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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 [[periodic function|pulsation periods]] in the order of a few days to months, are 4–20 times more massive than the Sun,<ref name=turner96>Turner, David G.[http://adsabs.harvard.edu/abs/1996JRASC..90...82T "The Progenitors of Classical Cepheid Variables"]. ''JRASC'' (1996)</ref> and up to 100,000 times more luminous.<ref name=turner10>Turner, David G.[http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0912.4864 "The PL calibration for Milky Way Cepheids and its implications for the distance scale"]. ''Ap&SS'' (2010)</ref> Classical Cepheids are yellow supergiants of [[spectral classification|spectral class]] F6 – K2 and their radii change by (~25% for the longer-period [[l Car]]) millions of kilometers during a pulsation cycle.<ref>Rodgers, A. W. [http://articles.adsabs.harvard.edu//full/1957MNRAS.117...85R/0000092.000.html "Radius variation and population type of cepheid variables"]. ''Monthly Notices of the Royal Astronomical Society''. 117 (1956) 84–94</ref><ref name="strohmeier1972">W. Strohmeier, ''Variable Stars'', Pergamon (1972)</ref> | |||
There exists a well-defined relationship between a Classical Cepheid variable's [[luminosity]] and pulsation period,<ref name=udalski99>Udalski, A.; Soszynski, I.; Szymanski, M.; Kubiak, M.; Pietrzynski, G.; Wozniak, P.; Zebrun, K.[http://adsabs.harvard.edu/abs/1999AcA....49..223U "The Optical Gravitational Lensing Experiment. Cepheids in the Magellanic Clouds. IV. Catalog of Cepheids from the Large Magellanic Cloud"]. ''Acta A.'' (1999)</ref><ref name=sos08>Soszynski, I.; Poleski, R.; Udalski, A.; Szymanski, M. K.; Kubiak, M.; Pietrzynski, G.; Wyrzykowski, L.; Szewczyk, O.; Ulaczyk, K. [http://adsabs.harvard.edu/abs/2008AcA....58..163S "The Optical Gravitational Lensing Experiment. The OGLE-III Catalog of Variable Stars. I. Classical Cepheids in the Large Magellanic Cloud"]. ''Acta A.'' (2008)</ref> securing Cepheids as viable [[standard candle]]s for establishing the Galactic and [[extragalactic distance scale]]s.<ref name=freedman2001/><ref name=tammannsandage2008/><ref name=majaess2009/><ref name=freedman2010>Freedman, Wendy L.; Madore, Barry F. [http://adsabs.harvard.edu/abs/2010ARA%26A..48..673F "The Hubble Constant"], ''Annual Review of Astronomy and Astrophysics'', 2010</ref> HST observations of Classical Cepheid variables have enabled firmer constraints on [[Hubble's law]].<ref name=freedman2001>Freedman, W. et al. [http://adsabs.harvard.edu/abs/2001ApJ...553...47F "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)</ref><ref name=tammannsandage2008/><ref name=freedman2010/><ref name=ngeow2006/><ref name=macririess2009/> 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.<ref name=majaess2009>Majaess D. J., Turner D. G., Lane D. J. [http://adsabs.harvard.edu/abs/2009arXiv0903.4206M "Characteristics of the Galaxy according to Cepheids"], ''Monthly Notices of the Royal Astronomical Society'' (2009)</ref> | |||
