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Zhanwen Han

Publications and source records attributed to Zhanwen Han.

At least 37 records · Page 2Linked to original sources

Radial Profiles of Binary Fraction in Elliptical Galaxies

The radial profile of binary fraction may vary with environment and is of significant importance for studying the formation mechanisms of binary stars and their dynamical evolution within globular clusters (GCs) and galaxies. However, existing studies remain limited to the Milky Way and its neighboring galaxies. Leveraging the method proposed by Zhang et al. for estimating the variation of binary fraction from integrated spectral features, we analyze a sample of 513 elliptical galaxies drawn from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey to measure their radial binary fraction profiles. Our results show that after accounting for the effect induced by radial variations in the stellar population (SP), the median SP-subtracted binary fraction, $r_{\rm b,sub}^{\rm med}$, becomes approximately flat. For nearly all elliptical galaxies in our sample, the variation in binary fraction relative to the galaxy center at $1R_e$ is less than 5%. No clear correlation is found between the binary fraction gradient and the gradients of SP properties. Moreover, we also compare differences between ultraviolet (UV) upturn and non-UV upturn galaxies. The overall binary fraction profiles and SP properties of the non-UV upturn galaxies in our sample are comparable to those of the UV upturn galaxies. This similarity may arise from the presence of residual star formation (RSF) in the non-UV upturn systems.

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Asteroseismic rotation rates of hot subdwarf B stars hint at transient accretion from leftover common envelope matter

Asteroseismology enabled measuring the rotation rate in the deep stellar interiors of stars across several evolutionary phases, advancing the theory of angular momentum transport in single stars from the main sequence to the white dwarf phase. However, binary stellar evolution products have not yet been studied in the context of angular momentum transport constrained by asteroseismology. Hot subdwarf B (sdB) stars can pulsate in non-radial modes, enabling probing of their internal rotation. Those in binary systems form through mass transfer, thus they can be used to probe theories of internal rotation in post-mass transfer stars. Here, we interpret observed asteroseismic core and envelope rotation rates of sdB stars in unsynchronised binary systems that formed through the common-envelope channel, using stellar evolution models of rotating sdB stars with internal magnetic fields. We find that when sdB stars form with the angular momentum content of red giant cores prior to common-envelope ejection, their predicted core rotation rates are two to ten times lower than measured asteroseismic rotation rates, and their envelope rotation rates are lower by two to five orders of magnitude. This suggests that the angular momentum content of sdB stars increases during their formation. Since sdB stars in close binary systems may host circumstellar matter from a past common-envelope ejection, we show that if they accrete a small amount of matter, the combination of internal magnetic fields with angular momentum transfer through accretion spins up both the core and envelope to match their measured asteroseismic rotation rates.

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Adiabatic Mass Loss In Binary Stars. VI. Massive Helium Binary Stars

The stability of binary mass transfer is a critical problem for binary evolution. We systematically calculate the adiabatic mass-loss model for naked helium stars with masses ranging from 10$M_{\odot}$ to 80$M_{\odot}$ to study the critical mass ratio ($q_\textrm{crit}$) of Wolf-Rayet binaries. We set up two prescriptions about Wolf-Rayet stellar wind and consider the isotropic re-emission effect during adiabatic mass loss. Results of the critical mass ratio for conserved dynamically unstable mass transfer show that most of the no-wind helium stars on the main sequence (HeMS) have $0.7<q_\textrm{crit}<3.0$ and on the Hertzsprung gap (HeHG) have $1.5<q_\textrm{crit}<27$. With the Wolf-Rayet star wind effect, the $q_\textrm{crit}$ gets lower on a certain evolutionary stage. With the isotropic re-emission effect, the $q_\textrm{crit}$ gets larger for early-evolutionary stage helium stars and lower for late-evolutionary stage helium stars. Based on fully non-conserved mass transfer, the criteria for HeMS stars are $1.0<q_\textrm{crit}<2.8$ and HeHG stars are $1.5<q_\textrm{crit}<5.0$. Compared with the widely used criterion $q_\textrm{crit}=3$ (HeMS) and $q_\textrm{crit}=4$ (HeHG), our result becomes more unstable for the HeMS stars and more stable for the HeHG stars. Our work could be applied to the binary mass transfer stage of massive helium binaries, such as Wolf-Rayet star binaries and high mass X-ray binaries with Wolf-Rayet star companions. It can be applied to the binary population synthesis studies for the formation of special objects, such as double black hole mergers.

