An evolutionary model for SAX J1808.4-3658

An evolutionary scenario to explain the transient nature and short total du ration of the X-ray burst of SAX J1808.4-3658 is proposed. An optical compa nion of the neutron star(a "turn-off" Main-Sequence star) fills its Roche l obe at the orbital period (P-orb) similar to 19 hours. During the initial h igh mass-transfer phase when the neutron star is a persistent X-ray source, the neutron star is spun up to a millisecond period. Due to its chemical c omposition gradient, the secondary does not become fully convective when it s mass decreases below 0.3 M., hence a magnetic braking remains an effectiv e mechanism to remove orbital angular momentum and the system evolves with Roche-lobe overflow towards a short orbital period. Near an orbital period of two hours the mass transfer rate becomes so small (similar to 10(-11) M. /yr) that the system can not continue to be observed as a persistent X-ray source. During further Roche-lobe filling evolution deep mixing allows the surface of secondary to become more and more helium rich. Since the accrete d matter is helium rich, it is easy to explain observed short total duratio n of the burst. This evolutionary picture suggest that radio emission can b e observed only at shorter wavelength's. Our model predicts a faster orbita l period decay than expected if the orbital evolution is driven only by gra vitational wave radiation.