Apparent magnitude

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measure of brightness for celestial objects, as seen from Earth




Asteroid 65 Cybele and two stars, with their magnitudes labeled


The apparent magnitude (m) of an astronomical object is a number that is a measure of its brightness as seen by an observer on Earth. The magnitude scale is logarithmic. A difference of 1 in magnitude corresponds to a change in brightness by a factor of 5100, or about 2.512. The brighter an object appears, the lower its magnitude value (i.e. inverse relation), with the brightest astronomical objects having negative apparent magnitudes: for example Sirius at −1.46.


The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry. Apparent magnitudes are used to quantify the brightness of sources at ultraviolet, visible, and infrared wavelengths. An apparent magnitude is usually measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V ("visual") filter band would be denoted either as mV or often simply as V, as in "mV = 15" or "V = 15" to describe a 15th-magnitude object.




Contents





  • 1 History


  • 2 Calculations

    • 2.1 Example: Sun and Moon


    • 2.2 Magnitude addition


    • 2.3 Absolute magnitude



  • 3 Standard reference values


  • 4 Table of notable celestial objects


  • 5 See also


  • 6 References


  • 7 External links




History















































Visible to
typical
human
eye[1]
Apparent
magnitude
Bright-
ness
relative
to Vega
Number of stars
brighter than
apparent magnitude[2]
in the night sky
Yes
−1.0251%1 (Sirius)

00.0
100%4

01.0
40%15

02.0
16%48

03.0
6.3%171

04.0
2.5%513

05.0
1.0%
7003160200000000000♠1602

06.0
0.4%
7003480000000000000♠4800

06.5
0.25%
7003910000000000000♠9100[3]
No

07.0
0.16%
7004140000000000000♠14000

08.0
0.063%
7004420000000000000♠42000

09.0
0.025%
7005121000000000000♠121000
10.00.010%
7005340000000000000♠340000

The scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars in the night sky were said to be of first magnitude (m = 1), whereas the faintest were of sixth magnitude (m = 6), which is the limit of human visual perception (without the aid of a telescope). Each grade of magnitude was considered twice the brightness of the following grade (a logarithmic scale), although that ratio was subjective as no photodetectors existed. This rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest and is generally believed to have originated with Hipparchus.


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 magnitude m is about 2.512 times as bright as a star of magnitude m + 1. This figure, the fifth root of 100, became known as Pogson's Ratio.[4] The zero point of Pogson's scale was originally defined by assigning Polaris a magnitude of exactly 2. Astronomers later discovered that Polaris is slightly variable, so they switched to Vega as the standard reference star, assigning the brightness of Vega as the definition of zero magnitude at any specified wavelength.


Apart from small corrections, the brightness of Vega still serves as the definition of zero magnitude for visible and near infrared wavelengths, where its spectral energy distribution (SED) closely approximates that of a black body for a temperature of 7004110000000000000♠11000 K. However, with the advent of infrared astronomy it was revealed that Vega's radiation includes an Infrared excess presumably due to a circumstellar disk consisting of dust at warm temperatures (but much cooler than the star's surface). At shorter (e.g. visible) wavelengths, there is negligible emission from dust at these temperatures. However, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the magnitude scale was extrapolated to all wavelengths on the basis of the black body radiation curve for an ideal stellar surface at 7004110000000000000♠11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance (usually expressed in janskys) for the zero magnitude point, as a function of wavelength, can be computed.[5] Small deviations are specified between systems using measurement apparatuses developed independently so that data obtained by different astronomers can be properly compared, but of greater practical importance is the definition of magnitude not at a single wavelength but applying to the response of standard spectral filters used in photometry over various wavelength bands.


With the modern magnitude systems, brightness over a very wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30 (for detectable measurements). The brightness of Vega is exceeded by four stars in the night sky at visible wavelengths (and more at infrared wavelengths) as well as the bright planets Venus, Mars, and Jupiter, and these must be described by negative magnitudes. For example, Sirius, the brightest star of the celestial sphere, has an apparent magnitude of −1.4 in the visible. Negative magnitudes for other very bright astronomical objects can be found in the table below.


