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Philipp M. Srivastava

Publications and source records attributed to Philipp M. Srivastava.

At least 19 recordsLinked to original sources

The Mass-Ratio Distribution of the Low-Mass Binary Black Hole Subpopulation: A Natural Outcome of Isolated Binary Evolution

The observed merging binary black hole population is increasingly consistent with being composed of a mixture of subpopulations, each likely the result of different formation mechanisms. In particular, the low-mass subpopulation, with primary black hole masses below $\approxeq 15\,M_{\odot}$, has been attributed to mergers formed through isolated binary evolution. We use the binary population synthesis code POSYDON to study the mass ratio $(q)$ distribution of binary black hole mergers from isolated binary evolution and compare to the observed low-mass subpopulation. We explore variations in supernova remnant prescriptions, common-envelope efficiency, and black hole accretion efficiency. We find that our models have a preference for asymmetric $q$, most with a broad peak near $q\approxeq0.5-0.7$, and a near-equal-mass component whose relative strength varies across models. This resultant $q$ distribution is consistent with the $q$ distribution of the low-mass subpopulation observed with gravitational waves. We find that for the majority of models these features arise from physically distinct formation subchannels: the asymmetric peak reflects contributions from common-envelope and stable mass-transfer systems, while the near-equal-mass component traces double-core common envelope and contact systems. We conclude that the features in the $q$ distribution of the observed low-mass subpopulation emerge naturally from isolated binary evolution across a range of model assumptions. As the gravitational-wave catalog continues to grow, the relative strength of these $q$ features will provide an increasingly powerful diagnostic of isolated binary evolution and its formation subchannels.

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High-mass binary black hole mergers from detailed binary evolution models

Gravitational-wave observations reveal a population of binary black hole (BBH) mergers with primary masses above ${\sim}40\,\mathrm{M}_\odot$, extending into and potentially beyond the pair-instability mass gap, with a possibly flat mass-ratio and broader χ_\mathrm{eff} distribution. We investigate whether super-Eddington accretion during stable mass transfer in isolated binary evolution can produce BBH mergers consistent with these properties across primary BH mass, mass-ratio, and χ_\mathrm{eff} distributions. Using POSYDON, we simulate BBH merger populations with primary BH masses above ${\sim}40\,\mathrm{M}_\odot$, under three BH accretion efficiencies: Eddington-limited, GRRMHD-informed, and fully conservative. We additionally vary the natal kick strength, including strong kicks at high BH masses. We find that super-Eddington accretion does not suppress BBH mergers in the high-mass regime. Fully-conservative accretion leads to an increase of BBH mergers in POSYDON with a strong kick-independent peak at $χ_\mathrm{eff}=0.6$ and a sharp mass-ratio peak at $q\sim0.5$, whereas observations favor $χ_\mathrm{eff}=0.0$ and a flatter mass-ratio distribution. The GRRMHD-informed and Eddington-limited accretion are compatible with the observed primary BH mass and mass ratio distribution, but require natal kicks to populate negative χ_\mathrm{eff}. A joint analysis of the primary BH mass, mass ratio, and χ_\mathrm{eff} distributions provides strong constraints on binary evolution physics, and disfavor fully-conservative BH accretion as the dominant formation mechanism for high-mass BBH mergers. The Eddington-limited and GRRMHD-informed prescriptions with modest kicks can explain part of the high-mass population, but an additional formation channel is still needed to account for the high fraction of negative χ_\mathrm{eff} systems and high secondary BH spins.

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Stellar Population Spectra Incorporating Detailed Binary Evolution using POSYDON

The accuracy of stellar population properties inferred through spectral energy distribution fitting hinges on the reliability of the underlying spectral models. Binary interactions are fundamental for massive star evolution, and ignoring their spectral contribution can lead to incorrect results. We use the POSYDON binary population synthesis code to generate spectral models of stellar populations that include binaries at solar metallicity. Our framework incorporates a collection of spectral libraries that is designed to address key outcomes of binary stellar evolution like Wolf-Rayet stars, stripped helium stars, and a treatment for stellar mergers. Our models confirm previous results showing that the inclusion of binary interactions has a significant effect on the UV and ionizing regime of the integrated spectrum. In particular we find that Wolf-Rayet stars and other massive stars dominate the production of ionizing radiation at earlier times, but after $\simeq$16 Myr stripped stars produced through mass transfer begin to dominate. Furthermore, we show that the production of ionizing He II photons is especially sensitive to the underlying population of stripped stars. While our results currently focus on high-mass stars ($\ge4~M_{\odot}$) at Solar metallicity, they provide the framework for binary spectral synthesis across a range of metallicities and masses and lay the foundation for calculations of the emergent emission-line spectra in the UV, optical, and IR regimes. We make the spectral models from this work publicly available for use in a format that can be integrated into fitting codes.

