Absolute magnitude is a measure of the luminosity of a celestial object, on a 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 light-years), with no extinction (or dimming) of its light due to absorption by interstellar dust particles. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared 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 MV 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 MV=3 would be 100 times more luminous than a star of absolute magnitude MV=8 as measured in the V filter band. The Sun has absolute magnitude MV=+4.83. Highly luminous objects can have negative absolute magnitudes: for example, the Milky Way galaxy has an absolute B magnitude of about −20.8.
An object's absolute bolometric magnitude 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 is applied.
In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 light-years, 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 point-like or star-like source, and computing the magnitude of that point-like 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, Mbol = MV + 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 1.4, which is brighter than the Sun, whose absolute visual magnitude is 4.83 (it actually serves as a reference point). The Sun's absolute bolometric magnitude is set arbitrarily, usually at 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 M87 has an absolute magnitude of −22 (i.e. as bright as about 60,000 stars of magnitude −10).
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. 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) is related by:
where F is the radiant flux measured at distance d (in parsecs), F10 the radiant flux measured at distance 10 pc. The relation can be written in terms of logarithm:
For objects at very large distances (outside the Milky Way) the luminosity distance dL (distance defined using luminosity measurements) must be used instead of d (in parsecs), because the Euclidean approximation is invalid for distant objects and general relativity must be taken into account. Moreover, the cosmological redshift complicates the relation 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 approximated using apparent magnitude m and stellar parallax p:
or using apparent magnitude m and distance modulus μ:
Rigel has a visual magnitude mV of 0.12 and distance about 860 light-years
Vega has a parallax p of 0.129″, and an apparent magnitude mV of 0.03
The Black Eye Galaxy has a visual magnitude mV of 9.36 and a distance modulus μ of 31.06
The bolometric magnitude Mbol, 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:
which makes by inversion:
In August 2015, the International Astronomical Union passed Resolution B2 defining the zero points of the absolute and apparent bolometric magnitude scales in SI units for power (watts) and irradiance (W/m2), respectively. Although bolometric magnitudes had been used by astronomers for many decades, there had been systematic differences in the absolute magnitude-luminosity scales presented in various astronomical references, and no international standardization. This led to systematic differences in bolometric corrections scales. Combined with incorrect assumed absolute bolometric magnitudes for the Sun could lead to systematic errors in estimated stellar luminosities (and stellar properties calculated which rely on stellar luminosity, such as radii, ages, and so on).
Resolution B2 defines an absolute bolometric magnitude scale where Mbol = 0 corresponds to luminosity L0 = 3.0128×1028 W, with the zero point luminosity L0 set such that the Sun (with nominal luminosity 3.828×1026 W) corresponds to absolute bolometric magnitude Mbol,⊙ = 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 mbol = 0 corresponds to irradiance f0 = 2.518021002×10−8 W/m2. Using the IAU 2015 scale, the nominal total solar irradiance ("solar constant") measured at 1 astronomical unit (1361 W/m2) corresponds to an apparent bolometric magnitude of the Sun of mbol,⊙ = −26.832.
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:
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 Mbol = 4.74, a value that was commonly adopted by astronomers before the 2015 IAU resolution.
The luminosity of the star in watts can be calculated as a function of its absolute bolometric magnitude Mbol as:
using the variables as defined previously.
For planets and asteroids a definition of absolute magnitude that is more meaningful for non-stellar objects is used. The absolute magnitude, commonly called , is defined as the apparent magnitude that the object would have if it were one Astronomical Unit (AU) from both the Sun and the observer, and in conditions of ideal solar opposition (an arrangement that is impossible in practice). Solar System bodies are illuminated by the Sun, therefore the magnitude varies as a function of illumination conditions, described by the phase angle. This relationship is referred to as the phase curve. The absolute magnitude is the brightness at phase angle zero, an arrangement known as opposition.
The absolute magnitude can be used to calculate the apparent magnitude of a body. For an object reflecting sunlight, and are connected by the relation
By the law of cosines, we have:
The value of depends on the properties of the reflecting surface, in particular on its roughness. In practice, different approximations are used based on the known or assumed properties of the surface.
A full-phase diffuse sphere reflects two-thirds as much light as a diffuse flat disk of the same diameter. A quarter phase () has as much light as full phase ().
For contrast, a diffuse disk reflector model is simply , which isn't realistic, but it does represent the opposition surge for rough surfaces that reflect more uniform light back at low phase angles.
