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Guoliang Lü

Publications and source records attributed to Guoliang Lü.

At least 19 recordsLinked to original sources

A Possible Triple Formation Scenario of Binary Black Hole Merge With One In Pair-instability Supernova Mass Gap

Observations of binary black hole (BBH) mergers detected by LIGO -- such as GW170729, GW190620, GW190706, GW230107, GW230820, and GW230928 -- feature high effective spins and primary black holes that fall squarely into the pair-instability supernova (PISN) mass gap ($\sim 45-130 \, M_{\odot}$). These events pose a significant challenge to standard stellar and binary evolution theories. To address this, we propose an isolated hierarchical triple stellar evolution channel. In this framework, tidal synchronization in tight inner binaries drives chemically homogeneous evolution (CHE), entirely bypassing giant expansion. A subsequent triple common envelope (TCE) evolution, triggered by the tertiary companion, rapidly drives the inner BBH to coalescence. Our model can provide a detailed evolutionary pathway that elegantly reproduces the properties of these GWs, such as GW190706. Assuming a low-metallicity environment ($Z = 0.001$), our framework predicts a volumetric merger rate of approximately $0.011 \, \mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$ at $z \approx 0.68$, accounting for $22\%$ of the empirical rate for this mass regime in the GWTC-4 catalog. This study demonstrates that primordial triple interactions are a highly efficient avenue for populating the PISN mass gap.

astro-ph.HE

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.

astro-ph.SR

Application of interpretable data-driven methods for the reconstruction of supernova neutrino energy spectra following fast neutrino flavor conversions

Neutrinos can experience fast flavor conversions (FFCs) in highly dense astrophysical environments, such as core-collapse supernovae and neutron star mergers, potentially affecting energy transport and other processes. Simulating fast flavor conversions under realistic astrophysical conditions requires substantial computational resources and poses significant analytical challenges. While machine learning methods such as multilayer perceptrons have been used to accurately predict the asymptotic outcomes of FFCs, their "black-box" nature limits the extraction of direct physical insight. To mitigate this limitation, we employ two distinct interpretable machine learning frameworks, Kolmogorov-Arnold Networks (KANs) and Sparse Identification of Nonlinear Dynamics (SINDy), to learn interpretable surrogates for the asymptotic input-output mapping from an FFC simulation dataset. Our analysis reveals a fundamental trade-off between predictive accuracy and model simplicity. KANs demonstrate high fidelity in reconstructing post-conversion neutrino energy spectra, achieving accuracies of up to 90%. In contrast, SINDy yields a low-rank, compact closed-form approximation of the input-output mapping, at the expense of some predictive accuracy. Critically, using these structured and sparse surrogates as diagnostic tools, we identify that the system's evolution is most sensitive to the initial number density of heavy-lepton neutrinos when FFCs are triggered, compared with other physical quantities. Ultimately, this work provides a methodological framework for interpretable machine learning that supports genuine data-driven scientific discovery in astronomy and astrophysics, going beyond prediction alone.

astro-ph.HE

A low mass and radius neutron star candidate in XTE J1810-189?

Photosphere radius expansion (PRE) bursts provide a crucial tool for constraining the mass and radius of neutron stars. In this study, we analyze time-resolved spectroscopic data from XTE J1810-189 in 2008, which exhibit evidence of a PRE event. We report here the possibility of a small-size and low-mass neutron star in XTE J1810-189 with use of the advantage of the direct cooling tail method. We obtained three sets of results, which can be broadly divided into high metal abundance (20 $\rm{Z}_{\odot}$ and 40 $\rm{Z}_{\odot}$), low metal abundance and hydrogen-rich (pure hydrogen, $\rm{Z}_{\odot}$, 0.3 $\rm{Z}_{\odot}$, 0.1 $\rm{Z}_{\odot}$, 0.01 $\rm{Z}_{\odot}$), and pure helium. In the high-metallicity scenario, the inferred neutron star mass is $<1.3\,M_{\odot}$ with a radius $<8\,\rm{km}$. In the low-metallicity, hydrogen-rich case, the mass ranges from 0.3 to 2.1 $M_{\odot}$ with radii of 7-13 km. For a pure-helium composition, we find two mass solutions: $1.08_{-0.22}^{+1.32}M_{\odot}$ (with $R>14\,\rm{km}$) and $2.5-2.9\,M_{\odot}$ (above the highest observed neutron star masses). Additionally, we applied the touchdown method combined with an MCMC analysis, the results are consistent with those from the direct cooling tail method, but with a broader range. Our analysis of the time-resolved spectrum of burst suggests a high-metallicity atmosphere, but new observations are required to confirm this result.

