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Classical Cepheids (also known as Population I Cepheids, Type I Cepheids, or Delta Cepheid variables) are a type of
Cepheid variable
A Cepheid variable () is a type of star that pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude.
A strong direct relationship between a Cepheid varia ...
star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
. They are
population I
During 1944, Walter Baade categorized groups of stars within the Milky Way into stellar populations.
In the abstract of the article by Baade, he recognizes that Jan Oort originally conceived this type of classification in 1926:
Baade noticed th ...
variable stars
A variable star is a star whose brightness as seen from Earth (its apparent magnitude) changes with time. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as e ...
that exhibit regular radial pulsations with periods of a few days to a few weeks and visual amplitudes from a few tenths of a magnitude to about 2 magnitudes.
There exists a well-defined
relationship between a classical Cepheid variable's
luminosity
Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a st ...
and pulsation period,
[ securing Cepheids as viable ]standard candle
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...
s for establishing the galactic and extragalactic distance scale
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...
s. Hubble Space Telescope
The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most versa ...
(HST) observations of classical Cepheid variables have enabled firmer constraints on Hubble's law
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
.[ Classical Cepheids have also been used to clarify many characteristics of our galaxy, such as the local spiral structure and the Sun's height above the galactic plane.]
Around 800 classical Cepheids are known in the Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
galaxy, out of an expected total of over 6,000. Several thousand more are known in the Magellanic Clouds
The Magellanic Clouds (''Magellanic system'' or ''Nubeculae Magellani'') are two irregular dwarf galaxies in the southern celestial hemisphere. Orbiting the Milky Way galaxy, these satellite galaxies are members of the Local Group. Because both ...
, with more known in other galaxies; the Hubble Space Telescope
The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most versa ...
has identified some in NGC 4603
NGC 4603 is a spiral galaxy located about 107 million light years away in the constellation Centaurus. It is a member of the Centaurus Cluster of galaxies, belonging to the section designated "Cen30". The morphological classification is SA(s)c, ...
, which is 100 million light year
A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (), or 5.88 trillion miles ().One trillion here is taken to be 1012 ...
s distant.
Properties
Classical Cepheid variables are 4–20 times more massive than the Sun, and around 1,000 to 50,000 (over 200,000 for the unusual V810 Centauri) times more luminous. Spectroscopically they are bright giants or low luminosity supergiants of spectral class
In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the ...
F6 – K2. The temperature and spectral type vary as they pulsate. Their radii are a few tens to a few hundred times that of the sun. More luminous Cepheids are cooler and larger and have longer periods. Along with the temperature changes their radii also change during each pulsation (e.g. by ~25% for the longer-period l Car), resulting in brightness variations up to two magnitudes. The brightness changes are more pronounced at shorter wavelengths.
Cepheid variables may pulsate in a fundamental mode
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies ...
, the first overtone
An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental i ...
, or rarely a mixed mode. Pulsations in an overtone higher than first are rare but interesting.[ The majority of classical Cepheids are thought to be fundamental mode pulsators, although it is not easy to distinguish the mode from the shape of the light curve. Stars pulsating in an overtone are more luminous and larger than a fundamental mode pulsator with the same period.]
When an intermediate mass star
A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth ma ...
(IMS) first evolves away from the main sequence
In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Her ...
, it crosses the instability strip very rapidly while the hydrogen shell is still burning. When the helium core ignites in an IMS, it may execute a blue loop
In the field of stellar evolution, a blue loop is a stage in the life of an evolved star where it changes from a cool star to a hotter one before cooling again. The name derives from the shape of the evolutionary track on a Hertzsprung–Russell ...
and crosses the instability strip again, once while evolving to high temperatures and again evolving back towards the asymptotic giant branch
The asymptotic giant branch (AGB) is a region of the Hertzsprung–Russell diagram populated by evolved cool luminous stars. This is a period of stellar evolution undertaken by all low- to intermediate-mass stars (about 0.5 to 8 solar masses) lat ...
. Stars more massive than about start core helium burning before reaching the red-giant branch
The red-giant branch (RGB), sometimes called the first giant branch, is the portion of the giant branch before helium ignition occurs in the course of stellar evolution. It is a stage that follows the main sequence for low- to intermediate-mass sta ...
and become red supergiant
Red supergiants (RSGs) are stars with a supergiant luminosity class ( Yerkes class I) of spectral type K or M. They are the largest stars in the universe in terms of volume, although they are not the most massive or luminous. Betelgeuse and Anta ...
s, but may still execute a blue loop through the instability strip. The duration and even existence of blue loops is very sensitive to the mass, metallicity
In astronomy, metallicity is the abundance of elements present in an object that are heavier than hydrogen and helium. Most of the normal physical matter in the Universe is either hydrogen or helium, and astronomers use the word ''"metals"'' as a ...
