It has been suggested that accretion-induced collapse (AIC) is a non-negligible path for the formation of the observed neutron stars (NSs). An ONe white dwarf (WD) that accretes material from a He star may experience AIC process and eventually produce intermediate-mass binary pulsars (IMBPs), named as the ONe WD+He star scenario. Note that previous studies can only account for part of the observed IMBPs with short orbital periods. In this work, we investigate the evolution of about 900 ONe WD+He star binaries to explore the distribution of IMBPs. We found that the ONe WD+He star scenario could form IMBPs including pulsars with 5 − 340 ms spin periods and 0.75 − 1.38 M ⊙ WD companions, in which the orbital periods range from 0.04 to 900 d. Compared with the 20 observed IMBPs, this scenario can cover the parameters of 13 sources in the final orbital period−WD mass plane and the Corbet diagram, most of which has short orbital periods. We found that the ONe WD+He star scenario can explain almost all the observed IMBPs with short orbital periods. This work can well match the observed parameters of PSR J1802−2124 (one of the two precisely observed IMBPs), providing a possible evolutional path for its formation. We also speculate that the compact companion of HD 49798 (a hydrogen depleted sdO6 star) may be not a NS based on the present work.
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 (MS) star through Roche-lobe overflow, where the mass-transfer is driven by the gravitational wave radiation. Firstly, we followed the long-term evolution of the NS+He MS 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 $\sim 3.1-11.9\, \rm Myr^{-1}$ 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.
Numerical comparisons of five screened potentials of dense plasma, namely, ion-sphere, Thomas-Fermi, generalized exponential-cosine, Shukla-Eliasson (SE), and Akbari-Moghanjoughi (AM), are conducted. Bound energy levels of ions in quantum plasma are calculated using the five screened potentials. Our results show that AM and SE models are different from the other three models.
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