The definition of the geometric albedo , a measure for the reflectivity of planetary surfaces, is based on the diffuse disk reflector model. The absolute magnitude , diameter (in kilometers) and geometric albedo of a body are related by
We have , At quarter phase, (according to the diffuse reflector model), this yields an apparent magnitude of The actual value is somewhat lower than that, The phase curve of the Moon is too complicated for the diffuse reflector model.
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. For planets, approximations for the correction term in the formula for m have been derived empirically, to match observations at different phase angles. The approximations recommended by the Astronomical Almanac are (with in degrees):
|Neptune||−7.00||(for and )|
Here is the effective inclination of Saturn's rings (their tilt relative to the observer), which as seen from Earth varies between 0° and 27° over the course of one Saturn orbit, and is a small correction term depending on Uranus' sub-Earth and sub-solar latitudes. is the Common Era year. Neptune's absolute magnitude is changing slowly due to seasonal effects as the planet moves along its 165-year orbit around the Sun, and the approximation above is only valid after the year 2000. For some circumstances, like for Venus, no observations are available, and the phase curve is unknown in those cases.
Example: On 1 January 2019, Venus was from the Sun, and from Earth, at a phase angle of (near quarter phase). Under full-phase conditions, Venus would have been visible at Accounting for the high phase angle, the correction term above yields an actual apparent magnitude of This is close to the value of predicted by the Jet Propulsion Laboratory.
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 . This rapid brightening near opposition is called the opposition effect. Its strength depends on the physical properties of the body's surface, and hence it differs from asteroid to asteroid.
In 1985, the IAU adopted the semi-empirical -system, based on two parameters and called absolute magnitude and slope, to model the opposition effect for the ephemerides published by the Minor Planet Center.
This relation is valid for phase angles , and works best when .
The slope parameter relates to the surge in brightness, typically 0.3 mag, when the object is near opposition. It is known accurately only for a small number of asteroids, hence for most asteroids a value of is assumed. In rare cases, can be negative. An example is 101955 Bennu, with .
In 2012, the -system was officially replaced by an improved system with three parameters , and , which produces more satisfactory results if the opposition effect is very small or restricted to very small phase angles. However, as of 2019, this -system has not been adopted by either the Minor Planet Center nor Jet Propulsion Laboratory.
The apparent magnitude of asteroids varies as they rotate, on time scales of seconds to weeks depending on their rotation period, by up to or more. In addition, their absolute magnitude can vary with the viewing direction, depending on their axial tilt. In many cases, neither the rotation period nor the axial tilt are known, limiting the predictability. The models presented here do not capture those effects.
The brightness of comets is given separately as total magnitude (, the brightness integrated over the entire visible extend of the coma) and nuclear magnitude (, the brightness of the core region alone). Both are different scales than the magnitude scale used for planets and asteroids, and can not be used for a size comparison with an asteroid's absolute magnitude H.
The activity of comets varies with their distance from the Sun. Their brightness can be approximated as
where are the total and nuclear apparent magnitudes of the comet, respectively, are its "absolute" total and nuclear magnitudes, and are the body-sun and body-observer distances, is the Astronomical Unit, and are the slope parameters characterising the comet's activity. For , this reduces to the formula for a purely reflecting body.
For example, the lightcurve of comet C/2011 L4 (PANSTARRS) can be approximated by  On the day of its perihelion passage, 10 March 2013, comet PANSTARRS was from the Sun and from Earth. The total apparent magnitude is predicted to have been at that time. The Minor Planet Center gives a value close to that, .
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.
(230965) 2004 XA192 is a Kuiper-belt object with a diameter of 339+120−95 km. It has an absolute magnitude of 4.11. It was discovered on 12 December 2004 at Palomar Observatory.
It is currently at 35.8 AU from the Sun, near its perihelion.(455502) 2003 UZ413
(455502) 2003 UZ413, also written as 2003 UZ413, is a trans-Neptunian object (TNO) with an absolute magnitude of 4.4. It has a 2:3 orbital resonance with Neptune, which makes it a plutino. It is likely large enough to be a dwarf planet.