Astronomers have developed other photometric zeropoint systems as alternatives to the Vega system. The most widely used is the AB magnitude system,[6] in which photometric zeropoints are based on a hypothetical reference spectrum having constant flux per unit frequency interval, rather than using a stellar spectrum or blackbody curve as the reference. The AB magnitude zeropoint is defined such that an object's AB and Vega-based magnitudes will be approximately equal in the V filter band.



Calculations




Image of 30 Doradus taken by ESO's VISTA. This nebula has an apparent magnitude of 8.




A graph of apparent magnitude against brightness


As the amount of light actually received by a telescope is reduced by transmission through the Earth's atmosphere, any measurement of apparent magnitude is corrected for what it would have been as seen from above the atmosphere. The dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Therefore, the apparent magnitude m, in the spectral band x, would be given by


mx=−5log100⁡(FxFx,0),displaystyle m_x=-5log _100left(frac F_xF_x,0right),displaystyle m_x=-5log _100left(frac F_xF_x,0right),

which is more commonly expressed in terms of common (base-10) logarithms as


mx=−2.5log10⁡(FxFx,0),displaystyle m_x=-2.5log _10left(frac F_xF_x,0right),displaystyle m_x=-2.5log _10left(frac F_xF_x,0right),

where Fx is the observed flux density using spectral filter x, and Fx,0 is the reference flux (zero-point) for that photometric 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 5100 ≈ 2.512 (Pogson's ratio). Inverting the above formula, a magnitude difference m1m2 = Δm implies a brightness factor of


F2F1=100Δm5=100.4Δm≈2.512Δm.displaystyle frac F_2F_1=100^frac Delta m5=10^0.4Delta mapprox 2.512^Delta m.displaystyle frac F_2F_1=100^frac Delta m5=10^0.4Delta mapprox 2.512^Delta m.


Example: Sun and Moon


What is the ratio in brightness between the Sun and the full Moon?


The apparent magnitude of the Sun is −26.74 (brighter), and the mean apparent magnitude of the full moon is −12.74 (dimmer).


Difference in magnitude:


x=m1−m2=(−12.74)−(−26.74)=14.00.displaystyle x=m_1-m_2=(-12.74)-(-26.74)=14.00.displaystyle x=m_1-m_2=(-12.74)-(-26.74)=14.00.

Brightness factor:


vb=100.4x=100.4×14.00≈398107.17.displaystyle v_b=10^0.4x=10^0.4times 14.00approx 398,107.17.displaystyle v_b=10^0.4x=10^0.4times 14.00approx 398,107.17.

The Sun appears about 7005400000000000000♠400000 times brighter than the full moon.



Magnitude addition


Sometimes one might wish to add brightnesses. For example, photometry on closely separated double stars may only be able to produce a measurement of their combined light output. How would we reckon the combined magnitude of that double star knowing only the magnitudes of the individual components? This can be done by adding the brightnesses (in linear units) corresponding to each magnitude.[7]


10−mf×0.4=10−m1×0.4+10−m2×0.4.displaystyle 10^-m_ftimes 0.4=10^-m_1times 0.4+10^-m_2times 0.4.displaystyle 10^-m_ftimes 0.4=10^-m_1times 0.4+10^-m_2times 0.4.

Solving for mfdisplaystyle m_fm_f yields


mf=−2.5log10⁡(10−m1×0.4+10−m2×0.4),displaystyle m_f=-2.5log _10left(10^-m_1times 0.4+10^-m_2times 0.4right),displaystyle m_f=-2.5log _10left(10^-m_1times 0.4+10^-m_2times 0.4right),

where mf is the resulting magnitude after adding the brightnesses referred to by m1 and m2.



Absolute magnitude



Since flux decreases with distance according to the inverse-square law, a particular apparent magnitude could equally well refer to a star at one distance, or a star four times brighter at twice that distance, and so on. When one is not interested in the brightness as viewed from Earth, but the intrinsic brightness of an astronomical object, then one refers not to the apparent magnitude but the absolute magnitude. The absolute magnitude M, of a star or astronomical object is defined as the apparent magnitude it would have as seen from a distance of 10 parsecs (about 32.6 light-years). The absolute magnitude of the Sun is 4.83 in the V band (yellow) and 5.48 in the B band (blue).[8] In the case of a planet or asteroid, the absolute magnitude H rather means the apparent magnitude it would have if it were 1 astronomical unit from both the observer and the Sun, and fully illuminated (a configuration that is only theoretically achievable, with the observer situated on the surface of the Sun).



