Unless stated otherwise, the wordmagnitude in astronomy usually refers to a celestial object's apparent magnitude. The magnitude scale likely dates to before the ancientRoman astronomerClaudius Ptolemy, whosestar catalog popularized the system by listing stars from1st magnitude (brightest) to 6th magnitude (dimmest).[1] The modern scale was mathematically defined to closely match this historical system byNorman Pogson in 1856.
The scale is reverselogarithmic: the brighter an object is, the lower itsmagnitude number. A difference of 1.0 in magnitude corresponds to the brightness ratio of, or about 2.512. For example, a magnitude 2.0 star is 2.512 times as bright as a magnitude 3.0 star, 6.31 times as magnitude 4.0, and 100 times magnitude 7.0.
The brightest astronomical objects have negative apparent magnitudes: for example,Venus at −4.2 orSirius at −1.46. The faintest stars visible with thenaked eye on the darkest night have apparent magnitudes of about +6.5, though this varies depending on a person'seyesight and withaltitude and atmospheric conditions.[2] The apparent magnitudes of known objects range from −26.832 to objects in deepHubble Space Telescope images of magnitude +31.5.[3]
Absolute magnitude is a related quantity which measures theluminosity that a celestial object emits, rather than its apparent brightness when observed, and is expressed on the same reverse logarithmic scale. Absolute magnitude is defined as the apparent magnitude that a star or object would have if it were observed from a distance of 10parsecs (33 light-years; 3.1×1014 kilometres; 1.9×1014 miles). Therefore, it is of greater use instellar astrophysics since it refers to a property of a star regardless of how close it is to Earth. But inobservational astronomy and popularstargazing, references to "magnitude" are understood to mean apparent magnitude.
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. This can be useful as a way of monitoring the spread oflight pollution.
Apparent magnitude is technically a measure ofilluminance, which can also be measured in photometric units such aslux.[4]
The scale used to indicate magnitude originates in theHellenistic practice of dividing stars visible to the naked eye into sixmagnitudes. Thebrightest stars in the night sky were said to be offirst magnitude (m = 1), whereas the faintest were of sixth magnitude (m = 6), which is the limit ofhumanvisual perception (without the aid of atelescope). Each grade of magnitude was considered twice the brightness of the following grade (alogarithmic scale), although that ratio was subjective as nophotodetectors existed. This rather crude scale for the brightness of stars was popularized byPtolemy in hisAlmagest and is generally believed to have originated withHipparchus. This cannot be proved or disproved because Hipparchus's original star catalogue is lost. The only preserved text by Hipparchus himself (a commentary to Aratus) clearly documents that he did not have a system to describe brightness with numbers: He always uses terms like "big" or "small", "bright" or "faint" or even descriptions such as "visible at full moon".[8]
In 1856,Norman Robert Pogson formalized the system by defining a first magnitude star as a star that is 100 times as bright as a sixth-magnitude star, thereby establishing the logarithmic scale still in use today. This implies that a star of magnitudem is about 2.512 times as bright as a star of magnitudem + 1. This figure, thefifth root of 100, became known asPogson's Ratio.[9] The1884 Harvard Photometry and 1886Potsdamer Durchmusterung star catalogs popularized Pogson's ratio, and eventually it became a de facto standard in modern astronomy to describe differences in brightness.[10]
Defining and calibrating what magnitude 0.0 means is difficult, and different types of measurements which detect different kinds of light (possibly by using filters) have different zero points. Pogson's original 1856 paper defined magnitude 6.0 to be the faintest star the unaided eye can see,[11] but the true limit for faintest possible visible star varies depending on the atmosphere and how high a star is in the sky. TheHarvard Photometry used an average of 100 stars close to Polaris to define magnitude 5.0.[12] Later, the Johnson UVB photometric system defined multiple types of photometric measurements with different filters, where magnitude 0.0 for each filter is defined to be the average of six stars with the same spectral type as Vega. This was done so thecolor index of these stars would be 0.[13] Although this system is often called "Vega normalized", Vega is slightly dimmer than the six-star average used to define magnitude 0.0, meaning Vega's magnitude is normalized to 0.03 by definition.
