  We study the angular momentum evolution of binaries containing two white
dwarfs which merge and become cool helium-rich supergiants. Our object is to
compare predicted rotation velocities with observations of highly evolved stars
believed to have formed from such a merger, including RCrB and extreme helium
stars. The principal study involves a binary containing a 0.6 solar mass CO
white dwarf, and a 0.3 solar mass He white dwarf. The initial condition for the
angular momentum distribution is defined where the secondary fills its Roche
Lobe. We assume conservation of angular momentum to compute the angular
momentum distribution in a collisionless disk and subsequently in the giant
envelope. At the end of shell-helium burning, the giant contracts to form a
white dwarf. We derive the surface rotation velocity during this contraction.
The calculation is repeated for a range of initial mass ratios, and also for
the case of mergers between two helium white dwarfs; the latter will contract
to the helium main-sequence rather than the white dwarf sequence. Assuming
complete conservation of angular momentum, we predict acceptable angular
rotation rates for cool giants and during the initial subsequent contraction.
However such stars will only survive spin-up to reach the white dwarf sequence
(CO+He merger) if the initial mass ratio is close to unity. He+He merger
products must lose angular momentum in order to reach the helium main sequence.
Minimum observed rotation velocities in extreme helium stars are lower than our
predictions by at least one half, indicating that CO+He mergers must lose at
least one half of their angular momentum.
