It is possible for one binary starsystems to end up in multiple of the cathegories below. For example, Cygnus X-1 is a spectroscopic binary, while it also is a high-mass x-ray binary.
A binary star is a pair of two stars, held together by the force of gravity. The brightest is called the primary star while the other is called the secondary star.
Appearance - On The Sky
Binary starsystems can be described as either optical, spectroscopic or visual, depending on how it appears to us on the night sky.
Optical binaries: Two stars that falsely appear to be binary stars, judging from their closeness on the sky are called optical binaries. The stars may in fact be located vast distances from each other, with no remarkable gravitational bond.
Spectroscopic binaries: Stars that orbit so close to each other (or are so far away), that both components can't be resolved through telescopes are called spectroscopic binaries, because they require a method of studying called spectroscopy to distinguish the stars. The star Mizar in Ursa Major is an example of both a spectroscopic binary and an visual binary: Two main stars can be distinguished through a telescope, but it turns out that both these stars have a companion each that can only be resolved through the use of spectroscopy.
Visual binary starsystems: A pair of stars, binary starsystems, that can be resolved through the use of telescopes (including interferometric methods) are called visual binaries.
Physical Composition
Furthermore, a binary starsystem can be put in one of the following three cathegories that describes the system physically:
Detached binary: There is no physical contact between the both stars. None has filled it's Roche lobe and they are both spherical in shape (unless one or both of them rotate really fast).
Semi-detached binary: One of the stars has filled its Roche lobe and has a shape which resembles an egg - due to the gravitational distortion of a very close neutron star or a black hole, which also rips gas from the surface of the distorted star. The gas often has a too high angular momentum while moving towards the compact object that the gas slowly forms an accretion disc.
Contact binary: In this case, both stars will have filled their Roche lobe, and may have become slightly egg-shaped. In this case the stars are relatively close to each other.
Eclipsing Binary Star Systems
In some cases, the orbital plane of of a binary starsystem happens to coincide almost perfectly with our line of sight (which is rare). In this case, we see one star passing infront of another, which will make it appear that the system has faded somewhat in brightness. The star Algol in the constellation of Perseus is a famous eclipsing binary and is a target for amateur astronomers. The system contains a K class giant which eclipses a B class star every 68.75 hours. The dimming of light when the smaller B class star eclipses the main star is visible to the naked eye. This phenomenon also occurs when a planet passes infront of its star and can be used to detect extrasolar planets. It will be used by the extrasolar mission Kepler.
Cataclysmic Binary Star Systems
Cataclysmic binaries are also known as cataclysmic variables. A cataclysmic binary consists of a primary white dwarf stellar remnant, and an orange/red K or M class main sequence (secondary) star, or in some cases, even a larger giant star.
The secondary star is tidally distorted by the white dwarf's gravitational field, which can weigh as much as 1.44 times more than our sun.
As matter from the secondary stars moves towards the small, compact white dwarf, it forms an accretion disc. The white dwarf, which consists of degenerated matter (plasma) is unable to fuse together the hydrogen, even though temperatures are sufficient. Eventually, the newly gained hydrogen on the surface quickly fuses to helium, in a heliumflash. This causes the white dwarf to brighten and display a celestial show called a nova, which can be seen from great distances.
There are occassions when the white dwarf's magnetic field disables the creation of an accretion disc. The light from these stars is known to sometimes be polarized. Depending on if the disc has been disrupted or prevented, these systems are also called intermediate polars and polars. These kinds of stars are also sometimes referred to as DQ Herculis and AM Herculis stars - after the first stars discovered of this type.
High-Mass X-Ray Binary Star Systems
High-mass X-Ray binaries (HMXB for short) contain a primary star that has a mass of, or larger than 10 MSun. The other companion is a compact object, usually a neutron star, or even a black hole. Matter is transferred to the compact object either by stellar winds, or by the compact object ripping gas off the surface. When the gas moves towards the compact object, it spirals inwards at an accelerating speed. Friction between the gas atoms makes the temperature rise to more than one million degrees Kelvin, which is hot enough to produce x-rays, hence the name high-mass x-ray binaries.
One of the most famous HMXB's is the system Cygnus X-1, which is thought to consist of an O9 class blue supergiant star, with a mass of 20-25 MSun and a black hole with a mass of 7-13 MSun. For more information, see the X-Ray binary starsystems page.
Low-Mass X-Ray Binary Star Systems
Low-mass X-Ray binaries are systems where the compact object is a neutron star, or a black hole. The primary star is a main sequence star with < 1 MSun. The black hole rips gas from the star's surface and creates an accretion disc, sometimes it may be a permanent disc. For more information, see the X-Ray binary starsystems page.
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