|MadSci Network: Astronomy|
The most famous case of flattening in the solar system is probably Saturn, which appears to be flattened due to the high rotation rate. The same effect is seen in interstellar clouds and other astronomical objects.
The amount of flattening depends on two main factors, the rate of the rotation and any other forces that are trying to keep the body spherical. In most cases what tries to keep the body as a sphere is pressure. When this pressure is balanced by the gravitational force which is trying to make the body collapse the body is in what is called hydrostatic equilibrium and the body will form a sphere. If we add rotation however we see a change in the shape of the object. If we start off with an initially spherical body which is in such a state of equilibrium, the rotation creates a force radial to the axis of rotation which tries to fling material off. The material along the axis of rotation feels no such force and will begin to collapse and both this movement outwards along the 'equator' of the body and inward movement at the 'poles'. This can then set up a new state of equilibrium from a state such as that shown in part (a) of the figure above to that shown in part (b). If the rotation speed was faster the figure would stop looking like an ellipse and eventually look like a disk, like that shown in part (c) of the figure.
In some cases it is possible that a torus could be formed although this will not happen under the sort of planetary or stellar conditions mentioned above. A torus will form if a cloud or large body of matter has been formed into a disk by the method mentioned above and there is a heavy compact body in the centre onto which the inner material accretes, such as a black hole. In the case of a black hole the material falling in is heated and as such emits radiation. Above a certain limit (called the Eddington limit) the pressure caused by this radiation stops any more material falling in and as the inner material has been used up a torus (doughnut shape) is formed. In some circumstances this situation can be stable although any disturbance is likely to cause further inflow of material and start the accretion process again with a disk forming. It is also possible, due to the different temperatures of different parts within the accretion disk to gain a toroidal shape as we see in Active Galactic Nuclei (AGN) which can be seen in the figure below.
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