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Vega

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For other uses, see Vega (disambiguation).
Vega

Location of Vega.
Observation data
Epoch J2000.0      Equinox J2000.0
Constellation Lyra
Right ascension 18h 36m 56.3364s[1]
Declination +38° 47′ 01.291″[1]
Apparent magnitude (V) 0.03[1]
Characteristics
Spectral type A0V[1]
U−B color index −0.01[1]
B−V color index +0.00[1]
Variable type Suspected Delta Scuti[2]
Astrometry
Radial velocity (Rv)−13.9[1] km/s
Proper motion (μ) RA: 201.03[1] mas/yr
Dec.: 287.47[1] mas/yr
Parallax (π)128.93 ± 0.55 mas[1]
Distance25.3 ± 0.1 ly
(7.76 ± 0.03 pc)
Absolute magnitude (MV)0.58[3]
Details
Mass2.11[4] M☉
Radius2.26×2.78[5] R☉
Luminosity37±3[5] L☉
Surface gravity (log g)4.1±0.1[5] cgs
Temperature9602±180[6] K
Metallicity[M/H]=−0.5[6]
Rotation12.5 h
Age3.86–5.72×108[4] years
Other designations
Wega,[7] Alpha Lyrae, α Lyrae, 3 Lyr, GJ 721, HR 7001, BD +38°3238, HD 172167, GCTP 4293.00, LTT 15486, SAO 67174, HIP 91262.[1]

Vega (α Lyr / α Lyrae / Alpha Lyrae) is the brightest star in the constellation Lyra, the fifth brightest star in the sky and the second brightest star in the Northern celestial hemisphere, after Arcturus. It is a relatively nearby star at only 25.3 light years from Earth, and, together with Arcturus and Sirius, one of the most luminous stars in the Sun's neighborhood.

This is a relatively young star that has an unusually low abundance of elements with higher atomic numbers than helium.[6] It is also a suspected variable star that may vary slightly in magnitude in a periodic manner.[8] Vega is rotating rapidly with a velocity of 274 km/s at the equator. This is causing the equator to bulge outward because of centrifugal effects, and, as a result, there is a variation of temperature across the star's photosphere that reaches a maximum at the poles. From the Earth, Vega is being observed from the direction of one of these poles.[4]

Based upon an excess emission of infrared radiation, Vega has a circumstellar disk of dust. This dust is likely the result of collisions between objects in an debris disk, which is analogous to the Kuiper belt in the Solar System.[9] Irregularities in this disk also suggest the presence of at least one planet in orbit around Vega.[10]

Etymology

The name Vega comes from the Arabic word waqi meaning "falling", via the phrase النسر الواقع an-nasr al-wāqi‘, which sources translate as "the falling eagle"[11] or "the swooping vulture",[12] as this constellation was represented as an eagle or vulture among the lore of ancient Egypt and India.[13] The name appeared in Christian Europe in the Alfonsine Tables[7] and, under the influence of the Spanish, the last component of this star's name gradually changed to Vega.[14]

Observation

Visibility

Vega can often be seen near the zenith in the mid-northern latitudes during the evening in the Northern Hemisphere summer,[15] and during these times from mid-southern latitudes it can be seen low above the northern horizon during the Southern Hemisphere winter. With a declination of +38.78°, Vega can only be viewed at latitudes north of 51° S.

The summer triangle.

This star lies at a vertex of the Summer Triangle, which consists of Vega in the constellation Lyra, Deneb in Cygnus and Altair in Aquila.[15] If one is to consider this asterism a right triangle, then Vega would correspond to its right angle. It is recognizable in the northern skies for there are few bright stars in its vicinity.[16]

In about AD 14,000, Vega will become the North Star when it comes within a few degrees of the north celestial pole owing to the precession of the equinoxes.[17] It is the brightest of the successive pole stars.[7]

The Lyrids are a strong meteor shower that peak each year between April 21–22. These meteors appear to originate from the direction of Lyra, and hence are sometimes called the Alpha Lyrids. However, they actually originated from debris emitted by the comet C/1861 G1 Thatcher and have nothing to do with the star.[18]

Magnitude scale

Professional astronomers have used Vega for the calibration of absolute photometric brightness scales. When the magnitude scale was fixed, Vega happened to be close to zero magnitude. Therefore the visual magnitude of Vega was decided to be, by definition, zero at all wavelengths for many years.[19] This is no longer the case, however, as the apparent magnitude zero point is now most commonly defined in terms of a particular numerically specified flux.

