In astronomy, magnitude is measure of the brightness of an object, usually in a defined passband. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus.
Magnitude values do not have a unit. 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 and absolute magnitude. The apparent magnitude (m) is the brightness of an object and 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 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. Venus at its brightest is -5. The International Space Station (ISS) sometimes reaches a magnitude of −6.
Amateur astronomers commonly express the darkness of the sky in terms of limiting 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 of illuminance, which can also be measured in photometric units such as lux. [1]
The Greek astronomer Hipparchus produced a catalogue which noted the apparent brightness of stars in the second century BC. In the second century AD the Alexandrian astronomer Ptolemy classified stars on a six-point scale, and originated the term magnitude. [2] To the unaided eye, a more prominent star such as Sirius 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. 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. [note 1] 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. [3]
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 (2′) in apparent diameter (1⁄30 of a degree, or 1⁄15 the diameter of the full moon), with second through sixth magnitude stars measuring 1+1⁄2′, 1+1⁄12′, 3⁄4′, 1⁄2′, and 1⁄3′, respectively. [4] 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. [5] 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. [5] [6] 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. [5] 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. [7]
However, by the mid-nineteenth century astronomers had measured the distances to stars via stellar parallax, 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 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 1856 Norman Pogson of Oxford proposed that a logarithmic scale of 5√100 ≈ 2.512 be adopted between magnitudes, so five magnitude steps corresponded precisely to a factor of 100 in brightness. [8] [9] Every interval of one magnitude equates to a variation in brightness of 5√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”, so Arcturus or Vega are magnitude 0, and Sirius 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 than Alpha 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, whose flux (i.e., brightness, a measure of power per unit area) in units such as watts per square metre (W m−2) are F1 and Fref, will have magnitudes m1 and mref related by
Astronomers use the term "flux" for what is often called "intensity" in physics, in order to avoid confusion with the specific 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 the list of brightest stars). For example, Sirius is magnitude −1.46, Arcturus is −0.04, Aldebaran 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), and for objects too faint for the human eye to see (such as Pluto).
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 d is the distance to the star measured in parsecs, m is the apparent magnitude, and M is the absolute magnitude.
If the line of sight between the object and observer is affected by extinction due to absorption of light by interstellar dust particles, then the object's apparent magnitude will be correspondingly fainter. For A 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 the V passband. A bolometric 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 in watts, 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. [10]
The following is a table giving apparent magnitudes for celestial objects and artificial satellites ranging from the Sun to the faintest object visible with the James 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 [11] | 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 of 8m telescopes | |||
−14 | 3.98×105 | 7 | 1.58×10−3 | Ceres (max.) faintest naked-eye stars visible from "dark" rural areas [12] | 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 of Hubble Space Telescope [13] | |||
−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 of James Webb Space Telescope [14] | |||
−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 |
Under Pogson's system the star Vega 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 (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. [15] 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.[ citation needed ]
Another logarithmic measure for intensity is the level, in 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 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 is 4 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.
Apparent magnitude is a measure of the brightness of a star or other astronomical object. An object's apparent magnitude depends on its intrinsic luminosity, its distance, and any extinction of the object's light caused by interstellar dust along the line of sight to the observer.
In astronomy, 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 were viewed from a distance of exactly 10 parsecs, without extinction of its light due to absorption by interstellar matter and cosmic dust. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared among each other on a magnitude scale. For Solar System bodies that shine in reflected light, a different definition of absolute magnitude (H) is used, based on a standard reference distance of one astronomical unit.
Canis Major is a constellation in the southern celestial hemisphere. In the second century, it was included in Ptolemy's 48 constellations, and is counted among the 88 modern constellations. Its name is Latin for "greater dog" in contrast to Canis Minor, the "lesser dog"; both figures are commonly represented as following the constellation of Orion the hunter through the sky. The Milky Way passes through Canis Major and several open clusters lie within its borders, most notably M41.
Sirius is the brightest star in the night sky. Its name is derived from the Greek word Σείριος, meaning lit. 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated α CMa or Alpha CMa. With a visual apparent magnitude of −1.46, Sirius is almost twice as bright as Canopus, the next brightest star. Sirius is a binary star consisting of a main-sequence star of spectral type A0 or A1, termed Sirius A, and a faint white dwarf companion of spectral type DA2, termed Sirius B. The distance between the two varies between 8.2 and 31.5 astronomical units as they orbit every 50 years.
Luminosity is an absolute measure of radiated electromagnetic energy (light) per unit time, and is synonymous with the radiant power emitted by a light-emitting object. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a star, galaxy, or other astronomical objects.
A binary star or binary star system is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in which case they are called visual binaries. Many visual binaries have long orbital periods of several centuries or millennia and therefore have orbits which are uncertain or poorly known. They may also be detected by indirect techniques, such as spectroscopy or astrometry. If a binary star happens to orbit in a plane along our line of sight, its components will eclipse and transit each other; these pairs are called eclipsing binaries, or, together with other binaries that change brightness as they orbit, photometric binaries.
Albireo is a double star designated Beta Cygni. The International Astronomical Union uses the name "Albireo" specifically for the brightest star in the system. Although designated 'beta', it is fainter than Gamma Cygni, Delta Cygni, and Epsilon Cygni and is the fifth-brightest point of light in the constellation of Cygnus. Appearing to the naked eye to be a single star of magnitude 3, viewing through even a low-magnification telescope resolves it into its two components. The brighter yellow star, itself a very close binary system, makes a striking colour contrast with its fainter blue companion.