Over 700 classical Cepheids are known in the [[Milky Way]] Galaxy,<ref name="cox1980">Cox, John P., ''Theory of Stellar Pulsations'', Princeton (1980)</ref> and several thousand extragalactic Cepheids have been discovered. The [[Hubble Space Telescope]] has identified classical Cepheids in [[NGC 4603]], which is 100 million [[light year]]s distant.<ref name="HST_NGC_4603_Cepheid_Distance">Jeffrey A. Newman, Stephen E. Zepf, Marc Davis, Wendy L. Freedman, Barry F. Madore, Peter B. Stetson, N. Silbermann and Randy Phelps [http://iopscience.iop.org/0004-637X/523/2/506/ "A Cepheid Distance to NGC 4603 in Centaurus"]. ''The Astrophysical Journal''. 523 (1999) 506–520</ref> | |||
==Discovery== | |||
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]]<ref | |||
name=dezeeuw1999>de Zeeuw, P. T.; Hoogerwerf, R.; de Bruijne, J. H. J.; Brown, A. G. A.; Blaauw, A. (1999). [http://adsabs.harvard.edu/abs/1999AJ....117..354D ''A HIPPARCOS Census of the Nearby OB Associations''], AJ</ref><ref name=majaess2012>Majaess, D.; Turner, D.; Gieren, W. (2012). [http://adsabs.harvard.edu/abs/2012ApJ...747..145M ''New Evidence Supporting Cluster Membership for the Keystone Calibrator Delta Cephei''], ApJ</ref> and the availability of precise [[Hubble Space Telescope]]/[[Hipparcos]] parallaxes.<ref name=benedict2002/> | |||
==Period-luminosity relation== | |||
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]].<ref>Leavitt, Henrietta S. [http://www.adsabs.harvard.edu/abs/1908AnHar..60...87L "1777 Variables in the Magellanic Clouds"]. ''Annals of Harvard College Observatory''. LX(IV) (1908) 87–110</ref> She published it in 1912<ref>Miss Leavitt in Pickering, Edward C. [http://adsabs.harvard.edu/abs/1912HarCi.173....1L "Periods of 25 Variable Stars in the Small Magellanic Cloud"] ''Harvard College Observatory Circular'' 173 (1912) 1–3.</ref> 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 [[Ejnar Hertzsprung|Hertzsprung]].<ref>Hertzsprung, E., "Über die räumliche Verteilung der Veränderlichen vom δ Cephei-Typus." ''Astronomischen Nachrichten'', 196 p. 201–210 (1913)</ref> 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.<ref name=benedict2007>Benedict, G. Fritz et al. [http://adsabs.harvard.edu/abs/2007AJ....133.1810B "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)</ref> Also, in 2008, [[European Southern Observatory|ESO]] astronomers estimated with a precision within 1% the distance to the Cepheid [[RS Puppis]], using [[light echo]]s from a nebula in which it is embedded.<ref>Kervella, Pierre: [http://www.eso.org/public/outreach/press-rel/pr-2008/pr-05-08.html ''Light echoes whisper the distance to a star'']</ref> However, that latter finding has been actively debated in the literature.<ref name=benedict2007>Bond, H. E., Sparks, W. B. [http://adsabs.harvard.edu/abs/2009A%26A...495..371B "On geometric distance determination to the Cepheid RS Puppis from its light echoes"], ''Astronomy and Astrophysics'', Volume 495, Issue 2, 2009, pp.371-377</ref> | |||
The following relationship between a Population I Cepheid's period <math>P</math> and its mean [[absolute magnitude]] <math>M_v</math> was established from [[Hubble Space Telescope]] [[trigonometric parallax]]es for 10 nearby Cepheids: | |||