Vega is also one of six A0V stars that were used to set the initial mean values for the UBV photometric system. The mean magnitude values for these stars gives U - B = B - V = 0, where U is the observed magnitude through an ultraviolet filter, B is the magnitude through a blue filter and V is the magnitude through a yellow filter. In effect, the magnitude of these stars is the same in the yellow, blue and ultraviolet parts of the spectrum.[20] Thus, Vega has a relatively flat electromagnetic spectrum in the visual region—wavelength range 350-850 nanometers, most of which can be seen with the human eye—so the flux densities are roughly equal, 2000-4000 Jy. The flux density of Vega drops rapidly in the infrared, and is near 100 Jy at 5 micrometers.[21]

Physical properties

Vega's spectral class is A0V, making it a main sequence star that is fusing hydrogen to helium in its core. Since more massive stars use their fusion fuel more quickly than smaller ones, Vega's lifetime is only one billion years, a tenth of our Sun's.[22] The current age of this star is between 386 and 511 million years, or up to about half its expected total main sequence life span. Vega has more than twice the mass[4] of the Sun and emits over thirty times the Sun's luminosity.

There is some question as to whether Vega displays variability in its luminosity. Small changes of order ±0.03 magnitude have been reported, but other observers have found no such variation. Thus the variability may be the result of systematic errors in measurement.[8] If Vega is variable, then it may be a Delta Scuti type with a period of about 0.107 days.[2] This is a category of stars that oscillate in a coherent manner, resulting in periodic pulsations in the star's luminosity.[23]

Rotation

From the Earth, Vega is seen from within 5 degrees of its polar rotation axis, but if viewed along the plane of its equator, Vega would look about 20% fainter than at the poles.[24] This is because the star has an equatorial rotation velocity if 274 km/s,[4] which is at 93% of the speed that would cause it to start breaking up from centrifugal effects (with a rotation period of about 12.5 hours). The local gravitational acceleration at the poles is greater than at the equator so the local luminosity is higher (Von Zeipel theorem). This is seen as a variation in effective temperature over the star: polar temperature is near 10,000 K (17,500 °F), while equatorial temperature is 7,600 K (13,200 °F).[4]

The rapid stellar rotation of Vega produces a pronounced equatorial bulge. The estimated polar radius of this star is 2.26±0.02 solar radii, while the equatorial radius is 2.78±0.02 solar radii. Thus the equator is 23% larger than the polar radius.[5] However, this bulge is not observed from the Earth (using an interferometer) as we are looking at the star from the direction of its pole.

Element abundance

Astronomers term "metals" those elements with higher atomic numbers than helium. The metallicity, or abundance of these heavy elements in Vega's photosphere is only about 32% relative to the Sun.[25] (Compare this, for example, to a three-fold metallicity abundance in the similar star Sirius as compared to the Sun.) For comparison, the Sun has an abundance of elements heavier than helium of about ZSol = 0.0172±0.002.[26] Thus, in terms of abundances, only about 0.54% of Vega consists of elements heavier than Helium.

The unusually low metallicity of Vega makes it a weak Lambda Boötis-type star.[27][28] However, the reason for the existence of such chemically-peculiar, spectral class A0-F0 stars remains unclear.[29]

The observed helium to hydrogen ratio in Vega is 0.030±0.005, which is about 40% lower than for the Sun. This may be caused by the disappearance of a helium convection zone near the surface. Instead, energy transfer is performed by the radiative process, which may be causing an abundance anomaly through diffusion.[30]

