Classical Cepheid variable

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Classical Cepheids (also known as Population I Cepheids, Type I Cepheids, or Delta Cephei variables) are a type of Cepheid variable star. They are population I, variable stars that exhibit pulsation periods in the order of a few days to months, are 4–20 times more massive than the Sun,[1] and up to 100,000 times more luminous.[2] Classical Cepheids are yellow supergiants of spectral class F6 – K2 and their radii change by (~25% for the longer-period l Car) millions of kilometers during a pulsation cycle.[3][4]

There exists a well-defined relationship between a classical Cepheid variable's luminosity and pulsation period,[5][6] securing Cepheids as viable standard candles for establishing the Galactic and extragalactic distance scales.[7][8][9][10] HST observations of classical Cepheid variables have enabled firmer constraints on Hubble's law.[7][8][10][11][12] Classical Cepheids have also been used to clarify many characteristics of our galaxy, such as the Sun's height above the galactic plane and the Galaxy's local spiral structure.[9]

Over 700 classical Cepheids are known in the Milky Way Galaxy,[13] and several thousand extragalactic Cepheids have been discovered. The Hubble Space Telescope has identified classical Cepheids in NGC 4603, which is 100 million light years distant.[14]

Discovery[edit]

On September 10, 1784 Edward Pigott detected the variability of Eta Aquilae, the first known representative of the class of classical Cepheid variables. However, the namesake for classical Cepheids is the star Delta Cephei, discovered to be variable by John Goodricke a few months later. Delta Cephei is also of particular importance as a calibrator for the period-luminosity relation since its distance is among the most precisely established for a Cepheid, thanks in part to its membership in a star cluster[15][16] and the availability of precise Hubble Space Telescope/Hipparcos parallaxes.[17]

Period-luminosity relation[edit]

A classical Cepheid's luminosity is directly related to its period of variation. The longer the pulsation period, the more luminous the star. The period-luminosity relation for classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt in an investigation of thousands of variable stars in the Magellanic Clouds.[18] She published it in 1912[19] with further evidence. Once the period-luminosity relationship is calibrated, the luminosity of a given Cepheid whose period is known can be established. Their distance is then found from their apparent brightness. The period-luminosity relationship has been calibrated by many astronomers throughout the twentieth century, beginning with Hertzsprung.[20] Calibrating the period-luminosity relation has been problematic, however, a firm Galactic calibration was established by Benedict et al. 2007 using precise HST parallaxes for 10 nearby classical Cepheids.[21] Also, in 2008, ESO astronomers estimated with a precision within 1% the distance to the Cepheid RS Puppis, using light echos from a nebula in which it is embedded.[22] However, that latter finding has been actively debated in the literature.[21]

The following relationship between a Population I Cepheid's period P and its mean absolute magnitude M_v was established from Hubble Space Telescope trigonometric parallaxes for 10 nearby Cepheids:

 M_v = (-2.43\pm0.12) (\log_{10}(P) - 1) - (4.05 \pm 0.02) \,

with P measured in days. [17][21] The following relations can also be used to calculate the distance d to classical Cepheids:

 5\log_{10}{d}=V+ (3.34) \log_{10}{P} - (2.45) (V-I) + 7.52 \,. [21]

or

 5\log_{10}{d}=V+ (3.37) \log_{10}{P} - (2.55) (V-I) + 7.48 \,. [23]

I and V represent near infrared and visual apparent mean magnitudes, respectively.

Uncertainties in Cepheid determined distances[edit]

Chief among the uncertainties tied to the Cepheid distance scale are: the nature of the period-luminosity relation in various passbands, the impact of metallicity on both the zero-point and slope of those relations, and the effects of photometric contamination (blending) and a changing (typically unknown) extinction law on classical Cepheid distances. All these topics are actively debated in the literature.[2][8][11][24][25][26][27][28][29][30][31][32]

These unresolved matters have resulted in cited values for the Hubble constant ranging between 60 km/s/Mpc and 80 km/s/Mpc.[7][8][10][11][12] Resolving this discrepancy is one of the foremost problems in astronomy since the cosmological parameters of the Universe may be constrained by supplying a precise value of the Hubble constant.[10][12]

Examples[edit]

Some fairly bright classical Cepheids which exhibit variations discernible with the naked eye include: Eta Aquilae, Zeta Geminorum, Beta Doradus, as well as the prototype Delta Cephei. The closest Classical Cepheid is the North Star (Polaris), although the star exhibits many peculiarities and its distance is a topic of active debate.[33]

