Absolute magnitude

This article is about the brightness of stars. For the science fiction magazine, see Absolute Magnitude (magazine). Absolute Magnitude is a discontinued semi-professional Science fiction magazine started in 1993 under the name Harsh Mistress.

In astronomy, absolute magnitude is the apparent magnitude an object would have if it were at a standard luminosity distance (10 parsecs) away from the observer, in the absence of interstellar extinction. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study The apparent magnitude ( m) of a celestial body is a measure of its Brightness as seen by an observer on Earth, normalized to the value Luminosity distance DL is defined in terms of the relationship between the Absolute magnitude M and Apparent magnitude m Observation is either an activity of a living being (such as a Human) which senses and assimilates the Knowledge of a Phenomenon, or the recording of data Extinction is a term used in Astronomy to describe the absorption and Scattering of Electromagnetic radiation emitted by Astronomical objects 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 ≈2. 512 difference in brightness between steps in magnitude. Brightness is an attribute of Visual perception in which a source appears to emit or reflect a given amount of Light. The Milky Way, for example, has an absolute magnitude of about −20. The Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias sometimes referred to simply 5. So a quasar at an absolute magnitude of −25. A quasar (contraction of QUASi-stellAR radio source) is an extremely powerful and distant Active galactic nucleus. 5 is 100 times brighter than our galaxy (because 2. A galaxy is a massive gravitationally bound system consisting of Stars an Interstellar medium of gas and dust, and Dark matter 512⁵ ≈ 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.

1 Absolute magnitude for stars and galaxies (M)
- 1.1 Computation
  - 1.1.1 Example
- 1.2 Apparent magnitude
2 Absolute magnitude for planets (H)
- 2.1 Apparent magnitude
  - 2.1.1 Example
3 See also
4 External links

Absolute magnitude for stars and galaxies (M)

In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32. Distance is a numerical description of how far apart objects are History The first direct measurements of an object at interstellar distances were undertaken by German Astronomer Friedrich Wilhelm Bessel in 1838 616 light years, or 3 × 10¹⁴ kilometres). A light-year or light year (symbol ly) is a unit of Length, equal to just under ten trillion Kilometres As defined by The kilometre ( American spelling: kilometer) symbol km is a unit of Length in the Metric system, equal to one thousand A star at ten parsecs has a parallax of 0. Parallax is an apparent displacement or difference of orientation of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between 1" (100 milli arc seconds).

In defining absolute magnitude it is necessary to specify the type of electromagnetic radiation being measured. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as When referring to total energy output, the proper term is bolometric magnitude. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός A bolometer is a device for measuring the energy of incident Electromagnetic radiation. The bolometric magnitude can be computed from the visual magnitude plus a bolometric correction, $M b o l = M V + B C$ . This correction is needed because very hot stars radiate mostly ultraviolet radiation, while very cool stars radiate mostly infrared radiation (see Planck's law). For a general introduction see Black body. In Physics, Planck's law describes the spectral radiance of Electromagnetic radiation 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 has different meanings in several different fields of science A mathematical equation relates apparent magnitude with absolute magnitude, via parallax. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent This article sets out the set-theoretic notion of relation For a more elementary point of view see Binary relations and Triadic relations

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. A shadow is an area where direct light from a light source cannot reach due to obstruction by an object Rigel (ˈraɪʤəl (β Ori / β Orionis / Beta Orionis is the brightest star in the constellation Orion and the sixth brightest star in the sky with Visual 0), Deneb (−7. Deneb (α Cyg / α Cygni / Alpha Cygni is the brightest Star in the Constellation Cygnus and one of the vertices of the Summer Triangle 2), Naos (−6. Zeta Puppis (ζ Pup / ζ Puppis is a Star in the Constellation of Puppis. 0), and Betelgeuse (−5. Betelgeuse (ˈbiːtəldʒuːz or /ˈbɛtəldʒuːz/ ( α Ori α Orionis Alpha Orionis is a Semiregular variable star located 640 Light-years away from 6).

For comparison, Sirius has an absolute magnitude of 1. Sirius is the brightest star in the night sky with a visual Apparent magnitude of &minus1 4 and the Sun has an absolute visual magnitude of 4. The Sun (Sol is the Star at the center of the Solar System. 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. In Descriptive statistics, the range is the length of the smallest interval which contains all the data The absolute magnitude for galaxies can be much lower (brighter). For example, the giant elliptical galaxy M87 has an absolute magnitude of −22. An elliptical galaxy is a Galaxy belonging to one of the three main classes of galaxy originally described by Edwin Hubble (whose name was dedicated Messier 87 (also known as M87, Virgo A or NGC 4486) is a giant Elliptical galaxy.

