Search

Observations show that globular clusters might be among the best places to find millisecond pulsars. However, the globular cluster Terzan 6 seems to be an exception without any pulsar discovered, although its high stellar encounter rate suggests that it harbors dozens of them. We report the discovery of the first radio pulsar, PSR J1751-3116A, likely associated with Terzan 6 in a search of C-band (4-8 GHz) data from the Green Bank Telescope with a spin period of 5.33 ms and dispersion measure, DM$\simeq$383 ${\rm pc~cm^{-3}}$. The mean flux density of this pulsar is approximately 3 ${\rm \mu Jy}$. The DM agrees well with predictions from the Galactic free electron density model, assuming a distance of 6.7 kpc for Terzan 6. PSR J1751-3116A is likely an isolated millisecond pulsar, potentially formed through dynamical interactions, considering the core-collapsed classification and the exceptionally high stellar encounter rate of Terzan 6. This is the highest radio frequency observation that has led to the discovery of a pulsar in a globular cluster to date. While L-band (1-2 GHz) observations of this cluster are unlikely to yield significant returns due to propagation effects, we predict that further pulsar discoveries in Terzan 6 will be made by existing radio telescopes at higher frequencies., Comment: 8 pages, 3 figures, 2 tables. Accepted for publication in ApJL

Swift J1858.6$-$0814 (hereafter J1858) is a transient neutron star low-mass X-ray binary (NS LMXB). There is controversy regarding its donor mass derived from observations and theoretical calculations. In this paper, we adopt seven magnetic braking (MB) prescriptions suggested in the literature and different metallicity $Z$ to simulate the evolution of the LMXB. Our results show that, employing the MB model proposed by \citet{2012ApJ...746...43R} ("rm12"), the Convection And Rotation Boosted ("carb") model \citep{2019ApJ...886L..31V}, as well as the Intermediate ("inter") and Convection-boosted ("cboost") models in \citet{2019MNRAS.483.5595V} can match (part of) the observational parameters of J1858 well. We then apply our method to other observed LMXBs and find that the "rm12" and "inter" MB laws are most promising in explaining transient LMXBs. In comparison, the simulations with the "cboost" and "carb" MB laws are more inclined to reproduce persistent LMXBs and ultra-compact X-ray binaries (UCXBs), respectively. Our results, though subject to computational and/or observational bias, show that it is challenging to find a unified MB law that applies to the NS LMXB sub-populations simultaneously, indicating our lack of understanding of the true MB law. In addition, we explore the influence of various MB laws on the magnitude of the bifurcation periods in LMXBs., Comment: 15 pages, 7 figures, 1 table and 1 appendix, accepted for publication in ApJ

Millisecond pulsar + helium white dwarf (MSP+He WD) binaries are thought to have descended from neutron star (NS) low-mass X-ray binaries (LMXBs). The NSs accreted from the progenitors of the WDs and their spin periods were accordingly accelerated to the equilibrium periods of order milliseconds. Thus, the initial spin periods of the ``recycled" NSs are critically determined by the mass transfer rate in the LMXB phase. However, the standard picture neglects the possible spin-down of the NSs when the donor star decouples from its Roche lobe at the end of the mass transfer, as well as the transient behavior of most LMXBs. Both imply more complicated spin evolution during the recycling process. In this work, we perform detailed calculations of the formation of MSP+He WD binaries. We take into account three magnetic braking (MB) prescriptions proposed in the literature, and examine the effects of both persistent and transient accretion. We find that the spin periods are not sensitively dependent on the efficiency of MB, but are considerably influenced by the accretion mode. In comparison with persistent accretion, transient accretion leads to shorter and longer spin periods of the NSs in narrow and wide systems, respectively. This may help account for the measured spin periods of MSPs in wide binaries, which seem to be longer than predicted by the persistent accretion model., Comment: 14 pages, 5 figures, 1 table. Accepted for publication in MNRAS

