Cepheid variable
A Cepheid (pronounced /ˈsɛfɪɪd/ or pronounced /ˈsiːfɪɪd/) is a member of a class of pulsating variable stars. The relationship between a Cepheid variable's luminosity and pulsation period is quite precise, securing Cepheids as viable standard candles and the foundation of the Extragalactic Distance Scale.
Typical classical Cepheids pulsate with periods of a few days to months, and their radii change by several million kilometers (30%) in the process[1]. They are large, luminous stars, of spectral class F6 – K2[2], they are 5–20 times as massive as the Sun and up to 30000 times more luminous.
Due to their high luminosity, classical Cepheids may be visible from great distances: the Hubble Space Telescope has identified classical Cepheids out to a distance of some 100 million light years[3].
Over 700 classical Cepheids are known in the Milky Way galaxy[4]—several thousand within the Local Group of galaxies. A few more have been identified outside the Local Group.
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Discovery
On September 10, 1784 Edward Pigott detected the variability of Eta Aquilae, the first known representative of the class of Cepheid variables. However, the namesake for classical Cepheids is the star Delta Cephei, discovered to be variable by John Goodricke a few months later.
The period-luminosity relation of Cepheids was discovered in 1908 by Henrietta Swan Leavitt in an investigation of thousands of variable stars in the Magellanic Clouds[5]. She published it in 1912[6] with further evidence.
Use as a "standard candle"
In 1915 Harlow Shapley used Cepheids to place initial constraints on the size and shape of the Milky Way, and of the placement of our Sun within it.
In 1924 Edwin Hubble discovered Cepheid variables in the Andromeda galaxy. This settled the Island Universe debate, concerning the question of whether the Milky Way and the Universe were synonymous, or was the Milky Way merely one in a plethora of galaxies that constitutes the Universe.[7]
Combining his calculations based on Cepheids of distances of galaxies with Vesto Slipher's measurements of the speed at which the galaxies recede from us, in 1929 Hubble and Milton L. Humason formulated what is now known as Hubble's law, concerning the expansion of the Universe.
The Hubble Space Telescope (HST) has found dozens of Cepheids in the galaxy M100 alone, whose distance has been estimated thereby to be about 53 million light-years[8]. It also made the most distant Cepheid measurement to date, of the galaxy NGC 4603 to be about 108 million light-years[3]. By means of HST Cepheid observations, better constraints on Hubble's law have been calculated[9], and many characteristics of our galaxy and our relationship to it have been clarified, for example: the Sun's height above the galactic plane, the distance to the galactic center, and the interpretation the local galactic spiral structure.[10]
Dynamics of the pulsation
The accepted explanation for the pulsation of Cepheids is called the Eddington valve,[11] or κ-mechanism, where the Greek letter κ (kappa) denotes gas opacity.
Helium is the gas thought to be most active in the process. Doubly-ionized helium (helium whose atoms are missing two electrons) is more opaque than singly-ionized helium. The more helium is heated, the more ionized it becomes.
At the dimmest part of a Cepheid's cycle, the ionized gas in the outer layers of the star is opaque, and so is heated by the star's radiation, and due to the increased temperature, begins to expand. As it expands, it cools, and so becomes less ionized and therefore more transparent, allowing the radiation to escape. Then the expansion stops, and reverses due to the star's gravitational attraction. The process then repeats.
The mechanics of the pulsation as a heat-engine was proposed in 1917 by Arthur Stanley Eddington[12] (who wrote at length on the dynamics of Cepheids), but it was not until 1953 that S. A. Zhevakin identified ionized helium[13] as a likely valve for the engine.
Cepheid-like variable stars
There are many variable stars that were originally called "Cepheid", but which are now considered as members of separate classes. While their pulsation is thought to be driven by similar mechanisms, they exhibit distinct period-luminosity relationships, are distributed differently within galaxies, and are thought to have different histories.
The RR Lyrae stars were recognized fairly early (by the 1930s) as being a separate class of variable, due to their short period and different association with galactic structures. Whereas the RR Lyrae stars are strongly associated with globular clusters, and can be found at any galactic latitude, classical Cepheids are strongly associated with the galactic plane.
The initial studies of Cepheid variable distances was complicated by the admixture of these other classes[14], which include the RR Lyrae variables as well as the W Virginis variables. It was in 1942 that Walter Baade realized that the Cepheids in the Andromeda Galaxy were of two populations[11].
The Cepheid variables are now divided into two subclasses, Population I or classical Cepheids, which are young, massive, metal-rich stars, and Population II or W Virginis Cepheids, which are older, fainter, metal-poor low-mass stars.[15] Population I and Population II Cepheids follow different period-luminosity relationships. The luminosity of Population II Cepheids is, on average, less than classical Cepheids by about 1.5 magnitudes (but still brighter than RR Lyrae stars).
All these stars lie within the instability strip of the Hertzsprung–Russell diagram of stellar types.
Any of these types of variable stars may be used as a standard candle for measuring distances within our own galaxy, but the types are associated with different structures, such as globular clusters and the galactic plane. The classical Cepheids, due to their luminosity, are always the first to be discerned in neighboring galaxies.
Period-luminosity relation
The precision of distance measurements based on the period-luminosity relation depends primarily on the precision with which the distance of some Cepheid is known. This calibration problem has long been a delicate issue, but in 2008, ESO astronomers have estimated with a precision within 1% the distance to the Cepheid RS Puppis, using light echos from a nebula in which it is embedded[16].
