Editing Variable star (section)

==={{Anchor|Pulsating variable}}Pulsating variable stars===
{{Main|Stellar pulsation}}
Pulsating stars swell and shrink, affecting their brightness and spectrum. Pulsations are generally split into: [[Radial pulsations|radial]], where the entire star expands and shrinks as a whole; and non-radial, where one part of the star expands while another part shrinks.

Depending on the type of pulsation and its location within the star, there is a natural or [[fundamental frequency]] which determines the period of the star. Stars may also pulsate in a [[harmonic]] or [[overtone]] which is a higher frequency, corresponding to a shorter period. Pulsating variable stars sometimes have a single well-defined period, but often they pulsate simultaneously with multiple frequencies and complex analysis is required to determine the separate [[Interference (wave propagation)|interfering]] periods. In some cases, the pulsations do not have a defined frequency, causing a random variation, referred to as [[stochastic]]. The study of stellar interiors using their pulsations is known as [[asteroseismology]].

The expansion phase of a pulsation is caused by the blocking of the internal energy flow by material with a high opacity, but this must occur at a particular depth of the star to create visible pulsations. If the expansion occurs below a convective zone then no variation will be visible at the surface. If the expansion occurs too close to the surface the restoring force will be too weak to create a pulsation. The restoring force to create the contraction phase of a pulsation can be pressure if the pulsation occurs in a non-degenerate layer deep inside a star, and this is called an [[Acoustics|acoustic]] or [[pressure]] mode of pulsation, abbreviated to [[P-mode star|p-mode]]. In other cases, the restoring force is [[gravity]] and this is called a [[gravity wave|g-mode]]. Pulsating variable stars typically pulsate in only one of these modes.

==== Cepheids and cepheid-like variables ====
{{Main|Cepheid variable}}
This group consists of several kinds of pulsating stars, all found on the [[instability strip]], that swell and shrink very regularly caused by the star's own mass [[resonance]], generally by the [[fundamental frequency]]. Generally the [[κ mechanism|Eddington valve]] mechanism for pulsating variables is believed to account for cepheid-like pulsations. Each of the subgroups on the instability strip has a fixed [[period-luminosity relation|relationship]] between period and absolute magnitude, as well as a relation between period and mean density of the star. The period-luminosity relationship was first established for Delta Cepheids by [[Henrietta Swan Leavitt|Henrietta Leavitt]], and makes these high luminosity Cepheids very useful for determining distances to galaxies within the [[Local Group]] and beyond. [[Edwin Hubble]] used this method to prove that the so-called spiral nebulae are in fact distant galaxies.

The Cepheids are named only for [[Delta Cephei]], while a completely separate class of variables is named after [[Beta Cephei]].

=====Classical Cepheid variables=====
{{Main|Classical Cepheid variable}}

Classical Cepheids (or Delta Cephei variables) are population I (young, massive, and luminous) yellow supergiants which undergo pulsations with very regular periods on the order of days to months. On September 10, 1784, [[Edward Pigott]] detected the variability of [[Eta Aquilae]], the first known representative of the class of Cepheid variables. However, the namesake for classical Cepheids is the star [[Delta Cephei]], discovered to be variable by [[John Goodricke]] a few months later.

=====Type II Cepheids=====
{{Main|Type II Cepheids}}

Type II Cepheids (historically termed W Virginis stars) have extremely regular light pulsations and a luminosity relation much like the δ Cephei variables, so initially they were confused with the latter category. Type II Cepheids stars belong to older [[Population II]] stars, than do the type I Cepheids. The Type II have somewhat lower [[metallicity]], much lower mass, somewhat lower luminosity, and a slightly offset period versus luminosity relationship, so it is always important to know which type of star is being observed.

=====RR Lyrae variables=====
{{Main|RR Lyrae variable}}

These stars are somewhat similar to Cepheids, but are not as luminous and have shorter periods. They are older than type I Cepheids, belonging to [[Population II]], but of lower mass than type II Cepheids. Due to their common occurrence in [[globular cluster]]s, they are occasionally referred to as ''cluster Cepheids''. They also have a well established period-luminosity relationship, and so are also useful as distance indicators. These A-type stars vary by about 0.2–2 magnitudes (20% to over 500% change in luminosity) over a period of several hours to a day or more.