Designation (name) Constellation Discovery Apparent magnitude (Maximum)[34] Apparent magnitude (Minimum)[34] Period Spectral class Comment
η Aql Aquila Pigott, 1784 3m.48 4m.39 07.17664 d F6 Ibv  
FF Aql Aquila 5m.18 5m.68 04.47 d F5Ia-F8Ia  
TT Aql Aquila 6m.46 7m.7 13.7546 d F6-G5  
U Aql Aquila 6m.08 6m.86 07.02393 d F5I-II-G1  
T Ant Antlia 5m.00 5m.82 05.898 d G5 has unseen companion, possibly associated with open cluster NGC 6649. Previously thought to be a type II Cepheid
RT Aur Auriga 5m.00 5m.82 03.73 d F8Ibv  
l Car Carina   3m.28 4m.18 35.53584 d G5 Iab/Ib  
δ Cep Cepheus John Goodricke, 1784 3m.48 4m.37 05.36634 d F5Ib-G2Ib double star, visible in binoculars
AX Cir Circinus   5m.65 6m.09 05.273268 d F2-G2II spectroscopic binary with 5 solar mass B6 companion
BP Cir Circinus   7m.31 7m.71 02.39810 d F2/3II-F6 spectroscopic binary with 4.7 solar mass B6 companion
BG Cru Crux   5m.34 5m.58 03.3428 d F5Ib-G0p  
R Cru Crux   6m.40 7m.23 05.82575 d F7Ib/II  
S Cru Crux   6m.22 6m.92 04.68997 d F6-G1Ib-II  
T Cru Crux   6m.32 6m.83 06.73331 d F6-G2Ib  
X Cyg Cygnus   5m.85 6m.91 16.38633 d F7Ib  
SU Cyg Cygnus   6m.44 7m.22 03.84555 d F2Iab  
β Dor Dorado   3m.46 4m.08 09.8426 d F4-G4Ia-II  
ζ Gem Gemini   3m.62 4m.18 10.15073 d F7Ib to G3Ib  
R Mus Musca   5m.93 6m.73 07.51 d F7Ib-G2  
S Mus Musca   5m.89 6m.49 09.66007 d F6Ib-G0  
S Nor Musca   6m.12 6m.77 09.75411 d F8-G0Ib  
BF Oph Ophiuchus   6m.93 7m.71 04.06775 d G0II  
RS Pup Puppis   6m.52 7m.67 41.3876 d F8Iab  
U Sgr Sagittarius (in M25)   6m.28 7m.15 06.74523 d G1Ib  
W Sgr Sagittarius   4m.29 5m.14 07.59503 d F4-G2Ib Optical double with γ Sgr
X Sgr Sagittarius   4m.20 4m.90 07.01283 d F5-G2II
V636 Sco Scorpius   6m.40 6m.92 06.79671 d F7/8Ib/II-G5  
R TrA Triangulum Australe   6m.4 6m.9 03.389 d F7Ib/II  
S TrA Triangulum Australe   6m.1 6m.8 06.323 d F8II  
α UMi (Polaris) Ursa Minor   1m.86 2m.13 03.9696 d F8Ib or F8II  
AH Vel Vela   5m.5 5m.89 04.227171 d F7Ib-II  
T Vul Vulpecula   5m.41 6m.09 04.435462 d F5Ib-G0Ib  

See also[edit]

References[edit]