Standard reference values










































































Standard apparent magnitudes and fluxes for typical bands[9]
Band

λ
(μm)

Δλ/λ
(FWHM)
Flux at m = 0, Fx,0

Jy
10−20 erg/(s·cm2·Hz)
U0.360.1518101.81
B0.440.2242604.26
V0.550.1636403.64
R0.640.2330803.08
I0.790.1925502.55
J1.260.1616001.60
H1.600.2310801.08
K2.220.23
0670
0.67
L3.50
g0.520.1437303.73
r0.670.1444904.49
i0.790.1647604.76
z0.910.1348104.81

It is important to note that the scale is logarithmic: the relative brightness of two objects is determined by the difference of their magnitudes. For example, a difference of 3.2 means that one object is about 19 times as bright as the other, because Pogson's Ratio raised to the power 3.2 is approximately 19.05.


A common misconception is that the logarithmic nature of the scale is because the human eye itself has a logarithmic response. In Pogson's time this was thought to be true (see Weber–Fechner law), but it is now believed that the response is a power law (see Stevens' power law).[10]


Magnitude is complicated by the fact that light is not monochromatic. 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 the UBV system is widely used, in which the magnitude is measured in three different wavelength bands: U (centred at about 350 nm, in the near ultraviolet), 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 light-adapted human eye, and when an apparent magnitude is given without any further qualification, it is usually the V magnitude that is meant, more or less the same as visual magnitude.


Because cooler stars, such as red giants and red dwarfs, emit little energy in the blue and UV regions of the spectrum their power is often under-represented by the UBV scale. Indeed, some L and T class stars have an estimated magnitude of well over 100, because they emit extremely little visible light, but are strongest in infrared.


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 blue supergiant Rigel and the red supergiant Betelgeuse 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 as photographic magnitudes, and are now considered obsolete.


For objects within the Milky 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 be adjusted for redshifts and for non-Euclidean distance measures due to general relativity.[11][12]


For planets and other Solar System bodies the apparent magnitude is derived from its phase curve and the distances to the Sun and observer.




Table of notable celestial objects































































































































































































































































































































































































































Apparent visual magnitudes of known celestial objects
Apparent
magnitude
(V)
Object
Seen from...
Notes
−67.57
gamma-ray burst GRB 080319B
seen from 1 AU away

−44.00star R136a1
seen from 1 AU away

−40.07star Zeta1 Scorpii
seen from 1 AU away

−38.00star Rigel
seen from 1 AU away
It would be seen as a large very bright bluish disk of 35° apparent diameter.
−30.30star Sirius Aseen from 1 AU away

−29.30star Sun
seen from Mercury at perihelion

−27.40star Sunseen from Venus at perihelion

−26.74star Sunseen from Earth[13]About 400,000 times brighter than mean full moon
−25.60star Sunseen from Mars at aphelion

−25.00
Minimum brightness that causes the typical eye slight pain to look at
−23.00star Sunseen from Jupiter at aphelion

−21.70star Sunseen from Saturn at aphelion

−20.20star Sunseen from Uranus at aphelion

−19.30star Sunseen from Neptune

−18.20star Sunseen from Pluto at aphelion

−16.70star Sunseen from Eris at aphelion

−14.20
An illumination level of 1 lux[14][15]
−12.90full moonseen from Earth at perihelion
maximum brightness of perigee + perihelion + full moon (mean distance value is −12.74,[16] though values are about 0.18 magnitude brighter when including the opposition effect)
−11.20star Sunseen from Sedna at aphelion

−10.00Comet Ikeya–Seki (1965)seen from Earth
which was the brightest Kreutz Sungrazer of modern times[17]
−9.50Iridium (satellite) flareseen from Earth
maximum brightness
−7.50supernova of 1006seen from Earth
the brightest stellar event in recorded history (7200 light-years away)[18]
−6.50The total integrated magnitude of the night skyseen from Earth