Kinematics

Based on this star's kinematic properties, it appears to belong to a stellar association called the Castor Moving Group. This group contains about 16 stars, including Alpha Librae, Alpha Cephei, Castor, Fomalhaut and Vega. All members of the group are moving in near parallel with similar space velocities. Membership in a moving group implies a common origin for these stars in a open cluster that has since become gravitationally unbound.[31] The estimated age of this moving group is 200±100 million years, and they have an average space velocity of 16.5 km/s.[32][33]

Vega has space velocity components of U=−13.9±0.9, V=−6.3±0.8 and W=−7.7±0.3, for a net space velocity of 17 km/s.[33] The radial component of this velocity, relative to the Sun, is −13.9 km/s while the traverse velocity is 9.9 km/s. Vega made its closest approach to the Sun about 360,000 years ago at a distance of 14.7 light years.[34] At that distance the star would have appeared as magnitude −1.1.

System

Infrared excess

A mid-infrared image of the debris disk around Vega. Credit: Spitzer Space Telescope/NASA.

One of the early results from the Infrared Astronomy Satellite (IRAS) was the discovery of excess infrared flux coming from Vega; beyond what would be expected from the star alone. This excess was measured at wavelengths of 25, 60 and 100 μm, and came from within an angular radius of 10 arcseconds (10″) centered on the star. At the measured distance of Vega, this corresponded to an actual radius of 80 astronomical units (AU), where an AU is the average radius of the Earth's orbit around the Sun. It was proposed that this radiation came from a field of orbiting particles with a dimension on the order of a millimeter, as anything smaller would eventually be removed from the system by radiation pressure or drawn into the star by means of Poynting-Robertson drag.[35] The latter is the result of radiation pressure creating an effective force that opposes the orbital motion of a dust particle, causing it to spiral inward. This effect is most pronounced for tiny particles that are closer to the star.[36]

Subsequent measurements of Vega at 193 μm showed a lower than expected flux for the hypothesized particles, suggesting that they must instead be on the order of 100 μm or less. To maintain this amount of dust in orbit around Vega, a continual source of replenishment would be required. A proposed mechanism for maintaining the dust was a disk of coalesced bodies that were in the process of collapsing to form a planet.[35]

Models fitted to the dust distribution around Vega indicates that it is a circular disk viewed from nearly pole-on. In addition, there is a hole in the center of the disk with a radius of no less than 80 AU.[37]

Debris disk

By 2005, the Spitzer Space Telescope had produced high resolution infrared images of the dust around Vega. It was shown to extend out to 43″ (330 AU) at a wavelength of 24 μm, 70″ (543 AU) at 70 μm and 105″ (815 AU) at 160 μm. These much wider disks were found to be circular and free of clumps, with dust particles ranging from 1–50 μm in size. The estimated total mass of this dust is 3×10-3 times the mass of the Earth. Production of the dust would require collisions between asteroids in a population corresponding to the Kuiper Belt around the Sun. Thus the dust is more likely created by a debris disk around Vega, rather than from a protoplanetary disk as was earlier thought.[9]

Artist concept illustrates how a massive collision of objects may have smashed together to create the dust ring around the star Vega.

The inner boundary of the debris disk was estimated at 11″±2″, or 70–102 AU. The disk of dust is produced as radiation pressure from Vega pushes debris from collisions of larger objects outward. However, continuous production of the amount of dust observed over the course of Vega's lifetime would require an enormous starting mass—estimated as hundreds of times the mass of Jupiter. Hence it is more likely to have been produced as the result of a relatively recent breakup of a moderate-sized (or larger) comet or asteroid, which then further fragmented as the result of collisions between the smaller components and other bodies. This dusty disk would be relatively young on the time scale of the star's age, and it will eventually be removed unless other collisional events supply more dust.[9]

Possible planetary system

In 1998 teams at the Joint Astronomy Centre and UCLA detected irregularities in the dust disk that suggest the presence of a planet.[38] Determining the nature of the planet has not been straightforward. A 2002 paper hypothesizes that the lumps are caused by a roughly Jupiter-mass planet on an eccentric orbit.[39] A 2003 paper hypothesizes these lumps could be caused by a roughly Neptune-mass planet having migrated from 40 to 65 AU over 56 million years,[10] an orbit large enough to allow the formation of smaller rocky planets closer to Vega. The migration of this planet would likely require gravitational interaction with a second, higher mass planet in a smaller orbit.[40]

