Evolutionary properties of helium-rich, degenerate dwarfs in binaries containing compact companions

The evolution of binaries containing low-mass donors (less than or equal to2 M(circle dot)) and degenerate accretors (i.e., white dwarfs [0.7 M(circle dot)] or neutron stars [1.4 M(circle dot)]) is systematically investigated over a wide expanse of parameter space. The donors are assumed to have metallicities in the range of 0.0001 less than or equal to Z less than or equal to 0.02 and could be either unevolved (zero- age main sequence) or ascending the red giant branch at the onset of mass transfer [ corresponding to 5 P P(orb)(hr) less than or similar to 2 x 10(3)]. The evolutionary tracks form part of a very detailed grid of nearly 200 sequences, each corresponding to a different set of initial conditions. During the initial phases of their evolution, the systems resemble either low-mass X-ray binaries or cataclysmic variables. However, as has been pointed out by several authors (e.g., Podsiadlowski et al.), the evolutionary tracks can exhibit a wide variety of behaviors and outcomes. We focus on systems that evolve to produce helium-rich degenerate dwarfs (HeDDs) that are either detached or still losing mass after a Hubble time. Of the systems that avoid dynamical instability, some evolve to ultrashort values of P(orb) (< 60 minutes), while others that lie above the bifurcation limit ( which we show to be quite sensitive to the assumed metallicity) produce wide binary millisecond pulsars (BMSPs) containing HeDD companions that have P(orb) values of less than or similar to 2 x 10(4) hr. We also show that the mass and composition of the envelopes of HeDDs that are about to descend the cooling branch are particularly sensitive to the input physics and this in turn dictates whether they experience extremely vigorous hydrogen shell flashes. Our computed values of the envelope mass, m(env) (corresponding to the mass of those layers below the surface containing some hydrogen), typically have a dependence on the final donor mass (m(f)) and metallicity (Z) that can be expressed as m(env) proportional to m(f) (-2.8)Z(-0.2). Furthermore, for systems that do not evolve too close to the bifurcation limit, we find that the final orbital period is given by P(orb),(f) (hr) congruent to 2.5 Z(0.3) x 10(10.7(mf/M circle dot)). Finally, we use our results to comment on the properties of the optical companions to binary millisecond pulsars and compare their inferred ages with the spin-down times of the pulsars. The structure of young HeDDs should be particularly useful as starting models for more sophisticated cooling calculations that take into account important long-term physical processes and thus we are making our models available for retrieval.