−6.00Crab Supernova of 1054seen from Earth
(6500 light-years away)[19]
−5.90International Space Stationseen from Earth
when the ISS is at its perigee and fully lit by the Sun[20]
−4.92planet Venusseen from Earth
maximum brightness[21] when illuminated as a crescent
−4.14planet Venusseen from Earth
mean brightness[21]
−4
Faintest objects observable during the day with naked eye when Sun is high
−3.99star Epsilon Canis Majoris
seen from Earth
maximum brightness of 4.7 million years ago, the historical brightest star of the last and next five million years
−2.98planet Venusseen from Earth
minimum brightness when it is on the far side of the Sun[21]
−2.94planet Jupiterseen from Earth
maximum brightness[21]
−2.94planet Marsseen from Earth
maximum brightness[21]
−2.5
Faintest objects visible during the day with naked eye when Sun is less than 10° above the horizon
−2.50new moonseen from Earth
minimum brightness
−2.48planet Mercuryseen from Earth
maximum brightness at superior conjunction (unlike Venus, Mercury is at its brightest when on the far side of the Sun, the reason being their different phase curves)[21]
−2.20planet Jupiterseen from Earth
mean brightness[21]
−1.66planet Jupiterseen from Earth
minimum brightness[21]
−1.47star system Siriusseen from Earth
Brightest star except for the Sun at visible wavelengths[22]
−0.83star Eta Carinae
seen from Earth
apparent brightness as a supernova impostor in April 1843
−0.72star Canopus
seen from Earth
2nd brightest star in night sky[23]
−0.55planet Saturnseen from Earth
maximum brightness near opposition and perihelion when the rings are angled toward Earth[21]
−0.3Halley's cometseen from Earth
Expected apparent magnitude at 2061 passage
−0.27star system Alpha Centauri ABseen from Earth
Combined magnitude (3rd brightest star in night sky)
−0.04star Arcturus
seen from Earth
4th brightest star to the naked eye[24]
−0.01star Alpha Centauri Aseen from Earth
4th brightest individual star visible telescopically in the night sky
+0.03star Vega
seen from Earth
which was originally chosen as a definition of the zero point[25]
+0.23planet Mercuryseen from Earth
mean brightness[21]
+0.50star Sunseen from Alpha Centauri

+0.46planet Saturnseen from Earth
mean brightness[21]
+0.71planet Marsseen from Earth
mean brightness[21]
+1.17planet Saturnseen from Earth
minimum brightness[21]
+1.86planet Marsseen from Earth
minimum brightness[21]
+3.03supernova SN 1987A
seen from Earth
in the Large Magellanic Cloud (160,000 light-years away)
+3 to +4
Faintest stars visible in an urban neighborhood with naked eye
+3.44Andromeda Galaxyseen from Earth
M31[26]
+4

Orion Nebula
seen from Earth
M42
+4.38moon Ganymede
seen from Earth
maximum brightness[27] (moon of Jupiter and the largest moon in the Solar System)
+4.50open cluster M41
seen from Earth
an open cluster that may have been seen by Aristotle[28]
+4.5