: <math> M_v = (-2.43\pm0.12) (\log_{10}(P) - 1) - (4.05 \pm 0.02) \, </math> | |||
with <math>P</math> measured in days. | |||
<ref | |||
name=benedict2002>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). [http://adsabs.harvard.edu/abs/2002AJ....124.1695B ''Astrometry with the Hubble Space Telescope: A Parallax of the Fundamental Distance Calibrator δ Cephei''], AJ</ref><ref | |||
name=benedict2007>Benedict, G. Fritz; McArthur, Barbara E.; Feast, Michael W.; Barnes, Thomas G.; Harrison, Thomas E.; Patterson, Richard J.; Menzies, John W.; Bean, Jacob L.; Freedman, Wendy L. (2007). [http://adsabs.harvard.edu/abs/2007AJ....133.1810B ''Hubble Space Telescope Fine Guidance Sensor Parallaxes of Galactic Cepheid Variable Stars: Period-Luminosity Relations''], AJ</ref> The following relations can also be used to calculate the distance <math>d</math> to classical Cepheids: | |||
: <math> 5\log_{10}{d}=V+ (3.34) \log_{10}{P} - (2.45) (V-I) + 7.52 \,. </math><ref name=benedict2007/> | |||
or | |||
: <math> 5\log_{10}{d}=V+ (3.37) \log_{10}{P} - (2.55) (V-I) + 7.48 \,. </math><ref name=majaess2011>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. [http://adsabs.harvard.edu/abs/2011ApJ...741L..27M "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)</ref> | |||
<math>I</math> and <math>V</math> represent near infrared and visual apparent mean magnitudes, respectively. | |||
==Uncertainties in Cepheid determined distances== | |||
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.<ref name=turner10/><ref name=tammannsandage2008>Tammann, G. A.; Sandage, A.; Reindl, B. [http://adsabs.harvard.edu/abs/2008A%26ARv..15..289T "The expansion field: the value of H 0"], ''Annual Review of Astronomy and Astrophysics'', 2008</ref><ref name=ngeow2006>Ngeow, C., Kanbur, S. M. [http://adsabs.harvard.edu/abs/2006ApJ...642L..29N "The Hubble Constant from Type Ia Supernovae Calibrated with the Linear and Nonlinear Cepheid Period-Luminosity Relations"], ''The Astrophysical Journal'', 2006</ref><ref>Feast, Michael W. & Robin M. Catchpole. [http://adsabs.harvard.edu/abs/1997MNRAS.286L...1F "The Cepheid period-luminosity zero-point from Hipparcos trigonometrical parallaxes"]. ''[[Monthly Notices of the Royal Astronomical Society]]''. 286 (1997) L 1–5.</ref><ref name=stanekudalski1999>Stanek, K. Z., Udalski, A. [http://adsabs.harvard.edu/abs/1999astro.ph..9346S "The Optical Gravitational Lensing Experiment. Investigating the Influence of Blending on the Cepheid Distance Scale with Cepheids in the Large Magellanic Cloud"], ''ApJ'', 1999</ref><ref name=udalski2001>Udalski, A. et al. [http://adsabs.harvard.edu/abs/2001AcA....51..221U "The Optical Gravitational Lensing Experiment. Cepheids in the Galaxy IC1613: No Dependence of the Period-Luminosity Relation on Metallicity"], ''Acta Astronomica'', 2001</ref><ref name=macri2006>Macri, L. M.; Stanek, K. Z.; Bersier, D.; Greenhill, L. J.; Reid, M. J. [http://adsabs.harvard.edu/abs/2006ApJ...652.1133M "A New Cepheid Distance to the Maser-Host Galaxy NGC 4258 and Its Implications for the Hubble Constant"], ''The Astrophysical Journal'', 2006</ref><ref name=bono2008>Bono, G.; Caputo, F.; Fiorentino, G.; Marconi, M.; Musella, I.