  A rotating star may be modeled as a continuous system of particles attracted
to each other by gravity and with a given total mass and prescribed angular
velocity. Mathematically this leads to the Euler-Poisson system. A white dwarf
star is modeled by a very particular, and rather delicate, equation of state
for the pressure as a function of the density. We prove an existence theorem
for rapidly rotating white dwarfs that depend continuously on the speed of
rotation. The key tool is global continuation theory, combined with a delicate
limiting process. The solutions form a connected set $\mathcal K$ in an
appropriate function space. As the speed of rotation increases, we prove that
either the supports of white dwarfs in $\mathcal K$ become unbounded or their
densities become unbounded. We also discuss the polytropic case with the
critical exponent $\gamma=4/3$.
