This characteristic of classical Cepheids was discovered in 1908 byHenrietta Swan Leavitt after studying thousands of variable stars in theMagellanic Clouds. The discovery establishes thetrue luminosity of a Cepheid by observing its pulsation period. This in turn gives the distance to the star by comparing its known luminosity to its observed brightness, calibrated by directly observing theparallax distance to the closest Cepheids such asRS Puppis andPolaris.
Cepheids change brightness due to theκ–mechanism,[1][2] which occurs when the opacity ofa star's atmosphere increases with temperature rather than decreasing.[3] The main gas involved is thought to behelium. On this analysis, the Cepheid cycle is driven by the factdoubly ionized helium, the form found at high temperatures, is more opaque than singly ionized helium. As a result the outer layer of the star cycles between compression and expansion: Compression heats the helium until it becomes doubly ionized. Due to its opacity when doubly ionized, the helium absorbs sufficient heat to expand. Once expanded the helium cools until it becomes singly ionized again and, due to its transparency when singly ionized, cools until it collapses. Cepheid variables become dimmest during the part of the cycle when the helium is doubly ionized.
On September 10, 1784,Edward Pigott detected the variability ofEta Aquilae, the first known representative of the class of classical Cepheid variables.[4] The eponymous star for classical Cepheids,Delta Cephei, was discovered to be variable byJohn Goodricke a few months later.[5] The number of similar variables grew to several dozen by the end of the 19th century, and they were referred to as a class as Cepheids.[6] Most of the Cepheids were known from the distinctive light curve shapes with the rapid increase in brightness and a hump, but some with more symmetrical light curves were known as Geminids after the prototypeζ Geminorum.[7]
A relationship between the period and luminosity for classical Cepheids was discovered in 1908 byHenrietta Swan Leavitt in an investigation of thousands of variable stars in theMagellanic Clouds.[8] She published it in 1912 with further evidence.[9] Cepheid variables were found to showradial velocity variation with the same period as the luminosity variation, and initially this was interpreted as evidence that these stars were part of abinary system. However, in 1914,Harlow Shapley demonstrated that this idea should be abandoned.[10] Two years later, Shapley and others had discovered that Cepheid variables changed theirspectral types over the course of a cycle.[11]
In 1913,Ejnar Hertzsprung attempted to find distances to 13 Cepheids using their motion through the sky.[12] (His results would later require revision.) In 1918, Harlow Shapley used Cepheids to place initial constraints on the size and shape of theMilky Way and of the placement of the Sun within it.[13] In 1924,Edwin Hubble established the distance to classical Cepheid variables in theAndromeda Galaxy, until then known as the "AndromedaNebula" and showed that those variables were not members of the Milky Way. Hubble's finding settled the question raised in the "Great Debate" of whether the Milky Way represented the entire Universe or was merely one of manygalaxies in the Universe.[14]
Illustration of Cepheid variables (red dots) at the center of the Milky Way[16]
In the mid 20th century, significant problems with the astronomical distance scale were resolved by dividing the Cepheids into different classes with very different properties. In the 1940s,Walter Baade recognized two separate populations of Cepheids (classical and type II). Classical Cepheids are younger and more massive population I stars, whereas type II Cepheids are older, fainter Population II stars.[17] Classical Cepheids and type II Cepheids follow different period-luminosity relationships. The luminosity of type II Cepheids is, on average, less than classical Cepheids by about 1.5magnitudes (but still brighter than RR Lyrae stars). Baade's seminal discovery led to a twofold increase in the distance to M31, and the extragalactic distance scale.[18][19] RR Lyrae stars, then known as Cluster Variables, were recognized fairly early as being a separate class of variable, due in part to their short periods.[20][21]
Cepheid variables are divided into two subclasses which exhibit markedly different masses, ages, and evolutionary histories:classical Cepheids andtype II Cepheids.Delta Scuti variables are A-type stars on or near the main sequence at the lower end of theinstability strip and were originally referred to as dwarf Cepheids.RR Lyrae variables have short periods and lie on the instability strip where it crosses thehorizontal branch. Delta Scuti variables and RR Lyrae variables are not generally treated with Cepheid variables although their pulsations originate with the same helium ionisationkappa mechanism.
