In
astronomy
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
, magnitude is a
unitless
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
measure of the
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. The perception is not linear to luminance, ...
of an
object
Object may refer to:
General meanings
* Object (philosophy), a thing, being, or concept
** Object (abstract), an object which does not exist at any particular time or place
** Physical object, an identifiable collection of matter
* Goal, an ...
in a defined
passband, often in the
visible or
infrared
Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...
spectrum, but sometimes across all wavelengths. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by
Hipparchus
Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the e ...
.
The scale is
logarithmic and defined such that a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. Thus each step of one magnitude is
times brighter than the magnitude 1 higher. 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
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's ...
and
absolute magnitude
Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse 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 ...
. The ''apparent'' magnitude () is the brightness of an object as it appears in the
night sky
The night sky is the nighttime appearance of celestial objects like stars, planets, and the Moon, which are visible in a clear sky between sunset and sunrise, when the Sun is below the horizon.
Natural light sources in a night sky in ...
from
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
. Apparent magnitude depends on an object's intrinsic
luminosity, its
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
, and the
extinction
Extinction is the termination of a kind of organism or of a group of kinds (taxon), usually a species. The moment of extinction is generally considered to be the death of the Endling, last individual of the species, although the Functional ext ...
reducing its brightness. The ''absolute'' magnitude () 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
planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s and
small Solar System bodies, based on its brightness at one
astronomical unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits ...
from the observer and the Sun.
The
Sun has an apparent magnitude of −27 and
Sirius
Sirius is the brightest star in the night sky. Its name is derived from the Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated Alpha CM ...
, the brightest visible star in the night sky, −1.46.
Venus at its brightest is -5. The
International Space Station
The International Space Station (ISS) is the largest Modular design, modular space station currently in low Earth orbit. It is a multinational collaborative project involving five participating space agencies: NASA (United States), Roscosmos ( ...
(ISS) sometimes reaches a magnitude of −6.
History
The Greek astronomer
Hipparchus
Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the e ...
produced a catalogue which noted the apparent brightness of stars in the second century BCE. In the second century CE the Alexandrian astronomer
Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
classified stars on a six point scale, and originated the term
magnitude.
To the unaided eye, a more prominent star such as
Sirius
Sirius is the brightest star in the night sky. Its name is derived from the Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated Alpha CM ...
or
Arcturus appears larger than a less prominent star such as
Mizar, which in turn appears larger than a truly faint star such as
Alcor
ALCOR (ALGOL Converter, acronym) is an early computer language definition created by the ALCOR Group, a consortium of universities, research institutions and manufacturers in Europe and the United States which was founded in 1959 and which had 60 m ...
. In 1736, the mathematician
John Keill described the ancient naked-eye magnitude system in this way:
The ''fixed Stars'' appear to be of different Bignesses, not because they really are so, but because they are not all equally distant from us. Those that are nearest will excel in Lustre and Bigness; the more remote ''Stars'' will give a fainter Light, and appear smaller to the Eye. Hence arise the Distribution of ''Stars'', according to their Order and Dignity, into ''Classes''; the first Class containing those which are nearest to us, are called ''Stars'' of the first Magnitude; those that are next to them, are ''Stars'' of the second Magnitude ... and so forth, 'till we come to the ''Stars'' of the sixth Magnitude, which comprehend the smallest ''Stars'' that can be discerned with the bare Eye. For all the other ''Stars'', which are only seen by the Help of a Telescope, and which are called Telescopical, are not reckoned among these six Orders. Altho' the Distinction of ''Stars'' into six Degrees of Magnitude is commonly received by ''Astronomers''; yet we are not to judge, that every particular ''Star'' is exactly to be ranked according to a certain Bigness, which is one of the Six; but rather in reality there are almost as many Orders of ''Stars'', as there are ''Stars'', few of them being exactly of the same Bigness and Lustre. And even among those ''Stars'' which are reckoned of the brightest Class, there appears a Variety of Magnitude; for ''Sirius'' or ''Arcturus'' are each of them brighter than ''Aldebaran'' or the ''Bull's'' Eye, or even than the ''Star'' in ''Spica''; and yet all these ''Stars'' are reckoned among the ''Stars'' of the first Order: And there are some ''Stars'' of such an intermedial Order, that the ''Astronomers'' have differed in classing of them; some putting the same ''Stars'' in one Class, others in another. For Example: The little ''Dog'' was by ''Tycho'' placed among the ''Stars'' of the second Magnitude, which ''Ptolemy'' reckoned among the ''Stars'' of the first Class: And therefore it is not truly either of the first or second Order, but ought to be ranked in a Place between both.