astro-ph.HE

Mass-Radius Constraints for 2S 0918-549 from an RXTE Superexpansion Burst: A Direct Cooling-Tail Analysis

Thermonuclear (Type I ) X-ray bursts from accreting neutron stars offer a means to determine neutron-star (NS) mass ($M$) and radius ($R$) and thereby probe the properties of matter at supranuclear density. A subset of these events, photospheric radius-expansion (PRE) bursts, provide a particularly powerful tool to constrain the neutron-star $M$ and $R$. Here, we apply the direct cooling-tail method to 2S~0918$-$549, using a rare superexpansion burst observed by \emph{RXTE}. We fit only the post-touchdown data within \(F/F_{\rm td}\in[0.6,0.95]\), employing modern atmosphere models (pure He and metal-enriched). The pure-He atmosphere yields a good description of the cooling tail (\(χ^{2}/ν=18.12/14\)), whereas metal-rich models fail; information-criterion tests (AIC/BIC) disfavor adding a free absorption edge in every time bin, indicating that heavy-element ashes are unnecessary. The joint fit gives a distance \(d=4.1-5.3\) kpc and mass-radius constraints \(M=1-2\,M_\odot\) and \(R=9.7-11.9\) km (99\% confidence). These results suggest that representative families of both gravity-bound and self-bound equations of state remain viable at the $1σ$ confidence level.

astro-ph.HE

Evolution of cataclysmic variables under different magnetic braking prescriptions

Context. The evolution of cataclysmic variables (CVs) - interacting binaries where a low-mass donor transfers matter to a white dwarf via an accretion disk - is critically controlled by magnetic braking (MB). Significant uncertainties persist regarding how distinct MB formalisms influence CV evolutionary pathways. Aims. We performed systematic simulations of CV evolution under five MB prescriptions using the MESA code: the classical Skumanich law and the Matt, Reiners & Mohanty (RM12), intermediate, and convection-boosted formalisms. Primary objectives included investigating their impact on orbital period distributions, mass-transfer rates, donor star evolution, and period gap characteristics. Methods. Evolutionary sequences were computed across all MB frameworks. We analyzed their effects on key observables: orbital period evolution, accretion rates, and period gap morphology. Results. Magnetic braking prescription selection fundamentally determines whether CV systems develop the characteristic period gap. The intermediate prescription provides optimal consistency with observations of nonmagnetic CVs, simultaneously reproducing the gap location and donor properties. Strong braking models (e.g., Skumanich) produce clear detachment phases, while self-consistent regulation models (Matt12 and RM12) maintain weak angular momentum loss and fail to form a gap, making them more prone to magnetic CVs. Conclusions. The presence or absence of the period gap is primarily governed by the strength and behavior of MB before the donor becomes fully convective. Future studies must further incorporate the regulatory effects of magnetic fields on donor structure to accurately predict the period distribution characteristics of magnetic CVs.

astro-ph.SR

Formation of the Dormant Black Holes with Luminous Companions from Binary or Triple Systems

Recently, a class of dormant black hole binaries with luminous companions (dBH-LC) has been observed, such as $Gaia$ BH1, BH2, and BH3. Unlike previously discovered X-ray BH binaries, this type of dBH-LC has relatively long orbital periods (typically more than several tens to a few hundred days) and shows very weak X-ray emission. Therefore, studying the formation and evolution of the whole dBH-LC population is also a very interesting problem. Our aim is to study the contribution of massive stars to the dBH-LC population under different evolutionary models (isolated binary evolution (IBE) and hierarchical triple evolution), and different formation channels (such as mass transfer, common envelope evolution). Using the Massive Objects in Binary Stellar Evolution (MOBSE) code, the Triple Stellar Evolution (TSE) code, and the latest initial multiple-star distributions, we model the populations of massive stars. Finally, we calculate the orbital properties, mass distributions, and birthrates of the BH-LC populations formed under these different conditions. In the Milky Way, we calculate that the birthrate of dBH-LC formed through IBE is about 4.35$\times$$10^{-5}$ ${\rm yr}^{-1}$, while the birthrate through triple evolution is about 1.47$\times$$10^{-3}$ ${\rm yr}^{-1}$. This means that the birthrate from triple evolution is one to two orders of magnitude higher than that from IBE. We find that in triple evolution, the main formation channel of dBH-LC is post-merger binaries formed from inner binary mergers triggered by von Zeipel$-$Lidov$-$Kozai oscillations.

