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The disc instability mechanism (DIM) is widely accepted to account for the transient behaviour of dwarf novae (DNe), which experience short outbursts separated by long quiescence. The duty cycle (the ratio between the outburst duration and the recurrence time) determines the amount of accreted mass by the white dwarf (WDs) during outbursts, thus playing an important role in the long-term binary evolution. Employing the code of Modules for Experiments in Stellar Astrophysics, we systemically investigate the influence of the duty cycles on the evolution of DNe and the mass growth of accreting carbon-oxygen (CO) WDs. Our calculations show that, while the DIM can considerably influence the accretion process, efficient WD-mass growth requires a particular range of the duty cycle. For WDs with the initial masses of 0.6, 0.7, and 1.1 M⊙, these duty cycles are 0.006$\, \le$d$\, \le$0.007, d = 0.005, and, d = 0.003 and the accumulated mass of the WDs can reach 0.1, 0.13, and 0.21 M⊙, respectively. In all of our simulations, no CO WDs can grow their masses to the explosion mass of Type Ia supernovae of about 1.38 M⊙. Because of a much short time-scale of the outburst state, the final donor-star masses and orbital periods are insensitive to the duty cycles. Therefore, we propose that the DIM in DNe could alleviate the WD mass problem to some extent.

The Hubble Space Telescope observation of the double white dwarf (WD) binary SDSS J125733.63$+$542850.5 reveal that the massive WD has a surface gravity log$g_1\sim8.7$ (which implies a mass of $M_1\sim1.06~{\rm M_\odot}$) and an effective temperature $T_1\sim13000$ K, while the effective temperature of the low-mass WD ($M_2

Recent timing analysis reveals that the orbital period of the first discovered accreting millisecond pulsar SAX J1808.4-3658 is increasing at a rate $\dot{P}_{\rm orb}=(3.89\pm0.15)\times 10^{-12}~\rm s\,s^{-1}$, which is at least one order of magnitude higher than the value arising from the conservative mass transfer. An ejection of mass loss rate of $10^{-9}~\rm M_{\odot}{\rm yr}^{-1}$ from the donor star at the inner Lagrangian point during the quiescence state could interpret the observed orbital period derivative. However, it is unknown whether this source can offer such a high mass loss rate. In this work, we attempt to investigate an evolutionary channel towards SAX J1808.4-3658. Once the accretion disk becomes thermally and viscously unstable, the spin-down luminosity of the millisecond pulsar and the X-ray luminosity during outbursts are assumed to evaporate the donor star, and the resulting winds carry away the specific orbital angular momentum at the inner Lagrangian point. Our scenario could yield the observed orbital period, the orbital period derivative, the peak X-ray luminosity during outbursts. Low-mass X-ray binaries with a $1.0~\rm M_{\odot}$ donor star, and an orbital period in the range of 0.8 - 1.5 d, may be the progenitor of SAX J1808.4-3658. Our numerical calculations propose that the current donor star mass is $0.044 ~\rm M_{\odot}$, which is in approximately agreement with the minimum mass of the donor star. In addition, our scenario can also account for the formation of black widows or the diamond planet like PSR J1719-1438., 7 pages, 5 figures, MNRAS in press

The recycling model suggested that low-mass X-ray binaries (LMXBs) could evolve into binary millisecond pulsars (BMSPs). In this work, we attempt to investigate the progenitor properties of BMSPs formed by the recycling evolutionary channel, and if sub-millisecond pulsars can be produced by this channel. Using Eggleton's stellar evolution code, considering that the dead pulsars can be spun up to a short spin period by the accreting material and angular momentum from the donor star, we have calculated the evolution of close binaries consisting of a neutron star and a low-mass main-sequence donor star, and the spin evolution of NSs. In calculation, some physical process such as the thermal and viscous instability of a accretion disk, propeller effect, and magnetic braking are included. Our calculated results indicate that, all LMXBs with a low-mass donor star of 1.0 - 2.0 $M_\odot$ and a short orbital period ($\la 3-4 \rm d$) can form millisecond pulsars with a spin period less than 10 ms. However, it is difficult to produce sub-millisecond pulsars by this evolutionary channel. In addition, our evolutionary scenario cannot account for the existence of BMSPs with a long orbital period ($P_{\rm orb}\ga 70-80\rm d$).

Justham, Rappaport & Podsiadlowski (2006) recently suggested that black-hole low-mass X-ray binaries (BHLMXBs) with short orbital periods may have evolved from black-hole intermediate-mass X-ray binaries (BHIMXBs). In their model the secondaries in BHIMXBs are assumed to possess anomalously high magnetic fields, so that magnetic braking can lead to substantial loss of angular momentum. In this paper we propose an alternative mechanism for orbital angular momentum loss in BHIMXBs. We assume that a small fraction $��$ of the transferred mass from the donor star form a circumbinary disc surrounding the binary system. The tidal torques exerted by the disc can effectively drain orbital angular momentum from the binary. We have numerically calculated the evolutionary sequences of BHIMXBs, to examine the influence of the circumbinary disc on the binary evolution. Our results indicate when $��\la 0.01-0.1$ (depending on the initial orbital periods), the circumbinary disc can cause secular orbital shrinking, leading to the formation of compact BHLMXBs, otherwise the orbits always expand during the evolution. This scenario also suggests the possible existence of luminous, persistent BHLMXBs, but it suffers the same problem as in Justham, Rappaport & Podsiadlowski (2006) that, the predicted effective temperatures of the donor stars are significantly higher than those of the observed donor stars in BHLMXBs., 7 pages, 5 figures, accepted for publication in MNRAS

Binary radio pulsars are generally believed to have been spun up to millisecond periods (i.e. recycling) via mass accretion from their donor stars, and they are the descendants of neutron star low-mass X-ray binaries. However, some studies indicate that the formation of pulsars from the accretion-induced collapse (AIC) of accreting white dwarfs (WDs) cannot be excluded. In this work, we use a population synthesis code to examine if the AIC channel can produce eccentric binary millisecond pulsars (BMSPs) in the Galaxy. Our simulated results indicate that, only when the natal MSPs receive a relatively strong kick ($\ga100\rm km\,s^{-1}$), can the AIC channel produce $\sim 10-180$ eccentric ($e>0.1$) BMSPs in the Galaxy, most of which are accompanied by a Helium star. Such a kick seems to be highly unlikely in the conventional AIC process, hence the probability of forming eccentric BMSPs via the AIC channel can be ruled out. Even if a high kick is allowed, the AIC channel cannot produce eccentric BMSPs with an orbital period of $\ga 20$ days. Therefore, we propose that the peculiar BMSP PSR J1903+0327 cannot be formed by the AIC channel. However, the AIC evolutionary channel may produce some fraction of isolated millisecond pulsars, and even sub-millisecond pulsars if they really exist.