IC 10 X-1 is one of close X-ray binaries containing a Wolf-Rayet donor, which can provide an evolutionary link between high-mass X-ray binaries and gravitational wave sources. It is still unclear about the precise nature of the accreting compact object in IC 10 X-1, although it looks more like a black hole than a neutron star. In this work, we use a binary population synthesis method to simulate the formation of IC 10 X-1 like binaries by assuming different common-envelope ejection efficiencies. This work represents a big step forward over previous studies since we adopt new criteria of mass-transfer stability. These criteria allow the formation of IC 10 X-1 like systems without experiencing common envelope evolution. Based on our calculations, we propose that the compact object in IC 10 X-1 is a black hole with mass of $\sim 10-30M_\odot$ and the progenitor evolution of this binary probably just experienced stable mass transfer., Comment: 17 pages, 10 figures, accepted by ApJ

Heartbeat stars (HBSs) with tidally excited oscillations (TEOs) are ideal astrophysical laboratories for studying the internal properties of the systems. In this paper, five new HBSs exhibiting TEOs are discovered using TESS photometric data. The orbital parameters are derived using a corrected version of Kumar et al.'s model based on the Markov Chain Monte Carlo (MCMC) method. The TEOs in these objects are examined, and their pulsation phases and modes are identified. The pulsation phases of the TEOs in TIC 266809405, TIC 266894805, and TIC 412881444 are consistent with the dominant $l=2$, $m=0$, or $\pm2$ spherical harmonic. For TIC 11619404, although the TEO phase is close to the $m=+2$ mode, the $m = 0$ mode cannot be excluded because of the low inclination in this system. The TEO phase in TIC 447927324 shows a large deviation ($>2\sigma$) from the adiabatic expectations, suggesting that it is expected to be a traveling wave rather than a standing wave. In addition, these TEOs occur at relatively low orbital harmonics, and we cautiously suggest that this may be an observational bias. These objects are valuable sources for studying the structure and evolution of eccentricity orbit binaries and extending the TESS HBS catalog with TEOs., Comment: 9pages, 5figures

Heartbeat stars (HBSs) are ideal astrophysical laboratories to study the formation and evolution of binary stars in eccentric orbits and the internal structural changes of their components under strong tidal action. We discover 23 new HBSs based on TESS photometric data. The orbital parameters, including orbital period, eccentricity, orbital inclination, argument of periastron, and epoch of periastron passage of these HBSs are derived by using a corrected version of Kumar et al.'s model based on the Markov Chain Monte Carlo (MCMC) method. The preliminary results show that these HBSs have orbital periods in the range from 2.7 to 20 days and eccentricities in the range from 0.08 to 0.70. The eccentricity-period relation of these objects shows a positive correlation between eccentricity and period, and also shows the existence of orbital circularization. The Hertzsprung-Russell diagram shows that the HBSs are not all located in a particular area. The distribution of the derived parameters suggests a selection bias within the TESS survey towards massive HBSs with shorter orbital periods, higher temperatures and luminosities. These objects are a very useful source to study the structure and evolution of eccentricity orbit binaries and to extend the TESS HBS catalog., Comment: 10 pages, 7 figures

4U 1954+31 is a high-mass X-ray binary (HMXB) that contains a neutron star and an M supergiant companion. The neutron star has a spin period of ~5.4 hr. The traditional wind-accreting model requires an ultra-strong magnetic field for the neutron star to explain its extremely long spin period, which seems problematic for the neutron star with an age of a few tens of million years. In this work, we take into account the unsteady feature of wind accretion, which results in alternation of the direction of the wind matter's angular momentum. Accordingly, the torque exerted by the accreted wind matter varies between positive and negative from time to time, and largely cancels out over long time. In such a scenario, neutron stars can naturally attain long spin periods without the requirement of a very strong magnetic field. This may also provide a reasonable explanation for the spin period distribution of long-period neutron stars in HMXBs., Comment: 9 pages, 6 figures, accepted for publication in MNRAS

In this paper, we use the information-theoretic approach to study curvature-dimension condition, rigidity theorems and entropy differential inequalities on Riemannian manifolds. We prove the equivalence of the ${\rm CD}(K, m)$-condition for $K\in \mathbb{R}$ and $m\in [n, \infty]$ and some entropy differential inequalities along the geodesics on the Wasserstein space over a Riemannian manifold. The rigidity models of the entropy differential inequalities are the $K$-Einstein manifolds and the $(K, m)$-Einstein manifolds with Hessian solitons. Moreover, we prove the monotonicity and rigidity theorem of the $W$-entropy along the geodesics on the Wasserstein space over Riemannian manifolds with CD$(0, m)$-condition. Finally, we compare our work with the synthetic geometry developed by Lott-Villani and Sturm.