=====Delta Scuti variables=====
{{Main|Delta Scuti variable}}

Delta Scuti (δ Sct) variables are similar to Cepheids but much fainter and with much shorter periods. They were once known as ''Dwarf Cepheids''. They often show many superimposed periods, which combine to form an extremely complex light curve. The typical δ Scuti star has an amplitude of 0.003–0.9 magnitudes (0.3% to about 130% change in luminosity) and a period of 0.01–0.2 days. Their [[stellar classification|spectral type]] is usually between A0 and F5.

=====SX Phoenicis variables=====
{{Main|SX Phoenicis variable}}
These stars of spectral type A2 to F5, similar to δ Scuti variables, are found mainly in globular clusters. They exhibit fluctuations in their brightness in the order of 0.7 magnitude (about 100% change in luminosity) or so every 1 to 2 hours.

=====Rapidly oscillating Ap variables=====
{{Main|Rapidly oscillating Ap star}}
These stars of spectral type A or occasionally F0, a sub-class of δ Scuti variables found on the main sequence. They have extremely rapid variations with periods of a few minutes and amplitudes of a few thousandths of a magnitude.

====Long period variables====
{{Main|Long period variable}}

The long period variables are cool evolved stars that pulsate with periods in the range of weeks to several years.

=====Mira variables=====
[[File:Chi Cygni light curve.png|thumb|[[Light curve]] of [[Mira variable]] [[χ Cygni]]]]
{{Main|Mira variable}}

Mira variables are [[Asymptotic giant branch]] (AGB) red giants. Over periods of many months they fade and brighten by between 2.5 and 11 [[apparent magnitude|magnitude]]s, a 6 fold to 30,000 fold change in luminosity. [[Mira]] itself, also known as Omicron Ceti (ο Cet), varies in brightness from almost 2nd magnitude to as faint as 10th magnitude with a period of roughly 332 days. The very large visual amplitudes are mainly due to the shifting of energy output between visual and infra-red as the temperature of the star changes. In a few cases, Mira variables show dramatic period changes over a period of decades, thought to be related to the thermal pulsing cycle of the most advanced AGB stars.

=====Semiregular variables=====
{{Main|Semiregular variable}}

These are [[red giants]] or [[red supergiant|supergiants]]. Semiregular variables may show a definite period on occasion, but more often show less well-defined variations that can sometimes be resolved into multiple periods. A well-known example of a semiregular variable is [[Betelgeuse]], which varies from about magnitudes +0.2 to +1.2 (a factor 2.5 change in luminosity). At least some of the semi-regular variables are very closely related to Mira variables, possibly the only difference being pulsating in a different harmonic.

=====Slow irregular variables=====
{{Main|Slow irregular variable}}

These are [[red giants]] or [[red supergiant|supergiants]] with little or no detectable periodicity. Some are poorly studied semiregular variables, often with multiple periods, but others may simply be chaotic.

=====Long secondary period variables=====
{{Main|Long-period variable star#Long secondary periods}}
Many variable red giants and supergiants show variations over several hundred to several thousand days. The brightness may change by several magnitudes although it is often much smaller, with the more rapid primary variations are superimposed. The reasons for this type of variation are not clearly understood, being variously ascribed to pulsations, binarity, and stellar rotation.<ref name=messina>{{cite journal|bibcode=2007NewA...12..556M|title=Evidence for the pulsational origin of the Long Secondary Periods: The red supergiant star V424 Lac (HD 216946)|journal=New Astronomy|volume=12|issue=7|pages=556–561|last1=Messina|first1=Sergio|year=2007|doi=10.1016/j.newast.2007.04.002}}</ref><ref>{{cite journal|bibcode=2007ApJ...660.1486S|arxiv=astro-ph/0701463|title=Long Secondary Periods and Binarity in Red Giant Stars|journal=The Astrophysical Journal|volume=660|issue=2|pages=1486–1491|last1=Soszyński|first1=I.|year=2007|doi=10.1086/513012|s2cid=2445038}}</ref><ref>{{cite journal|bibcode=2003ApJ...584.1035O|title=On the Origin of Long Secondary Periods in Semiregular Variables|journal=The Astrophysical Journal|volume=584|issue=2|pages=1035|last1=Olivier|first1=E. A.|last2=Wood|first2=P. R.|year=2003|doi=10.1086/345715|citeseerx=10.1.1.514.3679|s2cid=40373007 }}</ref>