  1. ^ Turner, David G."The Progenitors of Classical Cepheid Variables". JRASC (1996)
  2. ^ a b Turner, David G."The PL calibration for Milky Way Cepheids and its implications for the distance scale". Ap&SS (2010)
  3. ^ Rodgers, A. W. "Radius variation and population type of cepheid variables". Monthly Notices of the Royal Astronomical Society. 117 (1956) 84–94
  4. ^ W. Strohmeier, Variable Stars, Pergamon (1972)
  5. ^ Udalski, A.; Soszynski, I.; Szymanski, M.; Kubiak, M.; Pietrzynski, G.; Wozniak, P.; Zebrun, K."The Optical Gravitational Lensing Experiment. Cepheids in the Magellanic Clouds. IV. Catalog of Cepheids from the Large Magellanic Cloud". Acta A. (1999)
  6. ^ Soszynski, I.; Poleski, R.; Udalski, A.; Szymanski, M. K.; Kubiak, M.; Pietrzynski, G.; Wyrzykowski, L.; Szewczyk, O.; Ulaczyk, K. "The Optical Gravitational Lensing Experiment. The OGLE-III Catalog of Variable Stars. I. Classical Cepheids in the Large Magellanic Cloud". Acta A. (2008)
  7. ^ a b c Freedman, W. et al. "Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant", The Astrophysical Journal, Volume 553, Issue 1, pp. 47–72 (2001)
  8. ^ a b c d Tammann, G. A.; Sandage, A.; Reindl, B. "The expansion field: the value of H 0", Annual Review of Astronomy and Astrophysics, 2008
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  10. ^ a b c d Freedman, Wendy L.; Madore, Barry F. "The Hubble Constant", Annual Review of Astronomy and Astrophysics, 2010
  11. ^ a b c Ngeow, C., Kanbur, S. M. "The Hubble Constant from Type Ia Supernovae Calibrated with the Linear and Nonlinear Cepheid Period-Luminosity Relations", The Astrophysical Journal, 2006
  12. ^ a b c Macri, Lucas M.; Riess, Adam G. "The SH0ES Project: Observations of Cepheids in NGC 4258 and Type Ia SN Hosts", STELLAR PULSATION: CHALLENGES FOR THEORY AND OBSERVATION, 2009
  13. ^ Cox, John P., Theory of Stellar Pulsations, Princeton (1980)
  14. ^ Jeffrey A. Newman, Stephen E. Zepf, Marc Davis, Wendy L. Freedman, Barry F. Madore, Peter B. Stetson, N. Silbermann and Randy Phelps "A Cepheid Distance to NGC 4603 in Centaurus". The Astrophysical Journal. 523 (1999) 506–520
  15. ^ de Zeeuw, P. T.; Hoogerwerf, R.; de Bruijne, J. H. J.; Brown, A. G. A.; Blaauw, A. (1999). A HIPPARCOS Census of the Nearby OB Associations, AJ
  16. ^ Majaess, D.; Turner, D.; Gieren, W. (2012). New Evidence Supporting Cluster Membership for the Keystone Calibrator Delta Cephei, ApJ
  17. ^ a b Benedict, G. Fritz; McArthur, B. E.; Fredrick, L. W.; Harrison, T. E.; Slesnick, C. L.; Rhee, J.; Patterson, R. J.; Skrutskie, M. F.; Franz, O. G.; Wasserman, L. H.; Jefferys, W. H.; Nelan, E.; van Altena, W.; Shelus, P. J.; Hemenway, P. D.; Duncombe, R. L.; Story, D.; Whipple, A. L.; Bradley, A. J. (2002). Astrometry with the Hubble Space Telescope: A Parallax of the Fundamental Distance Calibrator δ Cephei, AJ
  18. ^ Leavitt, Henrietta S. "1777 Variables in the Magellanic Clouds". Annals of Harvard College Observatory. LX(IV) (1908) 87–110
  19. ^ Miss Leavitt in Pickering, Edward C. "Periods of 25 Variable Stars in the Small Magellanic Cloud" Harvard College Observatory Circular 173 (1912) 1–3.
  20. ^ Hertzsprung, E., "Über die räumliche Verteilung der Veränderlichen vom δ Cephei-Typus." Astronomischen Nachrichten, 196 p. 201–210 (1913)
  21. ^ a b c d Benedict, G. Fritz et al. "Hubble Space Telescope Fine Guidance Sensor Parallaxes of Galactic Cepheid Variable Stars: Period-Luminosity Relations", The Astronomical Journal, Volume 133, Issue 4, pp. 1810-1827 (2007)
  22. ^ Kervella, Pierre: Light echoes whisper the distance to a star
  23. ^ Majaess, Daniel; Turner, David; Moni Bidin, Christian; Mauro, Francesco; Geisler, Douglas; Gieren, Wolfgang; Minniti, Dante; Chené, André-Nicolas; Lucas, Philip; Borissova, Jura; Kurtev, Radostn; Dékány, Istvan; Saito, Roberto K. "New Evidence Supporting Membership for TW Nor in Lyngå 6 and the Centaurus Spiral Arm", ApJ Letters, Volume 741, Issue 2, article id. L2 (2011)
  24. ^ Feast, Michael W. & Robin M. Catchpole. "The Cepheid period-luminosity zero-point from Hipparcos trigonometrical parallaxes". Monthly Notices of the Royal Astronomical Society. 286 (1997) L 1–5.
  25. ^ Stanek, K. Z., Udalski, A. "The Optical Gravitational Lensing Experiment. Investigating the Influence of Blending on the Cepheid Distance Scale with Cepheids in the Large Magellanic Cloud", ApJ, 1999
  26. ^ Udalski, A. et al. "The Optical Gravitational Lensing Experiment. Cepheids in the Galaxy IC1613: No Dependence of the Period-Luminosity Relation on Metallicity", Acta Astronomica, 2001
  27. ^ Macri, L. M.; Stanek, K. Z.; Bersier, D.; Greenhill, L. J.; Reid, M. J. "A New Cepheid Distance to the Maser-Host Galaxy NGC 4258 and Its Implications for the Hubble Constant", The Astrophysical Journal, 2006
  28. ^ Bono, G.; Caputo, F.; Fiorentino, G.; Marconi, M.; Musella, I."Cepheids in External Galaxies. I. The Maser-Host Galaxy NGC 4258 and the Metallicity Dependence of Period-Luminosity and Period-Wesenheit Relations", The Astrophysical Journal, 2008
  29. ^ Majaess, D.; Turner, D.; Lane, D. "Type II Cepheids as Extragalactic Distance Candles", Acta Astronomica, 2009
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  31. ^ Scowcroft, V.; Bersier, D.; Mould, J. R.; Wood, P. R. "The effect of metallicity on Cepheid magnitudes and the distance to M33", Monthly Notices of the Royal Astronomical Society, Volume 396, Issue 3, pp. 1287-1296, 2009
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  33. ^ Turner, D. "Polaris and its Kin", STELLAR PULSATION: CHALLENGES FOR THEORY AND OBSERVATION, 2009
  34. ^ a b (visual magnitude, unless marked (B) (= blue) or (p) (= photographic))

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