It has been observed 79 times over 15 oppositions, with precovery images back to 1954.2003 QX113
2003 QX113, also written as 2003 QX113, is a detached object that was discovered when it was near aphelion. With an absolute magnitude of 4.7, it may be a dwarf planet.As of February 2016 located 59.9 AU from the Sun, it will have moved beyond 60 AU by 2017 and will reach its aphelion around 2058. It last came to perihelion around 1883. Its current distance makes it one of the twelve most distant known minor planets in the Solar System (see table below).2008 ST291
2008 ST291, also written as 2008 ST291, is a trans-Neptunian object with an absolute magnitude of 4.2, making it possibly a dwarf planet. It is located near the 1:6 Neptune resonance of 99.4 AU (compared to its 99.3 ± 0.2 AU), meaning that it completes roughly 1 orbit for every 6 orbits Neptune makes.2013 FY27
2013 FY27, also written 2013 FY27, is a trans-Neptunian object and binary system that belongs to the scattered disc (like Eris). Its discovery was announced on 31 March 2014. It has an absolute magnitude (H) of 3.0. 2013 FY27 is a binary object, with two components approximately 740 kilometres (460 mi) and 190 kilometres (120 mi) in diameter. It is the ninth-intrinsically-brightest known trans-Neptunian object, and is the largest unnumbered minor planet as of September 2018.2013 ND15
2013 ND15 (also written 2013 ND15) is an asteroid that is a temporary trojan of Venus, the first known Venus trojan.44P/Reinmuth
44P/Reinmuth or Reinmuth 2 is a Jupiter-family comet that is greatly perturbed by the gas giant Jupiter. The diameter of this comet is estimated at 3.22 km and its absolute magnitude at 11.Boötes I (dwarf galaxy)
The Boötes Dwarf Galaxy (Boo I dSph) is a galaxy, which appears faint, with a luminosity of 100,000 L☉ and an absolute magnitude of –5.8. It lies about 197 thousand light-years (60.4 kiloparsecs) away in the constellation Boötes. This dwarf spheroidal galaxy appears to be tidally disrupted by the Milky Way Galaxy, which it orbits, and has two stellar tails that cross over to form a cross. Tidally disrupted galaxies usually only form one tail.Like many of the ultrafaint dwarf spheroidals, the entire galaxy appears fainter than the Rigel system (absolute magnitude –7.84).Comet Humason
There is another long-period comet named Humason: C/1960 M1 (a.k.a. 1959 X, 1960e).Comet Humason, formally designated C/1961 R1 (a.k.a. 1962 VIII and 1961e), was a non-periodic comet discovered by Milton L. Humason on September 1, 1961. Its perihelion was well beyond the orbit of Mars, at 2.133 AU. Its period is 2940 years, and the diameter of its nucleus estimated at about 41 km.
It was a 'giant' comet, much more active than a normal comet for its distance to the Sun, with an absolute magnitude of +1.5, a hundred times brighter than an average new comet. It had an unusually disrupted or 'turbulent' appearance. It was also unusual in that the spectrum of its tail showed a strong predominance of the ion CO+, a result previously seen unambiguously only in Comet Morehouse (C/1908 R1).Comet of 1729
The Comet of 1729, also known as C/1729 P1 or Comet Sarabat, was a non-periodic comet with an absolute magnitude of −3, the brightest ever observed for a comet; it is therefore considered to be potentially the largest comet ever seen.DNA Publications
DNA Publications was an American publishing company which existed from 1993 to 2007 and was run by the husband-and wife team of Warren Lapine and Angela Kessler, who met at a science fiction convention in Virginia. Initially based in Massachusetts, DNA Publications relocated to Radford, Virginia. As of 2004 it was the second-largest genre magazine publisher in the US. Its first publication, in 1993, was the magazine Harsh Mistress, which Lapine produced in collaboration with Kevin Rogers and Tim Ballon.
DNA Publication distributed or published Aboriginal SF, Absolute Magnitude, Artemis, Dreams of Decadence, Fantastic Stories, Mythic Delirium, The Official KISS Magazine, Science Fiction Chronicle, and The Whole Cat Journal. It also published the book imprints Spyre Books and Wilder Publications. For their work on the magazines, DNA Publications was a 2000 World Fantasy Award nominee, in the "special award: professional" category. Absolute Magnitude was a 2002 Hugo Award nominee in the semiprozine category. Notable authors published by the DNA Publications magazines include Chris Bunch, Hal Clement, Harlan Ellison, Alan Dean Foster, and Allen Steele.
DNA Publications collapsed in early 2007. Weird Tales had been bought in 2005 by Wildside Press and Mythic Delirium, which parted with DNA Publications around the same time. Wilder Publications is now part of Tir Na Nog Press.HD 190647
HD 190647 is a yellow subgiant star located approximately 177 light years away in the constellation of Sagittarius. The apparent magnitude is 8 and absolute magnitude is 4. It is also called HIP 99115. In 2007, a planet was found to be orbiting the star.HD 218061
HD 218061 is a class K4III (orange giant) star in the constellation Aquarius. Its apparent magnitude is 6.16 and it is approximately 650 light years away based on parallax. It has a companion B of apparent magnitude 11.4 and separation 55.1", corresponding to roughly absolute magnitude 4.9 and a separation of 11000 AU if the distance from Earth is the same.HD 5319
HD 5319 is an 8th magnitude star approximately 397 light years away in the constellation Cetus. It is a subgiant star of spectral type K3, having run out of hydrogen in its core. When it was main-sequence, the spectral type was early F or late A.
