Apparent magnitude

Asteroid 65 Cybele and 2 stars with their magnitudes labeled

The apparent magnitude (m) of a celestial body is a measure of its brightness as seen by an observer on Earth, normalized to the value it would have in the absence of the atmosphere. The brighter the object appears, the lower the value of its magnitude.

Contents

History

The scale now used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars were said to be of first magnitude (m = 1), while the faintest were of sixth magnitude (m = 6), 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). This somewhat crude method of indicating the brightness of stars was popularized by Ptolemy in his Almagest, and is generally believed to originate with Hipparchus. This original system did not measure the magnitude of the Sun.

In 1856, Norman Robert Pogson formalized the system by defining a typical first magnitude star as a star that is 100 times as bright as a typical sixth magnitude star; thus, a first magnitude star is about 2.512 times as bright as a second magnitude star. The fifth root of 100 is known as Pogson's Ratio.[1] Pogson's scale was originally fixed by assigning Polaris a magnitude of 2. Astronomers later discovered that Polaris is slightly variable, so they first switched to Vega as the standard reference star, and then switched to using tabulated zero points for the measured fluxes.[2] The magnitude depends on the wavelength band (see below).

The modern system is no longer limited to 6 magnitudes or only to visible light. Very bright objects have negative magnitudes. For example, Sirius, the brightest star of the celestial sphere, has an apparent magnitude of –1.4. The modern scale includes the Moon and the Sun. The full Moon has a mean apparent magnitude of –12.74[3] and the Sun has an apparent magnitude of –26.74.[4] The Hubble Space Telescope has located stars with magnitudes of 30 at visible wavelengths and the Keck telescopes have located similarly faint stars in the infrared.

