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The General Catalogue of Variable Stars lists more than 46,000 variable stars in the Milky Way, as well as 10,000 in other galaxies, and over 10,000 'suspected' variables.[1]

SIMBAD recognizes some 36 types of variable stars including

  1. Long-period variables
  2. Semi-regular variables
  3. Ellipsoidal variables
  4. Cataclysmic variables
  5. DQ Her
  6. AM Her
  7. Nova-like stars
  8. Novas
  9. Dwarf Novas
  10. Variable stars
  11. Irregular variables
  12. Orion variables
  13. Rapid irregular variables
  14. Eruptive variables
  15. Flare stars
  16. FU Orionis variables
  17. Eruptive R CrB variables
  18. Rotational variables
  19. Rotational variables alfa2 CVn
  20. Pulsars
  21. BY Draconis variables
  22. RS CVn variables
  23. Pulsating variables
  24. RR Lyrae variables
  25. Cepheid variables
  26. Pulsing delta Sct variables
  27. Pulsing RV Tauri
  28. Pulsing W Virginis
  29. Pulsing beta Cep
  30. delta Cep
  31. gamma Dor
  32. Pulsing SX Phe
  33. Mira Cet long-period variables
  34. Semi-regular pulsating variables
  35. SN supernova
  36. Optically Violently Variable objects

Theoretical variable star[edit | edit source]

Def. "any star whose brightness varies"[2] is called a variable star.

Brightness can vary with time, space, or wavelength (spectrum).

Novae[edit | edit source]

Period: once in historical times.

Novae are "objects whose brightness has changed by ten to twenty magnitudes once in historical times".[3]

Recurrent novae[edit | edit source]

Period: seen to erupt more often than once.

Recurrent "novae whose amplitudes are on the small side but which have been seen to erupt more often than once".[3]

Long period variables[edit | edit source]

Mira A[edit | edit source]

This is a real visual image of the red giant Mira by the Hubble Space Telescope. Credit: Margarita Karovska (Harvard-Smithsonian Center for Astrophysics) and NASA.
Visual light curve of Mira, generated using the AAVSO light curve generator tool. Credit: Lithopsian.{{free media}}

Period: 175 to 1000 days.

Def. a variable star in which the long-period usual oscillation mode is the fundamental is called a long-period variable star.[4]

From the graph on the left one can see that Mira is a long period variable of some 332 days.

Long secondary period variables[edit | edit source]

Period: several hundred to several thousand days.

Many variable red giants and supergiants show variations over several hundred to several thousand days: the brightness may change by several magnitudes, rapid primary variations may be superimposed, or pulsations, binarity, and stellar rotation occur.[5][6][7]

Semiregular variables[edit | edit source]

Semiregular variable subtypes
Subtype[8] IAU definition[8] GCVS code[9] GCVS definition[9] Standard
SRa semi-regular variable giants of late spectral classes (M, C and S), which retain periodicity with comparative stability and possess, as a rule, small (less than 2m.5) light-variation amplitudes. Amplitudes and forms of light curves are usually liable to strong variations from period to period. Many of these stars differ from Mira Ceti type stars only owing to the smaller amplitude of light variation. SRA Semiregular late-type (M, C, S or Me, Ce, Se) giants displaying persistent periodicity and usually small (<2.5 mag in V) light amplitudes. Amplitudes and light-curve shapes generally vary and periods are in the range of 35–1200 days. Many of these stars differ from Miras only by showing smaller light amplitudes Z Aquarii (Z Aqr)[8][9]
SRb semi-regular variable giants of late spectral classes (M, C and S) with a poorly expressed periodicity, i.e. with a different duration of individual cycles (which leads to the impossibility of predicting the epochs of maximum and minimum brightness), or with the replacement of periodical changes by slow irregular variations, or even by the constancy of brightness. Some of them are characterised by a certain mean value of the period, given in the catalogue. SRB Semiregular late-type (M, C, S or Me, Ce, Se) giants with poorly defined periodicity (mean cycles in the range of 20 to 2300 days) or with alternating intervals of periodic and slow irregular changes, and even with light constancy intervals. Every star of this type may usually be assigned a certain mean period (cycle), which is the value given in the Catalogue. In a number of cases, the simultaneous presence of two or more periods of light variation is observed AF Cygni (AF Cyg)[8][9]
RR Coronae Borealis (RR CrB)[8][9]
SRc semi-regular variable super-giants of late spectral classes SRC Spectral-type (M, C, S or Me, Ce, Se) supergiants with amplitudes of about 1 mag and periods of light variation from 30 days to several thousand days. Mu Cephei (μ Cep)[8][9]
RW Cygni (RW Cyg)[8]
SRd semi-regular variable giants and super-giants belonging to spectral classes F, G, K SRD Semiregular variable giants and supergiants of F, G, or K spectral types, sometimes with emission lines in their spectra. Amplitudes of light variation are in the range from 0.1 to 4 mag, and the range of periods is from 30 to 1100 days S Vulpeculae (S Vul)[8]
UU Herculis (UU Her)[8]
AG Aurigae (AG Aur)[8]
SX Herculis (SX Her)[9]
SV Ursae Majoris (SV UMa)[9]
SRS Semiregular pulsating red giants with short period (several days to a month), probably high-overtone pulsators AU Arietis (AU Ari)[9]