, and helium abundance of the star. In some cases, stars may cross the instability strip for a fourth and fifth time when helium shell burning starts. The rate of change of the period of a Cepheid variable, along with chemical abundances detectable in the spectrum, can be used to deduce which crossing a particular star is making.
Classical Cepheid variables were B type main-sequence stars
In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar color index, color versus absolute magnitude, brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams afte ...
earlier than about B7, possibly late O stars, before they ran out of hydrogen in their cores. More massive and hotter stars develop into more luminous Cepheids with longer periods, although it is expected that young stars within our own galaxy, at near solar metallicity, will generally lose sufficient mass by the time they first reach the instability strip
The unqualified term instability strip usually refers to a region of the Hertzsprung–Russell diagram largely occupied by several related classes of pulsating variable stars: Delta Scuti variables, SX Phoenicis variables, and rapidly oscillati ...
that they will have periods of 50 days or less. Above a certain mass, depending on metallicity, red supergiants will evolve back to blue supergiants rather than execute a blue loop, but they will do so as unstable yellow hypergiant
A yellow hypergiant (YHG) is a massive star with an extended atmosphere, a spectral class from A to K, and, starting with an initial mass of about 20–60 solar masses, has lost as much as half that mass. They are amongst the most visually lumino ...
s rather than regularly pulsating Cepheid variables. Very massive stars never cool sufficiently to reach the instability strip and do not ever become Cepheids. At low metallicity, for example in the Magellanic Clouds, stars can retain more mass and become more luminous Cepheids with longer periods.[
]
Light curves
A Cepheid light curve is typically asymmetric with a rapid rise to maximum light followed by a slower fall to minimum (e.g. Delta Cephei
Delta Cephei (δ Cep, δ Cephei) is the Bayer designation for a quadruple star system located approximately 887 light-years away in the northern constellation of Cepheus, the King. At this distance, the visual magnitude of the star is ...
). This is due to the phase difference between the radius and temperature variations and is considered characteristic of a fundamental mode pulsator, the most common type of type I Cepheid. In some cases the smooth pseudo-sinusoidal light curve shows a "bump", a brief slowing of the decline or even a small rise in brightness, thought to be due to a resonance between the fundamental and second overtone. The bump is most commonly seen on the descending branch for stars with periods around 6 days (e.g. Eta Aquilae
Eta Aquilae (η Aql, η Aquilae) is the Bayer designation for a multiple star in the equatorial constellation of Aquila, the eagle. It was once part of the former constellation Antinous. On average, this star has an apparent visual magnitu ...
). As the period increases, the location of the bump moves closer to the maximum and may cause a double maximum, or become indistinguishable from the primary maximum, for stars having periods around 10 days (e.g. Zeta Geminorum
Zeta Geminorum (ζ Geminorum, abbreviated Zeta Gem, ζ Gem) is a bright star with cluster components, distant optical components and a likely spectroscopic partner in the zodiac constellation of Gemini — in its south, on the left 'leg' ...
). At longer periods the bump can be seen on the ascending branch of the light curve (e.g. X Cygni), but for period longer than 20 days the resonance disappears.
A minority of classical Cepheids show nearly symmetric sinusoidal light curves. These are referred to as s-Cepheids, usually have lower amplitudes, and commonly have short periods. The majority of these are thought to be first overtone (e.g. X Sagittarii
X Sagittarii is a variable star and candidate binary star system in the southern constellation of Sagittarius, near the western constellation boundary with Ophiuchus. It has a yellow-white hue and is visible to the naked eye with an appa ...
), or higher, pulsators, although some unusual stars apparently pulsating in the fundamental mode also show this shape of light curve (e.g. S Vulpeculae
S Vulpeculae is a variable star located in the constellation Vulpecula. A supergiant star, it is around 382 times the diameter of the Sun.
S Vulpeculae was first suspected of varying in brightness in 1836 and this was confirmed by 1862. ...
). Stars pulsating in the first overtone are expected to only occur with short periods in our galaxy, although they may have somewhat longer periods at lower metallicity, for example in the Magellanic Clouds. Higher overtone pulsators and Cepheids pulsating in two overtones at the same time are also more common in the Magellanic Clouds, and they usually have low amplitude somewhat irregular light curves.
