Inastronomy,magnitude is a measure of thebrightness of anobject, usually in a definedpassband. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times byHipparchus.
Magnitude values do not have a unit. The scale islogarithmic 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[1]. 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 andabsolute magnitude. Theapparent magnitude (m) is the brightness of an object and depends on an object's intrinsicluminosity, itsdistance, and theextinction reducing its brightness. Theabsolute 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, 10parsecs for stars. A more complex definition of absolute magnitude is used forplanets andsmall Solar System bodies, based on its brightness at oneastronomical unit from the observer and the Sun.
TheSun has an apparent magnitude of −27 andSirius, the brightest visible star in the night sky, −1.46.Venus at its brightest is -5. TheInternational Space Station (ISS) sometimes reaches a magnitude of −6.
Amateur astronomers commonly express the darkness of the sky in terms oflimiting magnitude, i.e. the apparent magnitude of the faintest star they can see with the naked eye. At a dark site, it is usual for people to see stars of 6th magnitude or fainter.
Apparent magnitude is really a measure ofilluminance, which can also be measured in photometric units such aslux.[2]
The Greek astronomerHipparchus produced a catalogue which noted the apparent brightness of stars in the second century BCE. In the second century CE, the Alexandrian astronomerPtolemy classified stars on a six-point scale, and originated the termmagnitude.[3] To the unaided eye, a more prominent star such asSirius orArcturus appears larger than a less prominent star such asMizar, which in turn appears larger than a truly faint star such asAlcor. In 1736, the mathematicianJohn Keill described the ancient naked-eye magnitude system in this way:
Thefixed Stars appear to be of different Bignesses, not because they really are so, but because they are not all equally distant from us.[note 1] Those that are nearest will excel in Lustre and Bigness; the more remoteStars will give a fainter Light, and appear smaller to the Eye. Hence arise the Distribution ofStars, according to their Order and Dignity, intoClasses; the first Class containing those which are nearest to us, are calledStars of the first Magnitude; those that are next to them, areStars of the second Magnitude ... and so forth, 'till we come to theStars of the sixth Magnitude, which comprehend the smallestStars that can be discerned with the bare Eye. For all the otherStars, 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 ofStars into six Degrees of Magnitude is commonly received byAstronomers; yet we are not to judge, that every particularStar 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 ofStars, as there areStars, few of them being exactly of the same Bigness and Lustre. And even among thoseStars which are reckoned of the brightest Class, there appears a Variety of Magnitude; forSirius orArcturus are each of them brighter thanAldebaran or theBull's Eye, or even than theStar inSpica; and yet all theseStars are reckoned among theStars of the first Order: And there are someStars of such an intermedial Order, that theAstronomers have differed in classing of them; some putting the sameStars in one Class, others in another. For Example: The littleDog was byTycho placed among theStars of the second Magnitude, whichPtolemy reckoned among theStars 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.[4]
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 2arc minutes (2′) in apparent diameter (1⁄30 of a degree, or1⁄15 the diameter of the full moon), with second through sixth magnitude stars measuring1+1⁄2′,1+1⁄12′,3⁄4′,1⁄2′, and1⁄3′, respectively.[5] 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 fromGalileo toJaques 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.[6]Johannes Hevelius produced a very precise table of star sizes measured telescopically, but now the measured diameters ranged from just over sixseconds of arc for first magnitude down to just under 2 seconds for sixth magnitude.[6][7] By the time ofWilliam 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.[6] Even into the early nineteenth century, the magnitude system continued to be described in terms of six classes determined by apparent size.[8]
However, by the mid-nineteenth century astronomers had measured the distances to stars viastellar parallax, and so understood that stars are so far away as to essentially appear aspoint sources of light. Following advances in understanding thediffraction of light andastronomical 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 per square metre) so that brighter stars appeared larger.
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 1856Norman Pogson of Oxford proposed that a logarithmic scale of5√100 ≈ 2.512 be adopted between magnitudes, so five magnitude steps corresponded precisely to a factor of 100 in brightness.[9][10] Every interval of one magnitude equates to a variation in brightness of5√100 or roughly 2.512 times. Consequently, a magnitude 1 star is about 2.5 times brighter than a magnitude 2 star, about 2.52 times brighter than a magnitude 3 star, about 2.53 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”, soArcturus orVega are magnitude 0, andSirius is magnitude −1.46.[citation needed]
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.
Two of the main types of magnitudes distinguished by astronomers are:
The difference between these concepts can be seen by comparing two stars.Betelgeuse (apparent magnitude 0.5, absolute magnitude −5.8) appears slightly dimmer in the sky thanAlpha Centauri A (apparent magnitude 0.0, absolute magnitude 4.4) even though it emits thousands of times more light, because Betelgeuse is much farther away.
Under the modern logarithmic magnitude scale, two objects, one of which is used as a reference or baseline, whoseflux (i.e., brightness, a measure of power per unit area) in units such as watts per square metre (W m−2) areF1 andFref, will have magnitudesm1 andmref related by
Astronomers use the term "flux" for what is often called "intensity" in physics, in order to avoid confusion with thespecific intensity. 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.Astronomers 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 thelist of brightest stars). For example,Sirius is magnitude −1.46,Arcturus is −0.04,Aldebaran is 0.85,Spica is 1.04, andProcyon 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 theSun andMoon), and for objects too faint for the human eye to see (such asPluto).