Betelgeuse[edit | edit source]

Light curve is of semiregular variable star Betelgeuse. Credit: American Association of Variable Star Observers (AAVSO).

Betelgeuse is classified as a semiregular variable star, indicating that some periodicity is noticeable in the brightness changes, but amplitudes may vary, cycles may have different lengths, and there may be standstills or periods of irregularity, placing it in subgroup SRc; these are pulsating red supergiants with amplitudes around one magnitude and periods from tens to hundreds of days.[9]

Rho Persei[edit | edit source]

Light curve of Rho Persei was taken with an automatic photoelectric telescope. Credit: Louis J. Boyd, Russell M. Genet, and Douglas S. Hall.{{fairuse}}

On the right is a light curve of Rho Persei taken with an automatic photoelectric telescope at Fairborn Observatory West, Phoenix, Arizona. The ordinate is differential magnitude, while the abscissa is JD 2445620.5 plus the value shown.

Rho Persei is a semiregular variable star, whose apparent magnitude varies between 3.3 and 4.0[10] with periods of 50, 120 and 250 days.[11] It is a bright giant star with a spectral type of M4 II.[12] The outer envelope has an effective temperature of 4,111 K,[13] giving it the red-orange hue of an M-type star.[14]

Dwarf novae[edit | edit source]

Period: some ten to one hundred days.

Dwarf "novae whose brightness keeps changing by three to five magnitudes in semi-periodic intervals of time of some ten to one hundred days".[3]

Nova-like stars[edit | edit source]

Period: some ten to one hundred days.

Nova-like "stars, which do not undergo outbursts but only irregular small-scale brightness changes or occasional drops in luminosity, but which in all other aspects are similar to the former group."[3]

Slowly pulsating B-type stars[edit | edit source]

Periods: between approximately half a day and five days.

Slowly pulsating B (SPB) stars are hot main-sequence stars slightly less luminous than the Beta Cephei stars, with longer periods and larger amplitudes.[15]

A slowly pulsating B-type star (SPB), formerly known as a 53 Persei variable, is a spectral type B2 to B9 (3 to 9 times as massive as the Sun) that pulsates with a period between approximately half a day and five days,[16] however within this most member stars have been found to have multiple periods of oscillations.[17]

They display variability both in their light emission and in their spectral line profile, where rhe variations in magnitude are generally smaller than 0.1 magnitudes.[16]

The variability increases with decreasing wavelength, so they are more obviously variable in ultraviolet spectrum than visible light.[17]

Their pulsations are non-radial, that is, they vary in shape rather than volume; different parts of the star are expanding and contracting simultaneously.[18]

Beta Cephei variables[edit | edit source]

Periods: in the order of 0.1–0.6 days.

Beta Cephei (β Cep) variables undergo short period pulsations in the order of 0.1–0.6 days with an amplitude of 0.01–0.3 magnitudes (1% to 30% change in luminosity) and are at their brightest during minimum contraction.[19]

Many stars of this kind exhibits multiple pulsation periods.[20]

Magnetic cataclysmic variables[edit | edit source]

Periods: between 2 and 3 hrs.

