# Stars/Variables

The General Catalogue of Variable Stars lists more than 46,000 variable stars in the Milky Way, as well as 10,000 in other galaxies, and over 10,000 'suspected' variables.
SIMBAD recognizes some 36 types of variable stars including
* Long-period variables
* Semi-regular variables
* Ellipsoidal variables
* Cataclysmic variables
* DQ Her
* AM Her
* Nova-like stars
* Novas
* Dwarf Novas
* Variable stars
* Irregular variables
* Orion variables
* Rapid irregular variables
* Eruptive variables
* Flare stars
* FU Orionis variables
* Eruptive R CrB variables
* Rotational variables
* Rotational variables alfa2 CVn
* Pulsars
* BY Draconis variables
* RS CVn variables
* Pulsating variables
* RR Lyrae variables
* Cepheid variables
* Pulsing delta Sct variables
* Pulsing RV Tauri
* Pulsing W Virginis
* Pulsing beta Cep
* delta Cep
* gamma Dor
* Pulsing SX Phe
* Mira Cet long-period variables
* Semi-regular pulsating variables
* SN supernova
* Optically Violently Variable objects

## Theoretical variable star

Def. "any star whose brightness varies" is called a variable star.
Brightness can vary with time, space, or wavelength (spectrum).

## Novae

Period: once in historical times.
Novae are "objects whose brightness has changed by ten to twenty magnitudes once in historical times".

## Recurrent novae

Period: seen to erupt more often than once.
Recurrent "novae whose amplitudes are on the small side but which have been seen to erupt more often than once".

## Mira A

Period: 175 to 1000 days.
Def. a variable star in which the long-period usual oscillation mode is the fundamental is called a long-period variable star.
From the graph on the left one can see that Mira is a long period variable of some 332 days.

## Long secondary period variables

Period: several hundred to several thousand days.
Many variable red giants and supergiants show variations over several hundred to several thousand days: the brightness may change by several magnitudes, rapid primary variations may be superimposed, or pulsations, binarity, and stellar rotation occur.

## Semiregular variables

Semiregular variable subtypes :
| Subtype | IAU definition | GCVS code | GCVS definition | Standard stars |
| SRa | semi-regular variable giants of late spectral classes (M, C and S), which retain periodicity with comparative stability and possess, as a rule, small (less than 2$^m$.5) light-variation amplitudes. Amplitudes and forms of light curves are usually liable to strong variations from period to period. Many of these stars differ from Mira Ceti type stars only owing to the smaller amplitude of light variation. | SRA | Semiregular late-type (M, C, S or Me, Ce, Se) giants displaying persistent periodicity and usually small (<2.5 mag in V) light amplitudes. Amplitudes and light-curve shapes generally vary and periods are in the range of 35–1200 days. Many of these stars differ from Miras only by showing smaller light amplitudes | Z Aquarii (Z Aqr) |
| SRb | semi-regular variable giants of late spectral classes (M, C and S) with a poorly expressed periodicity, i.e. with a different duration of individual cycles (which leads to the impossibility of predicting the epochs of maximum and minimum brightness), or with the replacement of periodical changes by slow irregular variations, or even by the constancy of brightness. Some of them are characterised by a certain mean value of the period, given in the catalogue. | SRB | Semiregular late-type (M, C, S or Me, Ce, Se) giants with poorly defined periodicity (mean cycles in the range of 20 to 2300 days) or with alternating intervals of periodic and slow irregular changes, and even with light constancy intervals. Every star of this type may usually be assigned a certain mean period (cycle), which is the value given in the Catalogue. In a number of cases, the simultaneous presence of two or more periods of light variation is observed | AF Cygni (AF Cyg) RR Coronae Borealis (RR CrB) |
| SRc | semi-regular variable super-giants of late spectral classes | SRC | Spectral-type (M, C, S or Me, Ce, Se) supergiants with amplitudes of about 1 mag and periods of light variation from 30 days to several thousand days. | Mu Cephei (μ Cep) RW Cygni (RW Cyg) |
| SRd | semi-regular variable giants and super-giants belonging to spectral classes F, G, K | SRD | Semiregular variable giants and supergiants of F, G, or K spectral types, sometimes with emission lines in their spectra. Amplitudes of light variation are in the range from 0.1 to 4 mag, and the range of periods is from 30 to 1100 days | S Vulpeculae (S Vul) UU Herculis (UU Her) AG Aurigae (AG Aur) SX Herculis (SX Her) SV Ursae Majoris (SV UMa) |
| | | SRS | Semiregular pulsating red giants with short period (several days to a month), probably high-overtone pulsators | AU Arietis (AU Ari) |

## Betelgeuse

Betelgeuse is classified as a semiregular variable star, indicating that some periodicity is noticeable in the brightness changes, but amplitudes may vary, cycles may have different lengths, and there may be standstills or periods of irregularity, placing it in subgroup SRc; these are pulsating red supergiants with amplitudes around one magnitude and periods from tens to hundreds of days.