astro-ph.SR

Dark Matter (S)pins the Planet

Dark matter heating in planets has been proposed as a potential probe for dark matter detection. Assuming near-equilibrium conditions, we find that the energy input from dark matter raises planetary temperatures and accelerates rotation. The distribution of energy between heating and rotational acceleration depends on both planetary properties and external inputs, suggesting that previous studies may have overestimated the heating contribution. At high dark matter densities, planetary rotation stabilizes earlier and becomes primarily governed by dark matter effects.

astro-ph.HE

A Core-Collapse Supernova Neutrino Parameterization with Enhanced Physical Interpretability

We introduce a novel parameterization of supernova neutrino energy spectra with a clear physical motivation. Its central parameter, $τ(t)$, quantifies the characteristic thermal-diffusion area during the explosion. When applied to the historic SN1987A data, this parameterization yields statistically significant fits and provides robust constraints on the unobserved low-energy portion of the spectrum. Beyond this specific application, we demonstrate the model's power on a suite of 3D core-collapse supernova simulations, finding that the temporal evolution of $τ(t)$ distinctly separates successful from failed explosions. Furthermore, we constrain the progenitor mass of SN 1987A to approximately 19 solar masses by applying Smoothed Isotonic Regression, while noting the sensitivity of this estimate to observational uncertainties. Moreover, in these simulations, $τ(t)$ and the gravitational-wave strain amplitude display a strong, synergistic co-evolution, directly linking the engine's energetic evolution to its geometric asymmetry. This implies that the thermodynamic state of the explosion is imprinted not only on the escaping neutrino flux, but also recorded in the shape of the energy spectrum. Our framework therefore offers a valuable tool for decoding the detailed core dynamics and multi-messenger processes of future galactic supernovae.

astro-ph.HE

Hunting Hidden Axion Signals in Pulsar Dispersion Measurements with Machine Learning

In axion models, interactions between axions and electromagnetic waves induce frequency-dependent time delays determined by the axion mass and decay constant. These small delays are difficult to detect, limiting the effectiveness of traditional methods. We compute such delays under realistic radio telescope conditions and identify a prominent dispersive feature near half the axion mass, which appears non-divergent within the limits of observational resolution. Based on this, we develop a machine learning method that achieves 90\% classification accuracy and demonstrates well performance in low signal-to-noise regimes. The method's robustness is confirmed against false positives using both simulated noisy data and real-world, known-null observations. Future improvements in optical clock precision and telescope bandwidth, particularly with instruments such as the Qitai Radio Telescope, may enhance constraints on the axion decay constant by up to four orders of magnitude in the $10^{-6} \sim 10^{-4}$ eV mass range.

astro-ph.HE

The influence of rotation and metallicity on the explodability of massive stars

During the late stages of massive stellar evolution, failed supernovae (FSN) may form through core-collapse processes. The traditional evaluation criterion $ξ_{2.5}$ $=$ 0.45, primarily established using non-rotating progenitor models, suffers from significant inaccuracies when applied to rotating pre-supernova systems. The effects of metallicity and rotation on the explodability landscapes of massive stars lack robust quantification. We aim to investigate how rotation and metallicity influence the explodability of massive stars. We investigate how rotation and metallicity affect stellar explodability using MESA simulations with initial rotational velocities of $0$, $300$, and $600~\mathrm{km,s^{-1}}$ at three metallicities ($Z_{\odot}$, $1/10,Z_{\odot}$, $1/50,Z_{\odot}$). Core-collapse phases are simulated with GR1D to determine critical heating efficiencies. Our results yield revised $ξ_{2.5}$ criteria: 0.45 for non-rotating models; 0.48 for $300~\mathrm{km,s^{-1}}$; 0.47 for $600~\mathrm{km,s^{-1}}$ at solar metallicity; and 0.59 for low-metallicity models. Chemically homogeneous evolution in rapidly rotating low-metallicity stars significantly raises the compactness limit for successful explosions and narrows the zero-age main sequence mass range for failed supernovae. Rotation substantially affects the explodability of low-metallicity massive stars, underscoring the importance of incorporating rotational effects in models of core-collapse supernova progenitors.