[http://adsabs.harvard.edu/abs/2008ApJ...684..102B "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</ref><ref name=majaess2009b>Majaess, D.; Turner, D.; Lane, D. [http://adsabs.harvard.edu/abs/2009AcA....59..403M "Type II Cepheids as Extragalactic Distance Candles"], ''Acta Astronomica'', 2009</ref><ref name=madore2009>Madore, Barry F., Freedman, Wendy L. [http://adsabs.harvard.edu/abs/2009ApJ...696.1498M " Concerning the Slope of the Cepheid Period-Luminosity Relation"], ''The Astrophysical Journal'', 2009</ref><ref name=scowcroft2009>Scowcroft, V.; Bersier, D.; Mould, J. R.; Wood, P. R. [http://adsabs.harvard.edu/abs/2009MNRAS.396.1287S "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</ref><ref name=majaess2010>Majaess, D. [http://adsabs.harvard.edu/abs/2010AcA....60..121M "The Cepheids of Centaurus A (NGC 5128) and Implications for H0"], ''Acta Astronomica'', 2010</ref> | |||
These unresolved matters have resulted in cited values for the Hubble constant ranging between 60 km/s/Mpc and 80 km/s/Mpc.<ref name=freedman2001/><ref name=tammannsandage2008/><ref name=freedman2010/><ref name=ngeow2006/><ref name=macririess2009/> 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.<ref name="freedman2010"/><ref name=macririess2009>Macri, Lucas M.; Riess, Adam G. [http://adsabs.harvard.edu/abs/2009AIPC.1170...23M "The SH0ES Project: Observations of Cepheids in NGC 4258 and Type Ia SN Hosts"], ''STELLAR PULSATION: CHALLENGES FOR THEORY AND OBSERVATION'', 2009</ref> | |||
==Examples== | |||
Some fairly bright Classical Cepheids which exhibit variations discernable 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.<ref name=turner2009>Turner, D. [http://adsabs.harvard.edu/abs/2010ARA%26A..48..673F "Polaris and its Kin"], ''STELLAR PULSATION: CHALLENGES FOR THEORY AND OBSERVATION'', 2009</ref> | |||
{| class="wikitable sortable" style="font-size:90%;" | |||
|- style="background:#efefef;" | |||
! style="width:10%;"|'''Designation (name)''' | |||
! style="width:10%;"|'''Constellation''' | |||
! style="width:15%;"|'''Discovery''' | |||
! style="width:10%;"|''[[Apparent magnitude]]'' (Maximum)<ref name="autogenerated1">''(visual magnitude, unless marked'' (B) ''(= blue) or'' (p) ''(= photographic))''</ref> | |||
! style="width:10%;"|''[[Apparent magnitude]]'' (Minimum)<ref name="autogenerated1"/> | |||
! style="width:15%;"|'''Period''' | |||
! style="width:15%;"|'''Spectral class''' | |||
! style="width:15%;"|'''Comment''' | |||
|- | |||
| [[Eta Aquilae|η Aql]] | |||
| [[Aquila (constellation)|Aquila]] | |||
| [[Nathaniel Pigott|Pigott]], 1784 | |||
| 3<sup>m</sup>.48 | |||
| 4<sup>m</sup>.39 | |||
| 7.17664 d | |||
| F6 Ibv | |||
| | |||
|- | |||
| [[FF Aquilae|FF Aql]] | |||
| [[Aquila (constellation)|Aquila]] | |||
| | |||
| 5<sup>m</sup>.18 | |||
| 5<sup>m</sup>.68 | |||
| 4.47 d | |||
| F5Ia-F8Ia | |||
| | |||
|- | |||
| [[TT Aquilae|TT Aql]] | |||
| [[Aquila (constellation)|Aquila]] | |||
| | |||
| 6<sup>m</sup>.46 | |||
| 7<sup>m</sup>.7 | |||
| 13.7546 d | |||
| F6-G5 | |||
| | |||
|- | |||
| [[U Aquilae|U Aql]] | |||
| [[Aquila (constellation)|Aquila]] | |||
| | |||