Note that the brighter the star, the smaller the magnitude: Bright "first magnitude" stars are "1st-class" stars, while stars barely visible to the naked eye are "sixth magnitude" or "6th-class".
The system was a simple delineation of stellar brightness into six distinct groups but made no allowance for the variations in brightness within a group.
Tycho Brahe attempted to directly measure the "bigness" of the stars in terms of angular size, which in theory meant that a star's magnitude could be determined by more than just the subjective judgment described in the above quote. He concluded that first magnitude stars measured 2
arc minutes
ARC may refer to:
Business
* Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s
* Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services
* ...
(2′) in apparent diameter ( of a degree, or the diameter of the full moon), with second through sixth magnitude stars measuring ′, ′, ′, ′, and ′, respectively. The development of the telescope showed that these large sizes were illusory—stars appeared much smaller through the telescope. However, early telescopes produced a spurious disk-like image of a star that was larger for brighter stars and smaller for fainter ones. Astronomers from
Galileo to
Jaques Cassini mistook these spurious disks for the physical bodies of stars, and thus into the eighteenth century continued to think of magnitude in terms of the physical size of a star.
Johannes Hevelius produced a very precise table of star sizes measured telescopically, but now the measured diameters ranged from just over six
''seconds'' of arc for first magnitude down to just under 2 seconds for sixth magnitude.
[
] By the time of
William Herschel astronomers recognized that the telescopic disks of stars were spurious and a function of the telescope as well as the brightness of the stars, but still spoke in terms of a star's size more than its brightness.
Even well into the nineteenth century the magnitude system continued to be described in terms of six classes determined by apparent size, in which
There is no other rule for classing the stars but the estimation of the observer; and hence it is that some astronomers reckon those stars of the first magnitude which others esteem to be of the second.
However, by the mid-nineteenth century astronomers had measured the distances to stars via
stellar parallax
Stellar parallax is the apparent shift of position of any nearby star (or other object) against the background of distant objects, and a basis for determining (through trigonometry) the distance of the object. Created by the different orbital p ...
, and so understood that stars are so far away as to essentially appear as
point sources of light. Following advances in understanding the
diffraction of light and
astronomical seeing, astronomers fully understood both that the apparent sizes of stars were spurious and how those sizes depended on the intensity of light coming from a star (this is the star's apparent brightness, which can be measured in units such as watts/cm
2) so that brighter stars appeared larger.
Modern definition
Early photometric measurements (made, for example, by using a light to project an artificial “star” into a telescope's field of view and adjusting it to match real stars in brightness) demonstrated that first magnitude stars are about 100 times brighter than sixth magnitude stars.
Thus in 1856
Norman Pogson
Norman Robert Pogson, CIE (23 March 1829 – 23 June 1891) was an English astronomer who worked in India at the Madras observatory. He discovered several minor planets and made observations on comets. He introduced a mathematical scale of stel ...
of Oxford proposed that a logarithmic scale of ≈ 2.512 be adopted between magnitudes, so five magnitude steps corresponded precisely to a factor of 100 in brightness. Every interval of one magnitude equates to a variation in brightness of or roughly 2.512 times. Consequently, a magnitude 1 star is about 2.5 times brighter than a magnitude 2 star, about 2.5
2 times brighter than a magnitude 3 star, about 2.5
3 times brighter than a magnitude 4 star, and so on.