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A Path to Constraints on Common Envelope Ejection in Massive Binaries: Full Evolutionary Reconstruction of Three Black Hole X-ray Binaries

The massive binary common envelope (CE) phase plays a pivotal role in the formation of close black hole/neutron star (BH/NS) binaries, yet significant uncertainties remain in our understanding of this process. In this study, we aim to constrain the massive binary CE phase by systematically reconstructing three observed BH X-ray binaries (BHXBs): GRO J1655-40, SAX J1819.3-2525, and 4U 1543-47. Through comprehensive binary evolution simulations and parametric supernova (SN) modeling, we establish lower limits for the CE efficiency parameters under different energy considerations within the standard energy formalism. Specifically, we derive minimum values for three cases: $α_{\rm 0.5U}$ and $α_{\rm U}$ representing CE efficiencies with half and all of the internal energy contributing to the envelope ejection, respectively, and $α_{\rm H}$ accounting for the envelope's enthalpy. Our analysis reveals that the self-consistent formation of these three BHXBs requires CE efficiency parameters satisfying: $α_{\rm 0.5U}\gtrsim 6.7$, $α_{\rm U}\gtrsim 4.2$ and $α_{\rm H}\gtrsim 1.7$. Notably, we find no viable solutions with CE efficiency values below unity, even when considering the most extreme scenarios in which the envelope binding energy is significantly reduced through enthalpy inclusion. {Our results strongly imply that either additional energy sources are required, or the formalism itself must be revised.} Furthermore, we quantitatively assess the impact of BH natal kicks on our results. A key finding is that 4U 1543-47's formation requires substantial natal kicks ($\gtrsim 50 \;\rm km/s$), as lower kick velocities are incompatible with isolated binary evolution.

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A New Pathway to Single Be Stars: Ejected Companions from Type Ia Supernovae

Be stars are rapid rotators generally produced by binary interactions. The single Be stars in the observations pose challenges to the Be star formation theory. In this paper, we propose a new pathway for the formation of single Be stars, in which the Be star is taken as the ejected companion star from a Type Ia supernova (SN Ia) explosion. Recent numerical simulations suggest that explosive oxygen burning, initiated via the convective Urca process in certain helium (He) stars near the Chandrasekhar mass limit, can set off a SN Ia. Based on this proposition, we further demonstrate that about $0.4\%$ of He star + main-sequence (MS) star binaries may evolve into single Be stars, where the MS star is spun up due to the mass accretion from the He star, and then the He star explodes as a SN Ia. We employ detailed binary evolutionary simulations and find the parameter space that would produce single Be stars via the SN Ia channel. Around $22\%$ of Be stars from the SN Ia progenitor channel exhibit peculiar tangential velocities exceeding $24\ \rm km/s$, classifying them as runaway stars. This suggests that the SN Ia channel plays a meaningful role in forming single Be stars, particularly within the runaway star population.

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Stellar Parameters and Orbital Period Estimates for Composite-Spectrum sdB+MS Binaries from LAMOST

Hot subdwarf (sdB) stars in binary systems with main-sequence (MS) companions provide valuable insights into mass transfer and envelope ejection processes in binary evolution. Their mass ratios, orbital periods, and stellar properties encode key information about their evolutionary histories. In this work, we analyze a sample of 123 composite-spectrum sdB+MS binaries identified from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope Low-Resolution Survey (LAMOST-LRS) Data Release (DR) 8. We adopt atmospheric parameters from spectral decomposition and estimate stellar masses and radii using theoretical evolutionary tracks. Radial velocities for both the hot subdwarfs and cool companions are measured independently through cross-correlation with synthetic templates. Orbital periods are statistically estimated using single-epoch RV separations and a Monte Carlo method that accounts for random inclination and orbital phase. We find that sdB masses are narrowly distributed around 0.5 Msun, consistent with expectations for core helium-burning stars, while MS companion masses span 0.6-1.9 Msun, with most falling between 1.0 and 1.4 Msun. The inferred orbital-period distribution shows a clear concentration toward long periods, broadly consistent with expectations for binaries formed through stable Roche-lobe overflow. Given that our sample consists of composite-spectrum sdB binaries, mainly sdB+FGK systems, the prevalence of long periods is largely driven by observational selection effects rather than the intrinsic period distribution of the sdB binary population. This study provides one of the largest uniform catalogs of composite spectrum sdB binaries to date, offering new observational constraints on their physical properties and formation channels.

