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Cepheid variable

A Cepheid variable (pron: ˈse-f(ē-)id or ˈsē-f(ē-)id) or Cepheid is a member of a particular class of variable stars, notable for a fairly tight correlation between their period of variability and absolute luminosity. The namesake and prototype of these variables is the star Delta Cephei, discovered to be variable by John Goodricke in 1784.

Because of this correlation (discovered and stated by Henrietta Swan Leavitt in 1908 and given precise mathematical form by her in 1912), a Cepheid variable can be used as a standard candle to determine the distance to its host cluster or galaxy. Since the period-luminosity relation can be calibrated with great precision using the nearest Cepheid stars, the distances found with this method are among the most accurate available.

Description

A Cepheid is usually a population I giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity. The luminosity of cepheid stars range from 103 to 104 times that of the Sun. Because Cepheids are from population I, they are sometimes called Type I Cepheids, while the similar (but belonging to population II) W Virginis variables are known as Type II Cepheids.

The exact mass of Cepheids with given brightness or oscillations is not known to any great precision, but astronomers hope to gather data for this from the newly-discovered third star of the Polaris system

The variation in luminosity is caused by a cycle of ionization of helium in the star's atmosphere, followed by expansion and deionization. While ionized, the atmosphere is more opaque to light. This cycle has a period equal to the star's dynamical time scale, therefore giving information on the mean density of the body as well as its luminosity.

Use as a "standard candle"

The relationship between a Cepheid variable's luminosity and variability period is quite precise, securing Cepheids as a viable standard candle and the foundation of the Extragalactic Distance Scale. This period / luminosity connection was discovered in 1912 by Henrietta Swan Leavitt. She measured the brightness of hundreds of Cepheid variables and discovered a distinct period-luminosity relationship. A three-day period Cepheid has a luminosity of about 800 times that of the Sun. A thirty-day period Cepheid is 10,000 times as bright as the Sun. The scale has been calibrated using nearby Cepheid stars and Cepheids which are members of open clusters.

Because of relatively high luminosity, Cepheid stars are visible from great distances. Edwin Hubble first identified some Cepheids in the Andromeda galaxy, thus proving its extragalactic nature (not known at that time). More recently, the Hubble Space Telescope succeeded in identifying some Cepheid stars in the Virgo cluster, at a distance of 60 million light years.

Period-luminosity relationship

The relationship between a Type I Cepheid's period $P$, and its absolute magnitude $M_v$ has been empirically derived by many astronomers throughout the Twentieth century. The relationship is calibrated using data collected from Cepheids whose distances are determined by other means. Ejnar Hertzsprung attempted the first calibration in 1913, but, due to his ignorance of interstellar absorption, his results were highly inaccurate.

A more recent calibration was published by Michael Feast and Robin Catchpole in 1997. Using data from the Hipparcos satellite, Feast and Catchpole calculated the distances to many Galactic Cepheids via trigonometric parallax. The resultant period-luminosity relationship was:

$M_v = -2.81 log\left(P\right) - \left(1.43 pm 0.1\right) ,$

with $P$ measured in days. In addition, the following Cepheid relations can be used to calculate the distance to Galactic and extragalactic Cepheids:

$5log_\left\{10\right\}\left\{d\right\}=V+ \left(3.43\right) log_\left\{10\right\}\left\{P\right\} - \left(2.58\right) \left(V-I\right) + 7.50 ,.$
$5log_\left\{10\right\}\left\{d\right\}=V+ \left(3.30\right) log_\left\{10\right\}\left\{P\right\} - \left(1.48\right) \left(V-J\right) + 7.63 ,.$

The use of Cepheid variable stars is not without its problems however. The largest source of error with Cepheids as standard candles is the possibility that the period-luminosity relation is affected by metallicity. For Galactic use only, the following relation is also valid in addition to those highlighted above:

$5log_\left\{10\right\}\left\{d\right\}=V+ \left(4.42\right) log_\left\{10\right\}\left\{P\right\} - \left(3.43\right) \left(B-V\right) + 7.15 ,.$

Similarly, in the absence of space reddenings, a first order estimate of a Galactic Cepheid's color excess can be approximated as:

$E\left(B-V\right)=-\left(0.27\right) log_\left\{10\right\}\left\{P\right\} + \left(0.41\right) \left(V-J\right) - 0.26 ,.$
Where J is on the 2MASS system.

Notes

• Some Cepheid stars (for example Polaris), have shown rapid period change.
• The distance to the Cepheid RS Puppis is estimated using light reflected off a large nebula surrounding the star.

Examples

Some Cepheid variables with fairly bright apparent magnitudes and variations in brightness large enough to easily distinguish with the naked eye include Eta Aquilae, Zeta Geminorum, Beta Doradus, as well as the prototype Delta Cephei.