This is the modern magnitude system, which measures the brightness, not the apparent size, of stars. Using this logarithmic scale, it is possible for a star to be brighter than “first class”, so
Arcturus or
Vega
Vega is the brightest star in the northern constellation of Lyra. It has the Bayer designation α Lyrae, which is Latinised to Alpha Lyrae and abbreviated Alpha Lyr or α Lyr. This star is relatively close at only from the Sun, a ...
are magnitude 0, and
Sirius
Sirius is the brightest star in the night sky. Its name is derived from the Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated Alpha CM ...
is magnitude −1.46.
Scale
As mentioned above, the scale appears to work 'in reverse', with objects with a negative magnitude being brighter than those with a positive magnitude. The more negative the value, the brighter the object.
Objects appearing farther to the left on this line are brighter, while objects appearing farther to the right are dimmer. Thus zero appears in the middle, with the brightest objects on the far left, and the dimmest objects on the far right.
Apparent and absolute magnitude
Two of the main types of magnitudes distinguished by astronomers are:
* Apparent magnitude, the brightness of an object as it appears in the night sky.
* Absolute magnitude, which measures the
luminosity of an object (or reflected light for non-luminous objects like
asteroids); it is the object's apparent magnitude as seen from a specific distance, conventionally 10
parsecs (32.6
light years).
The difference between these concepts can be seen by comparing two stars.
Betelgeuse
Betelgeuse is a red supergiant of spectral type M1-2 and one of the largest stars visible to the naked eye. It is usually the tenth-brightest star in the night sky and, after Rigel, the second-brightest in the constellation of O ...
(apparent magnitude 0.5, absolute magnitude −5.8) appears slightly dimmer in the sky than
Alpha Centauri A
Alpha Centauri (Latinisation of names, Latinized from α Centauri and often abbreviated Alpha Cen or α Cen) is a Star System, triple star system in the constellation of Centaurus (constellation), Centaurus. It consists of 3 stars: ...
(apparent magnitude 0.0, absolute magnitude 4.4) even though it emits thousands of times more light, because Betelgeuse is much farther away.
Apparent magnitude
Under the modern logarithmic magnitude scale, two objects, one of which is used as a reference or baseline, whose
intensities (brightnesses) measured from
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
in units of power per unit area (such as watts per square metre, W m
−2) are and , will have magnitudes and related by
:
Using this formula, the magnitude scale can be extended beyond the ancient magnitude 1–6 range, and it becomes a precise measure of brightness rather than simply a classification system.
Astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...
s now measure differences as small as one-hundredth of a magnitude. Stars that have magnitudes between 1.5 and 2.5 are called second-magnitude; there are some 20 stars brighter than 1.5, which are first-magnitude stars (see the
list of brightest stars
This is a list of stars arranged by their apparent magnitude – their brightness as observed from Earth. It includes all stars brighter than magnitude +2.50 in visible light, measured using a ''V''-band filter in the UBV photometric system. Sta ...
). For example,
Sirius
Sirius is the brightest star in the night sky. Its name is derived from the Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated Alpha CM ...
is magnitude −1.46,
Arcturus is −0.04,
Aldebaran
Aldebaran (Arabic: “The Follower”, "الدبران") is the brightest star in the zodiac constellation of Taurus. It has the Bayer designation α Tauri, which is Latinized to Alpha Tauri and abbreviated Alpha Tau or α Tau. Aldeba ...
is 0.85,
Spica is 1.04, and
Procyon is 0.34. Under the ancient magnitude system, all of these stars might have been classified as "stars of the first magnitude".
Magnitudes can also be calculated for objects far brighter than stars (such as the
Sun and
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
), and for objects too faint for the human eye to see (such as
Pluto
Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the S ...
).
Absolute magnitude
Often, only apparent magnitude is mentioned since it can be measured directly. Absolute magnitude can be calculated from apparent magnitude and distance from:
:
because intensity falls off proportionally to distance squared. This is known as the
distance modulus, where is the distance to the star measured in
parsecs, is the apparent magnitude, and is the absolute magnitude.