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Forming Double Neutron Stars using Detailed Binary Evolution Models with POSYDON: Comparison to the Galactic Systems

With over two dozen detections in the Milky Way, double neutron stars (DNSs) provide a unique window into massive binary evolution. We use the POSYDON binary population synthesis code to model DNS populations and compare them to the observed Galactic sample. By tracing their origins to underlying single and binary star physics, we place constraints on the detailed evolutionary stages leading to DNS formation. Our study reveals a bifurcation within the well-known common envelope (CE) formation channel for DNSs, which naturally explains an observed split in the orbital periods of the Galactic systems. The two subchannels are defined by whether the donor star has a helium core (Case B mass transfer) or a carbon-oxygen core (Case C) at the onset of the CE, with only the helium core systems eventually merging due to gravitational wave-modulated orbital decay. We find that across different treatments of the CE phase, the formation of DNSs through both subchannels requires either a generous core definition of $\simeq$ 30% H-fraction or a high CE ejection efficiency of $α_{\rm CE}\gtrsim1.2$. By testing different supernova kick velocity models, we find that galactic DNSs are best reproduced using a prescription that favors low velocity kicks ($\lesssim 50 \, \rm km/s$), in agreement with previous studies. Furthermore, our models indicate that merging DNSs are born from a stripped progenitor with a median pre-supernova envelope mass $\sim$ 0.2$M_{\odot}$. Our results highlight the value of detailed evolutionary models for improving our understanding of exotic binary star formation.

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Double Neutron Star Delay Times Across Cosmic Metallicities: The Role of Helium Star Progenitors

Metallicity can play a significant role in massive binary evolution through its impact on the opacity within stellar interiors and wind-driven mass loss. In this work, we investigate how the double neutron star (DNS) delay time distribution (DTD) is shaped by the metallicity-dependent evolution of the helium star$-$NS progenitor system. Drawing from insights rooted in single and binary star physics, we argue that at a given metallicity, the stellar radius during the helium main-sequence sets a lower limit on the size of the DNS orbit at birth. We then perform population synthesis with the detailed binary evolution code POSYDON to illustrate the resulting DTD across a range of metallicities. Our results indicate that, independent of the common envelope efficiency and reasonable natal kicks, the majority of DNS mergers across metallicities occur typically no earlier than $\simeq 40\,\rm{Myr}$ after star formation and peaks strongly between $80-250\,\rm{Myr}$. Roughly $15\%$ of DNSs merge within 80 Myr, which may explain $r$-process enrichment in environments with brief star formation histories, while $\gtrsim 20\%$ merge on delay times $>1$Gyr, providing an explanation for short gamma-ray bursts in old, metal-poor galaxies. The shape of the DTD can be complex, with a metallicity-dependent split in the dominant formation channel imprinting a characteristic double-peaked structure. Although ideally oriented natal kicks can produce very short merging DNS, we find that the required kick magnitudes are inconsistent with observations. Our work has implications for assessing the contribution of DNS mergers to $r$-process enrichment and gamma-ray bursts/kilonovae transients across cosmic time.

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A case for Case A: detailed look at binary black hole formation through stable mass transfer

In isolated binary evolution, binary black hole (BBH) mergers are generally formed through stable mass transfer (SMT) or common envelope evolution. In recent years, the SMT channel has received significant attention due to detailed binary models showing increased mass transfer stability compared to previous studies. In this work, we perform a full zero-age-main-sequence to compact object merger analysis using detailed binary models at eight metallicities between $10^{-4}Z_\odot$ and $2Z_\odot$ to self-consistently model the population properties of BBH mergers in the SMT channel, determined their progenitor initial conditional, and investigate the binary physics governing their formation and metallicity dependence. We use the population synthesis code POSYDON to determine the population of BBH mergers from SMT. Using its extended grids of MESA binary models, we determine the essential physics in the formation of BBH mergers. SMT produces BBH mergers predominantly from systems with $P_{ZAMS}\leq10$ days. In these systems, both the initial mass transfer between two stars and the subsequent interaction between the remaining star and the first-born BH take place while the respective donor star is on the main-sequence (Case A). We find a limited contribution from wider Case B/C systems. Without a natal kick, the SMT channel does not produce BBH mergers above $Z>0.2Z_\odot$ due to orbital widening from stellar wind mass loss. The primary BH mass distribution shows a strong dependence on metallicity, while the mass ratio prefers unity independent of metallicity due to mass ratio reversal. Additionally, the $χ_{eff}$ distributions contain peaks at $χ_{eff}=0$ and ~0.15 of which the former disappears at high metallicities. A mass-scaled natal kick leave this sub-population unchanged but introduce a low-mass, unequal mass ratio sub-population that merges due to their high eccentricity.