astro-ph.SR

The mixing of internal gravity waves and lithium production in intermediate-mass AGB stars

Context: Intermediate-mass asymptotic giant branch (AGB) stars influence Galactic lithium evolution by ejecting surface material (including Li) via stellar winds. Internal gravity waves (IGW), excited by convective motions, drive turbulent mixing in non-convective regions, altering stellar surface and wind chemistry. Aims: Investigate IGW-induced extra-mixing in the radiative zone between thermal pulses and convective envelopes of AGB stars and its impact on Li production. Derive the total Li contribution from intermediate-mass AGB stars using stellar models and initial mass functions. Methods: Construct stellar models (from zero-age main sequence to AGB end) with MESA, incorporating IGW-induced mixing and element diffusion. Calculate Li yields for stars of varying masses and metallicities using grids and population synthesis. Results: IGW triggers extra-mixing during He-shell flashes, transporting Be-7 from the radiative zone to the convective envelope, where it decays into Li-7. The positive effect of IGW on Li yield decreases with initial stellar mass but increases with metallicity. Most AGB stars (3.5-7.5 solar masses) produce positive Li yields. The total Li yield with IGW mixing (approximately 15 solar masses) is twice that without, contributing about 10 percent to Galactic Li. Conclusions: Through this extra-mixing mechanism induced by IGW, AGB stars can achieve a maximum A(Li) exceeding 5 and intermediate-mass AGB stars significantly contribute to Li in the Galactic ISM. These findings underscore the crucial role of IGW in stellar evolution, particularly in enhancing Li production.

astro-ph.SR

SN 2021hpr: A Normal Type Ia Supernova Showing Excess Emission in the Early Rising Phase

We present extensive optical observations of a nearby Type Ia supernova (SN Ia), SN 2021hpr, located in the spiral galaxy NGC 3147 at a distance of $\sim$ 45 Mpc. Our observations cover a phase within $\sim 1-2$ days to $\sim 290$ days after the explosion. SN 2021hpr is found to be a spectroscopically normal SN Ia, with an absolute B-band peak magnitude of $M_{max}(B) \approx -19.16 \pm 0.14$ mag and a post-peak decline rate of $Δm_{15}(B)= 1.00 \pm 0.01 $ mag. Early-time light curves showed a $\sim 7.0 \%$ excess emission compared to a homogeneously expanding fireball model, likely due to SN ejecta interacting with a companion or immediate circumstellar matter. The optical spectra of SN 2021hpr are overall similar to those of normal SNe Ia, but characterized by prominent detached high-velocity features (HVFs) of Si {\sc ii} and Ca {\sc ii} in the early phase. After examining a small sample of well-observed normal SNe Ia, we find that the HVFs are likely common for the subgroup with early-excess emission. The association of early bump feature with the HVFs could be attributed to density or abundance enhancement at the outer layer of the exploding star, likely as a result of interactions with companion$/$CSM or experiencing more complete burning. Nevertheless, the redshifted Fe {\sc ii} and Ni {\sc ii} lines in the nebular-phase spectra of SN 2021hpr, contrary to the blueshift trend seen in other SNe Ia showing early bump features, indicate its peculiarity in the explosion that remains to be understood.

astro-ph.HE

The Impact of Neutrino Magnetic Moments on the Evolution of the Helium Flash and Lithium-Rich Red Clump Stars

