  We have computed an extensive grid of binary evolution tracks to represent
low- and intermediate mass X-ray binaries (LMXBs and IMXBs). The grid includes
42,000 models which covers 60 initial donor masses over the range of 1-4 solar
masses and, for each of these, 700 initial orbital periods over the range of
10-250 hours. These results can be applied to understanding LMXBs and IMXBs:
those that evolve analogously to CVs; that form ultracompact binaries with
orbital periods in the range of 6-50 minutes; and that lead to wide orbits with
giant donors. We also investigate the relic binary recycled radio pulsars into
which these systems evolve. To evolve the donor stars in this study, we
utilized a newly developed stellar evolution code called "MESA" that was
designed, among other things, to be able to handle very low-mass and degenerate
donors. This first application of the results is aimed at an understanding of
the newly discovered pulsar PSR J1614-2230 which has a 1.97 solar masses
neutron star, orbital period = 8.7 days, and a companion star of 0.5 solar
mass. We show that (i) this system is a cousin to the LMXB Cyg X-2; (ii) for
neutron stars of canonical birth mass 1.4 solar masses, the initial donor stars
which produce the closest relatives to PSR J1614-2230 have a mass between
3.4-3.8 solar masses; (iii) neutron stars as massive as 1.97 solar masses are
not easy to produce in spite of the initially high mass of the donor star,
unless they were already born as relatively massive neutron stars; (iv) to
successfully produce a system like PSR J1614-2230 requires a minimum initial
neutron star mass of at least 1.6+-0.1 solar masses, as well as initial donor
masses and orbital period of ~ 4.25+-0.10 solar masses and ~49+-2 hrs,
respectively; and (v) the current companion star is largely composed of CO, but
should have a surface H abundance of ~10-15%.

High Energy Astrophysical Phenomena