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Irregularly Sampled Time Series Interpolation for Binary Evolution Simulations Using Dynamic Time Warping

Binary stellar evolution simulations are computationally expensive. Stellar population synthesis relies on these detailed evolution models at a fundamental level. Producing thousands of such models requires hundreds of CPU hours, but stellar track interpolation provides one approach to significantly reduce this computational cost. Although single-star track interpolation is straightforward, stellar interactions in binary systems introduce significant complexity to binary evolution, making traditional single-track interpolation methods inapplicable. Binary tracks present fundamentally different challenges compared to single stars, which possess relatively straightforward evolutionary phases identifiable through distinct physical properties. Binary systems are complicated by mutual interactions that can dramatically alter evolutionary trajectories and introduce discontinuities difficult to capture through standard interpolation. In this work, we introduce a novel approach for track alignment and iterative track averaging based on Dynamic Time Warping to address misalignments between neighboring tracks. Our method computes a single shared warping path across all physical parameters simultaneously, placing them on a consistent temporal grid that preserves the causal relationships between parameters. We demonstrate that this joint-alignment strategy maintains key physical relationships such as the Stefan-Boltzmann law in the interpolated tracks. Our comprehensive evaluation across multiple binary configurations demonstrates that proper temporal alignment is crucial for track interpolation methods. The proposed method consistently outperforms existing approaches and enables the efficient generation of more accurate binary population samples for astrophysical studies.

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Learning the Stellar Structure Equations via Self-supervised Physics-Informed Neural Networks

Stellar astrophysics relies critically on accurate descriptions of the physical conditions inside stars. Traditional solvers such as \texttt{MESA} (Modules for Experiments in Stellar Astrophysics), which employ adaptive finite-difference methods, can become computationally expensive and challenging to scale for large stellar population synthesis ($>10^9$ stars). In this work, we present an self-supervised physics-informed neural network (PINN) framework that provides a mesh-free and fully differentiable approach to solving the stellar structure equations under hydrostatic and thermal equilibrium. The model takes as input the stellar boundary conditions (at the center and surface) together with the chemical composition, and learns continuous radial profiles for mass $M_r(r)$, pressure $P(r)$, density $ρ(r)$, temperature $T(r)$, and luminosity $L_r(r)$ by enforcing the governing structure equations through physics-based loss terms. To incorporate realistic microphysics, we introduce auxiliary neural networks that approximate the equation of state and opacity tables as smooth, differentiable functions of the local thermodynamic state. These surrogates replace traditional tabulated inputs and enable end-to-end training. Once trained for a given star, the model produces continuous solutions across the entire radial domain without requiring discretization or interpolation. Validation against benchmark \texttt{MESA} models across a range of stellar masses yields a Mean Relative Absolute Error of $3.06\%$ and an average $R^2$ score of $99.98\%$. To our knowledge, this is the first demonstration that the stellar structure equations can be solved in a fully self-supervised and data-free fashion employing PINNs. This work establishes a foundation for scalable, physics-informed emulation of stellar interiors and opens the door to future extensions toward time-dependent stellar evolution.

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A binary merger product as the direct progenitor of a Type II-P supernova

Type II-P supernovae (SNe II-P) are the most common class of core-collapse SNe in the local Universe and play critical roles in many aspects of astrophysics. Since decades ago theorists have predicted that SNe II-P may originate not only from single stars but also from interacting binaries. While ~20 SNII-P progenitors have been directly detected on pre-explosion images, observational evidence still remains scarce for this speculated binary progenitor channel. In this work, we report the discovery of a red supergiant progenitor for the Type II-P SN 2018gj. While the progenitor resembles those of other SNe II-P in terms of effective temperature and luminosity, it is located in a very old environment and SN 2018gj has an abnormally short plateau in the light curve. With state-of-the-art binary evolution simulations, we find these characteristics can only be explained if the progenitor of SN 2018gj is the merger product of a close binary system, which developed a different interior structure and evolved over a longer timescale compared with single-star evolution. This work provides the first compelling evidence for the long-sought binary progenitor channel toward SNe II-P, and our methodology serves as an innovative and pragmatic tool to motivate further investigations into this previously hidden population of SNe II-P from binaries.

