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Ultraluminous X-ray sources (ULXs) are non-nuclear point-like objects observed with extremely high X-ray luminosity that exceeds the Eddington limit of a $\rm10\,M_\odot$ black hole. A fraction of ULXs has been confirmed to contain neutron star (NS) accretors due to the discovery of their X-ray pulsations. The donors detected in NS ULXs are usually luminous massive stars because of the observational biases. Recently, the He donor star in NGC 247 ULX-1 has been identified, which is the first evidence of a He donor star in ULXs. In this paper, we employed the stellar evolution code MESA to investigate the formation of ULXs through the NS+He star channel, in which a He star transfers its He-rich material onto the surface of a NS via Roche-lobe overflow. We evolved a large number of NS+He star systems and provided the parameter space for the production of ULXs. We found that the initial NS+He star systems should have $\rm\sim 0.7-2.6 \, M_\odot$ He star and $\rm \sim 0.1-2500\, d$ orbital period for producing ULXs, eventually evolving into intermediate-mass binary pulsars. According to binary population synthesis calculations, we estimated that the Galactic rate of NS ULXs with He donor stars is in the range of $\sim1.6-4.0\times10^{-4}\,{\rm yr}^{-1}$, and that there exist $\sim7-20$ detectable NS ULXs with He donor stars in the Galaxy., Comment: 19 pages, 6 figures, 2 tables

Millisecond pulsars (MSPs) are a kind of radio pulsars with short spin periods, playing a key role in many aspects of stellar astrophysics. In recent years, some more MSPs with wide orbits ($>30\,\rm d$) have been discovered, but their origin is still highly unclear. In the present work, according to an adiabatic power-law assumption for the mass-transfer process, we carried out a large number of complete binary evolution computations for the formation of MSPs with wide orbits through the iron core-collapse supernova (CCSN) channel, in which a neutron star (NS) originating from a CCSN accretes matter from a red-giant (RG) star and spun up to millisecond periods. We found that this channel can form the observed MSPs with wide orbits in the range of $30-1200\,{\rm d}$, in which the WD companions have masses in the range of $0.28-0.55\,\rm M_{\odot}$. We also found that almost all the observed MSPs can be reproduced by this channel in the WD companion mass versus orbital period diagram. We estimate that the Galactic numbers of the resulting MSPs from the CCSN channel are in the range of $\sim 4.8-8.5\times10^{5}$. Compared with the accretion-induced collapse channel, the CCSN channel provides a main way to produce MSPs with wide orbits., Comment: 19 pages, 8 figures, 3 tables. Accepted for publication in MNRAS

Black widows (BWs) are a type of eclipsing millisecond pulsars (MSPs) with low companion masses ($\lesssim0.05\,\rm M_\odot$) and tight orbits ($<1\,$d). PSR J1953+1844 is a BW with the shortest orbital period ($\sim53$ minutes) ever discovered, which was recently detected by Five-hundred-meter Aperture Spherical radio Telescope. Its companion mass is $\sim0.01\,\rm M_\odot$ according to its mass function, indicating that the companion may be a hydrogen-deficient star. However, the origin of PSR J1953+1844 is highly unclear. In this paper, we explored the origin of PSR J1953+1844 through the neutron star+He star channel, in which the system can experience ultracompact X-ray binary phase. We found that the He star donor channel can reproduce the characteristics of PSR J1953+1844, indicating that this work provides an alternative formation channel for this source. Meanwhile, the minimum orbital period of BWs formed by this channel is $\sim28$ minutes, corresponding to the companion mass of $0.058\,\rm M_\odot$. In addition, we note that even though PSR J1953+1844 has a short orbital period, it cannot be detected by the gravitational wave (GW) observatories like Laser Interferometer Space Antenna, TaiJi and TianQin. However, we still expect that the BWs with extremely tight orbit produced by this channel are the potential sources of future space-based GW observatories. Moreover, our simulations show that PSR J1953+1844 may eventually evolve into an isolated MSP., Comment: 6 pages, 3 figures, 1 table, accepted for publication in MNRAS, comments welcome!

