Pulsating Variables
In October 1595 the Dutchman David Fabricus observed the star ο Ceti to disappear. The same star was noted to vary in brightness during 1638-39 by another Dutch observer and became known as Mira (the "Wonderful") due to its behaviour. It was eventually found to have a period of about 334 days and was the first pulsating variable discovered. Its light curve was different to that of Algol which was correctly inferred to be an eclipsing binary by the brilliant young English astronomer John Goodricke in 1782.

Cepheids
Cepheids are very luminous, massive variables with periods of 1 -70 days. They are named after the first-such pulsating variable, δ Cephei discovered by John Goodricke in 1784. Cepheid light curves show a rapid rise in brightness followed by a more gradual decline, shaped like a shark fin. Their amplitude range is typically 0.5 to 2 magnitudes. The spectral class of a Cepheid actually changes as it pulsates, being about class F at maximum luminosity and down to class G or K at minimum.
There are in fact two types of Cepheids, the original Type I or Classical Cepheids of which δ Cephei is an example and the slightly dimmer Type II or W Virginis Cepheids.

Type I Classical Cepheids
These stars take their name from δ Cephei. Most have a period of between 5 -10 days and an amplitude range of 0.5 - 2.0 magnitudes in visible light. They are 1.5 - 2 magnitudes more luminous than Type II Cepheids.
The light curve for δ Cephei shows a distinctive rapid rise in brightness followed by a more gradual decrease. δ Cephei has a period of 5.366 days and a magnitude range of just under 1. This means that it is about twice as bright at its maximum than at its minimum.
Classical Cepheids follow a well-defined period-luminosity relationship. This means that the longer the period of the Cepheid, the more intrinsically luminous it is. This has important implications as it allows Cepheids to be used as standard candles for distance determination.

Type II W Virginis
Type II Cepheids are named after the first star identified in this group, W Virginis. It has a period of 17.2736 days, magnitude range of 9.46 - 10.75 and a spectral class range of F0Ib-G0Ib.
W Virginis -type Cepheids are intrinsically less luminous by 1.5 - 2 magnitudes than the Type I Classical Cepheids and have typical periods of 12 - 30 days. As they are older stars than Type I Cepheids and their spectra are characterised by having lower metallicities. Type II light curves show a characteristic bump on the decline side and they have an amplitude range of 0.3 - 1.2 magnitudes.
As with the Type I Cepheids they also display a similar well-defined period-luminosity relationship and can be used for distance determination.

RR Lyrae
These old population II giant stars are mostly found in globular clusters. They are characterised by their short periods, usually about 1.5 hours to a day and have a brightness range of 0.3 to 2 magnitudes. Spectral classes range from A7 to F5. RR Lyrae stars are less massive than Cepheids but they also follow their own period - luminosity relationship, with a mean absolute magnitude of +0.6. They are thus useful in determining distances to the globular clusters within which they are commonly found to a distance of about 200 kiloparsecs. Sub-types are classified according to the shape of their light curves.

RV Tauri
RV Tauri variables are yellow supergiants, mostly G and K-class stars. Their distinctive light curves show alternating deep and shallow minima with the period equal to the time between two successive deep minima. Typical values are 20 - 100 days.

Long-Period Variables (LPVs)
The first pulsating variable discovered was the long-period variable Mira. They are cool red giants or supergiants and have periods of months to years. Their luminosities can range from 10 to 10,000 × Sun. Long-period variables are further classified according to whether they exhibit regular periodicity, such as the Miras or more irregular behaviour.

Mira -Type
Mira or ο Ceti, established as a variable in 1638 gives its name to stars of this type. Mira itself has a period of 331 days and varies its brightness by almost 6 magnitudes in the visible waveband during a cycle. A red giant, its radius varies by 20 percent, peaking at 330 times that of our Sun. Its effective temperature ranges from 1,900 K to 2,600 K. It is also a visual binary and its companion is also a variable star.
The Mira-type stars have long periods, ranging from about 80 to 1,000 days, varying by 2.5 to 10 magnitudes visually. Their high luminosities mean they can, at maximum brightness, be detected at large distances. They have tenuous outer layers in their atmospheres which get shocked and heated from the regular pulsations. This can give rise to emission lines in their spectra. Dust grains in their outer atmosphere get heated so they are strong emitters in infrared wavebands. They also show evidence of molecules in these regions.

Semiregular Variables (SR)
These stars show some periodicity and variations in brightness but also exhibit irregularities where they appear to be stable. They are giant and supergiant stars with periods ranging from a few days to several years and the change in brightness is typically less than two magnitudes. The light curves of semiregulars have a variety of shapes. Prominent examples of this type include Antares, α Scorpius, and Betelgeuse, α Orionis.