Table of Notable Celestial Objects

Apparent visual magnitudes of known celestial objects
App. Mag. (V) Celestial object
–38.00 Rigel as seen from 1 astronomical unit. It is seen as a large very bright bluish scorching ball of 35° apparent diameter.
–30.40 Sun as seen from 1566 Icarus at perihelion
–30.30 Sirius as seen from 1 astronomical unit
–29.30 Sun as seen from Mercury at perihelion
–27.40 Sun as seen from Venus at perihelion
–26.74 Sun[4] (398,359 times brighter than mean full moon)
–25.60 Sun as seen from Mars at aphelion
–23.00 Sun as seen from Jupiter at aphelion
–21.70 Sun as seen from Saturn at aphelion
–20.20 Sun as seen from Uranus at aphelion
–19.30 Sun as seen from Neptune
–18.20 Sun as seen from Pluto at aphelion
–16.70 Sun as seen from Eris at aphelion
–12.92 Maximum brightness of Full Moon (mean is –12.74)[3]
–11.20 Sun as seen from Sedna at aphelion
–10.00 Sun as seen from scattered disc object 2006 SQ372 at aphelion
–9.50 Maximum brightness of an Iridium (satellite) flare
–8.30 Sun as seen from Comet Hyakutake at aphelion
–7.50 The SN 1006 supernova of AD 1006, the brightest stellar event in recorded history[5]
–6.00 The Crab Supernova (SN 1054) of AD 1054 (6500 light years away)[6]
–4.67 Maximum brightness of both Venus[7] when illuminated as a crescent and also the International Space Station (when the ISS is at its perigee and fully lit by the sun)[8]
–4.00 Faintest objects observable during the day with naked eye when Sun is high
–3.82 Minimum brightness of Venus when it is on the far side of the Sun
–2.94 Maximum brightness of Jupiter[9]
–2.91 Maximum brightness of Mars[10]
–2.50 Faintest objects visible during the day with naked eye when Sun is less than 10° above the horizon
–2.50 Minimum brightness of Moon when near the sun (New Moon)
–2.45 Maximum brightness of Mercury at superior conjunction (unlike Venus, Mercury is at its brightest when on the far side of the Sun)
–1.61 Minimum brightness of Jupiter
–1.47 Brightest star (except for the sun) at visible wavelengths: Sirius[11]
–0.83 Eta Carinae apparent brightness as a Supernova impostor in April 1843
–0.72 Second-brightest star: Canopus[12]
–0.49 Maximum brightness of Saturn at opposition and when the rings are full open (2003, 2018)
–0.27 The combined magnitude for the Alpha Centauri star system
–0.04 Third-brightest star: Arcturus[13]
0.03 Vega, which was originally chosen as a definition of the zero point[14]
0.50 Sun as seen from Alpha Centauri
1.47 Minimum brightness of Saturn
1.84 Minimum brightness of Mars
3.03 The SN 1987A supernova in the Large Magellanic Cloud 160,000 light-years away.
3 ... 4 Faintest stars visible in an urban neighborhood with naked eye
3.44 The well known Andromeda Galaxy (M31)[15]
4.38 Maximum brightness of Ganymede[16] (moon of Jupiter and the largest moon in the solar system)
4.50 M41 an open cluster that may have been seen by Aristotle[17]
5.14 Maximum brightness of brightest asteroid Vesta
5.32 Maximum brightness of Uranus[18]
5.72 The spiral galaxy M33, which is used as a test for naked eye seeing under dark skies[19][20]
5.73 Minimum brightness of Mercury
5.95 Minimum brightness of Uranus
6.40 Maximum brightness of asteroid Pallas
6.50 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.[21]
6.73 Maximum brightness of dwarf planet Ceres in the asteroid belt
6.75 Maximum brightness of asteroid Iris
6.90 The spiral galaxy M81 is an extreme naked eye target that pushes human eyesight and the Bortle Dark-Sky Scale to the limit[22]
7 ... 8 Extreme naked eye limit with class 1 Bortle Dark-Sky Scale, the darkest skies available on Earth[23]
7.72 The star HD 85828[24] is the faintest star known to be observed with the naked eye[25]
7.78 Maximum brightness of Neptune[26]
8.02 Minimum brightness of Neptune
8.10 Maximum brightness of Titan (largest moon of Saturn)[27][28] Mean opposition magnitude 8.4[29]
9.01 Maximum brightness of asteroid 10 Hygiea[30]
9.50 Faintest objects visible using common 7x50 binoculars under typical conditions
10.20 Maximum brightness of Iapetus[28] (brightest when west of Saturn and takes 40 days to switch sides)
12.00 Sun as seen from Rigel
12.91 Brightest quasar 3C 273 (luminosity distance of 2.4 Giga-light years)
13.42 Maximum brightness of Triton[29]
13.65 Maximum brightness of Pluto[31] (725 times fainter than magnitude 6.5 naked eye skies)
15.40 Maximum brightness of centaur Chiron[32]
15.55 Maximum brightness of Charon (the large moon of Pluto)
16.80 Current opposition brightness of Makemake[33]
17.27 Current opposition brightness of Haumea[34]
18.70 Current opposition brightness of Eris
20.70 Callirrhoe (small ~8km satellite of Jupiter)[29]
22.00 Approximate limiting magnitude of a 24" Ritchey-Chrétien telescope with 30 minutes of stacked images (6 subframes at 300s each) using a ccd detector[35]
22.91 Maximum brightness of Pluto's moon Hydra
23.38 Maximum brightness of Pluto's moon Nix
25.00 Fenrir (small ~4km satellite of Saturn)[36]
27.00 Faintest objects observable in visible light with 8m ground-based telescopes
28.00 Jupiter if it were located 5000AU from the Sun[37]
28.20 Halley's Comet in 2003 when it was 28AU from the Sun[38]
29.30 Sun as seen from Andromeda Galaxy
31.50 Faintest objects observable in visible light with Hubble Space Telescope
35.00 Sedna at aphelion (900 AU)
35.00 LBV 1806-20 is a luminous blue variable star at visible wavelengths
36.00 Faintest objects observable in visible light with E-ELT
(see also List of brightest stars)

The above are only approximate values at visible wavelengths (in reality the values depend on the precise bandpass used) — see airglow for more details of telescope sensitivity.