Although multidimensional simulations have investigated the processes of double WD mergers, post-merger evolution only focused on the carbon-oxygen (CO) WD or helium (He) WD merger remnants. In this work, we investigate for the first time the evolution of the remnants stemmed from the merger of oxygen-neon (ONe) WDs with CO WDs. Our simulation results indicate that the merger remnants can evolve to hydrogen- and helium-deficient giants with maximum radius of about 300Rsun. Our models show evidence that merger remnants more massive than 1.95Msun can ignite Ne before significant mass-loss ensues, and they thus would become electron-capture supernovae (ECSNe). However, remnants with initial masses less than 1.90Msun will experience further core contraction and longer evolutionary time before reaching at the conditions for Ne-burning. Therefore their fates are more dependent on mass-loss rates due to stellar winds, and thus more uncertain. Relatively high mass-loss rates would cause such remnants to end their lives as ONe WDs. Our evolutionary models can naturally explain the observational properties of the double WD merger remnant IRAS 00500+6713 (J005311). As previously suggested in the literature, we propose and justify that J005311 may be the remnant from the coalescence of an ONe WD and an CO WD. We deduce that the final outcome of J005311 would be a massive ONe WD rather than a supernova explosion. Our investigations may be able to provide possible constraints on the wind mass-loss properties of the giants which have CO-dominant envelopes., Comment: 22 pages, 10 figures, 8 tables, accepted for publication in ApJL

Black widows (BWs) are a type of eclipsing millisecond pulsars (MSPs) with companion masses $M_2$ $\lesssim 0.05\,\rm M_\odot$, which can be used to study the accretion history and the radiation of pulsars, as well as the origin of isolated MSPs. Recent observations indicate that there are two sub-types of BWs. One is the BWs with $M_2$ $\sim$ $0.01-0.05\,\rm M_\odot$, whereas another with $M_2$ $\lesssim 0.01\,\rm M_\odot$. However, the origin of the latter is still highly uncertain. In this paper, we investigated the formation of BWs with $M_2$ $\lesssim 0.01\,\rm M_\odot$ through ultra-compact X-ray binaries (UCXBs) with He star companions, in which a neutron star (NS) accretes material from a He star through Roche-lobe overflow. By considering different He star masses and evaporation efficiencies with the stellar evolution code Modules for Experiments in Stellar Astrophysics (MESA), we evolved a series of NS+He star systems that can undergo UCXB stage. We found that this channel can explain the formation of BWs with $M_2$ $\lesssim 0.01\,\rm M_\odot$ within the Hubble time, especially three widely studied BWs, i.e. PSRs J1719-1438, J2322-2650 and J1311-3430. We also found that X-ray irradiation feedback does not affect the evolutionary tracks of evaporation process. Our simulations indicate that the UCXB channel with He star companions are the potential progenitors of isolated MSPs, and that the origin of BWs with $M_2$ $\lesssim 0.01\,\rm M_\odot$ is different with another sub-type of BWs. In addition, the present work suggests that the BWs with $M_2$ $\lesssim 0.01\,\rm M_\odot$ may not be produced by redback systems., Comment: 13 pages, 5 figures, 2 tables, accepted for publication in MNRAS, comments welcome!

Context. Classical novae are powered by thermonuclear runaways occurring on the surface of accreting white dwarfs (WDs). In the observations, the enrichments of heavy elements in nova ejecta have been detected, indicating a mixing process between the accreted matter and the matter from the outer layers of the underlying WDs prior to nova outbursts. However, the mixing fraction in classical novae is still uncertain. Aims. The purpose of this article is to investigate some elemental abundance ratios during nova outbursts that can be used to estimate the WD mixing fraction in classical novae. Methods. By considering different WD mixing fractions with the stellar evolution code Modules for Experiments in Stellar Astrophysics (MESA), we carried out a series of simulations of nova outbursts, in which the initial CO WD masses range from $0.7-1.0\,M_\odot$. Results. We identified four elemental abundance ratios (i.e. $\rm (H+He)/\sum CNO$, $\rm (H+He)/Ne$, $\rm \sum CNO/Mg,$ and $\rm \sum CNO/Si$) that satisfy the conditions for determining the WD mixing fraction, in which $\rm (H+He)/\sum CNO$ is the most suitable mixing meter. We also estimated the WD mixing fraction in some representative classical novae. Additionally, we found that a higher metallicity (i.e. higher WD mixing fraction) is preferentially accompanied by a longer $t_{\rm 2}$ (the time of decline by two magnitudes from peak luminosity) during nova outbursts. Our results can be used to constrain the mixing process in classical novae., Comment: 14 pages, 6 figures, 2 tables, accepted for publication in A&A

