ACCRETION disks1,2 are found in many astrophysical objects, ranging fr
om newly formed stars and mass-transferring binary systems to quasars
and other active galactic nuclei. An important feature of accretion di
sks is the boundary layer-the interface between the disk and the accre
ting objects-where up to half the accretion luminosity may be liberate
d. The lack of a satisfactory description of the flow and thermal stru
cture of this layer has long been a handicap when modelling disk spect
ra. Here we report numerical solutions of a model of thin accretion di
sks around a central white dwarf which includes a self-consistent desc
ription of the boundary layer. We find two distinct kinds of solution
depending on the mass accretion rate M. At high rates, we find optical
ly thick boundary layers whose radial width and peak temperature decre
ase with decreasing M, but when the accretion rate falls below a criti
cal value, the boundary layer becomes optically thin, and the width an
d temperature increase dramatically. Our results provide an explanatio
n for the hard X-rays observed3 in cataclysmic variables, particularly
at low M. It should be possible to extend our analysis to other accre
tion-disk systems.