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.

Night sky with a very bright satellite flare
Hubble Ultra Deep Field part
CometBorrelly1002
  • Top: Light sources of different magnitudes. A very bright satellite flare can be seen in the night sky.
  • Bottom: The Hubble Ultra-Deep Field detected objects as faint as 30th magnitude (left). Comet Borrelly, the colors show its brightness over the range of three orders of magnitude (right).

History

The magnitude system dates back roughly 2000 years to the Greek astronomer Hipparchus (or the Alexandrian astronomer Ptolemy—references vary) who classified stars by their apparent brightness, which they saw as size (magnitude means "bigness, size"[1]). 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.[2]

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 (​130 of a degree, or ​115 the diameter of the full moon), with second through sixth magnitude stars measuring ​1 12′, ​1 112′, ​34′, ​12′, and ​13′, respectively.[3] 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.[4] 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.[4][5] 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.[4] 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.[6]

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/cm2) 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 of Oxford proposed that a logarithmic scale of 5100 ≈ 2.512 be adopted between magnitudes, so five magnitude steps corresponded precisely to a factor of 100 in brightness.[7][8] Every interval of one magnitude equates to a variation in brightness of 5100 or roughly 2.512 times. Consequently, a magnitude 1 star is about 2.5 times brighter than a magnitude 2 star, 2.52 brighter than a magnitude 3 star, 2.53 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.

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.

Number-line

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 (apparent magnitude 0.5, absolute magnitude −5.8) appears slightly dimmer in the sky than Alpha Centauri (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 in units of power per unit area (such as watts per square metre, W m−2) are I1 and Iref, will have magnitudes m1 and mref 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. Astronomers can 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).

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:

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.[9]

Examples

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 Hubble Space Telescope (HST):

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 −7 631 SN 1006 supernova 13 6.31×10−6 3C 273 quasar
limit of 4.5–6 in (11–15 cm) telescopes
−26 2.51×1010 −6 251 ISS (max.) 14 2.51×10−6 Pluto (max.)
limit of 8–10 in (20–25 cm) telescopes
−25 1×1010 −5 100 Venus (max.) 15 1×10−6
−24 3.98×109 −4 39.8 Faintest objects visible during the day with the naked eye when the sun is high[10] 16 3.98×10−7 Charon (max.)
−23 1.58×109 −3 15.8 Jupiter (max.), Mars (max.) 17 1.58×10−7
−22 6.31×108 −2 6.31 Mercury (max.) 18 6.31×10−8
−21 2.51×108 −1 2.51 Sirius 19 2.51×10−8
−20 1×108 0 1 Vega, Saturn (max.) 20 1×10−8
−19 3.98×107 1 0.398 Antares 21 3.98×10−9 Callirrhoe (satellite of Jupiter)
−18 1.58×107 2 0.158 Polaris 22 1.58×10−9
−17 6.31×106 3 0.0631 Cor Caroli 23 6.31×10−10
−16 2.51×106 4 0.0251 Acubens 24 2.51×10−10
−15 1×106 5 0.01 Vesta (max.), Uranus (max.) 25 1×10−10 Fenrir (satellite of Saturn)
−14 3.98×105 6 3.98×10−3 typical limit of naked eye[note 2] 26 3.98×10−11
−13 1.58×105 full moon 7 1.58×10−3 Ceres (max.) 27 1.58×10−11 visible light limit of 8m telescopes
−12 6.31×104 8 6.31×10−4 Neptune (max.) 28 6.31×10−12
−11 2.51×104 9 2.51×10−4 29 2.51×10−12
−10 1×104 10 1×10−4 typical limit of 7×50 binoculars 30 1×10−12
−9 3.98×103 Iridium flare (max.) 11 3.98×10−5 Proxima Centauri 31 3.98×10−13
−8 1.58×103 12 1.58×10−5 32 1.58×10−13 visible light limit of HST

Other scales

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.[11] 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.

Problems

The human eye is easily fooled, and Hipparchus's scale has had problems. For example, the human eye is more sensitive to yellow and red light than to blue, and photographic film more to blue than to yellow/red, giving different values of visual magnitude and photographic magnitude. Apparent magnitude can also be affected by factors such as dust in the atmosphere or light cloud cover absorbing some of the light.

Furthermore, many people find it counter-intuitive that a high magnitude star is dimmer than a low magnitude star.

