1. Evolutionary Sequences For Low- And-Intermediate-Mass X-Ray Binaries Ph. Podsiadlowski S. Rappaport E. D. Pfahl

2. Introduction LMXBs: discovered 40 yr ago Porb<10 days No luminous companion stars The only one case confirmed: Cyg X-2 LMXBs may descend from IMXBs

4. Binary Calculations Roche lobe radius: Mass transfer rate: Angular momentum loss:

5. Binary Calculations

6. (1): Systems evolving to long periods (2): Systems evolving to short periods (3): More massive systems Experiencing dynamical mass transfer and spiral-in Very few systems should be observable in the early rapid phase and X-ray binaries are mostly likely to have a relatively low mass secondary when they are observerd at the present epoch

9. Thermal Timescale Mass Transfer Mass-radius exponents:

10. In radiative stars, a large fraction of the envelope (in radius) contains very little mass

16. The systems becomes temporarily detached when the H-burning shell stars to move into the region with a gradient in hydrogen abundance, established during the hydrogen core burning phase and the giant shrinks significantly

17. The early mass transfer phase can be divided into two separate phases: (1):a phase of atmospheric Roche lobe overflow where the mass transfer rate increases exponentially, (2): a phase where the high-entropy material in the low-density envelope of the secondary is lost

20. The drop in Pmin at 13 hr occurs for a model where the secondary has just exhausted hydrogen in the center at the beginning of mass transfer

23. Application to The Population of X-Ray Binaries Issues: (1) how unique are the evolutionary paths we have found, (2) are types of systems suggested by other resonably long-lived phases of our binary evolutions represented in the observed binary X- ray source population (3) is our complete ensemble of binary evoltuion models consistent with the overall population of observed LMXBs and IMXBs?

26. Application to Binary Millisecond Pulsars In the Galaxy plane, binary radio pulsars classes: (1):one major class involves systems with low-mass companions. (2):the ones with substantially more massive white dwarf companions (3):systems containing planetary mass companions (4):systems consist of a pair of neutron stars

27. A outstanding problem: the birthrate problem Application to Binary Millisecond Pulsars