In two papers entitled ``Two generalizations of almost perfect nonlinearity" and ``On the vector subspaces of $\mathbb F_{2^n}$ over which the multiplicative inverse function sums to zero", the first author has introduced and studied the notion of sum-freedom of vectorial functions, which expresses that a function sums to nonzero values over all affine subspaces of $\Bbb F_{2^n}$ of a given dimension $k\geq 2$, and he then focused on the $k$th order sum-freedom of the multiplicative inverse function $x\in \Bbb F_{2^n}\mapsto x^{2^n-2}$. Some general results were given for this function (in particular, the case of affine spaces that do not contain 0 was solved positively), and the cases of $k\in \{3,n-3\}$ and of $k$ not co-prime with $n$ were solved as well (negatively); but the cases of those linear subspaces of dimension $k\in [\![ 4;n-4]\!]$, co-prime with $n$, were left open. The present paper is a continuation of the previous work. After studying, from two different angles, the particular case of those linear subspaces that are stable under the Frobenius automorphism, we deduce from the second approach that, for $k$ small enough (approximately, $3\le k\leq n/10$), the multiplicative inverse function is not $k$th order sum-free. Finally, we extend a result previously obtained in the second paper mentioned above, and we deduce in particular that, for any even $n$ and every $2\leq k\leq n-2$, the multiplicative inverse function is not $k$th order sum-free., Comment: 17 pages, 2 tables

Traditional manual driving and single-vehicle-based intelligent driving have limitations in real-time and accurate acquisition of the current driving status and intentions of surrounding vehicles, leading to vehicles typically maintaining appropriate safe distances from each other. Yet, accidents still frequently occur, especially in merging areas; meanwhile, it is difficult to comprehensively obtain the conditions of road infrastructure. These limitations not only restrict the further improvement of road capacity but also result in irreparable losses of life and property. To overcome this bottleneck, this paper constructs a space-time global view of the road traffic system based on a real-time sharing mechanism, enabling both road users and managers to timely access the driving intentions of nearby vehicles and the real-time status of road infrastructure.

The fallback disk model is widely accepted to explain long-period neutron stars (NSs) which can't be simulated by magnetic dipole radiation. However, no confirmed detection of disk was found from the newly discovered long period pulsars GLEAM-X 162759.5-523504.3, GPM J1839-10 and the known slowest isolated NSs 1E 161348-5055. This might be that the disks have either been in noninteracting/inactive state where its emission is too weak to be detected or have been disrupted. In this work, we conduct simulations to examine the lifetime of supernova fallback disks around isolated neutron stars. We assume that the disk's mass varies in a self-similar way and its interaction with the NS occurs only in interacting/active state. Our results reveal that nearly all the interacting lifetimes for the disk are shorter than 0.1 Myr while the existence lifetimes are considerably longer., Comment: Accepted in ApJ, comments are welcome

Within the framework of the Einstein-Maxwell-Dilaton (EMD) model, which incorporates information on the equation of state and baryon number susceptibility from lattice results, we have conducted a comprehensive analysis of the potential energy, running coupling, and dissociation time for heavy quark-antiquark pairs using gauge/gravity duality. This study encompasses various systems, including pure gluon systems, 2 flavor systems, 2+1 flavor systems, and 2+1+1 flavor systems under finite temperature and chemical potential. The results reveal that the linear component of the potential energy diminishes as the flavor increases. It is also found that our results are extremely close to the recent lattice results for 2+1 flavors at finite temperature. Moreover, we have thoroughly investigated the dissociation distance and running coupling constant of quark-antiquark pairs to gain a comprehensive understanding of their behavior across various flavors. Finally, we have examined real-time dynamics of quark dissociation. The findings indicate that the dissociation time of quark-antiquark pairs is dependent on temperature, chemical potential, and flavor of the systems.