Computation

One can compute the absolute magnitude $M\!\,$ of an object given its apparent magnitude $m\!\,$ and luminosity distance $D_L\!\,$ :

$M = m - 5 ((\log_{10}{D_L}) - 1)\!\,$

where $D_L\!\,$ is the star's luminosity distance in parsecs, which are (≈ 3. The apparent magnitude ( m) of a celestial body is a measure of its Brightness as seen by an observer on Earth, normalized to the value Luminosity distance DL is defined in terms of the relationship between the Absolute magnitude M and Apparent magnitude m History The first direct measurements of an object at interstellar distances were undertaken by German Astronomer Friedrich Wilhelm Bessel in 1838 2616 light-years)

For nearby astronomical objects (such as stars in our galaxy) the luminosity distance D_L is almost identical to the real distance to the object, because spacetime within our galaxy is almost Euclidean. A light-year or light year (symbol ly) is a unit of Length, equal to just under ten trillion Kilometres As defined by Luminosity distance DL is defined in terms of the relationship between the Absolute magnitude M and Apparent magnitude m Distance is a numerical description of how far apart objects are For much more distant objects the Euclidean approximation is not valid, and General Relativity must be taken into account when calculating the luminosity distance of an object. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916

In the Euclidean approximation for nearby objects, the absolute magnitude $M\!\,$ of a star can be calculated from its apparent magnitude and parallax:

$M = m + 5 (\log_{10}{p} + 1)\!\,$

where p is the star's parallax in arcseconds. The apparent magnitude ( m) of a celestial body is a measure of its Brightness as seen by an observer on Earth, normalized to the value Parallax is an apparent displacement or difference of orientation of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between

You can also compute the absolute magnitude $M\!\,$ of an object given its apparent magnitude $m\!\,$ and distance modulus $\mu\!\,$ :

$M = m - {\mu}\!\,$

Example

Rigel has a visual magnitude of

m V = 0. The distance modulus is a way of expressing distances that is often used in Astronomy. Rigel (ˈraɪʤəl (β Ori / β Orionis / Beta Orionis is the brightest star in the constellation Orion and the sixth brightest star in the sky with Visual 18

and distance about 773 light-years

$M_V = 0.18 - 5 \cdot (\log_{10} \frac{773}{3.2616} - 1) = -6.7$

Vega has a parallax of 0. A light-year or light year (symbol ly) is a unit of Length, equal to just under ten trillion Kilometres As defined by Vega (α Lyr / α Lyrae / Alpha Lyrae ( or) is the brightest Star in the Constellation Lyra, the fifth brightest star in the night Parallax is an apparent displacement or difference of orientation of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between 129", and an apparent magnitude of +0. 03

$M_V = 0.03 + 5 \cdot (1 +\log_{10}{0.129}) = +0.6$

Alpha Centauri A has a parallax of 0. Alpha Centauri (α Centauri / α Cen also known as Rigil Kentaurus, Rigil Kent, or Toliman, is the brightest Star in the southern Constellation 742" and an apparent magnitude of −0. 01

$M_V = -0.01 + 5 \cdot (1 +\log_{10}{0.742}) = +4.3$

Black Eye Galaxy has a visual magnitude of m_V=+9. The Black Eye Galaxy (also called Sleeping Beauty Galaxy; designated Messier 64, M64, or NGC 4826) was discovered by Edward Pigott 36 and a distance modulus of 31. 06.

M V = 9. 36 - 31. 06 = - 21. 7

Apparent magnitude

Given the absolute magnitude $M\!\,$ , for objects within our galaxy you can also calculate the apparent magnitude $m\!\,$ from any distance $d\!\,$ :

$m = M + 5 (\log_{10}{d} - 1)\!\,$

For objects at very great distances (outside our galaxy) the luminosity distance D_L must be used instead of d. Luminosity distance DL is defined in terms of the relationship between the Absolute magnitude M and Apparent magnitude m

Given the absolute magnitude $M\!\,$ , you can also compute apparent magnitude $m\!\,$ from its parallax $p\!\,$ :

$m = M - 5 (\log_{10}p + 1)\!\,$

Also calculating absolute magnitude $M\!\,$ from distance modulus $\mu\!\,$ :