The detection of the neutrino magnetic moment (NMM,$μ_v$) is one of the most significant challenges in physics. The additional energy loss due to NMM can significantly influence the He flash evolution in low-mass stars. Using the MESA code, we investigated the impact of NMM on the He flash evolution in low-mass stars. We found that NMM leads to an increase in both the critical He core mass required for the He flash and the luminosity of TRGB. For a typical $Z = 1 Z_{\odot}$ , $M$ = 1.0 $M_{\odot}$, and $μ_v = 3 \times 10^{-12} μ_{\mathrm{B}}$ model, the He core mass increases by $\sim 5\%$, and the TRGB luminosity increases by $\sim 35\%$ compared to the model without NMM. However, contrary to previous conclusions, our model indicates that the He flash occurs earlier, rather than delayed, with increasing NMM values. This is because the additional energy loss from NMM accelerates the contraction of the He core, releases more gravitational energy that heats the H shell and increases the hydrogen burning rate, thereby causing the He core to reach the critical mass faster and advancing the He flash. An increase in NMM results in a higher peak luminosity for the first He flash, a more off-center ignition position, and sub-flashes with higher luminosities, shorter intervals, and higher frequency. We found that the internal gravity wave (IGW) mixing generated by the He flash can induce sufficient mixing in the radiative zone, turning the overshoot region into a low-Dmix bottleneck within the stellar interior. The increase in NMM in the model narrows the overshoot bottleneck region, enabling Li to enter the surface convection zone more quickly, thereby enhancing the enrichment effect of IGW mixing on surface Li. For models incorporating both NMM and IGW mixing, the reduction in the overshoot bottleneck region allows them to effectively produce super Li-rich red clump star samples.

astro-ph.SR

Systematic study of the composition of Type I X-ray burst ashes: Neutron star structure v.s. Reaction rate uncertainties

In this study, we calculate for the first time the impacts of neutron star(NS) structure on the type I X-ray burst ashes using the \texttt{MESA} code. We find an increased mass fraction of the heavier elements with increasing surface gravity (increase mass or decrease radius), resulting in a higher average mass number ($A_{\rm ash}$) of burst ashes (except for higher mass NS due to the competition between the envelope temperature and the recurrence time). The burst strength ($α$) increases as surface gravity increases, which indicates the positive correlation between $A_{\rm ash}$ and $α$ with changes in surface gravity. If the $α$ value is higher, heavier $p$-nuclei should be produced by the type I X-ray burst nucleosynthesis. Besides, the effects of various burst input parameters, e.g. base heating ($Q_{\rm b}$), metallicity ($Z$) and some new reaction rates are calculated for comparison. We find that the heavier nuclei synthesis is inversely correlated to the base heating/metallicity, the smaller the base heating/metallicity, the greater the mass fraction of the heavier elements. The $α$ value decreases as $Q_{\rm b}$ or $Z$ decreases, which also indicates the positive correlation between $A_{\rm ash}$ and $α$ with variation in $Q_{\rm b}$ or $Z$. The new reaction rates from the $(p,γ)$ reactions on $^{17}\rm{F}$, $^{19}\rm{F}$, $^{26}\rm{P}$, $^{56}\rm{Cu}$, $^{65}\rm{As}$, and $(α,p)$ reaction on $^{22}\rm{Mg}$ have only minimal effects on burst ashes. In hydrogen-rich X-ray binary systems, nuclei heavier than $^{64}\rm{Ge}$ are fertile produced with larger NS mass, smaller NS radius, smaller base heating and smaller metallicity.

astro-ph.HE

The neutrino luminosity and energy spectrum of nova outburst

The nova outburst can produce a large number of neutrinos, whether it is the nuclear reaction process during the explosion or the shock wave acceleration proton process. We study the low-energy nuclear and thermal neutrino luminosity of novae with CO white dwarf (WD) mass ranging from 0.6 to 1.1 $\rm M_{\odot}$ with different accretion rates $\dot{M}$, core temperatures $(T_{\mathrm{C}})$, and mixing degrees. We find that during the accretion phase, low-energy neutrinos are mainly produced by pp chains and plasma decay, and photon luminosity is greater than low-energy nuclear and thermal neutrino luminosity. During the thermonuclear runaway (TNR) phase, low-energy neutrinos are mainly produced by the CNO cycle and photon-neutrino, and the low-energy nuclear and thermal neutrino luminosity far exceeds the photon luminosity. We find that the more massive the WD, the shorter the cycle time and the higher the low-energy nuclear neutrino luminosity. The higher the accretion rate, the lower the low-energy nuclear neutrino luminosity. If the accretion mixing effect is not taken into account, the outburst interval becomes longer, the low-energy nuclear neutrino luminosity will be increased. And for the cooler nova model $(T_{\mathrm{C}}=1\times10^{7}\rm K)$, the low-energy nuclear neutrino luminosity will be lower during the accretion phase and higher at the TNR. We also predict the neutrino luminosity and energy spectrum of the upcoming recurrent nova T Coronae Borealis (T CrB). We estimate that the next T CrB outburst has a low-energy nuclear neutrino peak luminosity of $2.7\times10^{8}\ \rm L_{ν,\odot}$ and a low-energy nuclear neutrino outburst duration of 88 days. In addition, we predict that the high-energy hadronic neutrino flux produced by T CrB nova can not be observed by the current-generation IceCube.

