears:
 $M_{\mathrm {V} }=0.125\left(\log _{10}{\frac {860}{3.2616}}1\right)=7.0.$
Vega has a parallax p of 0.129″, and an apparent magnitude m_{V} of 0.03:
 $M_{\mathrm {V} }=0.03+5\left(\log _{10}{0.129}+1\right)=+0.6.$
The Black Eye Galaxy has a visual magnitude m_{V} of 9.36 and a distance modulus μ of 31.06:
 $M_{\mathrm {V} }=9.3631.06=21.7.$
Bolometric magnitude
The bolometric magnitude M_{bol}, 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:^{[6]}
 $M_{\mathrm {bol,\star } }M_{\mathrm {bol,\odot } }=2.5\log _{10}\left({\frac {L_{\star }}{L_{\odot }}}\right)$
which makes by inversion:
 ${\frac {L_{\star }}{L_{\odot }}}=10^{0.4\left(M_{\mathrm {bol,\odot } }M_{\mathrm {bol,\star } }\right)}$
where
 L_{⊙} is the Sun's luminosity (bolometric luminosity)
 L_{★} is the star's luminosity (bolometric luminosity)
 M_{bol,⊙} is the bolometric magnitude of the Sun
 M_{bol,★} is the bolometric magnitude of the star.
In August 2015, the International Astronomical Union passed Resolution B2^{[8]} defining the zero points of the absolute and apparent bolometric magnitude scales in SI units for power (watts) and irradiance (W/m^{2}), respectively. Although bolometric magnitudes had been used by astronomers for many decades, there had been systematic differences in the absolute magnitudeluminosity scales presented in various astronomical references, and no international standardization. This led to systematic differences in bolometric corrections scales.^{[9]} 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 M_{bol} = 0 corresponds to luminosity L_{0} = 3.0128×10^{28} W, with the zero point luminosity L_{0} set such that the Sun (with nominal luminosity 3.828×10^{26} W) corresponds to absolute bolometric magnitude M_{bol,⊙} = 4.74. 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 m_{bol} = 0 corresponds to irradiance f_{0} = 2.518021002×10^{−8} W/m^{2}. Using the IAU 2015 scale, the nominal total solar irradiance ("solar constant") measured at 1 astronomical unit (1361 W/m^{2}) corresponds to an apparent bolometric magnitude of the Sun of m_{bol,⊙} = −26.832.^{[9]}
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:
 $M_{\mathrm {bol} }=2.5\log _{10}{\frac {L_{\star }}{L_{0}}}\approx 2.5\log _{10}L_{\star }+71.197425$
where
 L_{★} is the star's luminosity (bolometric luminosity) in watts
 L_{0} is the zero point luminosity 3.0128×10^{28} W
 M_{bol} 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 M_{bol} = 4.74, a value that was commonly adopted by astronomers before the 2015 IAU resolution.^{[9]}
The luminosity of the star in watts can be calculated as a function of its absolute bolometric magnitude M_{bol} as:
 $L_{\star }=L_{0}10^{0.4M_{\mathrm {bol} }}$
using the variables as defined previously.
Absolute magnitude Stars and galaxies articles: 37
Solar System bodies (H)
H  Diameter 