Discovery
On September 10, 1784 Edward Pigott
Edward Pigott (1753–1825) was an English astronomer notable for being one of the founders of the study of variable stars.
Biography
Son of the astronomer Nathaniel Pigott, Pigott's work focused on variable stars. Educated in France with ...
detected the variability of Eta Aquilae
Eta Aquilae (η Aql, η Aquilae) is the Bayer designation for a multiple star in the equatorial constellation of Aquila, the eagle. It was once part of the former constellation Antinous. On average, this star has an apparent visual magnitu ...
, the first known representative of the class of classical Cepheid variables. However, the namesake for classical Cepheids is the star Delta Cephei
Delta Cephei (δ Cep, δ Cephei) is the Bayer designation for a quadruple star system located approximately 887 light-years away in the northern constellation of Cepheus, the King. At this distance, the visual magnitude of the star is ...
, discovered to be variable by John Goodricke
John Goodricke FRS (17 September 1764 – 20 April 1786) was an English amateur astronomer. He is best known for his observations of the variable star Algol (Beta Persei) in 1782.
Life and work
John Goodricke, named after his great-grandfath ...
a month later. Delta Cephei is also of particular importance as a calibrator for the period-luminosity relation since its distance is among the most precisely established for a Cepheid, thanks in part to its membership in a star cluster
Star clusters are large groups of stars. Two main types of star clusters can be distinguished: globular clusters are tight groups of ten thousand to millions of old stars which are gravitationally bound, while open clusters are more loosely clust ...
and the availability of precise Hubble Space Telescope
The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most versa ...
and Hipparcos
''Hipparcos'' was a scientific satellite of the European Space Agency (ESA), launched in 1989 and operated until 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial obj ...
parallaxes.
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
Henrietta Swan Leavitt (; July 4, 1868 – December 12, 1921) was an American astronomer. A graduate of Radcliffe College, she worked at the Harvard College Observatory as a "computer", tasked with examining photographic plates in order to measu ...
in an investigation of thousands of variable stars in the Magellanic Clouds
The Magellanic Clouds (''Magellanic system'' or ''Nubeculae Magellani'') are two irregular dwarf galaxies in the southern celestial hemisphere. Orbiting the Milky Way galaxy, these satellite galaxies are members of the Local Group. Because both ...
. She published it in 1912 with further evidence. Once the period-luminosity relation 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 relation has been calibrated by many astronomers throughout the twentieth century, beginning with Hertzsprung. 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. Also, in 2008, ESO
The European Organisation for Astronomical Research in the Southern Hemisphere, commonly referred to as the European Southern Observatory (ESO), is an intergovernmental research organisation made up of 16 member states for ground-based ast ...
astronomers estimated with a precision within 1% the distance to the Cepheid RS Puppis
RS may refer to:
Businesses and organizations Sport
* RS Sailing, an international designer and builder of sailboats and dinghies
* Ford TeamRS, Ford Motor Company's European performance car and motorsport division
* Renault Sport, performance ...
, using light echo
309x309px, Reflected light following path B arrives shortly after the direct flash following path A but before light following path C. B and C have the same apparent distance from the star as seen from Earth.">Earth.html" ;"title="apparent distan ...
s from a nebula in which it is embedded. However, that latter finding has been actively debated in the literature.
The following experimental correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...
s between a Population I Cepheid's period ''P'' and its mean absolute magnitude
Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse Logarithmic scale, logarithmic Magnitude (astronomy), astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent mag ...
''M''v was established from Hubble Space Telescope
The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most versa ...
trigonometric parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different sightline, lines of sight and is measured by the angle or semi-angle of inclination between those two lines. Due to perspective (graphica ...
es for 10 nearby Cepheids:
: [
with ''P'' measured in days.
The following relations can also be used to calculate the distance ''d'' to classical Cepheids:
: ][
or
: ]
''I'' and ''V'' represent near infrared and visual apparent mean magnitudes, respectively. The distance ''d'' is in parsec
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...
s.
Small amplitude Cepheids
Classical Cepheid variables with visual amplitudes below 0.5 magnitudes, almost symmetrical sinusoidal light curves, and short periods, have been defined as a separate group called small amplitude Cepheids. They receive the acronym DCEPS in the GCVS. Periods are generally less than 7 days, although the exact cutoff is still debated.
