What Makes Cepheid Variables Standard Candles?

are cepheid variables standard candles

Cepheid variables are a class of extremely bright variable stars, named after the star delta Cephei in the Cepheus constellation. Their luminosity is related to the period of their pulsations, with longer-period stars being brighter than shorter-period ones. This makes them excellent standard candles, which are objects with known luminosities, allowing astronomers to calculate their distance by comparing their intrinsic brightness with their apparent brightness as viewed from Earth. The period-luminosity relation for Cepheid variables was discovered by Henrietta Leavitt, who noticed that the period of a Cepheid variable is proportional to its average brightness. This discovery has made Cepheid variables one of the most important standard candles in the universe, enabling cosmologists to measure the expansion of the universe.

Characteristics Values
Class Extremely bright variable stars
Luminosity High
Relation to distance The larger the distance, the brighter the star
Named after δ-Cephei (delta Cephei) in the constellation of Cepheus
Visibility Can be seen with the naked eye
Distance measurement Can measure distances up to about 100 million light-years
Calibration Difficult due to large uncertainties
Period-luminosity relation Discovered without knowing their distances or luminosities
Intrinsic luminosity Known
Apparent luminosity Can be compared with the intrinsic luminosity to get a measure of how far away the object is

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Cepheid variables are a class of extremely bright variable stars

The period-luminosity relation for Cepheid variables was discovered by Henrietta Leavitt, who noticed that the period of a Cepheid variable is proportional to its average brightness. This is called the Leavitt Relation or Leavitt Law, in her honour. By measuring the period of any Cepheid variable star, one can deduce its intrinsic brightness from the Leavitt period-luminosity relation.

Cepheid variables are good standard candles. Their luminosity is quite high (the most luminous Cepheids are 40,000 times more luminous than the Sun), so they can be seen at large distances. Their luminosities can be computed from the Leavitt period-luminosity relation. For instance, the star Delta Cephei has a period of P = 5.4 days. Any other Cepheid in the universe with the same period of variability will have the same average luminosity as Delta Cephei.

A standard candle is an object whose intrinsic luminosity is known. By comparing this with how much light from the object reaches us (its apparent luminosity), we can calculate how far away the object is from us. This is done by using the inverse-square law.

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Cepheid variables are a class of extremely bright variable stars. Their luminosity is related to the period of their pulsations. Longer-period Cepheid variables are brighter than shorter-period ones. This is known as the period-luminosity relation for Cepheids, sometimes also called the Leavitt Relation or Leavitt Law, after its discoverer Henrietta Swan Leavitt. Leavitt, who worked at the Harvard College Observatory, discovered the relation in 1908 by examining photographic plates to measure and catalog the brightness of stars.

The period-luminosity relation for Cepheids was discovered without knowing their distances or luminosities. Leavitt's discovery provided the first "standard candle" with which to measure the distance to faraway galaxies. The relation established Cepheids as foundational indicators of cosmic benchmarks for scaling galactic and extragalactic distances. Cepheids are now considered one of the most important standard candles in the universe.

The period-luminosity relation for classical Cepheids has been calibrated by many astronomers throughout the twentieth century, beginning with Hertzsprung. Calibrating the relation has been problematic, but a firm Galactic calibration was established by Benedict et al. in 2007 using precise HST parallaxes for 10 nearby classical Cepheids.

The logarithm of the period is linearly related to the logarithm of the star's average intrinsic optical luminosity. This means that the longer the pulsation period, the more luminous the star. Classical Cepheids are 4–20 times more massive than the Sun and up to 100,000 times more luminous.

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They are useful for measuring distances to galaxies

Cepheid variables are extremely bright variable stars. Their luminosity is related to the period of their pulsations: longer-period stars are brighter than shorter-period ones. This is known as the period-luminosity relation for Cepheids, or the Leavitt Relation/Law, named after its discoverer, Henrietta Leavitt.

The Leavitt Relation is useful for measuring distances to galaxies because it allows a simple timing measurement to be converted into a brightness measurement. This means that the intrinsic brightness of a Cepheid variable can be deduced from its period of pulsation. Then, by measuring the star's apparent brightness, its distance can be calculated using the inverse-square law.

