Introduction
- Eclipsing Binary Stars
Eclipsing binary stars are just one of the several types of variable stars. These stars appear as a single point of light to an observer, but based on its brightness variation and spectroscopic observations we can say certainly that the single point of light is actually two stars in close orbit around one another. The variations in light intensity from eclipsing binary stars are caused by one star passing in front of the other relative to an observer. An eclipsing binary star is a binary star in which the orbit plane of the two stars lies so nearly in the line of sight of the observer that the components undergo mutual eclipses. Algol and Ex Hya are the best-known example of an eclipsing binary[1]
Eclipsing binaries are variable stars, not because the light of the individual components vary but because of the eclipses. The light curve of an eclipsing binary is characterized by periods of practically constant light, with periodic drops in intensity. If one of the stars is larger than the other, one will be obscured by a total eclipse while the other will be obscured by an annular eclipse. The period of the orbit of an eclipsing binary may be determined from a study of the light curve, and the relative sizes of the individual stars can be determined in terms of the radius of the orbit by observing how quickly the brightness changes as the disc of the near star slides over the disc of the distant star[2].
- Cataclysmic variables (CVs)
These are binary star systems that have a white dwarf and a normal star companion. The white dwarf is often referred to as the “primary” star, and the normal star as the “companion” or the “secondary” star. The companion star, a star that is “normal,” like our Sun, loses material onto the white dwarf via accretion. The white dwarf is a dense compact object whose magnetic field is stronger at the poles; hence matter from the secondary companion is channeled to the magnetic poles during the accretion process. There are probably more than a million of these cataclysmic variables in the galaxy, but only few have been studied in X-rays so far (Warner 1995). Depending on the physical size of the white dwarf’s magnetosphere, the transferred material can either interact directly with the magnetosphere, e.g. in Polars, or result in the formation of an accretion disc, e.g. in intermediate polars. The accretion disc can be thought of as a machine, facilitating the extraction of angular momentum from the material, allowing it to accrete onto the white dwarf where gravitational potential energy of the gas is released as heat and radiation results in interesting observational properties of these systems (outbursts and brightening). Based on the observational properties of these systems, cataclysmic variables can be grouped into several categories e.g. classical novae, dwarf novae, recurrent novae, nova-like variables and Magnetic Cataclysmic Variables (mCVs) (Warner 1995).
- Formation of Cataclysmic Variables
Stars are born from gravitationally collapsing molecular and interstellar dust clouds. The collapse is induced through instability in the cloud which could be due to shock waves from a nearby supernova. A star develops when the core of the contracting protostar reaches a temperature that is enough for the ignition of nuclear fusion reactions. Less massive clouds require high densities to collapse while more massive clouds require lower densities to collapse thus more massive clouds collapse first (Kippenhahn & Weigert, 1990). As the density of the gas cloud increases, small parts of the cloud would collapse independently. Ultimately the cloud would fragment into many parts forming a whole cluster of stars. Stars therefore form in clusters finding themselves gravitationally bound in binaries, triplets, pairs of binaries or similar combinations. Stars destined to become CVs begin as binaries separated by a few hundred solar radii, orbiting each other approximately every ten years (Hellier 2001). One of the stars must be less than a solar mass and the other more massive. The more massive star evolves more rapidly, since the greater weight on its core ensures a higher pressure and temperature, and therefore a more vigorous nuclear burning rate. The more massive star eventually expands and becomes a red giant (Hellier 2001); hence overflowing its Roche lobe, and transfer its outer layers to the less massive companion. The more massive star is closer to the centre-of-mass (CM) of the binary, and material transferred to the less massive companion star therefore moves further from the CM. This results in increase of angular momentum of the material being transferred. Conserving the overall binary angular momentum will result in a decrease in the binary separation if the mass transfer is conservative (Frank et al. 1992). This dynamical mass transfer to the companion star will have dramatic consequences that will sculpture the further evolution of this system. This influx of material cannot be assimilated by the companion star, and the material overfills both Roche lobes forming a cloud surrounding the two stars. This is the “common envelope” phase in which the pre-cataclysmic variable is effectively orbiting within a massive red giant. The drag on the stars as they orbit drain their orbital energy causing them to spiral inwards, reducing their separation from about one hundred solar radii to about one solar radius in approximately one thousand years (Hellier 2001). The new-naked binary is either a cataclysmic binary, or if the separation is still too large for mass transfer, a detached binary is formed (Hellier 2001).
- Accretion Disc formation
Material transferred from the secondary star falls onto the magnetized rotating white dwarf due to gravitation, the spiralling-in process entails a loss of angular momentum by the magnetized rotating white dwarf, being transferred outwards by internal torques (Frank et al. 1992). The ring thus spreads out into a thin disc which continues spreading until the inner edge meets the compact star; or in the case of a magnetized primary, the radius where the disc ram pressure balances the magnetospheric pressure. This defines the so called magnetospheric radius of the white dwarf. The interaction of the disc with the primary star may lead to a spin-up or spin-down torque that affects the rotating compact star (Wang 1987). Angular momentum flowing outwards through the disc enables the inward flow of material thereby releasing energy. At the outer edge of the disc tidal interactions with the secondary star soak up the angular momentum and return it to the orbit of the secondary; limiting the outward spread of the disc, (Hellier 2001). This is replenished by mass transfer from the secondary star. Material will continue to flow inwards towards the white dwarf ( Frank et al. 1992) if: (i) Material in the disc loses angular momentum. (ii) The primary star rotates slowly enough allowing inflow of material instead of expelling it centrifugally. When a disc has been formed, the stream of material from the secondary star hits the edge of the disc, forming a “bright spot”. At this spot, the stream of material falling radially, encounters material moving across its path in a circular orbit. Not much is understood about the turbulent encounter, however, computer simulations suggest that the dense core of the stream punches a hole in the disc and is gradually assimilated into the circular flow, (Hellier 2001).
- Magnetic Cataclysmic Variables (mCVs)
In mCVs, the white dwarf usually has a substantial magnetic field that can either intercept the mass flow from the secondary from reaching down to the surface of the white dwarf, preventing the formation of an accretion disc, or disrupting the disc if present. The magnetospheric field also facilitates the mass inflow onto the surface of the compact white dwarf, a process called magnetic accretion[3]. These magnetic CVs can be subdivided into AM Her stars or polars in which the white dwarf rotation is phase locked to the orbital motion of the binary companion and the DQ Her stars or intermediate polars in which the rotation period of the white dwarf is shorter than the orbital period, (Rosen et al. 1988).
- Polars (also AM Herculis Star).
AM Her type systems are distinct from other CVs in that they completely lack an accretion disk. In polar systems, the magnetic field of the white dwarf is too strong for an accretion disk to form. The strong magnetic field of the white dwarf has the following important implications: (i) Polars are synchronously rotating systems (Prot = Porb), with orbital periods lying between ~ 81 and 222 minutes (Chanmugam & Ray 1984). The phase locked interaction is caused by the strong magnetic interaction between the white dwarf and the low mass secondary star. (ii) The formation of the disc is prevented (i.e. diskless accretion) because of its strong magnetic field (Chanmugam & Ray 1984).
[1] http://www.physics.sfasu.edu/astro/ebstar.
[2] http://en.wikipedia.org/wiki/Microsoft_PowerPoint.
[3] http://imagine.gsfc.nasa.gov/docs/science
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