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SN2024abfl: A Low-Luminosity Type IIP Supernova at the Low-Mass End of Core Collapse

We present optical photometric and spectroscopic observations of the low-luminosity (LL) Type IIP supernova SN\,2024abfl. The distance to its host galaxy is highly uncertain, with independent estimates of $9.5^{+2.3}_{-2.4}$ Mpc and $15.0^{+8.9}_{-1.9}$ Mpc. Even adopting the larger distance, the inferred plateau luminosity is only $\sim 10^{41}\rm erg\,s^{-1}$, placing SN 2024abfl at the extreme faint end of SNe IIP population. Its light curve exhibits a long-lasting plateau of approximately 110 days. The spectra show exceptionally low expansion velocities, with the \FeII\, velocity of $\sim1200\,\rm km\,s^{-1}$ at 50 days after the explosion, significantly lower than the typical values of $\sim2000-5500\,\rm km\,s^{-1}$ observed in SNe IIP, placing SN\,2024abfl among the slowest-expanding LL SNe IIP. Bolometric modeling yields a synthesized $^{56}$Ni mass of $\sim0.002-0.004\,\rm M_\odot$, though this estimate remains subject to significant uncertainty owing to the poorly constrained distance. Considering the plateau color and duration, the magnitude drop from plateau to tail, and the progenitor luminosity, we favor a low-mass core-collapse origin for SN\,2024abfl.

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Formation of black holes from He stars

Massive He stars are potential candidates of type Ib/c supernova (SN) progenitors. Understanding their final fates remains a key issue in astrophysics. In this work, we investigate the evolution of He stars with initial masses from 5 $M_\odot$ to 65 $M_\odot$, focusing on the presupernova (pre-SN) core structures to assess their explodability. Our simulations indicate that the final core structure is determined by the CO core mass and the central 12C mass fraction at the end of core He burning, affecting the properties of central C-burning and the locations of convective shells. The location of the last convective C-burning shell sets the mass of the C-free core, constraining the iron core mass and compactness. We found that the final compactness and iron core mass exhibit non-monotonic behavior with initial mass, suggesting that the boundary between neutron star and black hole formation is not a simple mass threshold. This is due to core C/Ne burning becoming neutrino dominated. This process drives stronger core contraction, ultimately increasing the iron core mass and the final compactness. In contrast, earlier core Ne/O/Si ignition and shell mergers inhibit core contraction, reducing both the iron core mass and final compactness. We also discuss the effects of metallicity and overshooting on the pre-SN core structure. These factors potentially affect the explodability of progenitors.

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Expected evolution of the binary system ATLAS J1138-5139

ATLAS J1138-5139 is a newly detected ultra-compact double white dwarf (DWD) system which is composed of a $1.02\,M_{\odot}$ carbon-oxygen white dwarf (CO WD) and a $0.24\,M_{\odot}$ helium (He) WD with an orbital period of about 27.68 min, making it one of the shortest-period DWD systems known. The future evolution and final fate of this system remain unexplored. In this work, we investigate the evolution of ATLAS J1138-5139 with the one-dimensional stellar evolution code Modules for Experiments in Stellar Astrophysics (MESA). We find that ATLAS J1138-5139 will evolve into an AM Canum Venaticorum (AM CVn) system in about \sim 6.3 Myr. Afterwards, the transferred material from the He WD companion start to build up to form a He shell near the surface of the CO WD. This accumulated He-shell masses can be up to approximately $0.12\,M_{\odot}$, which is likely to trigger a double-detonation (DDet) explosion of the CO WD. We therefore expect that ATLAS J1138-5139 will likely explode as a type Ia supernova eventually through the DDet explosion mechanism. Moreover, our calculations show that ATLAS J1138-5139 will be a promising target for gravitational-wave (GW) detection by future detectors like LISA, Tianqin and Taiji.