X-rays from magnetic cataclysmic variables are common because accretion provides a continuous supply of coronal gas.[21]

A plot of number of systems vs. orbit period shows a statistically significant minimum for periods between 2 and 3 hr which can probably be understood in terms of the effects of magnetic braking when the companion star becomes completely convective and the usual dynamo (which operates at the base of the convective envelope) can no longer give the companion a magnetic wind to carry off angular momentum.[21]

The rotation has been blamed on asymmetric ejection of planetary nubulae and winds[22] and the fields on in situ dynamos.[23]

Orbit and rotation periods are synchronized in strongly magnetized WDs.[21]

Those with no detectable field never are synchronized.[24]

With temperatures in the range 11,000 to 15,000 K, all the WDs with the most extreme fields are far too cool to be detectable EUV/X-ray sources, e.g., Grw +70°8247, LB 11146, SBS 1349+5434, PG 1031+234 and GD 229.[25]

Most highly magnetic WDs appear to be isolated objects, although G 23-46 (7.4 MG) and LB 1116 (670 MG) are in unresolved binary systems.[26]

RE J0317-853 is the hottest magnetic WD at 49,250 K, with an exceptionally intense magnetic field of ~340 MG, and implied rotation period of 725.4 s.[26]

Between 0.1 and 0.4 keV, RE J0317-853 was detectable by ROSAT, but not in the higher energy band from 0.4 to 2.4 keV.[27]

RE J0317-853 is associated with a blue star 16 arcsec from LB 9802 (also a blue WD) but not physically associated.[26]

A centered dipole field is not able to reproduce the observations, but an off-center dipole 664 MG at the south pole and 197 MG at the north pole does.[26]

Until recently (1995) only PG 1658+441 possessed an effective temperature > 30,000 K.[26]

Its polar field strength is only 3 MG.[26]

The ROSAT Wide Field Camera (WFC) source RE J0616-649 has an ~20 MG field.[28]

PG 1031+234 has a surface field that spans the range from ~200 MG to nearly 1000 MG and rotates with a period of 3h24m.[29]

The magnetic fields in CVs are confined to a narrow range of strengths, with a maximum of 7080 MG for RX J1938.4-4623.[30]

None of the single magnetic stars has been seen as of 1999 as an X-ray source, although fields are of direct relevance to the maintenance of coronae in main sequence stars.[21]

Pulsating white dwarfs[edit | edit source]

Period: hundreds to thousands of seconds.

Pulsating white dwarf (or pre-white dwarf) are non-radially pulsating stars with short periods of hundreds to thousands of seconds and tiny fluctuations of 0.001 to 0.2 magnitudes including the DAV, or ZZ Ceti, stars, with hydrogen-dominated atmospheres and the spectral type DA;[31] DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB;[32] and GW Vir stars, with atmospheres dominated by helium, carbon, and oxygen. GW Vir stars may be subdivided into DOV and PNNV stars.[33][34]

Very rapidly pulsating hot (subdwarf B) stars[edit | edit source]

Period: a few minutes.

The prototype of this rare class is V361 Hydrae, a 15th magnitude subdwarf B star that pulsates with a period of a few minutes and may simultaneously pulsate with multiple periods, have amplitudes of a few hundredths of a magnitude and are given the GCVS acronym RPHS, and are p-mode pulsators.[35]

Irregular variable stars[edit | edit source]

Def. stars or apparent stars where "light curves show seemingly regular variations interrupted by periods of irregular activity, [where some] isolated segments even show no variability" are called irregular variable stars.[36]

Pulsating variable stars[edit | edit source]

Pulsating stars swell and shrink, affecting their brightness and spectrum: radial, where the entire star expands and shrinks as a whole; and non-radial, where one part of the star expands while another part shrinks, although non-radial pulsations may encompass everything, with radial pulsations as a special case.[37][38]

Cataclysmic variables[edit | edit source]

"The term cataclysmic variable [...] comprises several related types of objects. For one there are the so-called novae, objects whose brightness has changed by ten to twenty magnitudes once in historical times, or recurrent novae whose amplitudes are on the small side but which have been seen to erupt more often than once; furthermore, dwarf novae whose brightness keeps changing by three to five magnitudes in semi-periodic intervals of time of some ten to one hundred days; and finally nova-like stars, which do not undergo outbursts but only irregular small-scale brightness changes or occasional drops in luminosity, but which in all other aspects are similar to the former group."[3]

"Cataclysmic variables (CVs) are close binary systems consisting of a white dwarf and a red-dwarf secondary transferring matter via the Roche lobe overflow."[39]

Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources.[40]

The accretion disk may be prone to instability leading to dwarf nova outbursts: a portion of the disk material falls onto the white dwarf, the cataclysmic outbursts occur when the density and temperature at the bottom of the accumulated hydrogen layer rise high enough to ignite nuclear fusion reactions, which rapidly burn the hydrogen layer to helium."[24]

