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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 $M_\odot$, these duty cycles are 0.006$\,\leq$$d$$\,\leq$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 $M_\odot$, respectively. In all of our simulations, no CO WDs can grow their masses to the explosion mass of Type Ia supernovae of about $1.38~M_\odot$. Because of a much short timescale 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., Comment: 9 pages, 6 figures, 4 tables. Published in MNRAS

Ultracompact cataclysmic variables (CVs) of the AM CVn type are deemed to be important verification sources for the future space gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA). We model the present-day Galactic population of AM CVn stars with He-star donors. Such a population has long expected to exist, though only a couple of candidates are known. We applied the hybrid method of binary population synthesis (BPS) which combines a simulation of the population of immediate precursors of AM CVn stars by a fast BPS code with subsequent tracking of their evolution by a full evolutionary code. The model predicts that the present birthrate of He-donor AM CVn stars in the Galaxy is $4.6\times 10^{-4}$ per yr and the Galaxy may harbour about 112000 objects of this class which have orbital periods less than 42-43 min. The foreground confusion limit and instrumental noise of LISA prevent the discovery of longer periods systems in gravitational waves. We find that about 500 He-star AM CVns may be detected by LISA with signal-to-noise ratio (S/N)>5 during a 4 yr mission. Within 1 Kpc from the Sun, there may exist up to 130 He-star AM CVns with the periods in the same range, which may serve as verification binaries, if detected in the electromagnetic spectrum. In the Milky Way, there are also about 14800 immediate precursors of AM CVn stars. They are detached systems with a stripped low-mass He-star and a white dwarf companion, out of which about 75 may potentially be observed by LISA during its mission., Comment: 9 pages, 4 figures, accepted by Astronomy and Astrophysics

PSR J$1946+3417$ is a millisecond pulsar (MSP) with a spin period $P\simeq3.17\rm~ms$. Harbored in a binary with an orbital period $P_{\rm b}\simeq27$ days, the MSP is accompanied by a white dwarf (WD). The masses of the MSP and the WD were determined to be $1.83\rm~M_\odot$ and $0.266\rm~M_\odot$, respectively. Specially, its orbital eccentricity is $e\simeq0.134$, which is challenging the recycling model of MSPs. Assuming that the neutron star in a binary may collapse to a strange star when its mass reaches a critical limit, we propose a phase transition (PT) scenario to account for the origin of the system. The sudden mass loss and the kick induced by asymmetric collapse during the PT may result in the orbital eccentricity. If the PT event takes place after the mass transfer ceases, the eccentric orbit can not be re-circularized in the Hubble time. Aiming at the masses of both components, we simulate the evolution of the progenitor of PSR J$1946+3417$ via \texttt{MESA}. The simulations show that a NS / main sequence star binary with initial masses of $1.4+1.6\rm~M_\odot$ in an initial orbit of 2.59 days will evolve into a binary consisting of a $2.0\rm~M_\odot$ MSP and a $0.27\rm~M_\odot$ WD in an orbit of $\sim21.5$ days. Assuming that the gravitational mass loss fraction during PT is $10\%$, we simulate the effect of PT via the kick program of \texttt{BSE} with a velocity of $\sigma_{\rm PT}=60~{\rm km~s}^{-1}$. The results show that the PT scenario can reproduce the observed orbital period and eccentricity with higher probability then other values., Comment: accepted to be published on RAA

The space gravitational wave (GW) detector Laser Interferometer Space Antenna (LISA) that was planed to launch in the early 2030s is to detect the low-frequency GW signals in the Galaxy. AM CVn stars were generally thought to be important low-frequency GW sources. Employing the MESA code, in this work we calculate the evolution of a great number of binary systems consisting of a white dwarf (WD) and a main sequence (MS) star, and diagnose whether their descendants-AM CVn stars can be visible by the LISA. The simulated results show that the progenitors of these LISA sources within a distance of 1 kpc are WD-MS binaries with a donor star of $1.0-1.4~M_\odot$ (for initial WD mass of $0.5~M_\odot$) or $1.0-2.0~M_\odot$ (for initial WD mass of $0.7~M_\odot$), and an initial orbital period slightly smaller than the bifurcation period. Our simulations also indicate ten verification AM CVn sources can be reproduced by the standard magnetic braking model, and are potential LISA sources. Based on the birthrate of AM CVns simulated by the population synthesis, the birthrate of AM CVn-LISA sources evolving from the evolved donor star channel within a distance of 1 kpc can be estimated to be $(0.6-1.4)\times10^{-6}~\rm yr^{-1}$, and the predicted number of AM CVn-LISA sources is about $340-810$. Therefore, the evolved donor star channel play an important role in forming AM CVn-LISA sources in the Galaxy., Comment: 8 pages, 5 figures, 2 tables, Accepted by ApJ

According to the recycling model, neutron stars in low-mass X-ray binaries were spun up to millisecond pulsars (MSPs), which indicates that all MSPs in the Galactic plane ought to be harbored in binaries. However, about $20\%$ Galactic field MSPs are found to be solitary. To interpret this problem, we assume that the accreting neutron star in binaries may collapse and become a strange star when it reaches some critical mass limit. Mass loss and a weak kick induced by asymmetric collapse during the phase transition (PT) from neutron star to strange star can result in isolated MSPs. In this work, we use a population-synthesis code to examine the PT model. The simulated results show that a kick velocity of $\sim60~{\rm km~s}^{-1}$ can produce $\sim6\times10^3$ isolated MSPs and birth rate of $\sim6.6\times10^{-7} {\rm ~yr}^{-1}$ in the Galaxy, which is approximately in agreement with predictions from observations. For the purpose of comparisons with future observation, we also give the mass distributions of radio and X-ray binary MSPs, along with the delay time distribution., Comment: 9 pages, 11 figures, accepted to publish on A&A

