Classical Cepheid variable

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][11][8][12][10]} 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.

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.^[15] She published it in 1912^[16] 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.^[17] 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.^[18] 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.^[19] However, that latter finding has been actively debated in the literature.^[18]

A calibration was published by Michael Feast and Robin Catchpole in 1997 using trigonometric parallaxes determined by the Hipparcos satellite. The relationship between a Population I Cepheid's period P, and its luminosity, measured as its mean absolute magnitude M_v was

$M_v = -2.81 \log_{10}(P) - (1.43 \pm 0.1) \,$

with P measured in days.^[20][21] The following relations can also be used to calculate the distance d and reddenings E(B − V) to classical Cepheids:

$5\log_{10}{d}=V+ (3.43) \log_{10}{P} - (2.58) (V-I) + 7.50 \,.$^[22]

$E(B-V)=-(0.27) \log_{10}{P} + (0.41) (V-J) - 0.26 \,.$

Where J is on the 2MASS photometric system, I and V represent near infrared and visual, 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.^{[23][24][11][25][8][26][27][28][29][2][30]}

These unresolved matters have resulted in cited values for the Hubble constant ranging between 60 km/s/Mpc and 80 km/s/Mpc.^{[7][11][8][12][10]} 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.^[12][10]

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.^[31]

See also

• Type II Cepheids
• RR Lyrae variables

References

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
9. ^ ^{a b} 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. ^ ^{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. ^ Leavitt, Henrietta S. "1777 Variables in the Magellanic Clouds". Annals of Harvard College Observatory. LX(IV) (1908) 87–110
16. ^ Miss Leavitt in Pickering, Edward C. "Periods of 25 Variable Stars in the Small Magellanic Cloud" Harvard College Observatory Circular 173 (1912) 1–3.
17. ^ Hertzsprung, E., "Über die räumliche Verteilung der Veränderlichen vom δ Cephei-Typus." Astronomischen Nachrichten, 196 p. 201–210 (1913)
18. ^ ^{a b} 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)
19. ^ Kervella, Pierre: Light echoes whisper the distance to a star
20. ^ Allen, Nick. The Cepheid Distance Scale: A History
21. ^ 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.
22. ^ Majaess D. J., Turner D. G., Lane D. J. "Assessing potential cluster Cepheids from a new distance and reddening parametrization and 2MASS photometry", Monthly Notices of the Royal Astronomical Society, Volume 390, Issue 4, pp. 1539–1548 (2008)
23. ^ 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
24. ^ 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
25. ^ 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
26. ^ 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
27. ^ Majaess, D.; Turner, D.; Lane, D. "Type II Cepheids as Extragalactic Distance Candles", Acta Astronomica, 2009
28. ^ Madore, Barry F., Freedman, Wendy L. " Concerning the Slope of the Cepheid Period-Luminosity Relation", The Astrophysical Journal, 2009
29. ^ 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
30. ^ Majaess, D. "The Cepheids of Centaurus A (NGC 5128) and Implications for H0", Acta Astronomica, 2010
31. ^ Turner, D. "Polaris and its Kin", STELLAR PULSATION: CHALLENGES FOR THEORY AND OBSERVATION, 2009

External links

• SEDS: Variable Stars
• McMaster Cepheid Photometry and Radial Velocity Data Archive
• American Association of Variable Star Observers
• Stellar pulsation theory - Regular versus irregular variability