The absolute magnitude (apparent magnitude at 10 parsecs) is 3.05, which would translate to easy naked eye visibility, but its distance is ten times greater, so its apparent magnitude is 8.05 (100 times fainter than its absolute magnitude), it is not visible to the naked eye and binoculars are needed.Luminosity
In astronomy, luminosity is the total amount of energy emitted per unit of time by a star, galaxy, or other astronomical object. As a term for energy emitted per unit time, luminosity is synonymous with power.In SI units luminosity is measured in joules per second or watts. Values for luminosity are often given in the terms of the luminosity of the Sun, L⊙. Luminosity can also be given in terms of the astronomical magnitude system: the absolute bolometric magnitude (Mbol) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band.
In contrast, the term brightness in astronomy is generally used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, and also on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness. The distance determined by luminosity measures can be somewhat ambiguous, and is thus sometimes called the luminosity distance.Magnitude (astronomy)
In astronomy, magnitude is a unitless measure of the brightness of an object in a defined passband, often in the visible or infrared spectrum, but sometimes across all wavelengths. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus.
The scale is logarithmic and defined such that each step of one magnitude changes the brightness by a factor of the fifth root of 100, or approximately 2.512. For example, a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. The brighter an object appears, the lower the value of its magnitude, with the brightest objects reaching negative values.
Astronomers use two different definitions of magnitude: apparent magnitude and absolute magnitude. The apparent magnitude (m) is the brightness of an object as it appears in the night sky from Earth. Apparent magnitude depends on an object's intrinsic luminosity, its distance, and the extinction reducing its brightness. The absolute magnitude (M) describes the intrinsic luminosity emitted by an object and is defined to be equal to the apparent magnitude that the object would have if it were placed at a certain distance from Earth, 10 parsecs for stars. A more complex definition of absolute magnitude is used for planets and small Solar System bodies, based on its brightness at one astronomical unit from the observer and the Sun.
The Sun has an apparent magnitude of −27 and Sirius, the brightest visible star in the night sky, −1.46. Apparent magnitudes can also be assigned to artificial objects in Earth orbit with the International Space Station (ISS) sometimes reaching a magnitude of −6.Red clump
The red clump is a clustering of red giants in the Hertzsprung–Russell diagram at around 5,000 K and absolute magnitude (MV) +0.5, slightly hotter than most red-giant-branch stars of the same luminosity. It is visible as a more dense region of the red giant branch or a bulge towards hotter temperatures. It is most distinct in many, but not all, galactic open clusters, but it is also noticeable in many intermediate-age globular clusters and in nearby field stars (e.g. the Hipparcos stars).
The red clump giants are cool horizontal branch stars, stars originally similar to the Sun which have undergone a helium flash and are now fusing helium in their cores.Standard asteroid physical characteristics
For the majority of numbered asteroids, almost nothing is known apart from a few physical parameters and orbital elements and some physical characteristics are often only estimated. The physical data is determined by making certain standard assumptions.Ursa Major I Dwarf
Ursa Major I Dwarf (UMa I dSph) is a dwarf spheroidal galaxy orbiting the Milky Way galaxy. Its discovery was revealed by Beth Willman et al. in 2005.Being a small dwarf galaxy, it measures only a few thousand light-years in diameter. As of 2006, it is the third least luminous galaxy known (discounting possible dark galaxies such as VIRGOHI21 in the Virgo cluster of galaxies), after the Boötes Dwarf (absolute magnitude −5.7) and the more recently discovered Ursa Major II Dwarf (absolute magnitude −3.8). The absolute magnitude of the galaxy is estimated to be only −6.75, meaning that it is less luminous than some stars, like Deneb in the Milky Way. It is comparable in luminosity to Rigel. It has been described as similar to the Sextans Dwarf Galaxy. Both galaxies are ancient and metal-deficient.
It estimated to be located at a distance of about 330,000 light-years (100 kpc) from the Earth. That is about twice the distance to the Large Magellanic Cloud; the largest and most luminous satellite galaxy of the Milky Way.
There was another object called "Ursa Major Dwarf", discovered by Edwin Hubble in 1949. It was designated as Palomar 4. Due to its peculiar look, it was temporarily suspected to be either a dwarf spheroidal or elliptical galaxy. However, it has since been found to be a very distant (about 360,000 ly) globular cluster belonging to our galaxy.
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