Apparently the only SSXS nonmagnetic cataclysmic variable is V Sge: bolometric luminosity of (1 - 10) x 1037, a binary including a blackbody (BB) accretor at T < 80 eV, and an orbital period of 0.514195 d.[41]

The accretion disk can become thermally stable in systems with high mass-transfer rates (Ṁ).[39] Such systems are called nova-like (NL) stars, because they lack outbursts characteristic of dwarf novae.[42]

VY Scl cataclysmic variables[edit | edit source]

Among the NL stars is a small group which shows a temporary reduction or cessation of Ṁ from the secondary. These are the VY Scl-type stars or anti-dwarf novae.[43]

V751 Cygni[edit | edit source]

V751 Cyg (BB, MW) is a VY Scl CV, has a bolometric luminosity of 6.5 x 1036 erg/s,[41] and emits soft X-rays at quiescence.[44]

The discovery of a weak soft X-ray source of V751 Cyg at minimum presents a challenge as this is unusual for CVs which commonly display weak hard X-ray emission at quiescence.[44]

The high luminosity (6.5 x 1036 erg/s) is particularly hard to understand in the context of VY Scl stars generally, because observations suggest that the binaries become simple red dwarf + white dwarf pairs at quiescence (the disk mostly disappears).[44]

"A high luminosity in soft X-rays poses an additional problem of understanding why the spectrum is of only modest excitation."[44]

The ratio He II λ4686/Hβ did not exceed ~0.5 in any of the spectra recorded up to 2001, which is typical for accretion-powered CVs and does not approach the ratio of 2 commonly seen in supersoft binaries (CBSS).[44]

Pushing the edge of acceptable X-ray fits toward lower luminosity suggests that the luminosity should not exceed ~2 x 1033 ergs/s, which gives only ~4 x 1031 ergs/s of reprocessed light in the WD about equal to the secondary's expected nuclear luminosity.[44]

Ellipsoidal variable star[edit | edit source]

Def. a variable star in which the "two stars are rather close to each other and the light variability is mainly due to the rotation of the distorted [ellipsoidal] primary" is called an ellipsoidal variable star.[45]

The distortion in the primary is towards the secondary star.[45]

Sun[edit | edit source]

The irradiance of the Sun varies by about 0.1% over an 11-year solar cycle.[46]

Algol[edit | edit source]

Ancient Egyptian calendars of lucky and unlucky days composed some 3,200 years ago may be the oldest preserved historical document of the discovery of a variable star, the eclipsing binary Algol.[47][48][49]

See also[edit | edit source]

References[edit | edit source]