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The environmental dependence of mid-IR luminous dusty Supernovae

Using the Spitzer and WISE images, we discovered 42 mid-IR luminous dusty supernovae with local integral-field spectroscopy data. The observed mid-IR emission indicates the presence of newly formed dust, or pre-existing dust heated by the radiation from the supernovae or circumstellar medium interactions. We carried out a systematic analysis of the supernova host environments and their dust properties, for understanding the dust-veiled exploding stars, and whether such an intense dust production process is associated with their local environments. We find that dusty supernovae prefer the locations with higher EW(Hα), lower metallicity, and heavier host extinctions compared to typical SN types, and they show the same increasing sequence in the values of EW(Hα) and oxygen abundance from hydrogen-rich, type IIn and hydrogen-poor dusty supernovae. These differences in environmental properties of different dusty SN types indicate the diversity of their progenitors. We also found that one marginal correlation is a negative correlation between the SN dust mass and star formation rate. This means that SNe would be more mid-IR luminous and more dust-rich at the region with lower star formation rate. However, the SN dust mass show no correlation with the metallicity and the host extinction, which were thought to be key factors affecting the mass-loss history of progenitors and the CSM environment of SNe. Therefore, the dust formation process in SNe might be insensitive to metallicity and the dust condition of their host environments.

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BayeSED-GALAXIES II. Bayesian full spectrum analysis of galaxies and application in the CSST wide-field slitless spectroscopy survey

The China Space Station Telescope (CSST) will conduct wide-field multiband photometric imaging and slitless spectroscopic surveys, advancing cosmology and galaxy evolution studies. Achieving CSST's cosmological goals requires precise redshifts ($σ_{\rm NMAD}\lesssim 0.002-0.005$) from low-resolution ($R\sim200$) and potentially blended slitless spectra. We present BayeSED3, extended for Bayesian full-spectrum analysis, including nebular emission modeling (via \textsc{Cloudy}) and a Bayesian treatment of the model scaling factor, improving reliability over optimization methods for low SNR spectra. Validated on realistic mock data generated with the CESS emulator (median SNR=1.65, including instrumental and self-blending effects), our method achieves excellent redshift precision with three-band (GU+GV+GI) spectroscopy: $σ_{\rm NMAD}=0.0008$ ($\sim$80% success) for star-forming and $σ_{\rm NMAD}=0.0015$ ($\sim$50% success) for quiescent galaxies. Stellar mass ($σ_{\rm NMAD}\approx0.015$ dex for SF, $\approx0.016$ dex for quiescent) and SFR ($σ_{\rm NMAD}\approx0.05$ dex for SF, especially at SNR>1) are reliably recovered. Self-blending increases scatter by $\gtrsim30%$, but combining spectroscopy with CSST's seven-band photometry significantly improves accuracy, especially for quiescent galaxies and data-limited cases. Single-band spectroscopy plus photometry yields reasonable redshifts: GU+photometry is limited, GI+photometry gives >60% (SF) and >40% (quiescent) success at $σ_{\rm NMAD}\lesssim0.002$, GV+photometry gives >35% (SF) and $\sim$40% (quiescent) at similar precision. The Bayesian framework offers a powerful method for accurate galaxy characterization, enhancing CSST's scientific outcomes despite the challenges of slitless spectroscopy.

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Pre-Supernova Eruptions Triggered by Sudden Energy Deposition in Low-Mass Core-Collapse Supernova Progenitors

In low-mass core-collapse supernova (CCSN) progenitors, nuclear burning beyond oxygen can become explosive under degenerate conditions, triggering eruptive mass loss before the final explosion. We investigate such pre-SN eruptions using \texttt{SNEC} hydrodynamic simulations and realistic stellar models, parameterizing the nuclear energy deposition as a fraction of the binding energy of the combined He layer and H-rich envelope. For the lowest-mass model (9 $M_\odot$), the ejecta mass ($M_{\rm ej}$) scales with the energy gained by the H-rich envelope via a power law (index$\sim$3.5). Across 9-10 $M_\odot$, this relation shows limited scatter within a factor of $\sim$2.6, enabling an estimation of the gained energy from $M_{\rm ej}$. The shock passage also flattens the bound envelope, which can affect the SN light curve morphology and provide another diagnostic for the eruption. Then, we compute the associated precursor light curves for the 9 $M_\odot$ model with the multi-group radiative-transfer code \texttt{STELLA}. These signals are typically faint, with bolometric luminosities of $\sim10^{39}$ erg s$^{-1}$ lasting hundreds of days. Their cool black-body spectra make them brighter in the infrared, yet several magnitudes fainter than observed pre-SN precursors at the threshold for full envelope ejection. To aid future studies, we make our post-eruption stellar profiles and precursor light curves publicly available.