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 thedistance modulus, whered is the distance to the star measured inparsecs,m is the apparent magnitude, andM is the absolute magnitude.
If the line of sight between the object and observer is affected byextinction due to absorption of light byinterstellar dust particles, then the object's apparent magnitude will be correspondingly fainter. ForA 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, MV is the magnitude at 10 parsecs in theV passband. Abolometric magnitude (Mbol) 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 inwatts, and are normalised to be approximately equal to MV 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.[11]
The following is a table givingapparent magnitudes forcelestial objects andartificial satellites ranging from the Sun to the faintest object visible with theJames Webb Space Telescope (JWST):
| Apparent magnitude | Brightness relative to magnitude 0 | Example | Apparent magnitude | Brightness relative to magnitude 0 | Example | Apparent magnitude | Brightness relative to magnitude 0 | Example | ||
|---|---|---|---|---|---|---|---|---|---|---|
| −27 | 6.31×1010 | Sun | −6 | 251 | ISS(max.) | 15 | 10−6 | |||
| −26 | 2.51×1010 | −5 | 100 | Venus(max.) | 16 | 3.98×10−7 | Charon(max.) | |||
| −25 | 1010 | −4 | 39.8 | Faintest objects visible during the day with the naked eye when the sun is high[12] | 17 | 1.58×10−7 | ||||
| −24 | 3.98×109 | −3 | 15.8 | Jupiter(max.),Mars(max.) | 18 | 6.31×10−8 | ||||
| −23 | 1.58×109 | −2 | 6.31 | Mercury(max.) | 19 | 2.51×10−8 | ||||
| −22 | 6.31×108 | −1 | 2.51 | Sirius | 20 | 10−8 | ||||
| −21 | 2.51×108 | 0 | 1 | Vega,Saturn(max.) | 21 | 3.98×10−9 | Callirrhoe(satellite of Jupiter) | |||
| −20 | 108 | 1 | 0.398 | Antares | 22 | 1.58×10−9 | ||||
| −19 | 3.98×107 | 2 | 0.158 | Polaris | 23 | 6.31×10−10 | ||||
| −18 | 1.58×107 | 3 | 0.0631 | Cor Caroli | 24 | 2.51×10−10 | ||||
| −17 | 6.31×106 | 4 | 0.0251 | Acubens | 25 | 10−10 | Fenrir(satellite of Saturn) | |||
| −16 | 2.51×106 | 5 | 0.01 | Vesta(max.),Uranus(max.) | 26 | 3.98×10−11 | ||||
| −15 | 106 | 6 | 3.98×10−3 | typical limit of naked eye[note 2] | 27 | 1.58×10−11 | visible light limit of8m telescopes | |||
| −14 | 3.98×105 | 7 | 1.58×10−3 | Ceres(max.) faintest naked-eye stars visible from "dark" rural areas[13] | 28 | 6.31×10−12 | ||||
| −13 | 1.58×105 | full moon | 8 | 6.31×10−4 | Neptune(max.) | 29 | 2.51×10−12 | |||
| −12 | 6.31×104 | 9 | 2.51×10−4 | 30 | 10−12 | |||||
| −11 | 2.51×104 | 10 | 10−4 | typical limit of 7×50 binoculars | 31 | 3.98×10−13 | ||||
| −10 | 104 | 11 | 3.98×10−5 | Proxima Centauri | 32 | 1.58×10−13 | visible light limit ofHubble Space Telescope[14] | |||
| −9 | 3.98×103 | Iridium flare(max.) | 12 | 1.58×10−5 | 33 | 6.29×10−14 | ||||
| −8 | 1.58×103 | 13 | 6.31×10−6 | 3C 273 quasar limit of 4.5–6 in (11–15 cm) telescopes | 34 | 2.50×10−14 | near-infrared light limit ofJames Webb Space Telescope[15] | |||
| −7 | 631 | SN 1006 supernova | 14 | 2.51×10−6 | Pluto(max.) limit of 8–10 in (20–25 cm) telescopes | 35 | 9.97×10−15 |
Any magnitude systems must be calibrated to define the brightness of magnitude zero. Many magnitude systems, such as the Johnson UBV system, assign the average brightness of several stars to a certain number to by definition, and all other magnitude measurements are compared to that reference point.[16] Other magnitude systems calibrate by measuring energy directly, without a reference point, and these are called "absolute" reference systems. Current absolute reference systems include theAB magnitude system, in which the reference is a source with a constant flux density per unit frequency,[17] and the STMAG system, in which the reference source is instead defined to have constant flux density per unit wavelength.[citation needed]
Another logarithmic measure for intensity is the level, indecibel. Although it is more commonly used for sound intensity, it is also used for light intensity. It is a parameter forphotomultiplier 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 level 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 is4 dB smaller (weaker) than the reference, which might need to be compensated by an increase in the capability of the camera by as many decibels.
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