Limiting Magnitudes for Visual Observation at High Magnification[14]
Telescope aperture (mm)
Limiting Magnitude
35
11.3
60
12.3
102
13.3
152
14.1
203
14.7
305
15.4
406
15.7
508
16.4
With the modern magnitude systems, brightness is described using Pogson's ratio. In practice, magnitude numbers rarely go above 30 before stars become too faint to detect. While Vega is close to magnitude 0, there are four brighter stars in the night sky at visible wavelengths (and more at infrared wavelengths) as well as the bright planets Venus, Mars, and Jupiter, and since brighter means smaller magnitude, these must be described bynegative magnitudes. For example,Sirius, the brightest star of thecelestial sphere, has a magnitude of −1.4 in the visible. Negative magnitudes for other very bright astronomical objects can be found in thetable below.
Astronomers have developed other photometric zero point systems as alternatives to Vega normalized systems. The most widely used is theAB magnitude system,[15] in which photometric zero points are based on a hypothetical reference spectrum having constantflux per unit frequency interval, rather than using a stellar spectrum or blackbody curve as the reference. The AB magnitude zero point is defined such that an object's AB and Vega-based magnitudes will be approximately equal in the V filter band. However, the AB magnitude system is defined assuming an idealized detector measuring only one wavelength of light, while real detectors accept energy from a range of wavelengths.
A scatter plot showing how familiar objects measure in magnitude, surfaceluminance, andangular diameter.
Precision measurement of magnitude (photometry) requires calibration of the photographic or (usually) electronic detection apparatus. This generally involves contemporaneous observation, under identical conditions, of standard stars whose magnitude using that spectral filter is accurately known. Moreover, as the amount of light actually received by a telescope is reduced due to transmission through theEarth's atmosphere, theairmasses of the target andcalibration stars must be taken into account. Typically one would observe a few different stars of known magnitude which are sufficiently similar. Calibrator stars close in the sky to the target are favoured (to avoid large differences in the atmospheric paths). If those stars have somewhat differentzenith angles (altitudes) then a correction factor as a function of airmass can be derived andapplied to the airmass at the target's position. Such calibration obtains the brightness as would be observed from above the atmosphere, where apparent magnitude is defined.[citation needed]
The apparent magnitude scale in astronomy reflects the received power of stars and not their amplitude. Newcomers should consider using the relative brightness measure in astrophotography to adjust exposure times between stars. Apparent magnitude also integrates over the entire object, regardless of its focus, and this needs to be taken into account when scaling exposure times for objects with significant apparent size, like the Sun, Moon and planets. For example, directly scaling the exposure time from the Moon to the Sun works because they are approximately the same size in the sky. However, scaling the exposure from the Moon to Saturn would result in an overexposure if the image of Saturn takes up a smaller area on your sensor than the Moon did (at the same magnification, or more generally, f/#).
Image of30 Doradus taken byESO'sVISTA. Thisnebula has a visual magnitude of 8.Graph of relative brightness versus magnitude
The dimmer an object appears, the higher the numerical value given to its magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Therefore, the magnitudem, in thespectral bandx, would be given bywhich is more commonly expressed in terms ofcommon (base-10) logarithms aswhereFx is the observedirradiance using spectral filterx, andFx,0 is the reference flux (zero-point) for thatphotometric filter. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor (Pogson's ratio). Inverting the above formula, a magnitude differencem1 −m2 = Δm implies a brightness factor of
Sometimes one might wish to add brightness. For example,photometry on closely separateddouble stars may only be able to produce a measurement of their combined light output. To find the combined magnitude of that double star knowing only the magnitudes of the individual components, this can be done by adding the brightness (in linear units) corresponding to each magnitude.[18]
Solving for yieldswheremf is the resulting magnitude after adding the brightnesses referred to bym1 andm2.