Eruptive or Cataclysmic Variables
Eruptive variables can exhibit significant and rapid changes in their luminosity due to violent outbursts caused by processes within the star. There is a wide variety of eruptive or cataclysmic variables. Some event, as implied by the term cataclysmic result in the destruction of the star whilst others can reoccur one or more times. More details on the different types are provided below. Some are also discussed in more detail in the pages on stellar evolution.

Supernovae
A supernova is a cataclysmic stage towards the end of a star's life that is characterised by a sudden and dramatic rise in brightness. A typical supernova may see a star become brighter by up to 20 magnitudes to an absolute magnitude of about -15. This means that a typical supernova may outshine the rest its galaxy for several days or a few weeks.
Supernovae are caused by one of two main mechanisms. The first (Type I) takes place when accreting material falling onto a white dwarf in a binary system takes it over the mass set by the Chandrasekhar limit. The resulting instability triggers a runaway thermonuclear explosion that destroys the star and releases large amounts of radioactive and heavy elements into space. The second (Type II) process occurs in very massive stars once all the material in their core has been fused into iron. As fusion cannot occur in elements heavier than iron the drop in outwards radiation pressure means that gravitational collapse overwhelms the core which rapidly implodes. The core material gets crushed to form degenerate neutron-density material whilst the extreme temperature and pressure in the surrounding layers cause rapid (R-process) nuclear reactions that synthesise the heaviest elements. A huge flux of neutrinos is thought to interact with the superdense material, ripping the star apart. Such core collapse supernovae may result in neutron stars and black holes forming from the remaining core material. More details are given in the later section on star death.
Observationally, supernovae are classified according to their spectra. Type I supernova exhibit no hydrogen lines in spectra taken soon after the supernova event. Those with silicon lines present are further classified as Type Ia and are thought to be due to thermonuclear explosions as in accreting white dwarfs. If no Si lines are present they are Type Ib or Ic depending on the high or low abundance of He lines respectively. These types occur due to core collapse following the outer layers being stripped away in Wolf-Rayet or binary stars.
Type II supernovae show hydrogen lines in their early spectra. They are all examples of core collapse events with most arising due to a massive progenitor star exhausting its core fuel. Perhaps the best known example of this was Supernova 1987A. This was the first supernova visible to the naked-eye since Kepler's supernovae of 1604. It took place in the Large Magellanic Cloud, a satellite galaxy of our own about 50,000 pc distant. Although we expect two or three stars to go supernova in our galaxy each century, these may not be visible in optical wavebands due to absorption and scattering by the galaxy's dust lanes so the occurrence of a supernova in an nearby galaxy was a major boon for astronomers. Observations of SN 1987A continue today at many wavebands.

Novae
A nova occurs in a close binary system and is characterised by a rapid and unpredictable rise in brightness of 7 - 16 magnitudes within a few days. The eruptive event is followed by a steady decline back to the pre-nova magnitude over a few months. This suggests that the event causing the nova does not destroy the original star. Our model for novae is that of an accreting white dwarf. It draws material off its close binary companion for about 10,000 to 100,000 years until there is sufficient material to trigger a thermonuclear explosion that then blasts the shell of material off into space.

Recurrent Novae
These are similar to novae with a change in magnitude of 7 - 16 and a period of outburst of up to about 200 days. They show two or more outburst over recorded observations.
T Pyxidis is a recurrent nova, erupting about every 20 years. HST observations revealed that the eruption is not uniform, rather it produces thousands of gaseous blobs, each about the size of our Solar System. The ring of material in the image is about 1 light year across. The interval between eruptions is much shorter for T Pyxidis than most nova because it is thought its white dwarf is right at the upper mass-limit for a white dwarf. It therefore needs to accrete less material before exploding.

Dwarf Novae
These are intrinsically faint stars that exhibit a sudden increase in brightness by 2 to 5 magnitudes over a few days with intervals of weeks or months between outbursts. Three subtypes are identified; U Geminorum , Z Camelopardalis and SU Ursae Majoris stars. Note as with other types of variables, the class or type name is normally based on the first such type of that class discovered. The U Geminorum type is thus named after the star U Geminorum.
As with other types of novae, dwarf novae are close binaries with a white dwarf as one of the component stars. The most popular model explaining their outbursts is the disk instability model in which thermal instabilities in the accretion disk cause outbursts but no explosion. There is no significant ejection of material in these events.

Symbiotic Stars
These systems have a red giant and a white dwarf in a semi-detached binary. Rather than material being accreted by gravitational attraction as with a recurrent novae, in symbiotic systems material is ejected from the surface of the red giant due to stellar wind. The resultant outbursts as material falls onto the white dwarf are less regular and smaller than in other eruptive variables brightening by up to three magnitudes. Examples include R Aquarii and BF Cygni.

Eclipsing Binaries
Eclipsing binaries are regarded as variable too in that as one of the component stars is eclipsed by the other, the total brightness of the system decreases. The light curves produced by eclipsing binaries show distinctive periodic minima.

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