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The Formation of Electron-capture Supernovae: A Review

It is generally believed that the electron-capture reactions happen when the oxygen-neon (ONe) cores grow in masses close to the Chandrasekhar limit, leading to the formation of neutron stars (NSs) via electron-capture supernovae (EC-SNe). EC-SNe are predicted to be the most likely short-lived and faint optical transients, and a small ejecta mass is expected during the collapse. This kind of SNe provide an alternative channel for producing isolated NSs and NS systems, especially for the formation of X-ray binaries and double NSs. Although EC-SNe were proposed ~45 yr ago, there are still some uncertainties for the origin of EC-SNe. In this article, we review recent studies on the two classic progenitor channels of EC-SNe, i.e., the single star channel and the binary star channel. In the single star channel, EC-SNe can happen in super asymptotic giant branch stars or He stars, whereas in the binary star channel EC-SNe can occur in He stars in binaries (involving He star+MS systems and NS+He star systems) or accretion-induced collapse in white dwarf binaries (involving the single-degenerate scenario and the double-degenerate scenario). Recent progress on the two progenitor channels is discussed, including the initial parameter range for EC-SNe, the evolutionary paths to EC-SNe, related objects and some observational constraints, etc. We also make some discussions on the possible candidates for EC-SNe in this article, and the impacts of EC-SNe on some research fields, e.g., the properties of NSs, double NS population and chemical products, etc. We also discuss the differences between EC-SNe and ultra-stripped SNe in this article. Research on EC-SNe is at a pivotal stage, with key theoretical uncertainties and observational challenges requiring integrated modeling and multi-wavelength observations for robust identification.

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Formation of Be stars via wind accretion: Case study on Black hole + Be star binaries

Be stars are rapidly rotating main-sequence (MS) stars that play a crucial role in understanding stellar evolution and binary interactions. In this letter, we propose a new formation scenario for black hole (BH) + Be star binaries (hereafter BHBe binaries), where the Be star is produced through the Wind Roche Lobe Overflow (WRLOF) mechanism. Our analysis is based on numerical simulations of the WRLOF process in massive binaries, building upon recent theoretical work. We demonstrate that the WRLOF model can efficiently form BHBe binaries under reasonable assumptions on stellar wind velocities. Using rapid binary population synthesis, we estimate the population of such systems in the Milky Way, predicting approximately $\sim$ {1800-3200} currently existing BHBe binaries originating from the WRLOF channel. These systems are characterized by high eccentricities and exceptionally wide orbits, with typical orbital periods exceeding 1000 days and a peak distribution around $\sim$10000 days. Due to their long orbital separations, these BHBe binaries are promising targets for future detection via astrometric {and interferometric} observations.

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The diverse morphology of gravitational wave signals from merging neutron-star white-dwarf binaries

In sufficiently compact neutron star-white dwarf (NSWD) binary systems, orbital decay means the white dwarf eventually fills its shrinking Roche lobe, initiating a phase of mass transfer. The exchange of angular momentum-both internal and external-plays a critical role in determining the binary's evolutionary outcome. For neutron stars with relatively low magnetic fields and spin frequencies, whether the orbital separation continues to shrink depends on the interplay between gravitational wave (GW) radiation and mass transfer dynamics. We compute the orbital evolution of NSWD binaries across a broad parameter space, incorporating four key variables. Our results reveal distinct boundaries in the NS-WD mass-mass diagram: binaries with white dwarf masses above these thresholds undergo rapid orbital decay and direct coalescence. The dependence of these boundaries on system parameters indicates that Roche-lobe-filling NSWD binaries can follow multiple evolutionary pathways -- a phenomenon we refer to as branched or polymorphic evolution. NSWD binary systems emit strong and diverse GW signals, many of which would be detectable by space-based GW observatories. The morphology of the evolving GW waveform provides a direct diagnostic for the NSWD binary configuration, including any contribution from an accretion disk. Our models can provide critical waveform templates for identifying merging binary signals in real-time GW data.