$m = M + {\mu}\!\,$

Absolute magnitude for planets (H)

For planets, comets and asteroids a different definition of absolute magnitude is used which is more meaningful for nonstellar objects. Parallax is an apparent displacement or difference of orientation of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between The distance modulus is a way of expressing distances that is often used in Astronomy. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is A comet is a small Solar System body that orbits the Sun and when close enough to the Sun exhibits a visible coma (atmosphere or a tail — Asteroids, sometimes called Minor planets or planetoids', are bodies—primarily of the inner Solar System —that are smaller than planets but

In this case, the absolute magnitude is defined as the apparent magnitude that the object would have if it were one astronomical unit (au) from both the Sun and the Earth and at a phase angle of zero degrees. The astronomical unit ( AU or au or au or sometimes ua) is a unit of Length based on the distance from the Earth to the The Sun (Sol is the Star at the center of the Solar System. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 Phase angle in astronomical observations is the angle between the light incident onto an observed object and the light reflected from the object This is a physical impossibility, as it requires the observing telescope to be 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.

Apparent magnitude

The absolute magnitude can be used to help calculate the apparent magnitude of a body under different conditions.

$m = H + 2.5 \log_{10}{(\frac{d_{BS}^2 d_{BO}^2}{p(\chi) d_0^4})}\!\,$

where

$d_0\!\,$ is 1 au, $\chi\!\,$ is the phase angle, the angle between the Sun-Body and Body-Observer lines; by the law of cosines, we have:

$\cos{\chi} = \frac{ d_{BO}^2 + d_{BS}^2 - d_{OS}^2 } {2 d_{BO} d_{BS}}\!\,$

$p(\chi)\!\,$ is the 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

$p(\chi) = \frac{2}{3} ( (1 - \frac{\chi}{\pi}) \cos{\chi} + (1/\pi) \sin{\chi} )\!\,$

A full-phase diffuse sphere reflects ⅔ as much light as a diffuse disc of the same diameter

Distances:

$d_{BO}\!\,$ is the distance between the observer and the body

$d_{BS}\!\,$ is the distance between the Sun and the body

$d_{OS}\!\,$ is the distance between the observer and the Sun

Example

Moon

$H_{Moon}\!\,$ = +0. Phase angle in astronomical observations is the angle between the light incident onto an observed object and the light reflected from the object In Trigonometry, the law of cosines (also known as Al-Kashi law or the cosine formula or cosine rule) is a statement about a general The Bond albedo is the fraction of power in the total electromagnetic radiation incident on an astronomical body that is scattered back out into space See also Lambertian reflectance Lambert's cosine law in Optics says that the Radiant intensity observed from a " Lambertian " "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe 25

$d_{OS}\!\,$ = $d_{BS}\!\,$ = 1 au

$d_{BO}\!\,$ = 384. 5 Mm = 2. 57 mau

How bright is the Moon from Earth?

Full Moon: $\chi\!\,$ = 0, ( $p(\chi)\!\,$ ≈ 2/3)

$m_{Moon} = 0.25 + 2.5 \log_{10}{(\frac{3}{2} 0.00257^2)} = -12.26\!\,$

(Actual -12. 7) A full Moon reflects 30% more light at full phase than a perfect diffuse reflector predicts.

Quarter Moon: $\chi\!\,$ = 90°, $p(\chi) \approx \frac{2}{3\pi}\!\,$ (if diffuse reflector)

$m_{Moon} = 0.25 + 2.5 \log_{10}{(\frac{3\pi}{2} 0.00257^2)} = -11.02\!\,$

(Actual approximately -11. 0) The diffuse reflector formula does better for smaller phases.

External links

In Radio astronomy, the flux unit or jansky (symbol Jy) is a non- SI unit of electromagnetic Flux density equivalent to Surface brightness is a concept used in Astronomy when describing extended Astronomical objects such as galaxies and Nebulae General For the missile mounting see Mistral missile SIMBAD (the S et of I dentifications M easurements and B ibliography for

Dictionary

-noun

(astronomy) the apparent magnitude that a star etc. would have if viewed from a distance of 10 parsecs. Opposed to apparent magnitude.

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Contents

Absolute magnitude for stars and galaxies (M)

Computation

Example

Apparent magnitude

Absolute magnitude for planets (H)

Apparent magnitude

Example

See also

External links

Dictionary

absolute magnitude

-noun