Absolute magnitude

Absolute magnitude

Overview
Absolute magnitude is the measure of a celestial object's intrinsic brightness. it is also the apparent magnitude
Apparent magnitude
The 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 parsec
Parsec
The 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 astronomy
Astronomy
Astronomy 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 magnitude
Apparent magnitude
The 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 magnitude
Apparent magnitude
The 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 parsec
Parsec
The 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 observer
Observation
Observation 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 extinction
Extinction (astronomy)
Extinction 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 luminosity
Luminosity
Luminosity 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 magnitude
Magnitude (astronomy)
Magnitude 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 100.4 (≈2.512) ratio of brightness
Brightness
Brightness 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.
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Encyclopedia
Absolute magnitude is the measure of a celestial object's intrinsic brightness. it is also the apparent magnitude
Apparent magnitude
The 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 parsec
Parsec
The 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 astronomy
Astronomy
Astronomy 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 magnitude
Apparent magnitude
The 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 magnitude
Apparent magnitude
The 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 parsec
Parsec
The 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 observer
Observation
Observation 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 extinction
Extinction (astronomy)
Extinction 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 luminosity
Luminosity
Luminosity 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 magnitude
Magnitude (astronomy)
Magnitude 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 100.4 (≈2.512) ratio of brightness
Brightness
Brightness 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 Way
Milky Way
The 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 quasar
Quasar
A 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 galaxy
Galaxy
A 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 (100.4)(-20.5-(-25.5)) = (100.4)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 × 1014 kilometres).
A star at 10 parsecs has a parallax
Parallax
Parallax 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 radiation
Electromagnetic radiation
Electromagnetic 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 bolometric
Bolometer
A 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 correction
Bolometric Correction
In 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 luminosity
Luminosity
Luminosity 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: Rigel
Rigel
Rigel is the brightest star in the constellation Orion and the sixth brightest star in the sky, with visual magnitude 0.18...

 (−7.0), Deneb
Deneb
Deneb 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), Naos
Zeta Puppis
Zeta 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 Betelgeuse
Betelgeuse
Betelgeuse, 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, Sirius
Sirius
Sirius 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 Sun
Sun
The 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 galaxy
Elliptical galaxy
An 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 correction
K correction
K 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 Relativity
General relativity
General 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
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

Vega
Vega
Vega 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 Galaxy
Black Eye Galaxy
The 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 mV=+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


Bolometric
Bolometer
A 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 luminosity
Luminosity
Luminosity 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 electromagnetic
Electromagnetic radiation
Electromagnetic 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 temperature
Effective temperature
The 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, comet
Comet
A 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 asteroid
Asteroid
Asteroids 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 magnitude
Apparent magnitude
The 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 unit
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

 (au) from both the Sun
Sun
The 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 angle
Phase angle (astronomy)
Phase 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 curve
Phase curve (astronomy)
In 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 angle
Phase angle (astronomy)
Phase 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 cosines
Law of cosines
In 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 sphere
Sphere
A 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 meteor
METEOR
METEOR 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 zenith
Zenith
The 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
    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
    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 luminosity
    Luminosity
    Luminosity 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 temperature
    Temperature
    Temperature 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
    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
    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