Several other issues arise in the calibration of Cepheids as a standard candle. Among these are effects on the light of the star by intervening galactic dust and gas: reddening (the alteration of the color), and extinction (the overall dimming of the light). Another issue is the actively debated effect of metallicity.
The period-luminosity relationship has been calibrated by many astronomers throughout the twentieth century, beginning with Hertzsprung[17].
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 
, and its luminosity, measured as its mean absolute magnitude 
was
with measured in days.[18][14] The following relations can also be used to calculate the distance 
and reddenings 
to classical Cepheids:
Where 
is on the 2MASS photometric system, and 
, 
and 
represent blue, near infrared, and visual, respectively.
Other information
Mass
The more massive Cepheids are more luminous and have more extended envelopes (the outer layers of gas in a star are sometimes called its "envelope"). Because these envelopes are more extended and the density in their envelopes is lower, their variability period, which is proportional to the inverse square root of the density in the layer, is longer.
Difficulties in using Cepheids to determine distances
There have been a number of difficulties associated with using Cepheids as distance indicators. Until recently, astronomers used photographic plates to measure the fluxes from stars. The plates were highly non-linear and often produced faulty flux measurements. Since massive stars are short-lived, they are always located near their dusty birthplaces. Dust absorbs light, particularly at blue wavelengths where most photographic images were taken, and if not properly corrected for, this dust absorption can lead to erroneous luminosity determinations. Finally, it has been very difficult to use ground-based telescopes to detect Cepheids in distant galaxies: Earth's fluctuating atmosphere makes it impossible to separate these stars from the diffuse light of their host galaxies.
Another difficulty with using Cepheids as distance indicators has been the problem of determining the distance to a sample of nearby Cepheids. In recent years, this problem has lessened, as several reliable and independent methods have been developed for determining the distances to the Magellanic Clouds. Since both of the Magellanic Clouds contain many Cepheids, they can be used to calibrate the distance scale.
Recent progress
Recent technological advances enabled astronomers to overcome a number of the other past difficulties. New detectors called CCDs (Charge-coupled devices) made more accurate flux measurements possible. These new detectors are also sensitive in the infrared wavelengths. Dust is much more transparent at these wavelengths. By measuring fluxes at multiple wavelengths however, corrections can be made for the effects of dust and make much more accurate distance determinations.
These advances enabled accurate study of the nearby galaxies that comprise the "Local Group" (the group of galaxies including our own Milky Way galaxy and our neighbor the Andromeda galaxy). Cepheids have been observed in both the metal rich inner region of the Andromeda Galaxy and its metal poor outer region, showing that the properties of Cepheids did not depend sensitively on chemical abundances. Despite these advances, limitations imposed by the Earth's atmosphere allowed only measurement of the distances to the nearest galaxies. In addition to the motion due to the expansion of the Universe, galaxies have "relative motions" due to the gravitational pull of neighboring galaxies. Because of these peculiar motions, measurements of the distances to more distant galaxies must be made to determine the Hubble constant.
Over the past few decades, values for the Hubble constant ranging between 50 km/s/Mpc and 100 km/s/Mpc have been reported. Resolving this discrepancy is one of the most important outstanding problems in observational cosmology.
Examples
Some fairly bright Cepheids whose brightnesses vary enough to easily discern with the naked eye include
- Eta Aquilae,
- Zeta Geminorum,
- Beta Doradus,
as well as the prototype
- Delta Cephei.
The best-known star which is a Cepheid (and also the closest Cepheid to us) is the "North star",
It has a period of 3.9696 days and varies .1 magnitudes in brightness, which is imperceptible by the human eye. Its period (and average luminosity, and the magnitude of its variation) have also changed substantially during the time they have been measured; this is unusual behavior for a Cepheid.
References
- ↑ 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)
- ↑ 3.0 3.1 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
- ↑ Cox, John P., Theory of Stellar Pulsations, Princeton (1980)
- ↑ 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.
- ↑ Hubble, E. "Cepheids in spiral nebulae", The Observatory, Vol. 48, p. 139–142 (1925)
- ↑ A. Mazumdar, "Cepheid distance to the virgo cluster" Pramana,V. 53, 6 (1999)
- ↑ 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)
- ↑ Majaess D. J., Turner D. G., Lane D. J. "Characteristics of the Galaxy according to Cepheids", Monthly Notices of the Royal Astronomical Society (2009)
- ↑ 11.0 11.1 Webb, Stephen, Measuring the Universe: The Cosmological Distance Ladder, Springer, (1999)
- ↑ Eddington, A. S., "The Pulsation Theory of Cepheid Variables.", The Observatory v. 40, 516, 290–293 (1917)
- ↑ Zhevakin, S. A., "К Теории Цефеид. I", Астрономический журнал, 30 161–179 (1953)
- ↑ 14.0 14.1 Allen, Nick. "The Cepheid Distance Scale: A History"
- ↑ Wallerstein, G. "The Cepheids of Population II and Related Stars", The Publications of the Astronomical Society of the Pacific, Volume 114, Issue 797, pp. 689–699 (2002)
- ↑ Kervella, Pierre: Light echoes whisper the distance to a star
- ↑ Hertzsprung, E., "Über die räumliche Verteilung der Veränderlichen vom δ Cephei-Typus." Astronomischen Nachrichten, 196 p. 201–210 (1913)
- ↑ 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.
- ↑ 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)
External links
- SEDS: Variable Stars
- Cepheid Variable Photometry and Radial Velocity Archive
- American Association of Variable Star Observers
- Stellar pulsation theory - Regular versus irregular variability
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