| 6<sup>m</sup>.08 | |||
| 6<sup>m</sup>.86 | |||
| 7.02393 d | |||
| F5I-II-G1 | |||
| | |||
|- | |||
| [[T Antliae|T Ant]] | |||
| [[Antlia]] | |||
| | |||
| 5<sup>m</sup>.00 | |||
| 5<sup>m</sup>.82 | |||
| 5.898 d | |||
| G5 | |||
| has unseen companion, possibly associated with open cluster [[NGC 6649]] | |||
|- | |||
| [[RT Aurigae|RT Aur]] | |||
| [[Auriga (constellation)|Auriga]] | |||
| | |||
| 5<sup>m</sup>.00 | |||
| 5<sup>m</sup>.82 | |||
| 3.73 d | |||
| F8Ibv | |||
| | |||
|- | |||
| [[HD 84810|l Car]] | |||
| [[Carina (constellation)|Carina]] | |||
| | |||
| 3<sup>m</sup>.28 | |||
| 4<sup>m</sup>.18 | |||
| 35.53584 d | |||
| G5 Iab/Ib | |||
| | |||
|- | |||
| [[Delta Cephei|δ Cep]] | |||
| [[Cepheus (constellation)|Cepheus]] | |||
| [[John Goodricke]], 1784 | |||
| 3<sup>m</sup>.48 | |||
| 4<sup>m</sup>.37 | |||
| 5.36634 d | |||
| F5Ib-G2Ib | |||
| double star, visible in binoculars | |||
|- | |||
| [[AX Circini|AX Cir]] | |||
| [[Circinus]] | |||
| | |||
| 5<sup>m</sup>.65 | |||
| 6<sup>m</sup>.09 | |||
| 5.273268 d | |||
| F2-G2II | |||
| spectroscopic binary with 5 solar mass B6 companion | |||
|- | |||
| [[BP Circini|BP Cir]] | |||
| [[Circinus]] | |||
| | |||
| 7<sup>m</sup>.31 | |||
| 7<sup>m</sup>.71 | |||
| 2.39810 d | |||
| F2/3II-F6 | |||
| spectroscopic binary with 4.7 solar mass B6 companion | |||
|- | |||
| [[BG Crucis|BG Cru]] | |||
| [[Crux]] | |||
| | |||
| 5<sup>m</sup>.34 | |||
| 5<sup>m</sup>.58 | |||
| 3.3428 d | |||
| F5Ib-G0p | |||
| | |||
|- | |||
| [[R Crucis|R Cru]] | |||
| [[Crux]] | |||
| | |||
| 6<sup>m</sup>.40 | |||
| 7<sup>m</sup>.23 | |||
| 5.82575 d | |||
| F7Ib/II | |||
| | |||
|- | |||
| [[X Cygni|X Cyg]] | |||
| [[Cygnus (constellation)|Cygnus]] | |||
| | |||
| 5<sup>m</sup>.85 | |||
| 6<sup>m</sup>.91 | |||
| 16.38633 d | |||
| F7Ib | |||
| | |||
|- | |||
| [[SU Cygni|SU Cyg]] | |||
| [[Cygnus (constellation)|Cygnus]] | |||
| | |||
| 6<sup>m</sup>.44 | |||
| 7<sup>m</sup>.22 | |||
| 3.84555 d | |||
| F2Iab | |||
| | |||
|- | |||
| [[Beta Doradus|β Dor]] | |||
| [[Dorado]] | |||
| | |||
| 3<sup>m</sup>.46 | |||
| 4<sup>m</sup>.08 | |||
| 9.8426 d | |||
| F4-G4Ia-II | |||
| | |||
|- | |||
| [[Zeta Geminorum|ζ Gem]] | |||
| [[Gemini (constellation)|Gemini]] | |||
| | |||
| 3<sup>m</sup>.62 | |||
| 4<sup>m</sup>.18 | |||
| 10.15073 d | |||
| F7Ib to G3Ib | |||
| | |||
|- | |||
| [[R Muscae|R Mus]] | |||
| [[Musca]] | |||
| | |||
| 5<sup>m</sup>.93 | |||
| 6<sup>m</sup>.73 | |||
| 7.51 d | |||
| F7Ib-G2 | |||
| | |||
|- | |||
| [[S Muscae|S Mus]] | |||
| [[Musca]] | |||
| | |||
| 5<sup>m</sup>.89 | |||
| 6<sup>m</sup>.49 | |||
| 9.66007 d | |||
| F6Ib-G0 | |||
| | |||
|- | |||
| [[BF Ophiuchi|BF Oph]] | |||
| [[Ophiuchus]] | |||
| | |||
| 6<sup>m</sup>.93 | |||
| 7<sup>m</sup>.71 | |||
| 4.06775 d | |||
| G0II | |||
| | |||
|- | |||
| [[Kappa Pavonis|κ Pav]] | |||
| [[Pavo (constellation)|Pavo]] | |||
| | |||
| 3<sup>m</sup>.91 | |||
| 4<sup>m</sup>.78 | |||
| 9.09423 d | |||
| F5Ib-II | |||
| | |||
|- | |||
| [[RS Puppis|RS Pup]] | |||
| [[Puppis]] | |||
| | |||
| 6<sup>m</sup>.52 | |||
| 7<sup>m</sup>.67 | |||
| 41.3876 d | |||
| F8Iab | |||
| | |||
|- | |||