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HST Deep Upper Limits Rule Out a Surviving Massive Binary Companion to the Type Ic Supernova 2012fh

Current explanations of the mass-loss mechanism for stripped-envelope supernovae remain divided between single and binary progenitor systems. Here we obtain deep ultraviolet (UV) imaging with the Hubble Space Telescope (HST) of the Type Ic SN 2012fh to search for the presence of a surviving companion star to the progenitor. We synthesize these observations with archival HST imaging, ground-based spectroscopy, and previous analyses from the literature to provide three independent constraints on the progenitor system. We fit the color-magnitude diagram of the surrounding population to constrain the most likely age of the system to be $<20$ Myr. Analysis of spectra of SN 2012fh provide an estimate of the He core mass of the progenitor star, $>5.6$ M$_{\odot}$. We analyze deep HST images at the precise location after the SN faded to constrain the luminosity of any remaining main-sequence binary companion to be $\log(L/L_{\odot}) \lesssim 3.35$. Combining observational constraints with current binary population synthesis models excludes the presence of a faint stellar companion to SN 2012fh at the $\lesssim10\%$ level. The progenitor was therefore either effectively isolated at the time of explosion or orbited by a black-hole companion. The latter scenario dominates if we only consider models that produce successful supernovae.

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POSYDON Version 2: Population Synthesis with Detailed Binary-Evolution Simulations across a Cosmological Range of Metallicities

Whether considering rare astrophysical events on cosmological scales or unresolved stellar populations, accurate models must account for the integrated contribution from the entire history of star formation upon which that population is built. Here, we describe the second version of POSYDON, an open-source binary population synthesis code based on extensive grids of detailed binary evolution models computed using the MESA code, which follows both stars' structures as a binary system evolves through its complete evolution from the zero-age main sequence, through multiple phases of mass transfer and supernovae, to their death as compact objects. To generate synthetic binary populations, POSYDON uses advanced methods to interpolate between our large, densely spaced grids of simulated binaries. In our updated version of POSYDON, we account for the evolution of stellar binaries across a cosmological range of metallicities, extending from $10^{-4}$ $Z_{\odot}$ to 2 $Z_{\odot}$, including grids specifically focused on the Small and Large Magellanic Clouds (0.2 $Z_{\odot}$ and 0.45 $Z_{\odot}$). In addition to describing our model grids and detailing our methodology, we outline several improvements to POSYDON. These include the incorporation of single stars in stellar populations, a treatment for stellar mergers, and a careful modeling of "reverse-mass transferring" binaries in which a once-accreting star later becomes a donor star. Our simulations are focused on binaries with at least one high-mass component, such as those that host neutron stars and black holes, and we provide post-processing methods to account for the cosmological evolution of metallicity and star formation as well as rate calculations for transient events.

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Mass-gap Black Holes in Coalescing Neutron Star Black Hole Binaries

The existence of a mass gap of $3-5\,M_{\odot}$ between the heaviest neutron stars (NSs) and the lightest black holes (BHs), inferred from the BH mass distribution in low mass X-ray binaries (LMXBs), has been suggested for decades. The recently reported gravitational-wave source GW230529 has been confidently identified as a NSBH merger, with the BH mass falling within this lower mass gap. This detection provides strong evidence against the existence of the latter and introduces new implications for the coalescing NSBH population, including a revised BH mass distribution and an updated local merger rate. In this study, we employ POSYDON, a binary population synthesis code that integrates detailed single- and binary-star models, to investigate coalescing NSBH binaries formed through isolated binary evolution. In particular, we focus on the BH mass distribution of the intrinsic NSBH merger population. We find that, with a high common-envelope efficiency of $α_{\rm{CE}} =2 $, the BH masses in NSBH mergers concentrate in the lower mass gap, aligning more closely with observations. However, after accounting for the constraints of the selection bias against mass-gap BHs in LMXBs, which suggests that the maximum NS birth mass is below $\simeq 2\,M_{\odot}$, we find that introducing a high $α_{\rm{CE}}$ is not required to match observations. Additionally, we explore the impact of core-collapse supernova kicks. Finally, we present the property distributions of observable NSBH mergers from our simulation and find that they match well with the observations. We find that the fraction of electromagnetic counterparts in observable populations is $\approx 4-30\%$, depending on different NS equations of state. Future detections of coalescing NSBH binaries would provide invaluable insights into SN mechanisms, common envelope evolution, and NS physics.

