Maximum mass ratio of AM CVn-type binary systems and maximum white dwarf mass in ultra-compact X-ray binaries

AM CVn-type stars and ultra-compact X-ray binaries are extremely interesting semi-detached close binary systems in which the Roche lobe filling component is a white dwarf transferring mass to another white dwarf, neutron star or a black hole. Earlier theoretical considerations show that there is a maximum mass ratio of AM CVn-type binary systems (qmax ≈ 2/3) below which the mass transfer is stable. In this paper we derive slightly different value for qmax and more interestingly, by applying the same procedure, we find the maximum expected white dwarf mass in ultra-compact X-ray binaries.