  1. N. N. Samus, E. V. Kazarovets, O. V. Durlevich (2001). "General Catalogue of Variable Stars". Odessa Astronomical Publications 14: 266. 
  2. SemperBlotto (17 December 2006). variable star. San Francisco, California: Wikimedia Foundation, Inc. Retrieved 24 October 2018. 
  3. 3.0 3.1 3.2 3.3 3.4 C. La Dous (March 1994). "Observations and Theory of Cataclysmic Variables: On Progress and Problems in Understanding Dwarf Novae and Nova-Like Stars". Space Science Reviews 67 (1-2): 1-221. doi:10.1007/BF00750527. Retrieved 2016-09-29. 
  4. G. H. Bowen (June 1, 1988). "Dynamical modeling of long-period variable star atmospheres". The Astrophysical Journal 329 (10.1086/166378): 299-317. doi:10.1086/166378. Retrieved 25 October 2018. 
  5. Sergio Messina (2007). "Evidence for the pulsational origin of the Long Secondary Periods: The red supergiant star V424 Lac (HD 216946)". New Astronomy 12 (7): 556. doi:10.1016/j.newast.2007.04.002. 
  6. I. Soszyński (2007). "Long Secondary Periods and Binarity in Red Giant Stars". The Astrophysical Journal 660 (2): 1486. doi:10.1086/513012. 
  7. E. A. Olivier and P. R. Wood (2003). "On the Origin of Long Secondary Periods in Semiregular Variables". The Astrophysical Journal 584 (2): 1035. doi:10.1086/345715. 
  8. 8.00 8.01 8.02 8.03 8.04 8.05 8.06 8.07 8.08 8.09 Kukarkin, B. V. (2016). "27. Commission des Etoiles Variables". Transactions of the International Astronomical Union 10: 398. doi:10.1017/S0251107X00020988. 
  9. 9.00 9.01 9.02 9.03 9.04 9.05 9.06 9.07 9.08 9.09 GCVS Variability Types. General Catalogue of Variable Stars @ Sternberg Astronomical Institute, Moscow, Russia. 12 Feb 2009. Retrieved 2010-11-24. 
  10. Kukarkin, B. V.; Kholopov, P. N.; Pskovsky, Y. P.; Efremov, Y. N.; Kukarkina, N. P.; Kurochkin, N. E.; Medvedeva, G. I. (1971). The third edition containing information on 20437 variable stars discovered and designated till 1968, In: General Catalogue of Variable Stars (3rd ed.). Bibcode: 1971GCVS3.C......0K. 
  11. Yeşilyaprak, C.; Aslan, Z. (December 2004). "Period-luminosity relation for M-type semiregular variables from Hipparcos parallaxes". Monthly Notices of the Royal Astronomical Society 355 (2): 601–607. doi:10.1111/j.1365-2966.2004.08344.x. 
  12. Ragland, S.; Traub, W. A.; Berger, J.-P.; Danchi, W. C.; Monnier, J. D.; Willson, L. A.; Carleton, N. P.; Lacasse, M. G. et al. (November 2006). "First Surface-resolved Results with the Infrared Optical Telescope Array Imaging Interferometer: Detection of Asymmetries in Asymptotic Giant Branch Stars". The Astrophysical Journal 652 (1): 650–660. doi:10.1086/507453. 
  13. Massarotti, Alessandro; Latham, David W.; Stefanik, Robert P.; Fogel, Jeffrey (January 2008). "Rotational and Radial Velocities for a Sample of 761 HIPPARCOS Giants and the Role of Binarity". The Astronomical Journal 135 (1): 209–231. doi:10.1088/0004-6256/135/1/209. 
  14. The Colour of Stars, In: Australia Telescope, Outreach and Education. Commonwealth Scientific and Industrial Research Organisation. December 21, 2004. Retrieved 2012-01-16. 
  15. De Cat, P. (2002). "An Observational Overview of Pulsations in β Cep Stars and Slowly Pulsating B Stars (invited paper)". Radial and Nonradial Pulsations as Probes of Stellar Physics 259: 196. 
  16. 16.0 16.1 Otero, S. A.; Watson, C.; Wils, P.. Variable Star Type Designations in the VSX. American Association of Variable Star Observers. Retrieved 11 May 2014. 
  17. 17.0 17.1 Waelkens, Christoffel (1993). J. M. NEMEC (Ed), Jaymie M. Matthews. ed. Slowly Pulsating B Stars, In: New Perspectives on Stellar Pulsation and Pulsating Variable Stars: IAU Colloquium 139. Cambridge University Press. pp. 180–82. ISBN 0521443822. 
  18. John R. Percy (2007). Understanding Variable Stars. Cambridge University Press. pp. 137–38, 200–02. ISBN 0-521-23253-8. 
  19. Variable Star Of The Season, Winter 2005: The Beta Cephei Stars and Their Relatives, John Percy, AAVSO. Accessed October 2, 2008.
  20. Lesh, J. R.; Aizenman, M. L. (1978). "The observational status of the Beta Cephei stars". Annual Review of Astronomy and Astrophysics 16: 215. doi:10.1146/annurev.aa.16.090178.001243. 
  21. 21.0 21.1 21.2 21.3 Trimble V (1999). "White dwarfs in the 1990's". Bull Astron Soc India 27: 549–66. 
