We have seen how main-sequence stars are supported against gravitational collapse by the enormous gas pressures sustained by the fusion energy .Since fuel for the nuclear reactions runs out eventually become important .Low-mass stars that have run out of energy are eventually stabilized against collapse by the electron degeneracy pressure discussed above and they are known as WHITE DWARFS

The structure of a white dwarf is a result of balance between the outward pressure of degeneracy forces and the inward-acting gravitational force. This latter force is proportional to the product of the density of the white dwarf and its mass, divided by the square of its radius: (this is a particular form of Newton law of gravitation). The density clearly also depends upon the mass of the star and the cube of its radius. Therefore we can say that the gravitational force increases as the square of the mass divided by the fifth power of the radius. We know from our discussion of the equation of state for degenerate matter that the pressure varies as the five-thirds power of the density. The outward radial force is just the pressure gradient, so we divide pressure by the star’s radius. The result is a force that is proportional to the five-thirds power of the mass divided by sixth power of radius. Hence at sufficiently small radii, the degeneracy pressure force exceeds the gravitation. If we now balance these two forces we obtain a radius which depends upon the inverse cube root of the mass. A curious feature of white dwarfs is that increasing the mass decreases the radius. The white dwarf has to become smaller because confining its electrons more is its only way of increasing its outward pressure forces and supporting the extra mass.

The mass of a white dwarf cannot exceed a certain critical value. If we consider higher-mass stars, the electrons move faster and faster with increasing mass until their speeds approach that of light. The equation of state now changes (as we have discussed immediately above) and the degeneracy pressure force is now proportional to the inverse sixth power of the radius. We can no longer bring the two opposing forces into equilibrium by suitable adjustment of the stellar radius and no stable solution for the star is possible using electron pressure. The critical mass at which this catastrophe occurs is known as the CHANDRASEKHAR, MASS for a white dwarf. It is about 1.4 solar masses for white dwarfs com¬posed of the proportions of material likely to result when a star approaches the end of its life. Note that a pure hydrogen white dwarf cannot exist, since at nuclear densities the hydrogen would immediately burn explosively to form helium.

In summary, a degenerate object decreases its size when increasing its mass. This is a consequence of the uncertainty principle, since a decrease of size means an increase in momentum and hence degeneracy pressure. The speed of light proves to be the limitation, for when the electron velocities approach this value the gravitational force increases at the same rate as the degeneracy pressure force, and equilibrium is unattainable (figure 6.2).
The fate of a white dwarf that captures so much matter that its mass exceeds the chandrasekhar limit is uncertain. Initially it would collapse, releasing a large quantity of gravitational energy. Some material is probably then blasted off and any remnant star would consist of exceedingly dense matter.

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