In some cases, limiting magnitude refers to the upper threshold of detection. In more formal uses, limiting magnitude is specified along with the strength of the signal (e.g., "10th magnitude at 20 sigma"). Sometimes limiting magnitude is qualified by the purpose of the instrument (e.g., "10th magnitude for photometry") This statement recognizes that a photometric detector can detect light far fainter than it can reliably measure.
The limiting magnitude of an instrument is often cited for ideal conditions, but environmental conditions impose further practical limits. These include weather, moonlight, skyglow, and light pollution. The International Dark-Sky Association has been vocal in championing the cause of reducing skyglow and light pollution.
The limiting magnitude for naked eye visibility refers to the faintest stars that can be seen with the unaided eye near the zenith on clear moonless nights. The quantity is most often used as an overall indicator of sky brightness, in that light polluted and humid areas generally have brighter limiting magnitudes than remote desert or high altitude areas. The limiting magnitude will depend on the observer, and will increase with the eye's dark adaptation. On a relatively clear sky, the limiting visibility will be about 6th magnitude.[2] However, the limiting visibility is 7th magnitude for faint stars visible from dark rural areas located 200km (120mi) from major cities.[3]
There is even variation within metropolitan areas. For those who live in the immediate suburbs of New York City, the limiting magnitude might be 4.0. This corresponds to roughly 250 visible stars, or one-tenth of the number that is visible under perfectly dark skies. From the boroughs of New York City outside Manhattan (Brooklyn, Queens, Staten Island, and the Bronx), the limiting magnitude might be 3.0, suggesting that at best, only about 50 stars might be seen at any one time. From brightly lit Midtown Manhattan, the limiting magnitude is possibly 2.0, meaning that from the heart of New York City only about 15 stars will be visible at any given time.
From relatively dark suburban areas, the limiting magnitude is frequently closer to 5 or somewhat fainter, but from very remote and clear sites, some amateur astronomers can see nearly as faint as 8th magnitude. Many basic observing references quote a limiting magnitude of 6, as this is the approximate limit of star maps which date from before the invention of the telescope. Ability in this area, which requires the use of averted vision, varies substantially from observer to observer, with both youth and experience being beneficial.
Limiting magnitude is traditionally estimated by searching for faint stars of known magnitude. In 2013 an app was developed based on Google's Sky Map that allows non-specialists to estimate the limiting magnitude in polluted areas using their phone.[4]
Modelling magnitude limits
We see stars if they have sufficient contrast against the background sky. A star's brightness (more precisely its illuminance) must exceed the sky's surface brightness (i.e. luminance) by a sufficient amount. Earth's sky is never completely black – even in the absence of light pollution there is a natural airglow that limits what can be seen. The astronomer H.D. Curtis reported his naked-eye limit as 6.53, but by looking at stars through a hole in a black screen (i.e. against a totally dark background) was able to see one of magnitude 8.3, and possibly one of 8.9.[5]
Naked-eye magnitude limits can be modelled theoretically using laboratory data on human contrast thresholds at various background brightness levels. Andrew Crumey has done this using data from experiments where subjects viewed artificial light sources under controlled conditions. Crumey showed that for a sky background with surface brightness , the visual limit could be expressed as:
where is a "field factor" specific to the observer and viewing situation.[6] The very darkest skies have a zenith surface brightness of approximately 22 mag arcsec−2, so it can be seen from the equation that such a sky would be expected to show stars approximately 0.4 mag fainter than one with a surface brightness of 21 mag arcsec−2. Crumey speculated that for most people will lie between about 1.4 and 2.4, with being typical. This would imply at the darkest sites, consistent with the traditionally accepted value, though substantially poorer than what is often claimed by modern amateur observers.
To explain the discrepancy, Crumey pointed out that his formula assumed sustained visibility rather than momentary glimpses. He reported that "scintillation can lead to sudden 'flashes' with a brightening of 1 to 2 mag lasting a hundredth of a second."[7] He commented, "The activities of amateur astronomers can lie anywhere between science and recreational sport. If the latter, then the individual's concern with limiting magnitude may be to maximise it, whereas for science a main interest should be consistency of measurement." He recommended that "For the purposes of visibility recommendations aimed at the general public it is preferable to consider typical rather than exceptional performance... Stars should be continuously visible (with direct or averted vision) for some extended period (e.g. at least a second or two) rather than be seen to flash momentarily."[8]
Crumey's formula, stated above, is an approximation to a more general one he obtained in photometric units.[9] He obtained other approximations in astronomical units for skies ranging from moderately light polluted to truly dark.[10]
If an observer knows their own SQM (i.e. sky brightness measured by a sky quality meter), and establishes their actual limiting magnitude, they can work out their own from these formulae. Crumey recommended that for accurate results, the observer should ascertain the V-magnitude of the faintest steadily visible star to one decimal place, and for highest accuracy should also record the colour index and convert to a standard value. Crumey showed that if the limit is at colour index , then the limit at colour index zero is approximately [10]
Some sample values are tabulated below. The general result is that a gain of 1 SQM in sky darkness equates to a gain in magnitude limit of roughly 0.3 to 0.4.
