Absolute magnitude is the measure of a celestial object's intrinsic brightness. it is also the
apparent magnitudeThe apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...
a star would have if it were 32.6 light years (10
parsecThe parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....
) away from Earth. In
astronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, to derive absolute magnitude from the observed
apparent magnitudeThe apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...
of a celestial object its value is corrected from distance to its observer. The absolute magnitude then equals the
apparent magnitudeThe apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...
an object would have if it were at a standard
luminosity distance (10
parsecThe parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....
) away from the
observerObservation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...
, in the absence of
astronomical extinctionExtinction is a term used in astronomy to describe the absorption and scattering of electromagnetic radiation by matter between an emitting astronomical object and the observer. Interstellar extinction—also called Galactic extinction, when it occurs in the Milky Way—was first...
.
It allows the true brightnesses of objects to be compared without regard to distance.
Bolometric magnitude is
luminosityLuminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...
expressed in magnitude units; it takes into account energy radiated at all wavelengths, whether observed or not.
The absolute magnitude uses the same convention as the visual
magnitudeMagnitude is the logarithmic measure of the brightness of an object, in astronomy, measured in a specific wavelength or passband, usually in optical or near-infrared wavelengths.-Background:...
: a factor of 10
0.4 (≈2.512) ratio of
brightnessBrightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target...
corresponds to a difference of 1.0 in magnitude. The
Milky WayThe Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...
, for example, has an absolute magnitude of about −20.5. So a
quasarA quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...
at an absolute magnitude of −25.5 is 100 times brighter than our
galaxyA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
(because (10
0.4)
(-20.5-(-25.5)) = (10
0.4)
5 = 100). If this particular quasar and our galaxy could be seen side by side at the same distance, the quasar would be 5 magnitudes (or 100 times) brighter than our galaxy.
Stars and galaxies (M)
In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 light years, or 3 × 10
14 kilometres).
A star at 10 parsecs has a
parallaxParallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. The term is derived from the Greek παράλλαξις , meaning "alteration"...
of 0.1" (100 milli arc seconds).
For galaxies (which are of course themselves much larger than 10 parsecs, and whose overall brightness cannot be directly observed from relatively short distances) the absolute magnitude is defined by reference to the apparent brightness of a point-like or star-like source of the same total luminosity as the galaxy, as it would appear if observed at the standard 10 parsecs distance.
In defining absolute magnitude one must specify the type of
electromagnetic radiationElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
being measured. When referring to total energy output, the proper term is
bolometricA bolometer is a device for measuring the power of incident electromagnetic radiation via the heating of a material with a temperature-dependent electrical resistance. It was invented in 1878 by the American astronomer Samuel Pierpont Langley...
magnitude. The bolometric magnitude can be computed from the visual magnitude plus a
bolometric correctionIn astronomy, a bolometric correction is a correction that must be made to the absolute magnitude of an object in order to convert an object's visible magnitude to its bolometric magnitude. Mathematically, such a calculation can be expressed: BC = M_b - M_v\!\,...
,
. This correction is needed because very hot stars radiate mostly ultraviolet radiation, while very cool stars radiate mostly infrared radiation (see Planck's law). The dimmer an object (at a distance of 10 parsecs) would appear, the higher its absolute magnitude. The lower an object's absolute magnitude, the higher its
luminosityLuminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...
. A mathematical equation relates apparent magnitude to absolute magnitude, via parallax.
Many stars visible to the naked eye have a such a low absolute magnitude that they would appear bright enough to cast shadows if they were only 10 parsecs from the Earth:
RigelRigel is the brightest star in the constellation Orion and the sixth brightest star in the sky, with visual magnitude 0.18...
(−7.0),
DenebDeneb is the brightest star in the constellation Cygnus and one of the vertices of the Summer Triangle. It is the 19th brightest star in the night sky, with an apparent magnitude of 1.25. A blue-white supergiant, Deneb is also one of the most luminous nearby stars...