| [[U Sagittarii|U Sgr]] | |||
| [[Sagittarius (constellation)|Sagittarius]] (in [[Messier 25|M25]]) | |||
| | |||
| 6<sup>m</sup>.28 | |||
| 7<sup>m</sup>.15 | |||
| 6.74523 d | |||
| G1Ib | |||
| | |||
|- | |||
| [[W Sagittarii|W Sgr]] | |||
| [[Sagittarius (constellation)|Sagittarius]] | |||
| | |||
| 4<sup>m</sup>.29 | |||
| 5<sup>m</sup>.14 | |||
| 7.59503 d | |||
| F4-G2Ib | |||
| Optical double with [[Gamma Sagittarii|γ Sgr]] | |||
|- | |||
| [[X Sagittarii|X Sgr]] | |||
| [[Sagittarius (constellation)|Sagittarius]] | |||
| | |||
| 4<sup>m</sup>.20 | |||
| 4<sup>m</sup>.90 | |||
| 7.01283 d | |||
| F5-G2II | |||
| | |||
|- | |||
| [[V636 Scorpii|V636 Sco]] | |||
| [[Scorpius]] | |||
| | |||
| 6<sup>m</sup>.40 | |||
| 6<sup>m</sup>.92 | |||
| 6.79671 d | |||
| F7/8Ib/II-G5 | |||
| | |||
|- | |||
| [[R Trianguli Australis|R TrA]] | |||
| [[Triangulum Australe]] | |||
| | |||
| 6<sup>m</sup>.4 | |||
| 6<sup>m</sup>.9 | |||
| 3.389 d | |||
| F7Ib/II | |||
| | |||
|- | |||
| [[S Trianguli Australis|S TrA]] | |||
| [[Triangulum Australe]] | |||
| | |||
| 6<sup>m</sup>.1 | |||
| 6<sup>m</sup>.8 | |||
| 6.323 d | |||
| F8II | |||
| | |||
|- | |||
| α UMi ([[Polaris]]) | |||
| [[Ursa Minor]] | |||
| | |||
| 1<sup>m</sup>.86 | |||
| 2<sup>m</sup>.13 | |||
| 3.9696 d | |||
| F8Ib or F8II | |||
| | |||
|- | |||
| [[AH Velorum|AH Vel]] | |||
| [[Vela (constellation)|Vela]] | |||
| | |||
| 5<sup>m</sup>.5 | |||
| 5<sup>m</sup>.89 | |||
| 4.227171 d | |||
| F7Ib-II | |||
| | |||
|- | |||
| [[T Vulpeculae|T Vul]] | |||
| [[Vulpecula]] | |||
| | |||
| 5<sup>m</sup>.41 | |||
| 6<sup>m</sup>.09 | |||
| 4.435462 d | |||
| F5Ib-G0Ib | |||
| | |||
|} | |||
==See also== | |||
*[[Type II Cepheids]] | |||
*[[RR Lyrae variables]] | |||
*[[Stellar pulsation theory - Regular versus irregular variability]] | |||
==References== | |||
{{Reflist|2}} | |||
==External links== | |||
*[http://www.institute-of-brilliant-failures.com The Cepheid Distance Scale: A History, by Nick Allen] | |||
*[http://www.seds.org/~spider/spider/ScholarX/variables.html SEDS: Variable Stars] | |||
*[http://crocus.physics.mcmaster.ca/Cepheid/HomePage.html McMaster Cepheid Photometry and Radial Velocity Data Archive] | |||
*[http://www.aavso.org/ American Association of Variable Star Observers] | |||
*[http://ogle.astrouw.edu.pl/atlas/classical_Cepheids.html OGLE Atlas of Variable Star Light Curves - Classical Cepheids] | |||
{{Variable star topics}} | |||
{{DEFAULTSORT:Cepheid Variable}} | |||
[[Category:Cepheid variables]] | |||
[[Category:Astrometry]] | |||
[[Category:Standard candles]] | |||
[[Category:Variable stars]] | |||
Revision as of 11:34, 5 November 2013
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
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
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 and its mean absolute magnitude was established from Hubble Space Telescope trigonometric parallaxes for 10 nearby Cepheids:
with measured in days. [17][21] The following relations can also be used to calculate the distance to classical Cepheids:
or
and represent near infrared and visual apparent mean magnitudes, respectively.