====Beta Cephei variables====
{{Main|Beta Cephei variable}}
Beta Cephei (β Cep) variables (sometimes called [[Beta Canis Majoris]] variables, especially in Europe)<ref>[http://www.aavso.org/vstar/vsots/winter05.shtml Variable Star Of The Season, Winter 2005: The Beta Cephei Stars and Their Relatives] {{Webarchive|url=https://web.archive.org/web/20100615085217/http://www.aavso.org/vstar/vsots/winter05.shtml |date=2010-06-15 }}, John Percy, [[AAVSO]].  Accessed October 2, 2008.</ref> undergo short period pulsations in the order of 0.1–0.6 days with an amplitude of 0.01–0.3 magnitudes (1% to 30% change in luminosity). They are at their brightest during minimum contraction. Many stars of this kind exhibits multiple pulsation periods.<ref>{{cite journal|bibcode=1978ARA&A..16..215L|title=The observational status of the Beta Cephei stars|journal=Annual Review of Astronomy and Astrophysics |volume=16|pages=215–240|last1=Lesh|first1=J. R.|last2=Aizenman|first2=M. L.|year=1978|doi=10.1146/annurev.aa.16.090178.001243}}</ref>

====Slowly pulsating B-type stars====
{{Main|Slowly pulsating B-type star}}
Slowly pulsating B (SPB) stars are hot main-sequence stars slightly less luminous than the Beta Cephei stars, with longer periods and larger amplitudes.<ref name=spb>{{cite journal|bibcode=2002ASPC..259..196D|title=An Observational Overview of Pulsations in β Cep Stars and Slowly Pulsating B Stars (invited paper)|journal=Radial and Nonradial Pulsations as Probes of Stellar Physics|volume=259|pages=196|last1=De Cat|first1=P.|year=2002}}</ref>

====Very rapidly pulsating hot (subdwarf B) stars====
{{Main|Subdwarf B star#Variables}}
The prototype of this rare class is [[V361 Hydrae]], a 15th magnitude [[subdwarf B star]]. They pulsate with periods of a few minutes and may simultaneous pulsate with multiple periods. They have amplitudes of a few hundredths of a magnitude and are given the GCVS acronym RPHS. They are [[P-mode star|p-mode]] pulsators.<ref name=kilkenny>{{cite journal|bibcode=2007CoAst.150..234K|title=Pulsating Hot Subdwarfs -- an Observational Review|journal= Communications in Asteroseismology|volume=150|pages=234–240|last1=Kilkenny|first1=D.|year=2007|doi=10.1553/cia150s234|doi-access=free}}</ref>

====PV Telescopii variables====
{{Main|PV Telescopii variable}}
Stars in this class are type Bp supergiants with a period of 0.1–1 day and an amplitude of 0.1 magnitude on average. Their spectra are peculiar by having weak [[hydrogen]] while on the other hand [[carbon]] and [[helium]] lines are extra strong, a type of [[extreme helium star]].

====RV Tauri variables====
{{Main|RV Tauri variable}}

These are yellow supergiant stars (actually low mass post-AGB stars at the most luminous stage of their lives) which have alternating deep and shallow minima. This double-peaked variation typically has periods of 30–100 days and amplitudes of 3–4 magnitudes. Superimposed on this variation, there may be long-term variations over periods of several years. Their spectra are of type F or G at maximum light and type K or M at minimum brightness. They lie near the instability strip, cooler than type I Cepheids more luminous than type II Cepheids. Their pulsations are caused by the same basic mechanisms related to helium opacity, but they are at a very different stage of their lives.

====Alpha Cygni variables====
{{Main|Alpha Cygni variable}}

Alpha Cygni (α Cyg) variables are nonradially pulsating supergiants of [[spectral class]]es B<sub>ep</sub> to A<sub>ep</sub>Ia. Their periods range from several days to several weeks, and their amplitudes of variation are typically of the order of 0.1 magnitudes. The light changes, which often seem irregular, are caused by the superposition of many oscillations with close periods. [[Deneb]], in the constellation of [[Cygnus (constellation)|Cygnus]] is the prototype of this class.