The high luminosity of Cepheid variables means that they can be seen at large distances, making them useful for measuring distances to distant galaxies. Cepheid variables can be used to measure distances out to about 100 million light-years. Beyond 30 megaparsecs, however, Cepheid variables are too dim to be detected, and brighter standard candles, such as Type Ia supernovae, are needed to measure distances.

Type Ia supernovae are the result of the thermonuclear explosion of a white dwarf star. They are extremely luminous, and can be seen at distances of thousands of megaparsecs. They are useful for measuring distances to galaxies because they all have roughly the same luminosity, so by comparing their apparent brightness as observed from Earth, their distance can be calculated.

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Henrietta Leavitt discovered the Leavitt Relation or Leavitt Law

Henrietta Swan Leavitt, an American astronomer, discovered the Leavitt Law or Leavitt Relation, also known as the period-luminosity relationship for Cepheid variables. Leavitt's work on Cepheids in the Magellanic Clouds led her to discover the relation between the luminosity and the period of Cepheid variables. Leavitt identified 1777 variable stars, of which 47 were Cepheids.

In 1908, Leavitt published her discovery of the period-luminosity relationship, which is the correlation between how bright a star is and the time it takes for the star to go from bright to dim. Leavitt examined Cepheids in the Small and Large Magellanic Clouds and observed a clear pattern: the brighter variable stars appeared to go from their faintest to brightest, no matter how far away they were from Earth. This was because these stars were all roughly the same distance away, and astronomers could measure their distance in the Magellanic Clouds. This meant that astronomers could use the period-luminosity relationship to calculate the distance of far more distant stars. The longer the star took to change brightness, the brighter the star.

Leavitt's discovery provided astronomers with the first standard candle with which to measure the distance to other galaxies. Before Leavitt's discovery, the only techniques available to astronomers for measuring the distance to a star were based on stellar parallax. Leavitt's work on the period-luminosity relationship for Cepheid variables allowed scientists to compute the distances to stars too remote for stellar parallax observations to be useful. Leavitt's discovery provided the basis for a fundamental shift in cosmology, as it prompted Harlow Shapley to move the Sun from the center of the galaxy in the "Great Debate" and, later, Hubble to move the Milky Way galaxy from the center of the universe.

Leavitt's work on the Leavitt Law or Leavitt Relation helped turn the sky into a three-dimensional map, allowing astronomers to solve the unknown in the equation: distance. Leavitt's groundbreaking research made it possible for Hubble to discover that the universe is expanding.

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Type Ia supernovae are also used as standard candles

The use of Type Ia supernovae to measure precise distances was pioneered by a collaboration of Chilean and US astronomers, the Calán/Tololo Supernova Survey. In a series of papers in the 1990s, the survey showed that while Type Ia supernovae do not all reach the same peak luminosity, a single parameter measured from the light curve can be used to correct unreddened Type Ia supernovae to standard candle values. The original correction to standard candle value is known as the Phillips relationship and was shown by this group to be able to measure relative distances to 7% accuracy.

The details of the pre-nova moments may help scientists better judge the quality of Type Ia supernovae as standard candles, which is an important link in the argument for dark energy. In July 2019, the Hubble Space Telescope took three images of a Type Ia supernova through a gravitational lens. This supernova appeared at three different times in the evolution of its brightness due to the differing path lengths of the light in the three images; at −24, 92, and 107 days from peak luminosity. A fourth image will appear in 2037, allowing observation of the entire luminosity cycle of the supernova.

The biggest problem with Type Ia supernovae is that they are infrequent. Even a large galaxy only has one supernova per century, on average.

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Frequently asked questions

Standard candles are objects with known intrinsic luminosity, i.e., the amount of light/radiation emitted by the object. By comparing the intrinsic luminosity with the apparent luminosity (how much light reaches us), we can measure how far away the object is.

Yes, Cepheid variables are a type of standard candle.

Cepheid variables are extremely bright variable stars with high luminosity, so they can be seen at large distances. Their luminosity can be computed from the Period-Luminosity Relation.

Henrietta Leavitt discovered the Period-Luminosity Relation for Cepheid variables. She noticed that the period of a Cepheid variable is proportional to its average brightness. This relation is sometimes called the Leavitt Relation or Leavitt Law.

Type Ia supernovae are another example of standard candles. They are the result of the thermonuclear explosion of a white dwarf star. They are 100,000 times more luminous than even the brightest Cepheid stars and can be seen at distances of thousands of megaparsecs.

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