The habitable zone around this star is the distance at which the energy flux from the Vega is comparable to the output of the Sun as received at Earth. As Vega is 37 times the luminosity of the Sun, the habitable zone is centered at a radius of about 6.1 AU.[41] The orbital period for a hypothetical planet at that radius would be 21.9 years.[42]

Cultural significance

The star has been the subject of many 'firsts' in Astronomy; in 1850 it became the first star to be photographed (by the daguerreotype process at Harvard Observatory),[7] and in 1872 the first to have its spectrum photographed.[43] It was also debatably the first star to have its parallax measured, in the pioneering experiments of Friedrich Struve in 1837.[44] Finally, it became the first star to have a car named after it, when Chevrolet launched the 'Vega' in 1971.[45]

At about 11–12,000 BCE, Vega was the pole star, when the Egyptians named it Ma'at, the Vulture-star. The Assyrians named this pole star Dayan-same, the "Judge of Heaven", while in Akkadian it was Tir-anna, "Life of Heaven". In Babylonian astronomy, Vega was one of the stars named Dilgan, "the Messenger of Light". For the Roman Empire, the start of Autumn was based upon the hour at which Vega set below the horizon.[7]

In Chinese mythology, there is a love story of Qi Xi 七夕 in which Niu Lang 牛郎 (Altair) and his two children (β and γ Aquilae) are separated forever from their mother Zhi Nü 織女 (Vega) who is on the far side of the river, the Milky Way 銀河.[46] The Japanese Tanabata festival is also based on this legend.[47]

Medieval astrologers counted Vega as one of the Behenian stars[48] and related it to chrysolite and winter savory. Cornelius Agrippa listed its kabbalistic sign under Vultur cadens, a literal Latin translation of the Arabic name.[49]