Calculations

As the amount of light received actually depends on the thickness of the Earth's atmosphere in the line of sight to the object, the apparent magnitudes are normalized to the value it would have in the absence of the atmosphere. The dimmer an object appears, the higher its apparent magnitude. Note that brightness varies with distance; an extremely bright object may appear quite dim, if it is far away. Brightness varies inversely with the square of the distance. The absolute magnitude, M, of a celestial body (outside of the solar system) is the apparent magnitude it would have if it were 10 parsecs (~32.6 light years) away; that of a planet (or other solar system body) is the apparent magnitude it would have if it were 1 astronomical unit away from both the Sun and Earth. The absolute magnitude of the Sun is 4.83 in the V band (yellow) and 5.48 in the B band (blue).[39]

The apparent magnitude, m, in the band, x, can be defined as mx below (noting that \log_{\sqrt[5]{100}} F = \frac{\log_{10} F }{\log_{10} 100^{1/5}} = 2.5\log_{10} F)

m_{x}= -2.5 \log_{10} (F_x/F_x^0)\,

where F_x\!\, is the observed flux in the band x, and F_x^0 is a reference flux in the same band x, such as the Vega star's for example. See Aller et al. 1982 for the most commonly used system.

The variation in brightness between two luminous objects can be calculated another way by subtracting the magnitude number of the brighter object from the magnitude number of the fainter object, then using the difference as an exponent for the base number 2.512; that is to say ( m_f - m_b = x ; and 2.512^x = variation in brightness).

Example 1 - Sun & Moon

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

m_f - m_b = x \!\

2.512^x = variation in brightness

The apparent magnitude of the Sun is -26.74, and the apparent magnitude of the full moon is -12.6. The full moon is the fainter of the two objects, while the Sun is the brighter.

Difference in magnitude

x = m_f - m_b \!\

x = (-12.74) - (-26.74) = 14 \!\

x = 14 \!\

Variation in Brightness

v_b = 2.512^x \!\

v_b = 2.512^{14} \!\

v_b = 398,359 \!\

variation in brightness = 398,359

In terms of apparent magnitude, the Sun is about 398,359 times brighter than the full moon.

Example 2 - Sirius & Polaris

What is the ratio in brightness between Sirius and Polaris?

m_f - m_b = x \!\

2.512^x = \!\ variation in brightness

The apparent magnitude of Sirius is -1.44, and the apparent magnitude of Polaris is 1.97. Polaris is the fainter of the two stars, while Sirius is the brighter.

Difference in magnitude

x = m_f - m_b \!\

x = 1.97 - (-1.44) = 3.41 \!\

x = 3.41 \!\

Variation in brightness

v_b = 2.512^x \!\

v_b = 2.512^{3.41} \!\

v_b = 23.124 \!\

In terms of apparent magnitude, Sirius is 23.124 times brighter than Polaris the North Star.

The second thing to notice is 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 19.054607... 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).[40]

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.

Since 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, since 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 our eyes see since 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 our Galaxy with a given absolute magnitude, 5 is added to the apparent magnitude for every tenfold increase in the distance to the object. This relationship does not apply for objects at very great distances (far beyond our galaxy), since a correction for General Relativity must then be taken into account due to the non-Euclidean nature of space.