See also

Notes

  1. ^ Today astronomers know that the brightness of stars is a function of both their distance and their own luminosity.
  2. ^ Under very dark skies, such as are found in remote rural areas

References

  1. ^ Heifetz, M.; Tirion, W. (2004). A Walk Through the Heavens: A Guide to Stars and Constellations and Their Legends. Cambridge: Cambridge University Press. p. 6.
  2. ^ Keill, J. (1739). An introduction to the true astronomy (3rd ed.). London. pp. 47–48.
  3. ^ Thoren, V. E. (1990). The Lord of Uraniborg. Cambridge: Cambridge University Press. p. 306.
  4. ^ a b c Graney, C. M.; Grayson, T. P. (2011). "On the Telescopic Disks of Stars: A Review and Analysis of Stellar Observations from the Early 17th through the Middle 19th Centuries". Annals of Science. 68 (3): 351–373. arXiv:1003.4918. doi:10.1080/00033790.2010.507472.
  5. ^ Graney, C. M. (2009). "17th Century Photometric Data in the Form of Telescopic Measurements of the Apparent Diameters of Stars by Johannes Hevelius". Baltic Astronomy. 18 (3–4): 253–263. arXiv:1001.1168. Bibcode:2009BaltA..18..253G.
  6. ^ Ewing, A.; Gemmere, J. (1812). Practical Astronomy. Burlington, NJ: Allison. p. 41.
  7. ^ Hoskin, M. (1999). The Cambridge Concise History of Astronomy. Cambridge: Cambridge University Press. p. 258.
  8. ^ Tassoul, J. L.; Tassoul, M. (2004). A Concise History of Solar and Stellar Physics. Princeton, NJ: Princeton University Press. p. 47.
  9. ^ "Glossary". JPL. Archived from the original on 2017-11-25. Retrieved 2017-11-23.
  10. ^ "Seeing stars and planets in the daylight". sky.velp.info. Archived from the original on 7 March 2016. Retrieved 8 May 2018.
  11. ^ Milone, E. F. (2011). Astronomical Photometry: Past, Present and Future. New York: Springer. pp. 182–184. ISBN 978-1-4419-8049-6.

External links

Cosmic Eye

Cosmic Eye is a short film and iOS app, developed by astrophysicist Danail Obreschkow. It shows the largest and smallest known scales of the universe by gradually zooming out from and then back into the face of a young lady called "Louise". According to the developer, the film and app were inspired by the essay Cosmic View (1957) and the short films Cosmic Zoom (1968) and Powers of Ten (1977), but use state-of-the-art know-how and new scientific imaging and computer simulations. Cosmic Eye was developed in 2012 and suddenly become famous in April 2016, when it scored 40 million views in ten days on the Facebook group page of "The Science Scoop". The video has since been viewed more than 200 Million times on Facebook (top-ten counts only) and was featured in major media, such as BBC World News.Cosmic Eye was re-released in 2018 in high-resolution landscape (16:9) format (the first version was portrait shaped).

Cosmic Voyage

Cosmic Voyage is a 1996 short documentary film produced in the IMAX format, directed by Bayley Silleck, produced by Jeffrey Marvin, and narrated by Morgan Freeman. The film was presented by the Smithsonian Institution's National Air and Space Museum,

and played in IMAX theaters worldwide. The film is available in the DVD format.

Index of physics articles (M)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

Intensity (physics)

In physics, intensity is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m2). It is used most frequently with waves ( Example - sound or light), in which case the average power transfer over one period of the wave is used. Intensity can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler.

The word "intensity" as used here is not synonymous with "strength", "amplitude", "magnitude", or "level", as it sometimes is in colloquial speech.

Intensity can be found by taking the energy density (energy per unit volume) at a point in space and multiplying it by the velocity at which the energy is moving. The resulting vector has the units of power divided by area (i.e., surface power density).

Photographic magnitude

Photographic magnitude (mph or mp ) 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.

Photographic observations have now been superseded by electronic photometry such as CCD charge-couple device cameras that convert the incoming light into an electric current by the photoelectric effect. Determination of magnitude is made using a photometer.

Star chart

A star chart or star map, also called a sky chart or sky map, is a map of the night sky. Astronomers divide these into grids to use them more easily. They are used to identify and locate constellations and astronomical objects such as stars, nebulae, and galaxies. They have been used for human navigation since time immemorial. Note that a star chart differs from an astronomical catalog, which is a listing or tabulation of astronomical objects for a particular purpose. Tools utilizing a star chart include the astrolabe and planisphere.

Formation
Evolution
Spectral
classification
Remnants
Hypothetical
Nucleosynthesis
Structure
Properties
Star systems
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