Cepheid variables

Cepheid in the Spiral Galaxy M100

A Cepheid (pron: ˈse-f(ē-)id or ˈsē-f(ē-)id) 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. They are large, hot stars, of spectral class F6 – K2^[1], that 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.

Over 700 classical Cepheids are known in the Milky Way galaxy^[2]—several thousand within the Local Group of galaxies. A few more have been identified outside the Local Group.

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^[3]. She published it in 1912^[4] 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.^[5]

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.

Cepheid variables have been used in a variety of ways, including placing cosmological constraints on the expansion of the Universe through the determination of distances to galaxies.^[6] They have also been used to measure many characteristics of our galaxy and our relationship to it, for example: to determine the Sun's height above the galactic plane, to establish the distance to the galactic center, and to interpret the local galactic spiral structure.^[7]

The 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]

Dynamics of the pulsation

The accepted explanation for the pulsation of Cepheids is called the Eddington valve^[9], 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^[10] (who wrote at length on the dynamics of Cepheids), but it was not until 1953 that S. A. Zhevakin identified ionized helium^[11] 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^[12], 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^[9].

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.^[13] 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.

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^[14].

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^[15].

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

with P measured in days.^[16][12] The following relations can also be used to calculate the distance d and reddenings E(B − V) to classical Cepheids:

^[17]

Where J is on the 2MASS photometric system, and B, I and V represent blue, near infrared, and visual, respectively.

Examples

Some fairly bright Cepheids with variations in brightness large 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",

• Polaris.

It has a period of about 4 days, but its variation in brightness at 1% would not be perceptible by 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

External links

• SEDS: Variable Stars
• Cepheid Variable Photometry and Radial Velocity Archive
• American Association of Variable Star Observers