We reported a cyclic variation of $O-C$ diagram with a semi-amplitude of 0.0033 days and a period of 1.05 years for the pulsating eclipsing binary HZ Dra. The cyclic variation can be explained by the light travel-time effect via the presence of a close-in third body orbiting around HZ Dra in an elliptical orbit with a maximum semi-major axis of 0.92 au. Based on the W-D code, the contribution of the third light to the total system is determined to be 29 $\%$, which is in agreement with the estimated value. Our light curve modelling indicates an evolving hot and cool spot on the surface of the primary and secondary components, respectively. Their positions are roughly symmetrical to the inner Lagrangian point L1, which could be used to explain the variation in the O$^{'}$Connell effect. Our frequency analysis detects 1 radial p-mode, 7 non-radial p-modes and 1 non-radial g-mode. In addition, a total of 6 multiplets are identified, spaced by the orbital frequency, which can be explained as a tidally split mode caused by the equilibrium tides of the close binary system with a circular orbit. These pulsating features suggest that the primary of HZ Dra is a $\delta$ Scuti star, pulsating in both p- and g-mode and influenced by tidal forces., Comment: 15 pages, 11 figures. The first version is Under Review in ApJ

We report the photometric analysis of SU UMa based on the observations of the Transiting Exoplanet Survey Satellite (TESS). TESS has released a large amount of data, which contains the light curves of a complete superoutburst and three normal outbursts of SU UMa. Based on the observations, the evolution of superhumps during the superoutburst was analyzed. By using the O - C method, the three stages were determined, and the superhump period for each stage was calculated. The mass ratio $q=0.137 (1)$ was estimated based on the stage A superhump method. A periodic oscillation with a period of 2.17(9) days was found in the superhump minimum O - C diagram, which is related to the precession of the accretion disk. We investigated the frequency information of quasiperiodic oscillations (QPOs) in the light curves. An ultralong period QPO of 0.18 days at the time of normal outburst and two ultralong periods QPOs of 0.19 days and 0.285 days in quiescence were found. No QPO was found in the superoutburst., Comment: 13 pages, 6 figures

We present the eclipsing Heartbeat Star KIC 9704906 with tidally excited oscillations (TEOs) and gamma Doradus/delta Scuti hybrid pulsations. The derived parameters show that it has an orbital period of $P$=8.7529108(1) days, a high eccentricity of $e$=0.467(3), and a high inclination of $i$=78$^{\circ}$.81(6). The mass ratio $q$=0.981(5), the relative radii (radius divided by semi-major axis) $r_1$=0.0639(2), and $r_2$=0.0715(4) indicate that the secondary component has a less mass and a larger radius, and may have evolved off the main sequence. The eight derived TEO candidates, $n$ = 3, 4, 5, 6, 7, 12, 40, and 44 harmonics, are consistent with or close to the dominant spherical harmonic $l=2$, $m=0$, or $\pm2$, assuming that the spin and orbital axes are aligned, and the pulsations are adiabatic and standing waves. We also identify ten independent frequency candidates, but one of them, $\mathit{f_{7}}$, is more like a modulation of a quasi-periodic signal and the orbits. According to the g-mode frequencies, we find that the rotation period of one component is 11.52(29) days. Although the masses and radii cannot be further constrained due to the lack of sufficient high-precision spectra, the fascinating phenomena in the Fourier spectra are evident and valuable in this system.

In this work, we discuss the description of neutral $\Sigma$ baryons with $I(J^P)=1(1/2^+)$ and $I(J^P)=1(3/2^+)$ using two bottom-up approaches: the deformed background and the static dilaton. In both models, we consider a non-linear Regge trajectory extension motivated by the \emph{strange} nature that $\Sigma$ baryons have. We found that both models describe these systems with an RMS error smaller than 10 $\%$. We also perform a configurational entropy calculation in both models to discuss hadronic stability.