Sagittarius Dwarf Spheroidal Galaxy
seen from Earth

+5.20asteroid Vesta
seen from Earth
maximum brightness
+5.38[29]planet Uranusseen from Earth
maximum brightness[21]
+5.68planet Uranusseen from Earth
mean brightness[21]
+5.72spiral galaxy M33
seen from Earth
which is used as a test for naked eye seeing under dark skies[30][31]
+5.8
gamma-ray burst GRB 080319B
seen from Earth
Peak visual magnitude (the "Clarke Event") seen on Earth on March 19, 2008 from a distance of 7.5 billion light-years.
+6.03planet Uranusseen from Earth
minimum brightness[21]
+6.49asteroid Pallas
seen from Earth
maximum brightness
+6.5
Approximate limit of stars observed by a mean naked eye observer under very good conditions. There are about 9,500 stars visible to mag 6.5.[1]
+6.64dwarf planet Ceres
seen from Earth
maximum brightness
+6.75asteroid Iris
seen from Earth
maximum brightness
+6.90spiral galaxy M81
seen from Earth
This is an extreme naked-eyetarget that pushes human eyesight and the Bortle scale to the limit[32]
+7 to +8
Extreme naked-eye limit, Class 1 on Bortle scale, the darkest skies available on Earth[33]
+7.25planet Mercuryseen from Earth
minimum brightness[21]
+7.67[34]planet Neptuneseen from Earth
maximum brightness[21]
+7.78planet Neptuneseen from Earth
mean brightness[21]
+8.00planet Neptuneseen from Earth
minimum brightness[21]
+8.10moon Titan
seen from Earth
maximum brightness; largest moon of Saturn;[35][36] mean opposition magnitude 8.4[37]
+8.29
star UY Scuti
seen from Earth
Maximum brightness; largest known star by radius
+8.94asteroid 10 Hygiea
seen from Earth
maximum brightness[38]
+9.50
Faintest objects visible using common 7×50 binoculars under typical conditions[39]
+10.20moon Iapetus
seen from Earth
maximum brightness[36], brightest when west of Saturn and takes 40 days to switch sides
+10.7

Luhman 16
seen from Earth
Closest brown dwarfs
+11.05
star Proxima Centauri
seen from Earth
2nd closest star
+11.8
moon Phobos
seen from Earth
Maximum brightness; brightest moon of Mars
+12.23
star R136a1
seen from Earth
Most luminous and massive star known[40]
+12.89
moon Deimos
seen from Earth
Maximum brightness
+12.91
quasar 3C 273
seen from Earth
brightest (luminosity distance of 2.4 billion light-years)
+13.42moon Triton
seen from Earth
Maximum brightness[37]
+13.65dwarf planet Pluto
seen from Earth
maximum brightness[41], 725 times fainter than magnitude 6.5 naked eye skies
+13.9
moon Titania
seen from Earth
Maximum brightness; brightest moon of Uranus
+14.1
star WR 102
seen from Earth
Hottest known star
+15.4
centaur Chiron
seen from Earth
maximum brightness[42]
+15.55moon Charon
seen from Earth
maximum brightness (the largest moon of Pluto)
+16.8dwarf planet Makemake
seen from Earth
Current opposition brightness[43]
+17.27dwarf planet Haumea
seen from Earth
Current opposition brightness[44]
+18.7dwarf planet Eris
seen from Earth
Current opposition brightness
+20.7moon Callirrhoe
seen from Earth
(small ~8 km satellite of Jupiter)[37]
+22
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 a CCD detector[45]
+22.91moon Hydra
seen from Earth
maximum brightness of Pluto's moon
+23.38moon Nix
seen from Earth
maximum brightness of Pluto's moon
+25.0moon Fenrir
seen from Earth
(small ~4 km satellite of Saturn)[46]
+27.6planet Jupiterseen from Earth
if it were located 5,000 AU (750 billion km) from the Sun[47]
+27.7
Faintest objects observable with an 8-meter class ground-based telescope such as the Subaru Telescope in a 10-hour image[48]
+28.2Halley's Cometseen from Earth
in 2003 when it was 28 AU from the Sun[49]
+28.4asteroid 2003 BH91
seen from Earth
observed magnitude of ~15-kilometer Kuiper belt object Seen by the Hubble Space Telescope (HST) in 2003, dimmest known directly-observed asteroid.
+31.5
Faintest objects observable in visible light with Hubble Space Telescope[50]
+34
Faintest objects observable in visible light with James Webb Space Telescope[51]
+35unnamed asteroidseen from Earth
expected magnitude of dimmest known asteroid, a 950-meter Kuiper belt object discovered by the HST passing in front of a star in 2009.[52]
+35star LBV 1806-20
seen from Earth
a luminous blue variable star, expected magnitude at visible wavelengths due to interstellar extinction


Some of the above magnitudes are only approximate. Telescope sensitivity also depends on observing time, optical bandpass, and interfering light from scattering and airglow.



See also



  • Luminosity in astronomy

  • List of nearest bright stars

  • List of nearest stars

  • Surface brightness

  • Distance modulus



References




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External links



  • "The astronomical magnitude scale". International Comet Quarterly.






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