See also

References

  1. ↑ Magnitudes of Thirty-six of the Minor Planets for the first day of each month of the year 1857, N. Pogson, MNRAS Vol. 17, p. 12 (1856)
  2. ↑ Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology - New Series " Gruppe/Group 6 Astronomy and Astrophysics " Volume 2 Schaifers/Voigt: Astronomy and Astrophysics / Astronomie und Astrophysik " Stars and Star Clusters / Sterne und Sternhaufen L. H. Aller et al., ISBN 3-540-10976-5 (1982)
  3. ↑ 3.0 3.1 Williams, Dr. David R. (2010-02-02). "Moon Fact Sheet". NASA (National Space Science Data Center). http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html. Retrieved 2010-04-09. 
  4. ↑ 4.0 4.1 Williams, Dr. David R. (2004-09-01). "Sun Fact Sheet". NASA (National Space Science Data Center). http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html. Retrieved 2010-07-03. 
  5. ↑ Winkler, P. Frank; Gupta, Gaurav; Long, Knox S. (2003). "The SN 1006 Remnant: Optical Proper Motions, Deep Imaging, Distance, and Brightness at Maximum". The Astrophysical Journal 585: 324–335. doi:10.1086/345985. 
  6. ↑ Supernova 1054 - Creation of the Crab Nebula
  7. ↑ Williams, David R. (2005-04-15). "Venus Fact Sheet". National Space Science Data Center. NASA. http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html. Retrieved 2010-06-24. 
  8. ↑ "ISS Information - Heavens-above.com". Heavens-above. http://www.heavens-above.com/satinfo.asp?SatID=25544. Retrieved 2007-12-22. 
  9. ↑ Williams, David R. (2007-11-02). "Jupiter Fact Sheet". National Space Science Data Center. NASA. http://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html. Retrieved 2010-06-25. 
  10. ↑ Williams, David R. (2007-11-29). "Mars Fact Sheet". National Space Science Data Center. NASA. http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html. Retrieved 2010-06-25. 
  11. ↑ "Sirius". SIMBAD Astronomical Database. http://simbad.u-strasbg.fr/simbad/sim-id?Ident=Sirius. Retrieved 2010-06-26. 
  12. ↑ "Canopus". SIMBAD Astronomical Database. http://simbad.u-strasbg.fr/simbad/sim-id?Ident=Canopus. Retrieved 2010-06-26. 
  13. ↑ "Arcturus". SIMBAD Astronomical Database. http://simbad.u-strasbg.fr/simbad/sim-id?Ident=Arcturus. Retrieved 2010-06-26. 
  14. ↑ "Vega". SIMBAD Astronomical Database. http://simbad.u-strasbg.fr/simbad/sim-id?Ident=Vega. Retrieved 2010-04-14. 
  15. ↑ "SIMBAD-M31". SIMBAD Astronomical Database. http://simbad.u-strasbg.fr/simbad/sim-id?Ident=M31. Retrieved 2009-11-29. 
  16. ↑ Yeomans and Chamberlin. "Horizon Online Ephemeris System for Ganymede (Major Body 503)". California Institute of Technology, Jet Propulsion Laboratory. http://ssd.jpl.nasa.gov/horizons.cgi?find_body=1&body_group=mb&sstr=503. Retrieved 2010-04-14.  (4.38 on 1951-Oct-03)
  17. ↑ "M41 possibly recorded by Aristotle". SEDS (Students for the Exploration and Development of Space). 2006-07-28. http://www.seds.org/messier/more/m041_ari.html. Retrieved 2009-11-29. 
  18. ↑ Williams, David R. (2005-01-31). "Uranus Fact Sheet". National Space Science Data Center. NASA. http://nssdc.gsfc.nasa.gov/planetary/factsheet/uranusfact.html. Retrieved 2010-06-25. 
  19. ↑ "SIMBAD-M33". SIMBAD Astronomical Database. http://simbad.u-strasbg.fr/simbad/sim-id?Ident=M33. Retrieved 2009-11-28. 
  20. ↑ Jerry Lodriguss (1993). "M33 (Triangulum Galaxy)". http://www.astropix.com/HTML/A_FALL/M33.HTM. Retrieved 2009-11-27.  (shows b mag not v mag)
  21. ↑ "Vmag<6.5". SIMBAD Astronomical Database. http://simbad.u-strasbg.fr/simbad/sim-sam?Criteria=Vmag%3C6.5. Retrieved 2010-06-25. 
  22. ↑ "Messier 81". SEDS (Students for the Exploration and Development of Space). 2007-09-02. http://www.seds.org/messier/m/m081.html. Retrieved 2009-11-28. 