Limiting magnitudes with F = 2
SQM 18.5
SQM 19.5
SQM 20.5
SQM 21.5
5.0
5.3
5.7
6.0
Visual magnitude limit with a telescope
The aperture (or more formally entrance pupil) of a telescope is larger than the human eye pupil, so collects more light, concentrating it at the exit pupil where the observer's own pupil is (usually) placed. The result is increased illuminance – stars are effectively brightened. At the same time, magnification darkens the background sky (i.e. reduces its luminance). Therefore stars normally invisible to the naked eye become visible in the telescope. Further increasing the magnification makes the sky look even darker in the eyepiece, but there is a limit to how far this can be taken. One reason is that as magnification increases, the exit pupil gets smaller, resulting in a poorer image – an effect that can be seen by looking through a small pinhole in daylight. Another reason is that star images are not perfect points of light; atmospheric turbulence creates a blurring effect referred to as seeing. A third reason is that if magnification can be pushed sufficiently high, the sky background will become effectively black, and cannot be darkened any further. This happens at a background surface brightness of approximately 25 mag arcsec−2, where only 'dark light' (neural noise) is perceived.[11]
Various authors[12] have stated the limiting magnitude of a telescope with entrance pupil centimetres to be of the form
with suggested values for the constant ranging from 6.8 to 8.7. Crumey obtained a formula for as a function of the sky surface brightness, telescope magnification, observer's eye pupil diameter and other parameters including the personal factor discussed above. Choosing parameter values thought typical of normal dark-site observations (e.g. eye pupil 0.7cm and ) he found .[13]
Fig. 13 from Crumey (2014). Magnitude limit as a function of sky brightness for a 100mm telescope at various magnifications.
Crumey obtained his formula as an approximation to one he derived in photometric units from his general model of human contrast threshold.[14] As an illustration, he calculated limiting magnitude as a function of sky brightness for a 100mm telescope at magnifications ranging from x25 to x200 (with other parameters given typical real-world values). Crumey found that a maximum of 12.7 mag could be achieved if magnification was sufficiently high and the sky sufficiently dark, so that the background in the eyepiece was effectively black.[15] That limit corresponds to = 7.7 in the formula above.
More generally, for situations where it is possible to raise a telescope's magnification high enough to make the sky background effectively black, the limiting magnitude is approximated by
where and are as stated above, is the observer's pupil diameter in centimetres, and is the telescope transmittance (e.g. 0.75 for a typical reflector).[16]
Fig. 14 from Crumey (2014). Magnitude limits determined by I.S. Bowen at Mount Wilson, compared with Crumey's formulae.
Telescopic limiting magnitudes were investigated empirically by I.S. Bowen at Mount Wilson Observatory in 1947,[17] and Crumey was able to use Bowen's data as a test of the theoretical model.[18] Bowen did not record parameters such as his eye pupil diameter, naked-eye magnitude limit, or the extent of light loss in his telescopes; but because he made observations at a range of magnifications using three telescopes (with apertures 0.33 inch, 6 inch and 60 inch), Crumey was able to construct a system of simultaneous equations from which the remaining parameters could be deduced. Because Crumey used astronomical-unit approximations, and plotted on log axes, the limit "curve" for each telescope consisted of three straight sections, corresponding to exit pupil larger than eye pupil, exit pupil smaller, and sky background effectively black. Bowen's anomalous limit at highest magnification with the 60-inch telescope was due to poor seeing. As well as vindicating the theoretical model, Crumey was able to show from this analysis that the sky brightness at the time of Bowen's observations was approximately 21.27 mag arcsec−2, highlighting the rapid growth of light pollution at Mount Wilson in the second half of the twentieth century.[19]
Large observatories
Telescopes at large observatories are typically located at sites selected for dark skies. They also increase the limiting magnitude by using long integration times on the detector, and by using image-processing techniques to increase the signal to noise ratio. Most 8 to 10 meter class telescopes can detect sources with a visual magnitude of about 27 using a one-hour integration time.[20]
Even higher limiting magnitudes can be achieved for telescopes above the Earth's atmosphere, such as the Hubble Space Telescope, where the sky brightness due to the atmosphere is not relevant. For orbital telescopes, the background sky brightness is set by the zodiacal light. The Hubble telescope can detect objects as faint as a magnitude of +31.5,[24] and the James Webb Space Telescope (operating in the infrared spectrum) is expected to exceed that.
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.
Proper motion is the astrometric measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars.