## Rho Persei

On the right is a light curve of Rho Persei taken with an automatic photoelectric telescope at Fairborn Observatory West, Phoenix, Arizona. The ordinate is differential magnitude, while the abscissa is JD 2445620.5 plus the value shown.
Rho Persei is a semiregular variable star, whose apparent magnitude varies between 3.3 and 4.0 with periods of 50, 120 and 250 days. It is a bright giant star with a spectral type of M4 II. The outer envelope has an effective temperature of 4,111 K, giving it the red-orange hue of an M-type star.

## Dwarf novae

Period: some ten to one hundred days.
Dwarf "novae whose brightness keeps changing by three to five magnitudes in semi-periodic intervals of time of some ten to one hundred days".

### Nova-like stars

Period: some ten to one hundred days.
Nova-like "stars, which do not undergo outbursts but only irregular small-scale brightness changes or occasional drops in luminosity, but which in all other aspects are similar to the former group."

## Slowly pulsating B-type stars

Periods: between approximately half a day and five days.
Slowly pulsating B (SPB) stars are hot main-sequence stars slightly less luminous than the Beta Cephei stars, with longer periods and larger amplitudes.
A slowly pulsating B-type star (SPB), formerly known as a 53 Persei variable, is a spectral type B2 to B9 (3 to 9 times as massive as the Sun) that pulsates with a period between approximately half a day and five days, however within this most member stars have been found to have multiple periods of oscillations.
They display variability both in their light emission and in their spectral line profile, where rhe variations in magnitude are generally smaller than 0.1 magnitudes.
The variability increases with decreasing wavelength, so they are more obviously variable in ultraviolet spectrum than visible light.
Their pulsations are non-radial, that is, they vary in shape rather than volume; different parts of the star are expanding and contracting simultaneously.

## Beta Cephei variables

Periods: in the order of 0.1–0.6 days.
Beta Cephei (β Cep) variables 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) and are at their brightest during minimum contraction.
Many stars of this kind exhibits multiple pulsation periods.

## Magnetic cataclysmic variables

Periods: between 2 and 3 hrs.
X-rays from magnetic cataclysmic variables are common because accretion provides a continuous supply of coronal gas.
A plot of number of systems vs. orbit period shows a statistically significant minimum for periods between 2 and 3 hr which can probably be understood in terms of the effects of magnetic braking when the companion star becomes completely convective and the usual dynamo (which operates at the base of the convective envelope) can no longer give the companion a magnetic wind to carry off angular momentum.
The rotation has been blamed on asymmetric ejection of planetary nubulae and winds and the fields on in situ dynamos.
Orbit and rotation periods are synchronized in strongly magnetized WDs.
Those with no detectable field never are synchronized.
With temperatures in the range 11,000 to 15,000 K, all the WDs with the most extreme fields are far too cool to be detectable EUV/X-ray sources, e.g., Grw +70°8247, LB 11146, SBS 1349+5434, PG 1031+234 and GD 229.
Most highly magnetic WDs appear to be isolated objects, although G 23-46 (7.4 MG) and LB 1116 (670 MG) are in unresolved binary systems.
RE J0317-853 is the hottest magnetic WD at 49,250 K, with an exceptionally intense magnetic field of ~340 MG, and implied rotation period of 725.4 s.
Between 0.1 and 0.4 keV, RE J0317-853 was detectable by ROSAT, but not in the higher energy band from 0.4 to 2.4 keV.
RE J0317-853 is associated with a blue star 16 arcsec from LB 9802 (also a blue WD) but not physically associated.
A centered dipole field is not able to reproduce the observations, but an off-center dipole 664 MG at the south pole and 197 MG at the north pole does.
Until recently (1995) only PG 1658+441 possessed an effective temperature > 30,000 K.
Its polar field strength is only 3 MG.
The ROSAT Wide Field Camera (WFC) source RE J0616-649 has an ~20 MG field.
PG 1031+234 has a surface field that spans the range from ~200 MG to nearly 1000 MG and rotates with a period of 3$^h$24$^m$.
The magnetic fields in CVs are confined to a narrow range of strengths, with a maximum of 7080 MG for RX J1938.4-4623.
None of the single magnetic stars has been seen as of 1999 as an X-ray source, although fields are of direct relevance to the maintenance of coronae in main sequence stars.

