Transients among binaries with evolved low-mass companions

We show that stable disk accretion should be very rare among low-mass X-ray binaries (LMXBs) and cataclysmic variables whose evolution is driven by the nuclear expansion of the secondary star on the first giant branch. Stable accretion is confined to neutron star systems in which the secondary is still relatively massive and to some supersoft white dwarf accretors. All other systems, including all black hole systems, appear as soft X-ray transients or dwarf novae. All long-period neutron star systems become transient well before most of the envelope mass is transferred and remain transient until envelope exhaustion. This complicates attempts to compare the numbers of millisecond pulsars in the Galactic disk with their LMXB progenitors and means that the pulsar spin rates are fixed in systems that are transient rather than steady, contrary to common assumption. The long-period persistent sources Sco X-2, LMC X-2, Cyg X-2, and V395 Car must have minimum companion masses, M-2, of about 0.75 M. if they contain neutron stars and still larger M-2 if they contain black holes. The neutron star transient GRO J1744-2844 must have M. less than or similar to 0.87 M.. The existence of any steady source at long periods supports the ideas that (1) the accretion disks in many, if not all, LMXBs are strongly irradiated by the central source and (2) mass transfer is thermally unstable in long-period supersoft X-ray sources.