Uncertainties in Cepheid determined distances
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
Some fairly bright Classical Cepheids which exhibit variations discernable 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 | 7.17664 d | F6 Ibv | |
| FF Aql | Aquila | 5m.18 | 5m.68 | 4.47 d | F5Ia-F8Ia | ||
| TT Aql | Aquila | 6m.46 | 7m.7 | 13.7546 d | F6-G5 | ||
| U Aql | Aquila | 6m.08 | 6m.86 | 7.02393 d | F5I-II-G1 | ||
| T Ant | Antlia | 5m.00 | 5m.82 | 5.898 d | G5 | has unseen companion, possibly associated with open cluster NGC 6649 | |
| RT Aur | Auriga | 5m.00 | 5m.82 | 3.73 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 | 5.36634 d | F5Ib-G2Ib | double star, visible in binoculars |
| AX Cir | Circinus | 5m.65 | 6m.09 | 5.273268 d | F2-G2II | spectroscopic binary with 5 solar mass B6 companion | |
| BP Cir | Circinus | 7m.31 | 7m.71 | 2.39810 d | F2/3II-F6 | spectroscopic binary with 4.7 solar mass B6 companion | |
| BG Cru | Crux | 5m.34 | 5m.58 | 3.3428 d | F5Ib-G0p | ||
| R Cru | Crux | 6m.40 | 7m.23 | 5.82575 d | F7Ib/II | ||
| X Cyg | Cygnus | 5m.85 | 6m.91 | 16.38633 d | F7Ib | ||
| SU Cyg | Cygnus | 6m.44 | 7m.22 | 3.84555 d | F2Iab | ||
| β Dor | Dorado | 3m.46 | 4m.08 | 9.8426 d | F4-G4Ia-II | ||
| ζ Gem | Gemini | 3m.62 | 4m.18 | 10.15073 d | F7Ib to G3Ib | ||
| R Mus | Musca | 5m.93 | 6m.73 | 7.51 d | F7Ib-G2 | ||
| S Mus | Musca | 5m.89 | 6m.49 | 9.66007 d | F6Ib-G0 | ||
| BF Oph | Ophiuchus | 6m.93 | 7m.71 | 4.06775 d | G0II | ||
| κ Pav | Pavo | 3m.91 | 4m.78 | 9.09423 d | F5Ib-II | ||
| RS Pup | Puppis | 6m.52 | 7m.67 | 41.3876 d | F8Iab | ||
| U Sgr | Sagittarius (in M25) | 6m.28 | 7m.15 | 6.74523 d | G1Ib | ||
| W Sgr | Sagittarius | 4m.29 | 5m.14 | 7.59503 d | F4-G2Ib | Optical double with γ Sgr | |
| X Sgr | Sagittarius | 4m.20 | 4m.90 | 7.01283 d | F5-G2II | ||
| V636 Sco | Scorpius | 6m.40 | 6m.92 | 6.79671 d | F7/8Ib/II-G5 | ||
| R TrA | Triangulum Australe | 6m.4 | 6m.9 | 3.389 d | F7Ib/II | ||
| S TrA | Triangulum Australe | 6m.1 | 6m.8 | 6.323 d | F8II | ||
| α UMi (Polaris) | Ursa Minor | 1m.86 | 2m.13 | 3.9696 d | F8Ib or F8II | ||
| AH Vel | Vela | 5m.5 | 5m.89 | 4.227171 d | F7Ib-II | ||
| T Vul | Vulpecula | 5m.41 | 6m.09 | 4.435462 d | F5Ib-G0Ib |
See also
References
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External links
- The Cepheid Distance Scale: A History, by Nick Allen
- SEDS: Variable Stars
- McMaster Cepheid Photometry and Radial Velocity Data Archive
- American Association of Variable Star Observers
- OGLE Atlas of Variable Star Light Curves - Classical Cepheids
- ↑ Turner, David G."The Progenitors of Classical Cepheid Variables". JRASC (1996)
- ↑ 2.0 2.1 Turner, David G."The PL calibration for Milky Way Cepheids and its implications for the distance scale". Ap&SS (2010)
- ↑ Rodgers, A. W. "Radius variation and population type of cepheid variables". Monthly Notices of the Royal Astronomical Society. 117 (1956) 84–94