The term s-Cepheid is used for short period small amplitude Cepheids with sinusoidal light curves that are considered to be first overtone pulsators. They are found near the red edge of the instability strip. Some authors use s-Cepheid as a synonym for the small amplitude DECPS stars, while others prefer to restrict it only to first overtone stars.
Small amplitude Cepheids (DCEPS) include Polaris
Polaris is a star in the northern circumpolar constellation of Ursa Minor. It is designated α Ursae Minoris ( Latinized to ''Alpha Ursae Minoris'') and is commonly called the North Star or Pole Star. With an apparent magnitude that ...
and FF Aquilae
FF Aquilae is a classical Cepheid variable star located in the constellation Aquila. It ranges from apparent magnitude 5.18 to 5.51 over a period of 4.470848 days, meaning it is faintly visible to the unaided eye in rural or suburban set ...
, although both may be pulsating in the fundamental mode. Confirmed first overtone pulsators include BG Crucis
BG Crucis is a suspected binary star system in the southern constellation of Crux. It is visible to the naked eye as a faint yellow-white hued point of light with an apparent visual magnitude that fluctuates around 5.49. The system is l ...
and BP Circini
BP Circini is a binary star system in the southern constellation of Circinus. It is located at a distance of approximately 3,300 light years from the Sun based on parallax.
The variability of this star was discovered by D. W. ...
.
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
In astronomy, metallicity is the abundance of elements present in an object that are heavier than hydrogen and helium. Most of the normal physical matter in the Universe is either hydrogen or helium, and astronomers use the word ''"metals"'' as a ...
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.
These unresolved matters have resulted in cited values for the Hubble constant
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
ranging between 60 km/s/Mpc and 80 km/s/Mpc.[ 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.]
Examples
Several classical Cepheids have variations that can be recorded with night-by-night, trained naked eye
Naked eye, also called bare eye or unaided eye, is the practice of engaging in visual perception unaided by a magnifying, light-collecting optical instrument, such as a telescope or microscope, or eye protection. Vision corrected to normal ...
observation, including the prototype Delta Cephei
Delta Cephei (δ Cep, δ Cephei) is the Bayer designation for a quadruple star system located approximately 887 light-years away in the northern constellation of Cepheus, the King. At this distance, the visual magnitude of the star is ...
in the far north, Zeta Geminorum
Zeta Geminorum (ζ Geminorum, abbreviated Zeta Gem, ζ Gem) is a bright star with cluster components, distant optical components and a likely spectroscopic partner in the zodiac constellation of Gemini — in its south, on the left 'leg' ...
and Eta Aquilae
Eta Aquilae (η Aql, η Aquilae) is the Bayer designation for a multiple star in the equatorial constellation of Aquila, the eagle. It was once part of the former constellation Antinous. On average, this star has an apparent visual magnitu ...
ideal for observation around the tropics (near the ecliptic and thus zodiac) and in the far south Beta Doradus
Beta Doradus, Latinized from β Doradus, is the second brightest star in the southern constellation of Dorado. It has a variable apparent visual magnitude, and is visible to the naked eye from the southern hemisphere. Based upon parallax ...
. The closest class member is the North Star (Polaris
Polaris is a star in the northern circumpolar constellation of Ursa Minor. It is designated α Ursae Minoris ( Latinized to ''Alpha Ursae Minoris'') and is commonly called the North Star or Pole Star. With an apparent magnitude that ...
) whose distance is debated and whose present variability is approximately 0.05 of a magnitude.[
]
See also
*RR Lyrae variable
RR Lyrae variables are periodic variable stars, commonly found in globular clusters. They are used as standard candles to measure (extra) galactic distances, assisting with the cosmic distance ladder. This class is named after the prototype and ...
*Stellar pulsation
Stellar pulsations are caused by expansions and contractions in the outer layers as a star seeks to maintain equilibrium. These fluctuations in stellar radius cause corresponding changes in the luminosity of the star. Astronomers are able to de ...
*Type II Cepheid
Type II Cepheids are variable stars which pulsate with periods typically between 1 and 50 days. They are population II stars: old, typically metal-poor, low mass objects.
Like all Cepheid variables, Type IIs exhibit a relationship between the st ...
References
External links
The Cepheid Distance Scale: A History, by Nick Allen
* ttp://www.aavso.org/ American Association of Variable Star Observersbr>OGLE Atlas of Variable Star Light Curves – Classical Cepheids
{{DEFAULTSORT:Cepheid Variable
Classical Cepheid variables
Astrometry
Standard candles