10  34 km 
12.6  10 km 
15  3.4 km 
17.6  1 km 
19.2  500 meter 
20  340 meter 
22.6  100 meter 
24.2  50 meter 
25  34 meter 
27.6  10 meter 
30  3.4 meter 
For planets and asteroids, a definition of absolute magnitude that is more meaningful for nonstellar objects is used. The absolute magnitude, commonly called $H$
Apparent magnitude
The absolute magnitude $H$
 $m=H+5\log _{10}{\left({\frac {d_{BS}d_{BO}}{d_{0}^{2}}}\right)}2.5\log _{10}{q(\alpha )},$
where $\alpha$
By the law of cosines, we have:
 $\cos {\alpha }={\frac {d_{\mathrm {BO} }^{2}+d_{\mathrm {BS} }^{2}d_{\mathrm {OS} }^{2}}{2d_{\mathrm {BO} }d_{\mathrm {BS} }}}.$
Distances:
 d_{BO} is the distance between the body and the observer
 d_{BS} is the distance between the body and the Sun
 d_{OS} is the distance between the observer and the Sun
 d_{0} is 1 AU, the average distance between the Earth and the Sun
Approximations for phase integral $q(\alpha )$
The value of $q(\alpha )$
Planets as diffuse spheres
Planetary bodies can be approximated reasonably well as ideal diffuse reflecting spheres. Let $\alpha$
 $q(\alpha )={\frac {2}{3}}\left(\left(1{\frac {\alpha }{180^{\circ }}}\right)\cos {\alpha }+{\frac {1}{\pi }}\sin {\alpha }\right).$
A fullphase diffuse sphere reflects twothirds as much light as a diffuse flat disk of the same diameter. A quarter phase ($\alpha =90^{\circ }$
For contrast, a diffuse disk reflector model is simply $q(\alpha )=\cos {\alpha }$
The definition of the geometric albedo $p$
 $D={\frac {1329}{\sqrt {p}}}\times 10^{0.2H}$
km.
Example: The Moon's absolute magnitude $H$
 $H=5\log _{10}{\frac {1329}{3474{\sqrt {0.113}}}}=+0.28.$
We have $d_{BS}=1{\text{ AU}}$
More advanced models
Because Solar System bodies are never perfect diffuse reflectors, astronomers use different models to predict apparent magnitudes based on known or assumed properties of the body.^{[12]} For planets, approximations for the correction term $2.5\log _{10}{q(\alpha )}$
Planet  $H$

Approximation for $2.5\log _{10}{q(\alpha )}$


Mercury  −0.613  $+6.328\times 10^{2}\alpha 1.6336\times 10^{3}\alpha ^{2}+3.3644\times 10^{5}\alpha ^{3}3.4265\times 10^{7}\alpha ^{4}+1.6893\times 10^{9}\alpha ^{5}3.0334\times 10^{12}\alpha ^{6}$

Venus  −4.384 

Earth  −3.99  $1.060\times 10^{3}\alpha +2.054\times 10^{4}\alpha ^{2}$

Mars  −1.601 

Jupiter  −9.395 

Saturn  −8.914 

Uranus  −7.110  $8.4\times 10^{4}\phi '+6.587\times 10^{3}\alpha +1.045\times 10^{4}\alpha ^{2}$

Neptune  −7.00  $+7.944\times 10^{3}\alpha +9.617\times 10^{5}\alpha ^{2}$

Here $\beta$
Example: On 1 January 2019, Venus was $d_{BS}=0.719{\text{ AU}}$
Earth's albedo varies by a factor of 6, from 0.12 in the cloudfree case to 0.76 in the case of altostratus cloud. The absolute magnitude here corresponds to an albedo of 0.434. Earth's apparent magnitude cannot be predicted as accurately as that of most other planets.^{[19]}
Asteroids
If an object has an atmosphere, it reflects light more or less isotropically in all directions, and its brightness can be modelled as a diffuse reflector. Atmosphereless bodies, like asteroids or moons, tend to reflect light more strongly to the direction of the incident light, and their brightness increases rapidly as the phase angle approaches $0^{\circ }$
In 1985, the IAU adopted the semiempirical $HG$
 $m=H+5\log _{10}{\left({\frac {d_{BS}d_{BO}}{d_{0}^{2}}}\right)}2.5\log _{10}{q(\alpha )},$
where
 the phase integral is $q(\alpha )=\left(1G\right)\phi _{1}\left(\alpha \right)+G\phi _{2}\left(\alpha \right)$
and
 $\phi _{i}\left(\alpha \right)=\exp {\left(A_{i}\left(\tan {\frac {\alpha }{2}}\right)^{B_{i}}\right)}$
for $i=1$ or $2$ , $A_{1}=3.332$ , $A_{2}=1.862$ , $B_{1}=0.631$ and $B_{2}=1.218$ .^{[22]}
This relation is valid for phase angles $\alpha <120^{\circ }$
The slope parameter $G$
In 2012, the $HG$
The apparent magnitude of asteroids varies as they rotate, on time scales of seconds to weeks depending on their rotation period, by up to $2{\text{ mag}}$
Cometary magnitudes
The brightness of comets is given separately as total magnitude ($m_{1}$
The activity of comets varies with their distance from the Sun. Their brightness can be approximated as
 $m_{1}=M_{1}+2.5\cdot K_{1}\log _{10}{\left({\frac {d_{BS}}{d_{0}}}\right)}+5\log _{10}{\left({\frac {d_{BO}}{d_{0}}}\right)}$
 $m_{2}=M_{2}+2.5\cdot K_{2}\log _{10}{\left({\frac {d_{BS}}{d_{0}}}\right)}+5\log _{10}{\left({\frac {d_{BO}}{d_{0}}}\right)},$
where $m_{1,2}$
For example, the lightcurve of comet C/2011 L4 (PANSTARRS) can be approximated by $M_{1}=5.41{\text{, }}K_{1}=3.69.$
Comet  Absolute magnitude $M_{1}$ 
Nucleus diameter 