In this paper, we give a new derivation of the incompressible Navier-Stokes equations on a compact Riemannian manifold $M$ via the Bellman dynamic programming principle on the infinite dimensional group of volume preserving diffeomorphisms $G={\rm SDiff}(M)$. In particular, when the viscosity vanishes, we give a new derivation of the incompressible Euler equation on a compact Riemannian manifold. The main result of this paper indicates an interesting relationship between the incompressible Navier-Stokes equations on $M$ and the Hamilton-Jacobi-Bellman equation on $G={\rm SDiff}(M)$.

Neutron star$-$white dwarf (NSWD) binaries are one of the most abundant sources of gravitational waves (GW) in the Milky Way. These GW sources are the evolutionary products of primordial binaries that experienced many processes of binary interaction. We employ a binary population synthesis method to investigate the properties of Galactic NSWD binaries detectable by the Laser Interferometer Space Antenna (LISA). In this paper, only the NSWD systems with a COWD or ONeWD component are included. We consider various models related to mass transfer efficiencies during primordial binary evolution, supernova explosion mechanisms at NS formation, common envelope ejection efficiencies, and critical WD masses that determining the stability of mass transfer between WDs and NSs. Based on our calculations, we estimate that tens to hundreds of LISA NSWD binaries exist in the Milky Way. We find that the detection of LISA NSWD binaries is able to provide profound insights into mass transfer efficiencies during the evolution of primordial binaries and critical WD masses during mass transfer from a WD to an NS., Comment: 11 pages, 5 figures, 1 table, accepted to MNRAS

Magnetars and central compact objects (CCOs) are subgroups of neutron stars that show a number of properties distinguished from canonical radio pulsars. We performed radio observations of three magnetars SGR 0418+5729, 1E 2259+586, 4U 0142+61, and a CCO PSR J1852+0040 with the Fivehundred-meter Aperture Spherical radio Telescope (FAST) at 1.25 GHz, aiming to search for radio pulsations in their quiescent states. During two observation epochs, no radio pulses have been detected towards any target above a significance of signal-to-noise ratio (S/N) = 7 from either the direct folding or blind search. We provided the most stringent upper limit of radio flux (<~ 2 -- 4 $\mu$Jy) for the magnetars and the CCO. For the magnetars with long periods, the real upper limits are likely an order of magnitude larger due to the red noise. The deep radio observations suggest that these magnetars and the CCO are indeed radio-quiet sources or unfavorably beamed., Comment: 7 pages, 3 figures, 2 tables; accepted for publication in ApJ

The detection of gravitational wave events has stimulated theoretical modeling of the formation and evolution of double compact objects (DCOs). However, even for the most studied isolated binary evolution channel, there exist large uncertainties in the input parameters and treatments of the binary evolution process. So far, double neutron stars (DNSs) are the only DCOs for which direct observations are available through traditional electromagnetic astronomy. In this work, we adopt a population synthesis method to investigate the formation and evolution of Galactic DNSs. We construct 324 models for the formation of Galactic DNSs, taking into account various possible combinations of critical input parameters and processes such as mass transfer efficiency, supernova type, common envelope efficiency, neutron star kick velocity, and pulsar selection effect. We employ Bayesian analysis to evaluate the adopted models by comparing with observations. We also compare the expected DNS merger rate in the Galaxy with that inferred from the known Galactic population of Pulsar-NS systems. Based on these analyses we derive favorable range of the aforementioned key parameters., Comment: 29 pages, 9 figures, 2 tables, accepted by ApJ

The popularity and diffusion of wearable devices provides new opportunities for sensor-based human activity recognition that leverages deep learning-based algorithms. Although impressive advances have been made, two major challenges remain. First, sensor data is often incomplete or noisy due to sensor placement and other issues as well as data transmission failure, calling for imputation of missing values, which also introduces noise. Second, human activity has multi-scale characteristics. Thus, different groups of people and even the same person may behave differently under different circumstances. To address these challenges, we propose a multilevel heterogeneous neural network, called MHNN, for sensor data analysis. We utilize multilevel discrete wavelet decomposition to extract multi-resolution features from sensor data. This enables distinguishing signals with different frequencies, thereby suppressing noise. As the components resulting from the decomposition are heterogeneous, we equip the proposed model with heterogeneous feature extractors that enable the learning of multi-scale features. Due to the complementarity of these features, we also include a cross aggregation module for enhancing their interactions. An experimental study using seven publicly available datasets offers evidence that MHNN can outperform other cutting-edge models and offers evidence of robustness to missing values and noise. An ablation study confirms the importance of each module., Comment: 14 pages, 7 figures

