- Absolute magnitude
astronomy, absolute magnitude (also known as absolute visual magnitude) is the apparent magnitudean object would have if it were at a standard luminosity distance(10 parsecs, 1 AU, or 100 km depending on object type) away from the observer, in the absence of astronomical extinction. It allows the overall brightnesses of objects to be compared without regard to distance.
The absolute magnitude uses the same convention as the visual magnitude, with a factor of about 2.512 difference in
brightnessbetween steps in magnitude. The Milky Way, for example, has an absolute magnitude of about −20.5. So a quasarat an absolute magnitude of −25.5 is 100 times brighter than our galaxy(because 2.5125 is approximately equal to 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 ten parsecs has a
parallaxof 0.1" (100 milli arc seconds).
In defining absolute magnitude it is necessary to specify the type of
electromagnetic radiationbeing measured. When referring to total energy output, the proper term is bolometric magnitude. The bolometric magnitude can be computed from the visual magnitude plus a bolometric correction, . 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. A mathematical equationrelates apparent magnitude with absolute magnitude, via parallax.
Many stars visible to the naked eye have an absolute magnitude which is capable of casting shadows from a distance of 10 parsecs;
Rigel(−7.0), Deneb(−7.2), Naos (−6.0), and Betelgeuse(−5.6). For comparison, Siriushas an absolute magnitude of 1.4 and the Sunhas an absolute visual magnitude of 4.83 (it actually serves as a reference point). The Sun's absolute bolometric magnitude is 4.75.
Absolute magnitudes for stars generally range from −10 to +17. The absolute magnitude for galaxies can be much lower (brighter). For example, the giant
elliptical galaxyM87 has an absolute magnitude of −22.
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, which are approximately 3.2616 light-years.
For nearby astronomical objects (such as stars in our galaxy) the 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 Relativitymust 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
Rigel has a visual magnitude of and distance about 773 light-years:
Vegahas a parallax of 0.129", and an apparent magnitude of +0.03: Alpha Centauri Ahas a parallax of 0.742" and an apparent magnitude of −0.01:
Black Eye Galaxyhas a visual magnitude of mV=+9.36 and a distance modulus of 31.06.:
Given the absolute magnitude , for objects within our galaxy you can also calculate the apparent magnitude from any distance :
For objects at very great distances (outside our galaxy) the luminosity distance "DL" must be used instead of "d".
Given the absolute magnitude , you can also compute apparent magnitude from its parallax :
Also calculating absolute magnitude from distance modulus :
planets, comets and asteroids 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 magnitudethat the object would have if it were one astronomical unit(au) from both the Sunand the observer and at a phase angle of zero degrees. This is a physical impossibility, as it requires the observer to be located at the centre of the Sun, but it is convenient for purposes of calculation.
To convert a stellar or galactic absolute magnitude into a planetary one, subtract 31.57.
The absolute magnitude can be used to help calculate the apparent magnitude of a body under different conditions.
is 1 au, is the phase angle, the angle between the Sun-Body and Body-Observer lines; by the
law of cosines, we have::
phase integral(integration of reflected light; a number in the 0 to 1 range):Example: (An ideal diffuse reflecting sphere) - 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
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.
meteor, the standard distanceis a height of 100 km at the observer's zenith. [citation | url=http://www.imo.net/glossary#term66 | contribution=Absolute magnitude of meteors | title=Glossary | publisher=International Meteor Organization | accessdate=2008-07-16] [citation | url=http://ssd.jpl.nasa.gov/?glossary&term=H | contribution=Absolute magnitude of Solar System bodies | publisher=NASA Jet Propulsion Laboratory | title=Solar System Dynamics Glossary | accessdate=2008-07-16]
* Hertzsprung-Russell diagram - Relates absolute magnitude or
luminosityversus spectral color or surface temperature.
Janskyradio astronomer's preferred unit - linear in power/unit area
Surface brightness- The "magnitude" for extended objects
* [http://astro.pas.rochester.edu/~aquillen/ast142/costanti.html Reference zero-magnitude fluxes]
* [http://www.astronomynotes.com/starprop/s4.htm The Magnitude system]
* [http://csep10.phys.utk.edu/astr162/lect/stars/magnitudes.html About stellar magnitudes]
* [http://simbad.u-strasbg.fr/sim-fid.pl Obtain the magnitude of any star] -
* [http://www.cfa.harvard.edu/iau/lists/Sizes.html Converting magnitude of minor planets to diameter]
* [http://neo.jpl.nasa.gov/glossary/h.html Another table for converting asteroid magnitude to estimated diameter]
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