astro-ph.SR

A possible formation scenario of the Gaia ID 3425577610762832384: inner binary merger inside a triple common envelope

Recently, an identified non-interacting black hole (BH) binary, Gaia ID 3425577610762832384 (hereafter G3425), contains a BH ($\sim$3.6 M$_{\odot}$) falling within the mass gap and has a nearly circular orbit, challenging the classical binary evolution and supernova theory. Here, we propose that G3425 originates from a triple through a triple common envelope (TCE) evolution. The G3425 progenitor originally may consist of three stars with masses of 1.49 M$_{\odot}$, 1.05 M$_{\odot}$, and 21.81 M$_{\odot}$, and inner and outer orbital periods of 4.22 days and 1961.78 days, respectively. As evolution proceeds, the tertiary fills its Roche lobe, leading to a TCE. We find that the orbital energy generated by the inspiral of the inner binary serves as an additional energy imparted for ejecting the common envelope (CE), accounting for $\sim$97\% of the binding energy in our calculations. This means that the outer orbit needs to expend only a small amount of the orbital energy to successfully eject CE. The outcome of the TCE is a binary consisting of a 2.54 M$_\odot$ merger produced by the inner binary merger and a 7.67 M$_\odot$ helium star whose CE successfully ejected, with an orbital period of 547.53 days. The resulting post-TCE binary (PTB) has an orbital period that is 1-2 orders of magnitude greater than the orbital period of a successfully ejected classical binary CE. In subsequent simulations, we find that the successfully ejected helium star has a 44.2\% probability of forming a BH. In the case of a non-complete fallback forming a BH, with an ejected mass of 2.6 M$_{\odot}$ and a relatively low natal kick ($11^{+16}_{-5}$ ${\rm km/s}$ to $49^{+39}_{-39}$ ${\rm km/s}$), this PTB can form G3425 in the Milky Way.

astro-ph.SR

A possible formation scenario of the Gaia BH1: inner binary merger in triple systems

Based on astrometric measurements and spectral analysis from $Gaia$ DR3, two quiescent black hole (BH) binaries, $Gaia$ BH1 and BH2, have been identified. Their origins remain controversial, particularly for $Gaia$ BH1. By considering a rapidly rotating ($ω/ω_{\rm crit} = 0.8$) and strongly magnetized ($B_{\rm 0} = 5000$ G) merger product, we find that, at typical Galactic metallicity, the merger product can undergo efficient chemically homogeneous evolution (CHE). This results in the merger product having a significantly smaller radius during its evolution compared to that of a normally evolving massive star. Under the condition that the initial triple stability is satisfied, we use the Multiple Stellar Evolution (MSE) code and the MESA code to identify an initial hierarchical triple that can evolve into $Gaia$ BH1. It initially consists of three stars with masses of 9.03 $M_{\odot}$, 3.12 $M_{\odot}$, and 1 $M_{\odot}$, with inner and outer orbital periods of 2.21 days and 121.92 days, and inner and outer eccentricities of 0.41 and 0.45, respectively. This triple initially experiences triple evolution dynamics instability (TEDI) followed by Roche lobe overflow (RLOF). During RLOF, the inner orbit shrinks, and tidal effects gradually suppress the TEDI. Eventually, the inner binary undergoes a merger through contact (or collision). Finally, using models of rapidly rotating and strongly magnetic stars, along with standard core-collapse supernova (SN) or failed supernova (FSN) models, we find that a PMB consisting of an 12.11 $M_{\odot}$ merger product and a 1 $M_{\odot}$ companion star (originally an outer tertiary) can avoid RLOF. After a SN or FSN with a low ejected mass of $\sim$0.22 $M_{\odot}$ and a low kick velocity ($46^{+25}_{-33}$ ${\rm km/s}$ or $9^{+16}_{-8}$ ${\rm km/s}$), the PMB can form $Gaia$ BH1 in the Galactic disk.

astro-ph.SR