If the line of sight between the object and observer is affected by
extinction
Extinction is the termination of a kind of organism or of a group of kinds (taxon), usually a species. The moment of extinction is generally considered to be the death of the Endling, last individual of the species, although the Functional ext ...
due to absorption of light by
interstellar dust particles, then the object's apparent magnitude will be correspondingly fainter. For magnitudes of extinction, the relationship between apparent and absolute magnitudes becomes
:
Stellar absolute magnitudes are usually designated with a capital M with a subscript to indicate the passband. For example, M
V is the magnitude at 10 parsecs in the
V passband. A
bolometric magnitude
Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse 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 w ...
(M
bol) is an absolute magnitude adjusted to take account of radiation across all wavelengths; it is typically smaller (i.e. brighter) than an absolute magnitude in a particular passband, especially for very hot or very cool objects. Bolometric magnitudes are formally defined based on stellar luminosity in
watt
The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James ...
s, and are normalised to be approximately equal to M
V for yellow stars.
Absolute magnitudes for solar system objects are frequently quoted based on a distance of 1 AU. These are referred to with a capital H symbol. Since these objects are lit primarily by reflected light from the sun, an H magnitude is defined as the apparent magnitude of the object at 1 AU from the sun and 1 AU from the observer.
Examples
The following is a table giving
apparent magnitude
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's ...
s for
celestial objects and
artificial satellites ranging from the Sun to the faintest object visible with the
Hubble Space Telescope (HST):
Other scales
Under
Pogson's system the star
Vega
Vega is the brightest star in the northern constellation of Lyra. It has the Bayer designation α Lyrae, which is Latinised to Alpha Lyrae and abbreviated Alpha Lyr or α Lyr. This star is relatively close at only from the Sun, a ...
was used as the fundamental reference star, with an apparent magnitude defined to be
zero, regardless of measurement technique or wavelength filter. This is why objects brighter than Vega, such as
Sirius
Sirius is the brightest star in the night sky. Its name is derived from the Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated Alpha CM ...
(Vega magnitude of −1.46. or −1.5), have negative magnitudes. However, in the late twentieth century Vega was found to vary in brightness making it unsuitable for an absolute reference, so the reference system was modernized to not depend on any particular star's stability. This is why the modern value for Vega' magnitude is close to, but no longer exactly zero, but rather 0.03 in the V (visual) band.
[
]
Current absolute reference systems include the
AB magnitude system, in which the reference is a source with a constant flux density per unit frequency, and the STMAG system, in which the reference source is instead defined to have constant flux density per unit wavelength.
Decibel
Another logarithmic scale for intensity is the
decibel. Although it is more commonly used for sound intensity, it is also used for light intensity. It is a parameter for
photomultiplier tubes and similar camera optics for telescopes and microscopes. Each factor of 10 in intensity corresponds to 10 decibels. In particular, a multiplier of 100 in intensity corresponds to an increase of 20 decibels and also corresponds to a decrease in magnitude by 5. Generally, the change in decibels is related to a change in magnitude by
:
For example, an object that is 1 magnitude larger (fainter) than a reference would produce a signal that is smaller (weaker) than the reference, which might need to be compensated by an increase in the capability of the camera by as many decibels.
See also
*
AB magnitude
*
Color–color diagram
A color–color diagram is a means of comparing the colors of an astronomical object at different wavelengths. Astronomers typically observe at narrow bands around certain wavelengths, and objects observed will have different brightnesses in each ...
*
List of brightest stars
This is a list of stars arranged by their apparent magnitude – their brightness as observed from Earth. It includes all stars brighter than magnitude +2.50 in visible light, measured using a ''V''-band filter in the UBV photometric system. Sta ...
*
Photometric-standard star
*
UBV photometric system
Notes
References
External links
*
{{Portal bar, Astronomy, Spaceflight, Outer space, Solar System
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Units of measurement in astronomy
Logarithmic scales of measurement
Concepts in astronomy
la:Magnitudo (astronomia)