(−7.2),
NaosZeta Puppis is a star in the constellation of Puppis. It is also known by the traditional names Naos and Suhail Hadar in Arabic....
(−6.0), and
BetelgeuseBetelgeuse, also known by its Bayer designation Alpha Orionis , is the eighth brightest star in the night sky and second brightest star in the constellation of Orion, outshining its neighbour Rigel only rarely...
(−5.6). For comparison,
SiriusSirius is the brightest star in the night sky. With a visual apparent magnitude of −1.46, it is almost twice as bright as Canopus, the next brightest star. The name "Sirius" is derived from the Ancient Greek: Seirios . The star has the Bayer designation Alpha Canis Majoris...
has an absolute magnitude of 1.4 which is greater than the
SunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
's absolute visual magnitude of 4.83 (it actually serves as a reference point). The Sun's absolute bolometric magnitude is 4.75.
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 galaxyAn elliptical galaxy is a galaxy having an approximately ellipsoidal shape and a smooth, nearly featureless brightness profile. They range in shape from nearly spherical to highly flat and in size from hundreds of millions to over one trillion stars...
M87 has an absolute magnitude of −22 (i.e. as bright as about 60,000 stars of magnitude -10).
Computation
One can compute the absolute magnitude
of an object given its apparent magnitude
and luminosity distance
:
where
is the star's luminosity distance in parsecs, wherein 1 parsec is approximately 3.2616 light-years. For very large distances, cosmological redshift complicates the relation between absolute and apparent magnitude, and an additional
k correctionK correction is a correction to an astronomical object's magnitude that allows a measurement of a quantity of light from an object at a redshift z to be converted to an equivalent measurement in the rest frame of the object. If one could measure all the light from an object at all wavelengths , a...
might be required.
For nearby astronomical objects (such as stars in our galaxy) luminosity distance
DL is almost identical to the real distance to the object, because spacetime within our galaxy is almost Euclidean. For much more distant objects the Euclidean approximation is not valid, and
General RelativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
must be taken into account when calculating the luminosity distance of an object.
In the Euclidean approximation for nearby objects, the absolute magnitude
of a star can be calculated from its apparent magnitude and parallax:
where p is the star's parallax in arcseconds.
You can also compute the absolute magnitude
of an object given its apparent magnitude
and
distance modulus-Definition:The distance modulus \mu=m-M is the difference between the apparent magnitude m and the absolute magnitude M of an astronomical object...
:
Examples
Rigel has a visual magnitude of
and distance about 773 light-years
VegaVega is the brightest star in the constellation Lyra, the fifth brightest star in the night sky and the second brightest star in the northern celestial hemisphere, after Arcturus...
has a parallax of 0.129", and an apparent magnitude of +0.03
Alpha Centauri A has a parallax of 0.742" and an apparent magnitude of −0.01
The
Black Eye GalaxyThe Black Eye Galaxy was discovered by Edward Pigott in March 1779, and independently by Johann Elert Bode in April of the same year, as well as by Charles Messier in 1780...
has a visual magnitude of m
V=+9.36 and a distance modulus of 31.06.
Apparent magnitude
Given the absolute magnitude
, for objects within our galaxy you can also calculate the apparent magnitude
from any distance
(in parsecs):
For objects at very great distances (outside our galaxy) the luminosity distance
DL must be used instead of
d (in parsecs).
Given the absolute magnitude
, you can also compute apparent magnitude
from its parallax
:
Also calculating absolute magnitude
from distance modulus
:
Bolometric magnitude
BolometricA bolometer is a device for measuring the power of incident electromagnetic radiation via the heating of a material with a temperature-dependent electrical resistance. It was invented in 1878 by the American astronomer Samuel Pierpont Langley...
magnitude corresponds to
luminosityLuminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...
, expressed in magnitude units; that is, after taking into account all
electromagneticElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
wavelengths, including those unobserved due to instrumental pass-band, the Earth's atmospheric absorption, or extinction by interstellar dust. For stars, in the absence of extensive observations at many wavelengths, it usually must be computed assuming an
effective temperatureThe effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation...