The Carte du Ciel and the Astrographic Catalogue were two distinct but connected components of a massive international astronomical project, initiated in the late 19th century, to catalogue and map the positions of millions of stars as faint as 11th or 12th magnitude. Twenty observatories from around the world participated in exposing and measuring more than 22,000 (glass) photographic plates in an enormous observing programme extending over several decades. Despite, or because of, its vast scale, the project was only ever partially successful – the Carte du Ciel component was never completed, and for almost half a century the Astrographic Catalogue part was largely ignored. However, the appearance of the Hipparcos Catalogue in 1997 has led to an important development in the use of this historical plate material.
An optical telescope is a telescope that gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electronic image sensors.
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.
An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is named because it is usually the lens that is closest to the eye when someone looks through an optical device to observe an object or sample. The objective lens or mirror collects light from an object or sample and brings it to focus creating an image of the object. The eyepiece is placed near the focal point of the objective to magnify this image to the eyes. The amount of magnification depends on the focal length of the eyepiece.
The Guide Star Catalog (GSC), also known as the Hubble Space Telescope, Guide Catalog (HSTGC), is a star catalog compiled to support the Hubble Space Telescope with targeting off-axis stars. GSC-I contained approximately 20,000,000 stars with apparent magnitudes of 6 to 15. GSC-II contains 945,592,683 stars out to magnitude 21. As far as possible, binary stars and non-stellar objects have been excluded or flagged as not meeting the requirements of Fine Guidance Sensors. This is the first full sky star catalog created specifically for navigation in outer space.
Satellite flare, also known as satellite glint, is a satellite pass visible to the naked eye as a brief, bright "flare". It is caused by the reflection toward the Earth below of sunlight incident on satellite surfaces such as solar panels and antennas. Streaks from satellite flare are a form of light pollution that can negatively affect ground-based astronomy, stargazing, and indigenous people.
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 distance modulus is a way of expressing distances that is often used in astronomy. It describes distances on a logarithmic scale based on the astronomical magnitude system.
Riccò's law, discovered by astronomer Annibale Riccò, is one of several laws that describe a human's ability to visually detect targets on a uniform background. It says that for visual targets below a certain size, threshold visibility depends on the area of the target, and hence on the total light received. The "certain size", is small in daylight conditions, larger in low light levels. The law is of special significance in visual astronomy, since it concerns the ability to distinguish between faint point sources and small, faint extended objects ("DSOs").
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.
Sky brightness refers to the visual perception of the sky and how it scatters and diffuses light. The fact that the sky is not completely dark at night is easily visible. If light sources were removed from the night sky, only direct starlight would be visible.
Eigengrau, also called Eigenlicht, dark light, or brain gray, is the uniform dark gray background color that many people report seeing in the absence of light. The term Eigenlicht dates back to the nineteenth century, and has rarely been used in recent scientific publications. Common scientific terms for the phenomenon include "visual noise" or "background adaptation". These terms arise due to the perception of an ever-changing field of tiny black and white dots seen in the phenomenon.
The Bortle dark-sky scale is a nine-level numeric scale that measures the night sky's brightness of a particular location. It quantifies the astronomical observability of celestial objects and the interference caused by light pollution. John E. Bortle created the scale and published it in the February 2001 edition of Sky & Telescope magazine to help amateur astronomers evaluate the darkness of an observing site, and secondarily, to compare the darkness of observing sites. The scale ranges from Class 1, the darkest skies available on Earth, through to Class 9, inner-city skies. It gives several criteria for each level beyond naked-eye limiting magnitude (NELM). The accuracy and utility of the scale have been questioned in recent research. The table below summarizes Bortle's descriptions of the classes. For some classes, there can be very drastic differences from one class to the next, e.g, Bortle 4 to 5.
The Millennium Star Atlas was constructed as a collaboration between a team at Sky & Telescope led by Roger Sinnott, and the European Space Agency's Hipparcos project, led by Michael Perryman. This 1997 work was the first sky atlas to include the Hipparcos and Tycho Catalogue data, extending earlier undertakings in terms of completeness and uniformity to a magnitude limit of around 10–11 magnitude. It appeared as a stand-alone publication, and as three volumes of the 17-volume Hipparcos Catalogue.
Iota1 Librae, Latinized from ι1 Librae, is a quadruple star system in the constellation Libra. Its apparent magnitude is 4.54. It is located 379 light years from earth.
↑ Illingworth, G. D.; Magee, D.; Oesch, P. A.; Bouwens, R. J.; Labbé, I.; Stiavelli, M.; van Dokkum, P. G.; Franx, M.; Trenti, M.; Carollo, C. M.; Gonzalez, V. (21 October 2013). "The HST eXtreme Deep Field XDF: Combining all ACS and WFC3/IR Data on the HUDF Region into the Deepest Field Ever". The Astrophysical Journal Supplement Series. 209 (1): 6. arXiv:1305.1931. Bibcode:2013ApJS..209....6I. doi:10.1088/0067-0049/209/1/6. S2CID55052332.
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