  23. ↑ John E. Bortle (February 2001). "The Bortle Dark-Sky Scale". Sky & Telescope. http://www.skyandtelescope.com/resources/darksky/3304011.html. Retrieved 2009-11-18. 
  24. ↑ "HD 85828". SIMBAD Astronomical Database. http://simbad.u-strasbg.fr/simbad/sim-id?Ident=HD+85828. Retrieved 2009-11-28. 
  25. ↑ Brian Skiff of Lowell Observatory (1997-01-10). "Messier 81 naked-eye". sci.astro.amateur. http://www.seds.org/messier/xtra/supp/m81naked.txt. Retrieved 2009-11-28. 
  26. ↑ Williams, David R. (2007-11-29). "Neptune Fact Sheet". National Space Science Data Center. NASA. http://nssdc.gsfc.nasa.gov/planetary/factsheet/neptunefact.html. Retrieved 2010-06-25. 
  27. ↑ Yeomans and Chamberlin. "Horizon Online Ephemeris System for Titan (Major Body 606)". California Institute of Technology, Jet Propulsion Laboratory. http://ssd.jpl.nasa.gov/horizons.cgi?find_body=1&body_group=mb&sstr=606. Retrieved 2010-06-28.  (8.10 on 2003-Dec-30)
  28. ↑ 28.0 28.1 "Classic Satellites of the Solar System". Observatorio ARVAL. http://www.oarval.org/ClasSaten.htm. Retrieved 2010-06-25. 
  29. ↑ 29.0 29.1 29.2 "Planetary Satellite Physical Parameters". JPL (Solar System Dynamics). 2009-04-03. http://ssd.jpl.nasa.gov/?sat_phys_par. Retrieved 2009-07-25. 
  30. ↑ "AstDys (10) Hygiea Ephemerides". Department of Mathematics, University of Pisa, Italy. http://hamilton.dm.unipi.it/astdys/index.php?pc=1.1.3.1&n=10&oc=500&y0=2095&m0=6&d0=27&h0=00&mi0=00&y1=2095&m1=6&d1=28&h1=00&mi1=00&ti=1.0&tiu=days. Retrieved 2010-06-26. 
  31. ↑ Williams, David R. (2006-09-07). "Pluto Fact Sheet". National Space Science Data Center. NASA. http://nssdc.gsfc.nasa.gov/planetary/factsheet/plutofact.html. Retrieved 2010-06-26. 
  32. ↑ "AstDys (2060) Chiron Ephemerides". Department of Mathematics, University of Pisa, Italy. http://hamilton.dm.unipi.it/astdys/index.php?pc=1.1.3.1&n=2060&oc=500&y0=2097&m0=4&d0=3&h0=00&mi0=00&y1=2097&m1=4&d1=3&h1=00&mi1=00&ti=1.0&tiu=days. Retrieved 2010-06-26. 
  33. ↑ "AstDys (136472) Makemake Ephemerides". Department of Mathematics, University of Pisa, Italy. http://hamilton.dm.unipi.it/astdys/index.php?pc=1.1.3.1&n=136472&oc=500&y0=2010&m0=3&d0=17&h0=00&mi0=00&y1=2010&m1=3&d1=17&h1=00&mi1=00&ti=1.0&tiu=days. Retrieved 2010-06-26. 
  34. ↑ "AstDys (136108) Haumea Ephemerides". Department of Mathematics, University of Pisa, Italy. http://hamilton.dm.unipi.it/astdys/index.php?pc=1.1.3.1&n=136108&oc=500&y0=2010&m0=4&d0=6&h0=00&mi0=00&y1=2010&m1=4&d1=6&h1=00&mi1=00&ti=1.0&tiu=days. Retrieved 2010-06-26. 
  35. ↑ Steve Cullen (sgcullen) (2009-10-05). "17 New Asteroids Found by LightBuckets". LightBuckets. http://www.lightbuckets.com/news/37/17-new-asteroids-found-by-lightbuckets/. Retrieved 2009-11-15. 
  36. ↑ Scott S. Sheppard. "Saturn's Known Satellites". Carnegie Institution (Department of Terrestrial Magnetism). http://www.dtm.ciw.edu/users/sheppard/satellites/satsatdata.html. Retrieved 2010-06-28. 
  37. ↑ Magnitude difference is 2.512*log10[(5000/5)^2 X (4999/4)^2] ≈ 30.6, so Jupiter is 30.6 mag fainter at 5000 AU
  38. ↑ "New Image of Comet Halley in the Cold". ESO. 2003-09-01. http://www.eso.org/public/outreach/press-rel/pr-2003/phot-27-03.html. Retrieved 2009-02-22. 
  39. ↑ Prof. Aaron Evans. "Some Useful Astronomical Definitions". Stony Brook Astronomy Program. http://www.astro.sunysb.edu/aevans/PHY523/classnotes523/useful-definitions-pp.pdf. Retrieved 2009-07-12. 
  40. ↑ E. Schulman and C. V. Cox (1997). "Misconceptions About Astronomical Magnitudes". American Journal of Physics 65: 1003. 

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