attain the necessary mass by colliding with one another. It may be that in elliptical galaxies such collisions are the major source of supernovae. This hypothesis is based on the fact that the X-rays produced by those galaxies are 30 to 50 times less than what is expected to be produced by type Ia supernovas of that galaxy as matter accretes on the white dwarf from its encircling companion. It has been concluded that no more than 5 percent of the supernovae in such galaxies could be created by the process of accretion onto white dwarfs. The significance of this finding is that there could be two types of supernovae, which could mean that the Chandrasekhar limit might not always apply in determining when a white dwarf goes supernova, given that two colliding white dwarfs could have a range of masses. This in turn would confuse efforts to use exploding white dwarfs as standard candles in determining distances. White dwarfs have low luminosity and therefore occupy a strip at the bottom of the Hertzsprung–Russell diagram, a graph of stellar luminosity versus color or temperature. They should not be confused with low-luminosity objects at the low-mass end of the main sequence, such as the hydrogen-fusing red dwarfs, whose cores are supported in part by thermal pressure, or the even lower-temperature brown dwarfs. Mass–radius relationship The relationship between the mass and radius of low-mass white dwarfs can be estimated using the nonrelativistic Fermi gas equation of state, which gives where is the radius, is the total mass of the star, is the number of electrons per unit mass (dependent only on composition), is the electron mass, is the reduced Planck constant, and is the gravitational constant. Since this analysis uses the non-relativistic formula for the kinetic energy, it is non-relativistic. When the electron velocity in a white dwarf is close to the speed of light, the kinetic energy formula approaches where is the speed of light, and it can be shown that there is no stable equilibrium in the ultrarelativistic limit. In particular, this analysis yields the maximum mass of a white dwarf, which is 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