Evolutionary paths of binaries with a neutron star. I. The case of SAX J1808.4-3658

Abstract

The evolutionary status of the low mass X-ray binary SAX J1808.4-3658 is simulated by following the binary evolution of its possible progenitor system through mass transfer, starting at a period of ∼6.6 hr. The evolution includes angular momentum losses via magnetic braking and gravitational radiation. It also takes into account the effects of illumination of the donor by both the X-ray emission and the spin down luminosity of the pulsar. The system goes through stages of mass transfer and stages during which it is detached, where only the rotationally powered pulsar irradiates the donor. We show that the pulsar irradiation is a necessary ingredient to reach SAX J1808.4-3658 orbital period when the donor mass is reduced to 0.04-0.06 M . We also show that the models reproduce important properties of the system, including the orbital period derivative, which is shown to be directly linked to the evolution through mass transfer cycles. Moreover we find that the effects of the irradiation on the internal structure of the donor are non negligible, causing the companion star to be non completely convective at the values of mass observed for the system and significantly altering its long term evolution, as the magnetic braking remains active along the whole evolution.

Origin and binary evolution of millisecond pulsars

“…This kind of cycles is compatible with the positive 𝑃 orb 's found for some AMXPs. In particular, the 𝑃 orb =3.6÷3.8 × 10 −12 [97] measured during the outbursts in SAX J1808, can be reproduced by standard evolution including X-ray irradiation and MSP irradiation with 𝜖 = 0.01 [108]. The cyclic evolution also accounts for the higher frequency of systems at 0.1 𝑀/𝑀 0.2 .…”

“…Below 𝑃 bif , starting from 0.85 𝑀 , the dash-dotted magenta line is a standard binary evolution starting in late case A, with no illumination and reaching a minimum period well below 76 m, as the hydrogen content of the core is very small. The violet and blue lines are taken from [108] and represent a standard case A evolution (no illumination) and an evolution with illumination 𝜖 𝑋 = 𝜖 𝑀 𝑆 𝑃 = 0.01. This latter passes through the location of the AMXP SaX J 1808.4-3658.…”

“…The cycles of mass-transfer due to X-rays illumination in LMXBs are particularly important, as they may be relevant to understand: After early computations [48,26,47], recently the evolution of LMXBs with illumination has been afforded in [11,12,13,108]. Eq.…”

“…8, considering the shorter recurrence between cycles (𝜖=0.005), the LMXB phase is ∼1/15, 1/10 and 1/4 of the entire cycle, thus fully solving the birthrate problem. In the case displayed, and in [108], each cycle spans from 30-50 Myr (0.75 𝑀 ) to 20-90 Myr (0.6 𝑀 ) to 70-140 Myr. This kind of cycles is compatible with the positive 𝑃 orb 's found for some AMXPs.…”

“…The spin-up problem has been afforded numerically in early works in e.g. [75,64] and more recently in [108].…”