It has been shown that the rate of angular momentum loss (AML) in cataclysmic variables (CVs) below the period gap is about 2.47 times that caused by gravitational radiation, suggesting extra AML mechanism besides gravitational radiation. Several potential mechanisms have been proposed but none of them has been verified. In this work we examine whether AML caused by friction between the expanding nova envelope and the donor star can account for the required AML rate. By adopting various expanding velocities of the envelope, we have calculated the evolution of CVs with typical initial parameters. Our results show that this friction interaction unlikely solve the extra AML problem unless the expanding velocities are extremely low. Thus there should be a more efficient AML mechanism that plays a role in the CV evolution., Comment: 19 pages, 4 figures, 5 tables, accepted by ApJ on November 15

Accretion-induced collapse (AIC) is widely accepted to be one of the formation channels for millisecond pulsars (MSPs). Since the MSPs have high spindown luminosities, they can immediately start to evaporate their companion stars after birth. In this paper we present a detailed investigation on the evolution of the post-AIC binaries, taking into account the effect of evaporation both before and during the Roche-lobe overflow process. We discuss the possible influence of the input parameters including the evaporation efficiency, the initial spin period and the initial surface magnetic field of the newborn neutron star. We compare the calculated results with the traditional low-mass X-ray binary evolution, and suggest that they may reproduce at least part of the observed redbacks and black widows in the companion mass - orbital period plane depending on the mechanisms of angular momentum loss associated with evaporation., Comment: 25 pages, 13 figures, accepted for publication in ApJ

Recent observations show that the white dwarfs (WDs) in cataclysmic Variables (CVs) have an average mass significantly higher than isolated WDs and WDs in post-common envelope binaries (PCEBs), which are thought to the progenitors of CVs. This suggests that either the WDs have grown in mass during the PCEB/CV evolution or the binaries with low-mass WDs are unable to evolve to be CVs. In this paper, we calculate the evolution of accreting WD binaries with updated hydrogen accumulation efficiency and angular momentum loss prescriptions. We show that thermal timescale mass transfer is not effective in changing the average WD mass distribution. The WD mass discrepancy is most likely related to unstable mass transfer in WD binaries in which an efficient mechanism of angular momentum loss is required., Comment: 22 pages, 10 figures, accepted for publication in ApJ

It is difficult for the intermediate-mass X-ray binaries (IMXBs) evolutionary channel to form intermediate-mass binary pulsars (IMBPs) with a short orbital period (less than 3 d) via stable mass transfer. The main reason is that the magnetic braking mechanisms are generally thought not to work for donor stars with a mass of greater than 1.5 $\rm M_{\odot}$ in the canonical model. However, some intermediate-mass stars have anomalously strong magnetic fields (about 100 -- 10000 G), i. e. so-called Ap or Bp stars. With the coupling between the magnetic field and the irradiation-driven wind from the surface of Ap/Bp stars, a plausible magnetic braking mechanism should be expected. In this work, we attempt to investigate if IMXBs with Ap/Bp stars can produce IMBPs with a short orbital period (less than 3 d) by such an anomalous magnetic braking mechanism. Using a stellar evolution code, we have simulated the evolution of a large number of IMXBs consisting of a NS and an Ap/Bp star. For the spin evolution of the NS, we consider the accretion torque, the propeller torque, and the spin-down torque caused by the interaction between the magnetic field and the accretion disc. The calculated results show that, employing anomalous magnetic braking of Ap/Bp stars, IMXBs can evolve into compact IMBPs with short orbital periods of less than 3 d. However, there exists significant discrepancy between the spin periods of IMBPs in our simulated results and those observed., Comment: 8 pages, 6 figures. Accepted for publication in MNRAS

It is difficult for intermediate-mass X-ray binaries to form compact intermediate-mass binary pulsars (IMBPs) with a short orbital-period ($\la 3 \rm d$), which have a heavy ($\ga 0.4 M_{\odot}$) CO or ONeMg white dwarf companions. Since neutron star + He star binaries may experience common-envelope evolution, they have some advantage to account for the formation of short orbital-period IMBPs. In this work, we explore the probability of IMBPs formed by this evolutionary channel. Using Eggleton's stellar evolution code, considering that the dead pulsars were spun up by the accreting material and angular momentum from the He star companions, we have calculated the evolution of a large number of neutron star + He star binaries. Our simulated results indicate that, the NS + He star evolutionary channel can produce IMBPs with a WD of $\sim0.5 - 1.1 M_{\odot}$ and an orbital period of $0.03 - 20$ d, in which pulsars have a spin-period of $1.4 - 200$ ms. Comparing the calculated results with the observational parameters (spin period and orbital period) of 9 compact IMBPs, the NS + He star evolutionary channel can account for the formation of 4 sources. Therefore, NS + He star binaries offer an alternative evolutionary channel to compact IMBPs., Comment: 5 pages, 4 figures, accepted for publication in MNRAS letters

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 ($P_{\rm orb}\ga 70-80\rm d$)., Comment: 7 pages,5 figures, MNRAS in press