While magnitude generally refers to a measurement in a particular filter band corresponding to some range of wavelengths, the apparent or absolutebolometric magnitude (mbol) is a measure of an object's apparent or absolute brightness integrated over all wavelengths of the electromagnetic spectrum (also known as the object'sirradiance or power, respectively). The zero point of the apparent bolometric magnitude scale is based on the definition that an apparent bolometric magnitude of 0 mag is equivalent to a received irradiance of 2.518×10−8watts per square metre (W·m−2).[16]
While apparent magnitude is a measure of the brightness of an object as seen by a particular observer, absolute magnitude is a measure of theintrinsic brightness of an object. Flux decreases with distance according to aninverse-square law, so the apparent magnitude of a star depends on both its absolute brightness and its distance (and any extinction). For example, a star at one distance will have the same apparent magnitude as a star four times as bright at twice that distance. In contrast, the intrinsic brightness of an astronomical object, does not depend on the distance of the observer or anyextinction.[19]
The absolute magnitudeM, of a star or astronomical object is defined as the apparent magnitude it would have as seen from a distance of 10 parsecs (33 ly). The absolute magnitude of the Sun is 4.83 in the V band (visual), 4.68 in theGaia satellite's G band (green) and 5.48 in the B band (blue).[20][21][22]
In the case of a planet or asteroid, the absolute magnitudeH rather means the apparent magnitude it would have if it were 1astronomical unit (150,000,000 km) from both the observer and the Sun, and fully illuminated at maximum opposition (a configuration that is only theoretically achievable, with the observer situated on the surface of the Sun).[23]
The magnitude scale is a reverse logarithmic scale. A common misconception is that the logarithmic nature of the scale is because thehuman eye itself has a logarithmic response. In Pogson's time this was thought to be true (seeWeber–Fechner law), but it is now believed that the response is apower law(seeStevens' power law).[25]
Magnitude is complicated by the fact that light is notmonochromatic. The sensitivity of a light detector varies according to the wavelength of the light, and the way it varies depends on the type of light detector. For this reason, it is necessary to specify how the magnitude is measured for the value to be meaningful. For this purpose theUBV system is widely used, in which the magnitude is measured in three different wavelength bands: U (centred at about 350 nm, in the nearultraviolet), B (about 435 nm, in the blue region) and V (about 555 nm, in the middle of the human visual range in daylight). The V band was chosen for spectral purposes and gives magnitudes closely corresponding to those seen by the human eye. When an apparent magnitude is discussed without further qualification, the V magnitude is generally understood.[26]
Because cooler stars, such asred giants andred dwarfs, emit little energy in the blue and UV regions of the spectrum, their power is often under-represented by the UBV scale. Indeed, someL and T class stars have an estimated magnitude of well over 100, because they emit extremely little visible light, but are strongest ininfrared.[27]
Measures of magnitude need cautious treatment and it is extremely important to measure like with like. On early 20th century and older orthochromatic (blue-sensitive)photographic film, the relative brightnesses of the bluesupergiantRigel and the red supergiantBetelgeuse irregular variable star (at maximum) are reversed compared to what human eyes perceive, because this archaic film is more sensitive to blue light than it is to red light. Magnitudes obtained from this method are known asphotographic magnitudes, and are now considered obsolete.[28]
For objects within theMilky Way with a given absolute magnitude, 5 is added to the apparent magnitude for every tenfold increase in the distance to the object. For objects at very great distances (far beyond the Milky Way), this relationship must beadjusted for redshifts and fornon-Euclidean distance measures due togeneral relativity.[29][30]
For planets and other Solar System bodies, the apparent magnitude is derived from itsphase curve and the distances to the Sun and observer.[31]
Some of the listed magnitudes are approximate. Telescope sensitivity depends on observing time, optical bandpass, and interfering light fromscattering andairglow.
maximum brightness of perigee + perihelion + full Moon (~0.267 lux; mean distance value is −12.74,[17] though values are about 0.18 magnitude brighter when including theopposition effect)
Faintest objects observable during the day with naked eye when Sun is high. An astronomical object casts human-visible shadows when its apparent magnitude is equal to or lower than −4[44]
maximum brightness atsuperior conjunction (unlike Venus, Mercury is at its brightest when on the far side of the Sun, the reason being their different phase curves)[43]
Faintest objects observable in visible light with a 600 mm (24″)Ritchey-Chrétien telescope with 30 minutes of stacked images (6 subframes at 5 minutes each) using aCCD detector[73]
Faintest objects observable with thePan-STARRS 1.8-meter telescope using a 60-second exposure[75] This is currently the limiting magnitude of automated allskyastronomical surveys.
in 2003 when it was 28 AU (4.2 billion km) from the Sun, imaged using 3 of 4 synchronised individual scopes in theESO'sVery Large Telescope array using a total exposure time of about 9 hours[78]
Discovered by theJames Webb Space Telescope. One of the furthest objects discovered.[79] Approximately a billion times fainter than can be observed with the naked eye.
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