Tidally excited oscillations (TEOs) in Heartbeat Stars (HBSs) are an essential probe of the internal properties of the systems, but their potential has yet to be fully exploited. Based on the orbital parameters of TEO candidates from our previous works, we identify the pulsation phases and amplitudes of TEOs in fourteen Kepler HBSs. Most pulsation phases of most systems can be explained by the dominant being $l=2$, $m=0$, or $\pm2$ spherical harmonic, assuming that the spin and orbital axes are aligned, and the pulsations are adiabatic and standing waves. The largest deviation ($>6\sigma$) occurs in KIC 8459354, which can be explained by the spin-orbit misalignment, and KIC 5877364 has a similar scenario. For KIC 11122789, almost half of the harmonics show large deviations; we cautiously suggest that these harmonics may not be considered TEO candidates. A similar scenario also exists in KIC 6290740. This phases and mode identification approach can also be used inversely to verify the TEO candidates derived by the Fourier analysis. Furthermore, the harmonics with large deviations ($>2\sigma$) in KIC 4377638, KIC 5090937, and KIC 11403032 can be expected to be travelling waves rather than standing waves. In addition, we also suggest that the apsidal motion could cause large deviations in TEO phases from theoretical values., Comment: published on MNRAS

TV Col is a long-period eclipsing intermediate polar (IPs) prototype star for the negative superhump (NSH) system. We investigate the eclipse minima, eclipse depth, and NSH amplitude based on TESS photometry. Using the same analytical method as SDSS J081256.85+191157.8, we find periodic variations of the O-C for eclipse minima and NSH amplitudes with periods of 3.939(25) d and 3.907(30) d, respectively. The periodic variation of the NSH amplitude of TV Col confirms that periodic NSH amplitude changes in response to the tilted disk precession may be universal, which is another evidence that the origin of the NSHs is related to the tilted disk precession. We suggest that the NSH amplitude variation may be similar to the superorbital signal, coming from the periodic change in visual brightness of the energy released by streams touching the tilted disk with tilted disk precession. Finally, we find for the first time that the eclipse depth exhibits bi-periodic variations with periods of P1 = 3.905(11) d and P2 = 1.953(4) d, respectively. P2 is about half of P1 and the disk precession period (P1~ Pprec ~ 2 * P2). We suggest that P1 may come from the periodic change in the brightness of the eclipse center due to tilted disk precession, while P2 may come from two accretion curtains precessing together with the tilted disk, but more verification and discussion are necessary. The discovery of bi-periodic variations in eclipse depth provides a new window for studying IPs and tilted disk precession., Comment: 18 pages, 7 figures, 3 tables; Accepted for publication in The Astrophysical Journal

Electron-capture supernovae (EC-SNe) provide an alternative channel for producing neutron stars (NSs). They play an important role in the formation of double NS (DNS) systems and the chemical evolution of galaxies, and contribute to the NS mass distribution in observations. It is generally believed that EC-SNe originate from $e$-captures on $\rm^{24}Mg$ and $\rm^{20}Ne$ in the massive degenerate oxygen-neon (ONe) cores with masses close to the Chandrasekhar limit ($M_{\rm Ch}$). However, the origin of EC-SNe is still uncertain. In this paper, we systematically studied the EC-SNe in NS+He star systems by considering the explosive oxygen burning that may occur in the near-$M_{\rm Ch}$ ONe core. We provided the initial parameter spaces for producing EC-SNe in the initial orbital period $-$ initial He star mass (log$P_{\rm orb}^{\rm i}-M_{\rm He}^{\rm i}$) diagram, and found that both $M_{\rm He}^{\rm i}$ and minimum $P_{\rm orb}^{\rm i}$ for EC-SNe increase with metallicity. Then, by considering NS kicks added to the newborn NS, we investigated the properties of the formed DNS systems after the He star companions collapse into NSs, such as the orbital periods, eccentricities and spin periods of recycle pulsars ($P_{\rm spin}$), etc. The results show that most of the observed DNS systems can be produced by NS kicks of $\lesssim50\rm\,km\,s^{-1}$. In addition, we found that NSs could accrete more material if the residual H envelope on the He star companions is considered, which can form the mildly recycled pulsars ($P_{\rm spin}\sim20\,$ms) in DNS systems., Comment: 13 pages, 14 figures, 3 tables, accepted for publication in MNRAS, comments welcome!