Light curve ofDelta Cephei, the prototype of classical cepheids, showing the regular variations produced by intrinsic stellar pulsations
Classical Cepheids (also known as Population I Cepheids, type I Cepheids, or Delta Cepheid variables) undergo pulsations with very regular periods on the order of days to months. Classical Cepheids arePopulation Ivariable stars which are 4–20 times more massive than the Sun,[24] and up to 100,000 times more luminous.[25] These Cepheids are yellow bright giants and supergiants ofspectral class F6 – K2 and their radii change by (~25% for the longer-periodI Carinae) millions of kilometers during a pulsation cycle.[26]
Classical Cepheids are used to determine distances to galaxies within theLocal Group and beyond, and are a means by which theHubble constant can be established.[27][28][29][30][31] Classical Cepheids have also been used to clarify many characteristics of the Milky Way galaxy, such as the Sun's height above the galactic plane and the Galaxy's local spiral structure.[32]
A group of classical Cepheids with small amplitudes andsinusoidal light curves are often separated out as Small Amplitude Cepheids or s-Cepheids, many of them pulsating in the first overtone.
Type II Cepheids (also termed Population II Cepheids) arepopulation II variable stars which pulsate with periods typically between 1 and 50 days.[17][33] Type II Cepheids are typicallymetal-poor, old (~10 Gyr), low mass objects (~half the mass of the Sun). Type II Cepheids are divided into several subgroups by period. Stars with periods between 1 and 4 days are of theBL Her subclass, 10–20 days belong to theW Virginis subclass, and stars with periods greater than 20 days belong to theRV Tauri subclass.[17][33]
A group of pulsating stars on the instability strip have periods of less than 2 days, similar to RR Lyrae variables but with higher luminosities. Anomalous Cepheid variables have masses higher than type II Cepheids, RR Lyrae variables, and the Sun. It is unclear whether they are young stars on a "turned-back" horizontal branch,blue stragglers formed throughmass transfer in binary systems, or a mix of both.[40][41]
A small proportion of Cepheid variables have been observed to pulsate in two modes at the same time, usually the fundamental and first overtone, occasionally the second overtone.[42] A very small number pulsate in three modes, or an unusual combination of modes including higher overtones.[43]
Chief among the uncertainties tied to the classical and type II Cepheid distance scale are: the nature of the period-luminosity relation in variouspassbands, the impact ofmetallicity on both the zero-point and slope of those relations, and the effects of photometric contamination (blending with other stars) and a changing (typically unknown)extinction law on Cepheid distances. All these topics are actively debated in the literature.[28][25][30][37][44][45][46][47][48][49][50][51]
These unresolved matters have resulted in cited values for theHubble constant (established from Classical Cepheids) ranging between 60 km/s/Mpc and 80 km/s/Mpc.[27][28][29][30][31] 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.[29][31] Uncertainties have diminished over the years, due in part to discoveries such asRS Puppis.
Delta Cephei is also of particular importance as acalibrator of the Cepheid period-luminosity relation since its distance is among the most precisely established for a Cepheid, partly because it is a member of astar cluster[52][53] and the availability of precise parallaxes observed by theHubble,Hipparcos, andGaia space telescopes.[54] The accuracy ofparallax distance measurements to Cepheid variables and other bodies within 7,500 light-years is vastly improved by comparing images from Hubble taken six months apart, from opposite points in the Earth's orbit. (Between two such observations 2AU apart, a star at a distance of 7500 light-years = 2300parsecs would appear to move an angle of2/2300 arc-seconds = 2 x 10−7 degrees, theresolution limit of the available telescopes.)[55]
The accepted explanation for the pulsation of Cepheids is called the Eddington valve,[1][2] or "κ-mechanism", where the Greek letter κ (kappa) is the usual symbol for the gas opacity.
Helium is the gas thought to be most active in the process. Doublyionized helium (helium whose atoms are missing both electrons) is more opaque than singly ionized helium. As helium is heated, its temperature rises until it reaches the point at which double ionisation spontaneously occurs and is sustained throughout the layer in much the same way a fluorescent tube 'strikes'. At the dimmest part of a Cepheid's cycle, this ionized gas in the outer layers of the star is relatively opaque, and so is heated by the star's radiation, and due to the increasing temperature, begins to expand. As it expands, it cools, but remains ionised until another threshold is reached at which point double ionization cannot be sustained and the layer becomes singly ionized hence more transparent, which allows radiation to escape. The expansion then stops, and reverses due to the star's gravitational attraction. The star's states are held to be either expanding or contracting by thehysteresis[56] generated by the doubly ionized helium and indefinitely flip-flops between the two states reversing every time the upper or lower threshold is crossed. This process is rather analogous to therelaxation oscillator found in electronics.[citation needed]
In 1879,August Ritter (1826–1908) demonstrated that the adiabatic radial pulsation period for a homogeneous sphere is related to itssurface gravity and radius through the relation:
where k is a proportionality constant. Now, since the surface gravity is related to the sphere mass and radius through the relation:
one finally obtains:
whereQ is a constant, called the pulsation constant.[57]
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