See also

References

  1. ^ a b c d e f g h i j k Staff (October 30, 2007). "SIMBAD query result: V* alf Lyr -- Variable Star". Centre de Données astronomiques de Strasbourg. Retrieved 2007-10-30. {{cite web}}: Check date values in: |date= (help)—use the "display all measurements" option to show additional parameters.
  2. ^ a b Fernie, J. D. (1981). "On the variability of VEGA". Astronomical Society of the Pacific. 93 (2): 333–337. Retrieved 2007-10-30.
  3. ^ For apparent magnitude m and parallax π, the absolute magnitude Mv is given by:
  4. ^ a b c d e f Peterson, D. M. (1999). "Vega is a rapidly rotating star" (PDF). Nature. 440 (7086): 896–899. Retrieved 2007-10-29. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  5. ^ a b c d Aufdenberg, J.P. (2006). "First results from the CHARA Array: VII. Long-Baseline Interferometric Measurements of Vega Consistent with a Pole-On, Rapidly Rotating Star?". Astrophysical Journal. 645: 664–675. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  6. ^ a b c Kinman, T. (2002). "The determination of Teff for metal-poor A-type stars using V and 2MASS J, H and K magnitudes". Astronomy and Astrophysics. 391: 1039–1052. Retrieved 2007-10-30. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  7. ^ a b c d e Allen, Richard Hinckley (1963). Star Names: Their Lore and Meaning. Courier Dover Publications. ISBN 0486210790.
  8. ^ a b I.A., Vasil'yev (March 17, 1989). "On the Variability of Vega". Commission 27 of the I.A.U. Retrieved 2007-10-30. {{cite web}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  9. ^ a b c K. Y. L. Su; et al. (2005). "The Vega Debris Disk: A Surprise from Spitzer". The Astrophysical Journal. 628: 487–500. Retrieved 2007-11-02. {{cite journal}}: Explicit use of et al. in: |author= (help)
  10. ^ a b Wyatt, M. (2002). "Resonant Trapping of Planetesimals by Planet Migration: Debris Disk Clumps and Vega's Similarity to the Solar System". The Astrophysical Journal. 598: 1321–1340. Retrieved 2007-10-30.
  11. ^ Glasse, Cyril (2001). The New Encyclopedia of Islam. Rowman Altamira. ISBN 0759101906.—"astronomy" entry.
  12. ^ Harper, Douglas (November 2001). "Vega". Online Etymology Dictionary. Retrieved 2007-11-01.
  13. ^ Houlding, Deborah (December 2005). "Lyra: The Lyre". Sktscript. Retrieved 2007-11-04.
  14. ^ Houtsma, M. Th. (1987). E.J. Brill's First Encyclopaedia of Islam, 1913-1936. Vol. VII. E.J. Brill. pp. p. 292. {{cite book}}: |pages= has extra text (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  15. ^ a b Pasachoff, Jay M. (2000). A Field Guide to Stars and Planets (Fourth edition ed.). Houghton Mifflin Field Guides. ISBN 0395934311. {{cite book}}: |edition= has extra text (help)
  16. ^ Upgren, Arthur R. (1998). Night Has a Thousand Eyes: A Naked-Eye Guide to the Sky, Its Science, and Lore. Basic Books. ISBN 0306457903.
  17. ^ Roy, Archie E. (2003). Astronomy: Principles and Practice. CRC Press. ISBN 0750309172. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  18. ^ Arter, T. R. (1997). "The mean orbit of the April Lyrids". Monthly Notices of the Royal Astronomical Society. 289 (3): 721–728. Retrieved 2007-11-02. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  19. ^ Garfinkle, Robert A. (1997). Star-Hopping: Your Visa to Viewing the Universe. Cambridge University Press. ISBN 0521598893.
  20. ^ Johnson, H. L. (1953). "Fundamental stellar photometry for standards of spectral type on the revised system of the Yerkes spectral atlas". Astrophysical Journal. 117: 313–352. Retrieved 2007-11-05. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  21. ^ McMahon, Richard G. (November 23, 2005). "Notes on Vega and magnitudes" (Text). University of Cambridge. Retrieved 2007-11-07. {{cite web}}: Check date values in: |date= (help)
  22. ^ For stars in the range 1.75<M<2.2, 0.2<Y<0.3 and 0.004<Z<0.01, stellar models give an age range of 0.43–1.64×109 years between a star joining the main sequence and turning off to the red giant branch. With a mass closer to 2.2, however, the interpolated age for Vega is less than a billion. See pages 769–778 on:
    Mengel, J. G. (1979). "Stellar evolution from the zero-age main sequence". Astrophysical Journal Supplement Series. 40: 733–791. Retrieved 2007-11-05. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  23. ^ A. Gautschy, H. Saio (1995). "Stellar Pulsations Across The HR Diagram: Part 1". Annual Review of Astronomy and Astrophysics. 33: 75–114. Retrieved 2007-05-14.
  24. ^ Gulliver, Hill, Austin F. (1994). "Vega: A rapidly rotating pole-on star". The Astrophysical Journal. 429 (2): L81–L84. Retrieved 2007-10-29. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  25. ^ For a metallicity of −0.5, the proportion of metals relative to the Sun is given by:
    .