Comet Sarabat  −3.0  ≈100 km? 
Comet HaleBopp  −1.3  60 ± 20 km 
Comet Halley  4.0  14.9 x 8.2 km 
average new comet  6.5  ≈2 km^{[33]} 
289P/Blanpain (during 1819 outburst)  8.5^{[34]}  320 m^{[35]} 
289P/Blanpain (normal activity)  22.9^{[36]}  320 m 
The absolute magnitude of any given comet can vary dramatically. It can change as the comet becomes more or less active over time, or if it undergoes an outburst. This makes it difficult to use the absolute magnitude for a size estimate. When comet 289P/Blanpain was discovered in 1819, its absolute magnitude was estimated as $M_{1}=8.5$
For some comets that have been observed at heliocentric distances large enough to distinguish between light reflected from the coma, and light from the nucleus itself, an absolute magnitude analogous to that used for asteroids has been calculated, allowing to estimate the sizes of their nuclei.^{[37]}
Absolute magnitude Solar System bodies (H) articles: 46
Meteors
For a meteor, the standard distance for measurement of magnitudes is at an altitude of 100 km (62 mi) at the observer's zenith.^{[38]}^{[39]}
Absolute magnitude Meteors articles: 2
See also
 Hertzsprung–Russell diagram – relates absolute magnitude or luminosity versus spectral color or surface temperature.
 Jansky radio astronomer's preferred unit – linear in power/unit area
 List of most luminous stars
 Photographic magnitude
 Surface brightness – the magnitude for extended objects
 Zero point (photometry) – the typical calibration point for star flux
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factor for a diffuse disk reflector can be computed as $2{\text{ AU}}\cdot 10^{H_{\text{Sun}}/5}$ , where $H_{\text{Sun}}=26.76$ , the absolute magnitude of the Sun, and $1{\text{ AU}}=1.4959787\times 10^{8}{\text{ km}}.$  ^ Chesley, Steven R.; Chodas, Paul W.; Milani, Andrea; Valsecchi, Giovanni B.; Yeomans, Donald K. (October 2002). "Quantifying the Risk Posed by Potential Earth Impacts" (PDF). Icarus. 159 (2): 425. Bibcode:2002Icar..159..423C. doi:10.1006/icar.2002.6910. Archived from the original (PDF) on 4 November 2003. Retrieved 15 April 2020.
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External links
 Reference zeromagnitude fluxes
 International Astronomical Union
 Absolute Magnitude of a Star calculator
 The Magnitude system
 About stellar magnitudes
 Obtain the magnitude of any star – SIMBAD
 Converting magnitude of minor planets to diameter
 Another table for converting asteroid magnitude to estimated diameter