====Gamma Doradus variables====
{{Main|Gamma Doradus variable}}
Gamma Doradus (γ Dor) variables are non-radially pulsating main-sequence stars of [[spectral classes]] F to late A. Their periods are around one day and their amplitudes typically of the order of 0.1 magnitudes.

====Pulsating white dwarfs====
{{Main|Pulsating white dwarf}}
These non-radially pulsating stars have short periods of hundreds to thousands of seconds with tiny fluctuations of 0.001 to 0.2 magnitudes. Known types of pulsating white dwarf (or pre-white dwarf) include the ''DAV'', or ''[[ZZ Ceti]]'', stars, with hydrogen-dominated atmospheres and the spectral type DA;<ref name="physrev">{{cite journal|bibcode=1990RPPh...53..837K|title=REVIEW: Physics of white dwarf stars|journal=Reports on Progress in Physics|volume=53|issue=7|pages=837|last1=Koester|first1=D.|last2=Chanmugam|first2=G.|year=1990|doi=10.1088/0034-4885/53/7/001|s2cid=122582479|url=https://semanticscholar.org/paper/fde3294fc2ec8d89f95f7c3eaad91e7b0416601c}}</ref> ''DBV'', or ''[[V777 Her]]'', stars, with helium-dominated atmospheres and the spectral type DB;<ref name="wden">{{cite book|bibcode=2002eaa..book.....M|isbn=0-333-75088-8|title=Encyclopedia of Astronomy and Astrophysics|last1=Murdin|first1=Paul|year=2002}}</ref> and ''[[GW Vir]]'' stars, with atmospheres dominated by helium, carbon, and oxygen. GW Vir stars may be subdivided into ''DOV'' and ''PNNV'' stars.<ref name="quirion">{{cite journal|bibcode=2007ApJS..171..219Q|title=Mapping the Instability Domains of GW Vir Stars in the Effective Temperature-Surface Gravity Diagram|journal=The Astrophysical Journal Supplement Series|volume=171|issue=1|pages=219–248|last1=Quirion|first1=P.-O.|last2=Fontaine|first2=G.|last3=Brassard|first3=P.|year=2007|doi=10.1086/513870|doi-access=free}}</ref><ref>{{cite journal|bibcode=2004A&A...426L..45N|title=Detection of non-radial g-mode pulsations in the newly discovered PG 1159 star HE 1429-1209|journal=Astronomy and Astrophysics|volume=426|issue=2|pages=L45|last1=Nagel|first1=T.|last2=Werner|first2=K.|year=2004|doi=10.1051/0004-6361:200400079|arxiv = astro-ph/0409243 |s2cid=9481357}}</ref>

==== Solar-like oscillations ====
The [[Sun]] oscillates with very low amplitude in a large number of modes having periods around 5 minutes. The study of these oscillations is known as [[helioseismology]]. Oscillations in the Sun are driven stochastically by [[convection]] in its outer layers. The term [[solar-like oscillations]] is used to describe oscillations in other stars that are excited in the same way and the study of these oscillations is one of the main areas of active research in the field of [[asteroseismology]].

==== BLAP variables ====
{{Main|BLAP (Blue Large-Amplitude Pulsators)}}
A Blue Large-Amplitude Pulsator (BLAP) is a pulsating star characterized by changes of 0.2 to 0.4 magnitudes with typical periods of 20 to 40 minutes.

==== Fast yellow pulsating supergiants ====
A fast yellow pulsating supergiant (FYPS) is a luminous yellow supergiant with pulsations shorter than a day.  They are thought to have evolved beyond a red supergiant phase, but the mechanism for the pulsations is unknown.  The class was named in 2020 through analysis of [[TESS]] observations.<ref name=trevor2020>{{cite journal|arxiv=2008.11723|last1=Dorn-Wallenstein|first1=Trevor Z.|last2=Levesque|first2=Emily M.|last3=Neugent|first3=Kathryn F.|last4=Davenport|first4=James R. A.|last5=Morris|first5=Brett M.|last6=Gootkin|first6=Keyan|title=Short Term Variability of Evolved Massive Stars with TESS II: A New Class of Cool, Pulsating Supergiants|journal=The Astrophysical Journal|year=2020|volume=902|issue=1|page=24|doi=10.3847/1538-4357/abb318|bibcode=2020ApJ...902...24D|s2cid=221340538 |doi-access=free }}</ref>