Andromeda is one of the 48 constellations listed by the 2nd-century Greco-Roman astronomer Ptolemy, and one of the 88 modern constellations. Located in the northern celestial hemisphere, it is named for Andromeda, daughter of Cassiopeia, in the Greek myth, who was chained to a rock to be eaten by the sea monster Cetus. Andromeda is most prominent during autumn evenings in the Northern Hemisphere, along with several other constellations named for characters in the Perseus myth. Because of its northern declination, Andromeda is visible only north of 40° south latitude; for observers farther south, it lies below the horizon. It is one of the largest constellations, with an area of 722 square degrees. This is over 1,400 times the size of the full moon, 55% of the size of the largest constellation, Hydra, and over 10 times the size of the smallest constellation, Crux.
Lynx is a constellation named after the animal, usually observed in the Northern Celestial Hemisphere. The constellation was introduced in the late 17th century by Johannes Hevelius. It is a faint constellation, with its brightest stars forming a zigzag line. The orange giant Alpha Lyncis is the brightest star in the constellation, and the semiregular variable star Y Lyncis is a target for amateur astronomers. Six star systems have been found to contain planets. Those of 6 Lyncis and HD 75898 were discovered by the Doppler method; those of XO-2, XO-4, XO-5 and WASP-13 were observed as they passed in front of the host star.
Photometry, from Greek photo- ("light") and -metry ("measure"), is a technique used in astronomy that is concerned with measuring the flux or intensity of light radiated by astronomical objects. This light is measured through a telescope using a photometer, often made using electronic devices such as a CCD photometer or a photoelectric photometer that converts light into an electric current by the photoelectric effect. When calibrated against standard stars of known intensity and colour, photometers can measure the brightness or apparent magnitude of celestial objects.
Circinus is a small, faint constellation in the southern sky, first defined in 1756 by the French astronomer Nicolas-Louis de Lacaille. Its name is Latin for compass, referring to the drafting tool used for drawing circles. Its brightest star is Alpha Circini, with an apparent magnitude of 3.19. Slightly variable, it is the brightest rapidly oscillating Ap star in the night sky. AX Circini is a Cepheid variable visible with the unaided eye, and BX Circini is a faint star thought to have been formed from the merger of two white dwarfs. Two sun-like stars have planetary systems: HD 134060 has two small planets, and HD 129445 has a Jupiter-like planet. Supernova SN 185 appeared in Circinus in 185 AD and was recorded by Chinese observers. Two novae have been observed more recently, in the 20th century.
Naked eye, also called bare eye or unaided eye, is the practice of engaging in visual perception unaided by a magnifying, light-collecting optical instrument, such as a telescope or microscope, or eye protection.
The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A direct distance measurement of an astronomical object is possible only for those objects that are "close enough" to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances and methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity.
NGC 3982(also known as UGC 6918) is an intermediate spiral galaxy approximately 68 million light-years away in the constellation Ursa Major. It was discovered by William Herschel on April 14, 1789, and misclassified as a planetary nebula. NGC 3982 is a part of the M109 Group.
In astronomy, surface brightness (SB) quantifies the apparent brightness or flux density per unit angular area of a spatially extended object such as a galaxy or nebula, or of the night sky background. An object's surface brightness depends on its surface luminosity density, i.e., its luminosity emitted per unit surface area. In visible and infrared astronomy, surface brightness is often quoted on a magnitude scale, in magnitudes per square arcsecond (MPSAS) in a particular filter band or photometric system.
The Malmquist bias is an effect in observational astronomy which leads to the preferential detection of intrinsically bright objects. It was first described in 1922 by Swedish astronomer Gunnar Malmquist (1893–1982), who then greatly elaborated upon this work in 1925. In statistics, this bias is referred to as a selection bias or data censoring. It affects the results in a brightness-limited survey, where stars below a certain apparent brightness cannot be included. Since observed stars and galaxies appear dimmer when farther away, the brightness that is measured will fall off with distance until their brightness falls below the observational threshold. Objects which are more luminous, or intrinsically brighter, can be observed at a greater distance, creating a false trend of increasing intrinsic brightness, and other related quantities, with distance. This effect has led to many spurious claims in the field of astronomy. Properly correcting for these effects has become an area of great focus.
Photographic magnitude is a measure of the relative brightness of a star or other astronomical object as imaged on a photographic film emulsion with a camera attached to a telescope. An object's apparent photographic magnitude depends on its intrinsic luminosity, its distance and any extinction of light by interstellar matter existing along the line of sight to the observer.
The Solar System and all of the visible stars are in different orbits about the core of the Milky Way galaxy. Thus, their relative positions change over time, and for the nearer stars this movement can be measured. As a star moves toward or away from us, its apparent brightness changes. Sirius is currently the brightest star in Earth's night sky, but it has not always been so. Canopus has persistently been the brightest star over the ages; other stars appear brighter only during relatively temporary periods, during which they are passing the Solar System at a much closer distance than Canopus.
First-magnitude stars are the brightest stars in the night sky, with apparent magnitudes lower than +1.50. Hipparchus, in the 1st century BC, introduced the magnitude scale. He allocated the first magnitude to the 20 brightest stars and the sixth magnitude to the faintest stars visible to the naked eye.