  26. ^ Antia, H. M. (2006). "Determining Solar Abundances Using Helioseismology". The Astrophysical Journal. 644 (2): 1292–1298. Retrieved 2007-11-05. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  27. ^ Renson, P. (1990). "Catalogue of Lambda Bootis Candidates". Bulletin d'Information Centre Donnees Stellaires. 38: 137–149. Retrieved 2007-11-07. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)—Entry for HD 172167 on p. 144.
  28. ^ Qiu, H. M. (2001). "The Abundance Patterns of Sirius and Vega". The Astrophysical Journal. 548 (2): 77–115. Retrieved 2007-10-30. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  29. ^ Martinez, Peter (1998). "The pulsating lambda Bootis star HD 105759". Monthly Notices of the Royal Astronomical Society. 301 (4): 1099–1103. Retrieved 2007-11-05. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  30. ^ Adelman, Saul J. (1990). "An elemental abundance analysis of the superficially normal A star VEGA". Astrophysical Journal, Part 1. 348: 712–717. Retrieved 2007-11-07. {{cite journal}}: Unknown parameter |coauthor= ignored (|author= suggested) (help)
  31. ^ Inglis, Mike (2003). Observer's Guide to Stellar Evolution: The Birth, Life, and Death of Stars. Springer. ISBN 1852334657.
  32. ^ U=−10.7±3.5, V=−8.0±2.4, W=−9.7±3.0 km/s. The net velocity is:
  33. ^ a b Barrado y Navascues, D. (1998). "The Castor moving group. The age of Fomalhaut and VEGA". Astronomy and Astrophysics. 339: 831–839. Retrieved 2007-10-31.
  34. ^ Let θ represent the angle between the line-of-sight to Vega and its velocity vector. Then, for radial velocity vr and traverse velocity vt:
    For current distance D, the closest approach occurs at D sin(θ) = 14.7 ly, while the distance travelled is D cos(θ) = 20.6 ly. Use of the net space velocity provides the duration t needed to travel the latter distance:
  35. ^ a b Harper, D. A. (1984). "On the nature of the material surrounding VEGA". Astrophysical Journal, Part 1. 285: 808–812. Retrieved 2007-11-02. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  36. ^ Robertson, H. P. (1937). "Dynamical effects of radiation in the solar system". Monthly Notices of the Royal Astronomical Society. 97. Royal Astronomical Society: 423–438. Retrieved 2007-11-02. {{cite journal}}: Cite has empty unknown parameter: |1= (help); Unknown parameter |month= ignored (help)
  37. ^ Dent, W. R. F. (2000). "Models of the dust structures around Vega-excess stars". Monthly Notices of the Royal Astronomical Society. 314 (4): 702–712. Retrieved 2007-11-07. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  38. ^ Staff (April 21, 1998). "Astronomers discover possible new Solar Systems in formation around the nearby stars Vega and Fomalhaut". Joint Astronomy Centre. Retrieved 2007-10-29. {{cite news}}: Check date values in: |date= (help)
  39. ^ Wilner, D. (2002). "Structure in the Dusty Debris around Vega". The Astrophysical Journal. 569: L115–L119. Retrieved 2007-10-30. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  40. ^ Gilchrist, E. (December 1, 2003). "New evidence for Solar-like planetary system around nearby star". Royal Observatory, Edinburgh. Retrieved 2007-10-30. {{cite news}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  41. ^ Per the inverse square law, the habitable zone is centered at:
    where rAU is the mean radius of the habitable zone in AU and Lstar is the luminosity of the star compared to the Sun.
  42. ^ The solution for the orbital period of a small body is given by:
    where P is the orbital period, M is the mass of the central body, a is the length of the orbit's semi-major axis, and G is the gravitational constant. See formula 3.9 at:
    Braeunig, Robert A. (2007). "Orbital Mechanics". Rocket and Space Technology. Retrieved 2007-11-02.
    It follows that for a hypothetical, relatively small planet in orbit around Vega:
    giving an orbital period of 21.9 Earth years.
  43. ^ Barker, George F. (1887). "On the Henry Draper Memorial Photographs of Stellar Spectra". Proceedings of the American Philosophical Society. 24: 166–172.
  44. ^ Débarbat, Suzanne (1988). "The First Successful Attempts to Determine Stellar Parallaxes in the Light of the Bessel/Struve Correspondances". Mapping the Sky: Past Heritage and Future Directions. Springer. ISBN 9027728100.
  45. ^ Frommert, Hartmut. "Vega, Alpha Lyrae". SEDS. Retrieved 2007-11-02.
  46. ^ Wei, Liming (2005). Chinese Festivals. Chinese Intercontinental Press. ISBN 750850836X. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  47. ^ Kippax, John Robert (1919). The Call of the Stars: A Popular Introduction to a Knowledge of the Starry Skies with their Romance and Legend. G. P. Putnam's Sons.
  48. ^ Tyson, Donald (1993). Three Books of Occult Philosophy. Llewellyn Worldwide. ISBN 0875428320. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  49. ^ Agrippa, Heinrich Cornelius (1533). De Occulta Philosophia.
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