## Pulsating white dwarfs

Period: hundreds to thousands of seconds.
Pulsating white dwarf (or pre-white dwarf) are non-radially pulsating stars with short periods of hundreds to thousands of seconds and tiny fluctuations of 0.001 to 0.2 magnitudes including the DAV, or ZZ Ceti, stars, with hydrogen-dominated atmospheres and the spectral type DA; DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB; and GW Vir stars, with atmospheres dominated by helium, carbon, and oxygen. GW Vir stars may be subdivided into DOV and PNNV stars.

## Very rapidly pulsating hot (subdwarf B) stars

Period: a few minutes.
The prototype of this rare class is V361 Hydrae, a 15th magnitude subdwarf B star that pulsates with a period of a few minutes and may simultaneously pulsate with multiple periods, have amplitudes of a few hundredths of a magnitude and are given the GCVS acronym RPHS, and are p-mode pulsators.

## Irregular variable stars

Def. stars or apparent stars where "light curves show seemingly regular variations interrupted by periods of irregular activity, [where some] isolated segments even show no variability" are called irregular variable stars.

## Pulsating variable stars

Pulsating stars swell and shrink, affecting their brightness and spectrum: 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, although non-radial pulsations may encompass everything, with radial pulsations as a special case.

## Cataclysmic variables

"The term cataclysmic variable [...] comprises several related types of objects. For one there are the so-called novae, objects whose brightness has changed by ten to twenty magnitudes once in historical times, or recurrent novae whose amplitudes are on the small side but which have been seen to erupt more often than once; furthermore, dwarf novae whose brightness keeps changing by three to five magnitudes in semi-periodic intervals of time of some ten to one hundred days; and finally nova-like stars, which do not undergo outbursts but only irregular small-scale brightness changes or occasional drops in luminosity, but which in all other aspects are similar to the former group."
"Cataclysmic variables (CVs) are close binary systems consisting of a white dwarf and a red-dwarf secondary transferring matter via the Roche lobe overflow."
Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources.
The accretion disk may be prone to instability leading to dwarf nova outbursts: a portion of the disk material falls onto the white dwarf, the cataclysmic outbursts occur when the density and temperature at the bottom of the accumulated hydrogen layer rise high enough to ignite nuclear fusion reactions, which rapidly burn the hydrogen layer to helium."
Apparently the only SSXS nonmagnetic cataclysmic variable is V Sge: bolometric luminosity of (1 - 10) x 10$^{37}$, a binary including a blackbody (BB) accretor at T < 80 eV, and an orbital period of 0.514195 d.
The accretion disk can become thermally stable in systems with high mass-transfer rates (Ṁ). Such systems are called nova-like (NL) stars, because they lack outbursts characteristic of dwarf novae.

### VY Scl cataclysmic variables

Among the NL stars is a small group which shows a temporary reduction or cessation of Ṁ from the secondary. These are the VY Scl-type stars or anti-dwarf novae.

### V751 Cygni

V751 Cyg (BB, MW) is a VY Scl CV, has a bolometric luminosity of 6.5 x 10$^{36}$ erg/s, and emits soft X-rays at quiescence.
The discovery of a weak soft X-ray source of V751 Cyg at minimum presents a challenge as this is unusual for CVs which commonly display weak hard X-ray emission at quiescence.
The high luminosity (6.5 x 10$^{36}$ erg/s) is particularly hard to understand in the context of VY Scl stars generally, because observations suggest that the binaries become simple red dwarf + white dwarf pairs at quiescence (the disk mostly disappears).
"A high luminosity in soft X-rays poses an additional problem of understanding why the spectrum is of only modest excitation."
The ratio He II λ4686/Hβ did not exceed ~0.5 in any of the spectra recorded up to 2001, which is typical for accretion-powered CVs and does not approach the ratio of 2 commonly seen in supersoft binaries (CBSS).
Pushing the edge of acceptable X-ray fits toward lower luminosity suggests that the luminosity should not exceed ~2 x 10$^{33}$ ergs/s, which gives only ~4 x 10$^{31}$ ergs/s of reprocessed light in the WD about equal to the secondary's expected nuclear luminosity.

## Ellipsoidal variable star

Def. a variable star in which the "two stars are rather close to each other and the light variability is mainly due to the rotation of the distorted [ellipsoidal] primary" is called an ellipsoidal variable star.
The distortion in the primary is towards the secondary star.

## Sun

The irradiance of the Sun varies by about 0.1% over an 11-year solar cycle.

## Algol

Ancient Egyptian calendars of lucky and unlucky days composed some 3,200 years ago may be the oldest preserved historical document of the discovery of a variable star, the eclipsing binary Algol.