Negative superhumps (NSHs) are signals a few percent shorter than the orbital period of a binary star and are considered to originate from the reverse precession of the tilted disk. Based on TESS photometry, we find nine new cataclysmic variable stars (CVs) with NSHs. Three (ASAS J1420, TZ Per, and V392 Hya) of these stars similar to AH Her still have NSHs during dwarf nova outbursts, and the NSH amplitude varies with the outburst. The variation in the radius of the accretion disk partially explains this phenomenon. However, it does not explain the rebound of the NSH amplitude after the peak of the outburst and the fact that the NSH amplitude of the quiescence is sometimes not the largest, and it is necessary to combine the disk instability model (DIM) and add other ingredients. Therefore, we suggest that the variation of NSH amplitude with outburst can be an essential basis for studying the origin of NSHs and improving the DIM. The six ( ASASSN-V J1137, ASASSN-V J0611, 2MASS J0715, LAMOST J0925, ASASSN-17qj, and ZTF18acakuxo) remaining stars have been poorly studied, and for the first time we determine their orbital periods, NSHs and Superorbital signal (SOR) periods. The NSH periods and amplitudes of ASASSN-V J1137 and ASASSN-17qj vary with the SOR, and based on the comparison of the observations with the theory, we suggest that a single change in tilted disk angle does not explain the observations of the SOR and that other ingredients need to be considered as well., Comment: 21 pages, 12 figures, accepted for publication in the Astrophysical Journal

We will develop some elements in stochastic analysis in the Wasserstein space $\mathbb{P}_2(M)$ over a compact Riemannian manifold $M$, such as intrinsic It$\^o$ formulae, stochastic regular curves and parallel translations along them. We will establish the existence of parallel translations along regular curves, or stochastic regular curves in case of $\mathbb{P}_2(\mathbb{T})$. Surprisingly enough, in this last case, the equation defining stochastic parallel translations is a SDE on a Hilbert space, instead of a SPDE.

An irreducible polynomial $f\in\Bbb F_q[X]$ of degree $n$ is {\em normal} over $\Bbb F_q$ if and only if its roots $r, r^q,\dots,r^{q^{n-1}}$ satisfy the condition $\Delta_n(r, r^q,\dots,r^{q^{n-1}})\ne 0$, where $\Delta_n(X_0,\dots,X_{n-1})$ is the $n\times n$ circulant determinant. By finding a suitable {\em symmetrization} of $\Delta_n$ (A multiple of $\Delta_n$ which is symmetric in $X_0,\dots,X_{n-1}$), we obtain a condition on the coefficients of $f$ that is sufficient for $f$ to be normal. This approach works well for $n\le 5$ but encounters computational difficulties when $n\ge 6$. In the present paper, we consider irreducible polynomials of the form $f=X^n+X^{n-1}+a\in\Bbb F_q[X]$. For $n=6$ and $7$, by an indirect method, we are able to find simple conditions on $a$ that are sufficient for $f$ to be normal. In a more general context, we also explore the normal polynomials of a finite Galois extension through the irreducible characters of the Galois group., Comment: 28 pages