  22. Spruit HC (1998). Astron Astrophys. 333: 603. 
  23. Schmidt GD, Grauer AD (1997). "Upper Limits for Magnetic Fields on Pulsating White Dwarfs". Ap J. 488 (2): 827. doi:10.1086/304746. 
  24. 24.0 24.1 Marshallsumter (March 8, 2013). Super soft X-ray source. San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2013-05-18. 
  25. Schmidt GD, Smith PS (1995). "A Search for Magnetic Fields among DA White Dwarfs". Ap J. 448: 305. doi:10.1086/175962. 
  26. 26.0 26.1 26.2 26.3 26.4 26.5 Barstow MA, Jordan S, O'Donoghue D, Burleigh MR, Napiwotzki R, Harrop-Allin MK (1995). "RE J0317-853: the hottest known highly magnetic DA white dwarf". MNRAS 277 (3): 931–85. 
  27. Fleming TA (1995). 
  28. Jordan, Finley. 
  29. Latter WB, Schmidt GD, Green RF (1987). "The rotationally modulated Zeeman spectrum at nearly 10 to the 9th Gauss of the white dwarf PG 1031 + 234". Ap J. 320: 308. doi:10.1086/165543. 
  30. Schwope AD, "et al." (1995). Astron Astrophys. 293: 764. 
  31. Koester, D.; Chanmugam, G. (1990). "REVIEW: Physics of white dwarf stars". Reports on Progress in Physics 53 (7): 837. doi:10.1088/0034-4885/53/7/001. 
  32. Murdin, Paul (2002). Encyclopedia of Astronomy and Astrophysics. ISBN 0-333-75088-8. Bibcode: 
  33. Quirion, P.-O.; Fontaine, G.; Brassard, P. (2007). "Mapping the Instability Domains of GW Vir Stars in the Effective Temperature-Surface Gravity Diagram". The Astrophysical Journal Supplement Series 171: 219. doi:10.1086/513870. 
  34. Nagel, T.; Werner, K. (2004). "Detection of non-radial g-mode pulsations in the newly discovered PG 1159 star HE 1429-1209". Astronomy and Astrophysics 426 (2): L45. doi:10.1051/0004-6361:200400079. 
  35. D. Kilkenny (2007). "Pulsating Hot Subdwarfs -- an Observational Review". Communications in Astroseismology 150: 234. doi:10.1553/cia150s234. 
  36. James R. Webb, Alex G. Smith, Robert J. Leacock, Gregory L. Fitzgibbons, Paul P. Gombola, and David W. Sheppard (February 1988). "Optical observations of 22 violently variable extragalactic sources - 1968-1986". The Astronomical Journal 95 (2): 374-97. doi:10.1086/114641. Retrieved 25 October 2018. 
  37. Brown, T. M.; Gilliland, R. L. (1994). "Asteroseismology". Annual Review of Astronomy and Astrophysics 32: 37. doi:10.1146/annurev.aa.32.090194.000345. 
  38. Cox, John P., Theory of Stellar Pulsation, Princeton, (1980)
  39. 39.0 39.1 Kato T, Ishioka R, Uemura M (Dec 2002). "Photometric Study of KR Aurigae during the High State in 2001". Publ Astron Soc Japan 54 (6): 1033–9. 
  40. Introduction to Cataclysmic Variables (CVs). 
  41. 41.0 41.1 Greiner J (2000). "Catalog of supersoft X-ray sources". New Astron. 5 (3): 137–41. doi:10.1016/S1384-1076(00)00018-X. 
  42. Osaki, Yoji (1996). "Dwarf-Nova Outbursts". PASP 108: 39. doi:10.1086/133689. 
  43. Warner B (1995). Cataclysmic Variable Stars. Cambridge: Cambridge University Press. 
  44. 44.0 44.1 44.2 44.3 44.4 44.5 Patterson J, Thorstensen JR, Fried R, Skillman DR, Cook LM, Jensen L (Jan 2001). "Superhumps in Cataclysmic Binaries. XX. V751 Cygni". Publ Astron Soc Pacific (PASP) 113 (779): 72–81. doi:10.1086/317973. 
  45. 45.0 45.1 L. Mantegazza and E. Poretti (February 1995). "HD 96008: an ellipsoidal variable star, not an unusual F-type variable". Astronomy and Astrophysics 294 (2): 190-194. Retrieved 25 October 2018. 
  46. Fröhlich, C. (2006). "Solar Irradiance Variability Since 1978". Space Science Reviews 125: 53. doi:10.1007/s11214-006-9046-5. 
  47. Porceddu, S., Jetsu, L., Lyytinen, J., Kajatkari, P., Lehtinen, J., Markkanen, T., Toivari-Viitala, J. (2008). "Evidence of Periodicity in Ancient Egyptian Calendars of Lucky and Unlucky Days". Cambridge Archaeological Journal 18 (3): 327–339. doi:10.1017/S0959774308000395. 
  48. Jetsu, L., Porceddu, S., Lyytinen, J., Kajatkari, P., Lehtinen, J., Markkanen, T., Toivari-Viitala, J. (2013). "Did the Ancient Egyptians Record the Period of the Eclipsing Binary Algol - The Raging One?". The Astrophysical Journal 773 (1): A1 (14pp). doi:10.1088/0004-637X/773/1/1. 
  49. Jetsu, L., Porceddu, S. (2015). "Shifting Milestones of Natural Sciences: The Ancient Egyptian Discovery of Algol's Period Confirmed". PLoS ONE 10 (12): e.0144140 (23pp). doi:10.1371/journal.pone.0144140. 

External links[edit | edit source]