Ultra-compact X-ray binaries (UCXBs) are low-mass X-ray binaries with hydrogen-deficient mass-donors and ultra-short orbital periods. They have been suggested to be the potential Laser Interferometer Space Antenna (LISA) sources in the low-frequency region. Several channels for the formation of UCXBs have been proposed so far. In this article, we carried out a systematic study on the He star donor channel, in which a neutron star (NS) accretes matter from a He main-sequence star through Roche-lobe overflow, where the mass-transfer is driven by gravitational wave radiation. Firstly, we followed the long-term evolution of the NS+He main-sequence star binaries by employing the stellar evolution code Modules for Experiments in Stellar Astrophysics, and thereby obtained the initial parameter spaces for the production of UCXBs. We then used these results to perform a detailed binary population synthesis approach to obtain the Galactic rates of UCXBs through this channel. We estimate the Galactic rates of UCXBs appearing as LISA sources to be $\sim3.1-11.9\, \rm Myr^{-1}$ through this channel, and the number of such UCXB-LISA sources in the Galaxy can reach about $1-26$ calibrated by observations. The present work indicates that the He star donor channel may contribute significantly to the Galactic UCXB formation rate. We found that the evolutionary tracks of UCXBs through this channel can account for the location of the five transient sources with relatively long orbital periods quite well. We also found that such UCXBs can be identified by their locations in the mass-transfer rate versus the orbital period diagram., Comment: 21 pages, 9 figures, 1 table, accepted for publication in MNRAS

Nova outbursts play an important role in the chemical evolution of galaxies, especially they are the main source of synthetic $^{13}\rm C$, $^{15}\rm N$, $^{17}\rm O$ and some radioactive isotopes like $^{22}\rm Na$ and $^{26}\rm Al$. The enrichment of He in nova ejecta indicates that the accreted material may mix with the He-shell (He-mixing). The purpose of this work is to investigate how the He-mixing affects the nova outbursts in a systematic way. We evolved a series of accreting WD models, and found that the mass fraction of H and He in nova ejecta can be influenced by different He-mixing fractions significantly. We also found that both the nova cycle duration and ejected mass increase with the He-mixing fractions. Meanwhile, the nuclear energy production from $p$-$p$ chains decreases with the He-mixing fraction during the nova outbursts, whereas the CNO-cycle increases. The present work can reproduce the chemical abundances in the ejecta of some novae, such as GQ Mus, ASASSN-18fv, HR Del, T Aur and V443 Sct. This implies that the He-mixing process cannot be neglected when studying nova outbursts. This study also develops a He-mixing meter (i.e. $\rm He/H$) that can be used to estimate the He-mixing fraction in classical nova systems., Comment: 15 pages, 9 figures, accepted by MNRAS, comments welcome!

Accretion induced collapse (AIC) may be responsible for the formation of some interesting neutron star binaries, e.g., millisecond pulsars, intermediate-mass binary pulsars, etc. It has been suggested that oxygen-neon white dwarfs (ONe WDs) can increase their mass to the Chandrasekhar limit by multiple He-shell flashes, leading to AIC events. However, the properties of He-shell flashes on the surface of ONe WDs are still not well understood. In this article, we aim to study He-shell flashes on the surface of ONe WDs in a systematic approach. We investigated the long-term evolution of ONe WDs accreting He-rich material with various constant mass-accretion rates by time-dependent calculations with the stellar evolution code Modules for Experiments in Stellar Astrophysics (MESA), in which the initial ONe WD masses range from 1.1 to 1.35 M . We found that the mass-retention efficiency increases with the ONe WD mass and the mass-accretion rate, whereas both the nova cycle duration and the ignition mass decrease with the ONe WD mass and the mass-accretion rate. We also present the nuclear products in different accretion scenarios. The results presented in this article can be used in the future binary population synthesis studies of AIC events., Comment: 13 pages, 6 figures, accepted by Research in Astronomy and Astrophysics