- ↑ W. Strohmeier, Variable Stars, Pergamon (1972)
- ↑ 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)
- ↑ 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)
- ↑ 7.0 7.1 7.2 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)
- ↑ 8.0 8.1 8.2 8.3 Tammann, G. A.; Sandage, A.; Reindl, B. "The expansion field: the value of H 0", Annual Review of Astronomy and Astrophysics, 2008
- ↑ 9.0 9.1 Majaess D. J., Turner D. G., Lane D. J. "Characteristics of the Galaxy according to Cepheids", Monthly Notices of the Royal Astronomical Society (2009)
- ↑ 10.0 10.1 10.2 10.3 Freedman, Wendy L.; Madore, Barry F. "The Hubble Constant", Annual Review of Astronomy and Astrophysics, 2010
- ↑ 11.0 11.1 11.2 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
- ↑ 12.0 12.1 12.2 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
- ↑ Cox, John P., Theory of Stellar Pulsations, Princeton (1980)
- ↑ 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
- ↑ 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
- ↑ Majaess, D.; Turner, D.; Gieren, W. (2012). New Evidence Supporting Cluster Membership for the Keystone Calibrator Delta Cephei, ApJ
- ↑ 17.0 17.1 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
- ↑ Leavitt, Henrietta S. "1777 Variables in the Magellanic Clouds". Annals of Harvard College Observatory. LX(IV) (1908) 87–110
- ↑ Miss Leavitt in Pickering, Edward C. "Periods of 25 Variable Stars in the Small Magellanic Cloud" Harvard College Observatory Circular 173 (1912) 1–3.
- ↑ Hertzsprung, E., "Über die räumliche Verteilung der Veränderlichen vom δ Cephei-Typus." Astronomischen Nachrichten, 196 p. 201–210 (1913)
- ↑ 21.0 21.1 21.2 21.3 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) Cite error: Invalid
<ref>tag; name "benedict2007" defined multiple times with different content Cite error: Invalid<ref>tag; name "benedict2007" defined multiple times with different content - ↑ Kervella, Pierre: Light echoes whisper the distance to a star
- ↑ 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)
- ↑ 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.
- ↑ 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
- ↑ 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
- ↑ 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
- ↑ 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
- ↑ Majaess, D.; Turner, D.; Lane, D. "Type II Cepheids as Extragalactic Distance Candles", Acta Astronomica, 2009
- ↑ Madore, Barry F., Freedman, Wendy L. " Concerning the Slope of the Cepheid Period-Luminosity Relation", The Astrophysical Journal, 2009
- ↑ 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
- ↑ Majaess, D. "The Cepheids of Centaurus A (NGC 5128) and Implications for H0", Acta Astronomica, 2010
- ↑ Turner, D. "Polaris and its Kin", STELLAR PULSATION: CHALLENGES FOR THEORY AND OBSERVATION, 2009
- ↑ 34.0 34.1 (visual magnitude, unless marked (B) (= blue) or (p) (= photographic))