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The relation between helium white dwarf mass and orbital period under two types of opacity

Helium white dwarfs (He WDs) are end products of low-mass red giant donors in close binary systems via stable mass transfer or common envelope evolution. At the end of stable mass transfer, there is a well-known relation between the He WD mass and orbital period. Although this relation has been widely investigated, the influence of different types of opacity at low temperatures is ignored. In this work, we modeled the evolution of WD binaries with stellar evolution code MESA and two types of opacity at low temperatures from Ferguson et al. (2005) and Freedman et al. (2008, 2014). We investigated the relation between the WD mass and orbital period and compared these results with observations. We find that the relation derived from the opacity of Freedman et al. (2008, 2014) is below that from the opacity of Ferguson et al. (2005) and the relation derived from the opacity of Freedman et al. (2008, 2014) can better explain the observations. In addition, we provided fitting formulae for the relations derived from the opacity of Freedman et al. (2008,2014) at different metallicities.

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The origin of B-type runaway stars based on kinematics

Runaway stars depart their birthplaces with high peculiar velocities. Two mechanisms are commonly invoked to explain their origin, the binary supernova scenario (BSS) and the dynamical ejection scenario (DES). Investigating the kinematic properties of runaway stars is key to understanding their origins.We intend to investigate the origins of 39 B-type runaway stars from LAMOST using orbital traceback analysis. From the catalog of LAMOST, we selected 39 B-type runaway stars and determined their spectral subtypes from key absorption lines. We then derived atmospheric parameters for each star using the Stellar Label Machine (SLAM), which is trained on TLUSTY synthetic spectra computed under the non-local thermodynamic equilibrium (NLTE) assumption. Using the derived atmospheric parameters as input, we estimated stellar masses and ages with a machine learning model trained on PARSEC evolutionary tracks. We finally performed orbital traceback with GALPY to analyze their origins. Through orbital traceback, we find that 29 stars have trajectories entirely within the Galactic disk, whereas 10 are disk-passing yet still trace back to the disk. Two stars have trajectories that intersect those of known clusters. Their orbits show similar morphologies in both the $X-Y$ and $R-Z$ planes, and their [M/H] values are comparable, suggesting possible cluster origins. However, definitive confirmation will require additional evidence. In addition, the $V_{\rm Sp} - v\sin{i}$ plane shows that runaway stars with low peculiar space velocities but high $v\sin{i}$ remain on the Galactic disk, whereas those with high peculiar space velocities but low $v\sin{i}$ pass through the disk, possibly reflecting two distinct origins.

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A New Algol-type Binary with an Accretion disk

We present a comprehensive photometric and spectroscopic analysis of the Algol-type binary \textit{Gaia} DR3 1892576067672499328. We identified the system as a spectroscopic binary based on medium-resolution LAMOST spectra. Combined with \textit{TESS} photometry, we determine an orbital period of \( P = 2.47757 (1) \) days, a low mass ratio of \( q = 0.098 \pm 0.002 \), and an orbital inclination of \( i = 46.934^{+2.613}_{-1.11} \) degrees. The orbit is consistent with being circular (\( e = 0 \)). The binary comprises a \( M_1 = 1.817 ^{ +0.106}_{-0.202} \,M_\odot \), \( R_1 = 1.265^{+0.121}_{-0.160}\,R_\odot \) A-type primary and a Roche-lobe-filling secondary of \( M_2 = 0.179 ^{ +0.011}_{-0.020} \,M_\odot \), \( R_2 = 1.994 ^{ +0.041}_{-0.077} \,R_\odot \). The double-peak H$α$ emission line indicates the possible existence of a Keplerian accretion disc. We established a simple standard accretion disc model and modeled the geometric and dynamical properties of the accretion disc. The obtained outer disc radius $R_{\mathrm{out}} \approx 3.36 \pm 0.43\,R_\odot$ is consistent with the values inferred from the emission velocity of H$α$. Systemic velocity variations observed over time suggest the possible presence of a tertiary companion, with a minimum mass of $M_3 > 0.369 \pm 0.024 \,M_\odot$. Given the low mass ratio, the secondary may evolve into a proto-helium white dwarf, forming an \text{EL CVn}-type system in the future. This system offers valuable insights into accretion dynamics and the formation of binaries.

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