<P> Since this analysis uses the non-relativistic formula p ∕ 2m for the kinetic energy, it is non-relativistic . If we wish to analyze the situation where the electron velocity in a white dwarf is close to the speed of light, c, we should replace p ∕ 2m by the extreme relativistic approximation p c for the kinetic energy . With this substitution, we find </P> <P> If we equate this to the magnitude of E, we find that R drops out and the mass, M, is forced to be </P> <P> To interpret this result, observe that as we add mass to a white dwarf, its radius will decrease, so, by the uncertainty principle, the momentum, and hence the velocity, of its electrons will increase . As this velocity approaches c, the extreme relativistic analysis becomes more exact, meaning that the mass M of the white dwarf must approach a limiting mass of M. Therefore, no white dwarf can be heavier than the limiting mass M, or 1.4 M . </P> <P> For a more accurate computation of the mass - radius relationship and limiting mass of a white dwarf, one must compute the equation of state which describes the relationship between density and pressure in the white dwarf material . If the density and pressure are both set equal to functions of the radius from the center of the star, the system of equations consisting of the hydrostatic equation together with the equation of state can then be solved to find the structure of the white dwarf at equilibrium . In the non-relativistic case, we will still find that the radius is inversely proportional to the cube root of the mass . Relativistic corrections will alter the result so that the radius becomes zero at a finite value of the mass . This is the limiting value of the mass--called the Chandrasekhar limit--at which the white dwarf can no longer be supported by electron degeneracy pressure . The graph on the right shows the result of such a computation . It shows how radius varies with mass for non-relativistic (blue curve) and relativistic (green curve) models of a white dwarf . Both models treat the white dwarf as a cold Fermi gas in hydrostatic equilibrium . The average molecular weight per electron, μ, has been set equal to 2 . Radius is measured in standard solar radii and mass in standard solar masses . </P>

White dwarfs are made out of degenerate matter . what does this term mean