Heartbeat stars (HBSs) with tidally excited oscillations (TEOs) are ideal laboratories for studying the effect of equilibrium and dynamical tides. However, studies of TEOs in Kepler HBSs are rare due to the need for better modeling of the equilibrium tide in light curves. We revisit the HBSs in our previous work and study the TEOs in these HBSs based on the derived orbital parameters that could express the equilibrium tide. We also compile a set of analytic procedures to examine the harmonic and anharmonic TEOs in their Fourier spectra. The TEOs of 21 HBSs have been newly analyzed and presented. Twelve of these HBSs show prominent TEOs (signal-to-noise ratio of the harmonics $S/N \ge 10$). The relation between the orbital eccentricities and the harmonic number of the TEOs shows a positive correlation. The relation between the orbital periods and the harmonic number also shows a positive correlation. Furthermore, the distribution of HBSs with TEOs in the Hertzsprung-Russell (H-R) diagram shows that TEOs are more visible in hot stars with surface effective temperatures $T$ $\gtrsim$ 6500 K. These samples may also be valuable targets for future studies of the effect of tidal action in eccentric orbits., Comment: Published on ApJ

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

Helium white dwarfs (HeWDs) are thought to form from low-mass red giant stars experiencing binary interaction. Because the helium core mass of a red giant star is closely related to the stellar radius, there exists well-known relation between the orbital period ($P_{\rm orb}$) and the mass ($M_{\rm WD}$) of the HeWDs, which is almost independent of the type of the companion star. Traditional derivation of the $M_{\rm WD}$-$P_{\rm orb}$ relation generally neglected the effect of wind mass loss from the red giants, while observations show that wind mass loss from red giants in binary systems is systematically higher than that from isolated stars. In this work, we calculate binary evolution with tidally enhanced stellar wind (TEW) and find that it causes significantly scatter of the traditional $M_{\rm WD}$-$P_{\rm orb}$ relation. The TEW can prevent the red giants from overflowing their Roche lobes and slow down the growth of the helium core, leaving a lower-mass HeWD for given orbital period. This scenario may account for some of the HeWD binaries that deviate from the traditional $M_{\rm WD}$-$P_{\rm orb}$ relation. However, we point out that observations of more HeWD binaries in wide orbits are needed to test the TEW model and to constrain the enhanced wind factor., Comment: 11 pages, 8 figures, 3 tables, accepted for publication in MNRAS, comments are welcome!

Observations of elliptical galaxies suggest that black holes (BHs) might serve as dark energy candidates, coupled to the expansion of the Universe. According to this hypothesis, the mass of a BH could increase as the Universe expands. BH low-mass X-ray binaries (LMXBs) in the Galactic disk were born several gigayears ago, making the coupling effect potentially significant. In this work, we calculate the evolution of BH binaries with a binary population synthesis method to examine the possible influence of cosmologically-coupled growth of BHs, if it really exists. The measured masses of the compact objects in LMXBs show a gap around $\sim 2.5-5~{\rm M_\odot}$, separating the most massive neutron stars from the least massive BHs. Our calculated results indicate that, considering the mass growth seem to (partially) account for the mass gap and the formation of compact BH LMXBs, alleviating the challenges in modeling the formation and evolution of BH LMXBs with traditional theory. However, critical observational evidence like the detection of intermediate-mass black hole binaries is required to test this hypothesis., Comment: 10 pages, 4 figures, 3 tables, accepted for publication in ApJ, comments are welcome

It is widely accepted that quite a number of double compact objects (DCOs) in the Milky Way can be identified by future space-based gravitational wave (GW) detectors, while systematic investigations on the detection of the GW sources in nearby galaxies are still lacking. In this paper, we present calculations of potential populations of GW sources for all types of DCOs in the Local Group galaxy M31. For M31, we use an age-dependent model for the evolution of the metallicity and the star-formation rate. By varying assumptions of common-envelope ejection efficiencies and supernova-explosion mechanisms during binary evolution, we make predictions on the properties of DCOs that can be detected by the Laser Interferometer Space Antenna (LISA). Our calculations indicate that a few (a dozen) DCOs are likely to be observed by LISA during its 4 (10) yr mission. We expect that the sources with black-hole components are more likely to be firstly identified during a 4-yr mission since these binaries have relatively large chirp masses, while the systems with white-dwarf components dominate the overall population of detectable GW sources during a 10-yr mission. LISA can only detect very tight fast-merging systems in M31, corresponding to the peak of orbital period distribution from $\sim 2$ min for double white dwarfs to $\sim 20$~min for double black holes., Comment: 15 pages, 7 figures, 1 table, accepted by ApJ