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Degenerate Objects

Types of Cataclysmic Variable

Our galaxy contains numerous cataclysmic variables. One estimate is that it contains 10-7 cataclysmic variables per cubic parsec, which implies that the Galaxy contains tens of thousands of cataclysmic variables. We see only a fraction of these binaries, however, because they are not unusually bright. The brightest are modestly more luminous than the Sun, generating up to about 10 times the power generated by the Sun.

The power generated by a cataclysmic variable depends both on the rate of decay of the orbit and on the depth of the degenerate dwarf's gravitational potential. With a mass comparable to the Sun's and a radius comparable to Earth's, a degenerate dwarf causes an object falling onto it to release around 0.02% of the object's rest mass energy. For hydrogen, this is only 3% of the energy that can be released through nuclear fusion to helium. The characteristic temperature associated with this potential is nearly 200 keV (2 &times 109° Kelvin), but the whole process of converting gravitational potential energy into radiation usually drives the temperature much lower, because the gravitational potential energy is dumped into the degenerate dwarf's atmosphere before it is radiated away. Most of the energy is radiated at visible and ultraviolet wavelengths, with some radiation appearing at x-ray wavelengths.

Other than the orbital period of the binary system, which changes over time, few properties vary among cataclysmic variables—the mass and magnetic field of the degenerate dwarf and the rate at which mass flows to the degenerate dwarf from its companion fusion-powered star. The properties of the companion star are effectively set by the orbital period and the degenerate dwarf's mass. Despite this, cataclysmic variables display a rich variety of behavior that is a manifestation of three pieces of physics: the accretion disk surrounding the degenerate dwarf, the interaction of accreting gas with the magnetic field of the degenerate dwarf, and the nuclear fusion of hydrogen and helium accumulated at the surface of the degenerate dwarf. While this physics divides cataclysmic variables into many classes, we will limit ourselves to the most important. One point to make is that these classes are not mutually exclusive.

The effect of a strong magnetic field on the degenerate dwarf is most dramatically seen in the AM Herculis binaries, which are also given the unfortunate name of “polars,” pronounced to rhyme with star. The surface magnetic field of the degenerate dwarf in these systems is typically over 107 Gauss, compared to the 0.3 Gauss magnetic field of Earth and the 104 Gauss magnetic field found in the solar flares of the Sun. The magnetic field filling the space around the degenerate dwarf is so strong that an accretion disk cannot form. Instead, the gas is forced by the magnetic field to flow to the star's magnetic poles, where it passes through a standing shock wave in the star's atmosphere, releasing its gravitational potential energy as visible and x-ray light. The magnetic field also locks the degenerate dwarf to its companion star, so that the degenerate dwarf completes one rotation in one orbit of its companion.

What is interesting about the AM Herculis binaries is that we can easily see the signature of the magnetic field. Energetic electrons in a strong magnetic field move in a helix along the direction of the magnetic field lines. As they move, they radiate light, called cyclotron radiation. The characteristic frequency of this radiation, the cyclotron frequency, is proportional to the magnetic field strength, and is identical to the number of times the electrons twists around the magnetic field in a unit of time. The light is highly polarized (the inspiration for the name polar), with the orientation of the polarization set by the direction of the magnetic field. Because the radiation is emitted from the magnetic poles, we can see the light from the degenerate dwarf change in a predictable way as the star rotates. AM Herculis binaries therefore give the observer a tremendous amount of information in the polarization and variability of its visible light about the magnetic field in the system and about the orientation of the both the degenerate star and the binary system.

A type of system though to be related to the AM Herculis binaries is the DQ Herculis binaries. These systems have strong magnetic fields, but the fields are not sufficiently strong to lock the degenerate dwarf into synchronous rotation with its companion. They may have partial accretions disks, disks that are disrupted by the magnetic field before they touch the atmospheres of the degenerate dwarfs. This difference with the AM Herculis binaries may arise because the magnetic field is somewhat weaker than found in the AM Herculis binaries.

In the absence of a strong magnetic field, the light we see from a cataclysmic variable comes from an accretion disk that extends down to the atmosphere of the degenerate dwarf. These cataclysmic variables are characterized by their outbursts of energy rather than by the characteristics of their light. Principally, these are the classical novae and the dwarf novae. As the names imply, the outbursts of the second systems are much less intense than from the first. These two systems differ fundamentally in the physics causing their outbursts, for the first is created by a thermonuclear runaway at the surface of the degenerate dwarf, while the second is an event occurring in the accretion disk.

The classical novae were recognized back in the 19th century. It is to these events that the supernova is superior. During its normal life, the classical nova accretes gas onto itself through an accretion disk. Over time, hydrogen and helium from the companion build up over layers of carbon and oxygen in the atmosphere of the degenerate dwarf. Eventually the pressure at the bottom of the hydrogen and helium layer is sufficient to induce nuclear fusion. This event is explosive, because the thermonuclear fusion rate is strongly dependent on the temperature of the gas. Once the fusion begins, the temperature rises, causing thermonuclear burning to spread throughout the atmosphere. The atmosphere of hydrogen and helium that has built up over time suddenly burns to carbon, releasing all of its nuclear energy. This causes a cataclysmic variable to become hundreds of millions of times brighter. Once over, the degenerate dwarf cools and returns to accreting gas from its companion. The time between explosions ranges from hundreds to a thousand years.

The outburst from a dwarf nova is much less dramatic, brightening the system by a factor of ten to a hundred, but they are much more frequent, reoccurring on a time scale of weeks or months. The outbursts in these systems is caused by an instability in the accretion disk that suddenly causes gas in the disk to flow more rapidly onto the degenerate dwarf.

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