.
Solar System bodies (H)
For planets,
cometA comet is an icy small Solar System body that, when close enough to the Sun, displays a visible coma and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet...
s and
asteroidAsteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
s a different definition of absolute magnitude is used which is more meaningful for nonstellar objects.
In this case, the absolute magnitude is defined as the
apparent magnitudeThe apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...
that the object would have if it were one
astronomical unitAn astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....
(au) from both the
SunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
and the observer. Because the object is illuminated by the Sun absolute magnitude is a function of
phase anglePhase angle in astronomical observations is the angle between the light incident onto an observed object and the light reflected from the object...
and this relationship is referred to as the
phase curveIn astronomy a phase curve describes the brightness of a reflecting body as a function of its phase angle. The brightness usually refers the object’s absolute magnitude which, in turn, is its apparent magnitude at a distance of one astronomical unit from the Earth and Sun...
.
To convert a stellar or galactic absolute magnitude into a planetary one, subtract 31.57.
Apparent magnitude
The absolute magnitude can be used to help calculate the apparent magnitude of a body under different conditions.
where
is 1 au,
is the
phase anglePhase angle in astronomical observations is the angle between the light incident onto an observed object and the light reflected from the object...
, the angle between the Sun–Body and Body–Observer lines. By the
law of cosinesIn trigonometry, the law of cosines relates the lengths of the sides of a plane triangle to the cosine of one of its angles. Using notation as in Fig...
, we have:
is the phase integral (integration of reflected light; a number in the 0 to 1 range).
Example: Ideal diffuse reflecting
sphereA sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
. A reasonable first approximation for planetary bodies
A full-phase diffuse sphere reflects ⅔ as much light as a diffuse disc of the same diameter.
Distances:
-
is the distance between the observer and the body
-
is the distance between the Sun and the body
-
is the distance between the observer and the Sun
Note: because Solar System bodies are never perfect diffuse reflectors, astronomers use empirically derived relationships to predict apparent magnitudes when accuracy is required.
Example
Moon:
-
= +0.25
-
= 
= 1 au
-
= 384.5 Mm = 2.57 mau
How bright is the Moon from Earth?
- Full Moon:
= 0, (
≈ 2/3)
-
- (Actual -12.7) A full Moon reflects 30% more light at full phase than a perfect diffuse reflector predicts.
- Quarter Moon:
= 90°, 
(if diffuse reflector)
-
- (Actual approximately -11.0) The diffuse reflector formula does better for smaller phases.
Meteors
For a
meteorMETEOR is a metric for the evaluation of machine translation output. The metric is based on the harmonic mean of unigram precision and recall, with recall weighted higher than precision...
, the standard distance for measurement of magnitudes is at an altitude of 100 km (62 mi) at the observer's
zenithThe zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...
.
See also
- Photographic magnitude
Before the advent of photometers which accurately measure the brightness of astronomical objects, the apparent magnitude of an object was obtained by taking a picture of it with a camera. These images, made on photoemulsive film or plates, were more sensitive to the blue end of the visual spectrum...
- Hertzsprung–Russell diagram
The Hertzsprung–Russell diagram is a scatter graph of stars showing the relationship between the stars' absolute magnitudes or luminosities versus their spectral types or classifications and effective temperatures. Hertzsprung–Russell diagrams are not pictures or maps of the locations of the stars...
- Relates absolute magnitude or luminosityLuminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...
versus spectral color or surface temperatureTemperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
.
- Jansky
The flux unit or jansky is a non-SI unit of spectral flux density equivalent to 10−26 watts per square metre per hertz...
radio astronomer's preferred unit - linear in power/unit area
- Surface brightness
The overall brightness of an extended astronomical object such as a galaxy, star cluster, or nebula, can be measured by its total magnitude, integrated magnitude or integrated visual magnitude; a related concept is surface brightness, which specifies the brightness of a standard-sized piece of an...
- The magnitude for extended objects
- List of most luminous stars
External links