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Emulators for stellar profiles in binary population modeling

Knowledge about the internal physical structure of stars is crucial to understanding their evolution. The novel binary population synthesis code POSYDON includes a module for interpolating the stellar and binary properties of any system at the end of binary MESA evolution based on a pre-computed set of models. In this work, we present a new emulation method for predicting stellar profiles, i.e., the internal stellar structure along the radial axis, using machine learning techniques. We use principal component analysis for dimensionality reduction and fully-connected feed-forward neural networks for making predictions. We find accuracy to be comparable to that of nearest neighbor approximation, with a strong advantage in terms of memory and storage efficiency. By providing a versatile framework for modeling stellar internal structure, the emulation method presented here will enable faster simulations of higher physical fidelity, offering a foundation for a wide range of large-scale population studies of stellar and binary evolution.

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Challenges in Forming Millisecond Pulsar-Black Holes from Isolated Binaries

Binaries harboring a millisecond pulsar (MSP) and a black hole (BH) are a key observing target for current and upcoming pulsar surveys. We model the formation and evolution of such binaries in isolation at solar metallicity using the next-generation binary population synthesis code POSYDON. We examine neutron star (NS)-BH binaries where the NS forms first (labeled NSBH), as the NS must be able to spin-up to MSP rotation periods before the BH forms in these systems. We find that NSBHs are very rare and have a birth rate < 1 Myr$^{-1}$ for a Milky Way-like galaxy in our typical models. The NSBH birth rate is 2-3 orders of magnitude smaller than that for NS-BHs where the BH forms first (labeled BHNS). These rates are also sensitive to model assumptions about the supernova (SN) remnant masses, natal kicks, and common-envelope efficiency. We find that 100% of NSBHs undergo a mass ratio reversal before the first SN and up to 64% of NSBHs undergo a double common envelope phase after the mass ratio reversal occurs. Most importantly, no NSBH binaries in our populations undergo a mass transfer phase, either stable or unstable, after the first SN. This implies that there is no possibility of pulsar spin-up via accretion, and thus MSP-BH binaries cannot form. Thus, dynamical environments and processes may provide the only formation channels for such MSP-BH binaries.

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Irregularly Sampled Time Series Interpolation for Detailed Binary Evolution Simulations

Modeling of large populations of binary stellar systems is an intergral part of a many areas of astrophysics, from radio pulsars and supernovae to X-ray binaries, gamma-ray bursts, and gravitational-wave mergers. Binary population synthesis codes that employ self-consistently the most advanced physics treatment available for stellar interiors and their evolution and are at the same time computationally tractable have started to emerge only recently. One element that is still missing from these codes is the ability to generate the complete time evolution of binaries with arbitrary initial conditions using pre-computed three-dimensional grids of binary sequences. Here we present a highly interpretable method, from binary evolution track interpolation. Our method implements simulation generation from irregularly sampled time series. Our results indicate that this method is appropriate for applications within binary population synthesis and computational astrophysics with time-dependent simulations in general. Furthermore we point out and offer solutions to the difficulty surrounding evaluating performance of signals exhibiting extreme morphologies akin to discontinuities.

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The Formation of Black Holes in Non-interacting, Isolated Binaries. Gaia Black Holes as Calibrators of Stellar Winds From Massive Stars

Context. The black holes discovered using Gaia, especially Gaia BH1 and BH2, have low mass companions of solar-like metallicity in wide orbits. For standard isolated binary evolution formation channels including interactions such an extreme mass ratio is unexpected; especially in orbits of hundreds to thousands of days. Aims. Here, we investigate a non-interacting formation path for isolated binaries to explain the formation of Gaia BH1 and BH2. Methods. We use single star models computed with MESA to constrain the main characteristics of possible progenitors of long-period black hole binaries like Gaia BH1 and BH2. Then, we incorporate these model grids into the binary population synthesis code POSYDON, to explore whether the formation of the observed binaries at solar metallicity is indeed possible. Results. We find that winds of massive stars ($\gtrsim 80\,M_\odot$), especially during the Wolf-Rayet phase, tend to cause a plateau in the initial stellar mass to final black hole mass relation (at about $13\,M_\odot$ in our default wind prescription). However, stellar winds at earlier evolutionary phases are also important at high metallicity, as they prevent the most massive stars from expanding ($<100\,R_\odot$) and filling their Roche lobe. Consequently, the strength of the applied winds affects the range of the final black hole masses in non-interacting binaries, making it possible to form systems similar to Gaia BH1 and BH2. Conclusions. We deduce that wide binaries with a black hole and a low mass companion can form at high metallicity without binary interactions. There could be hundreds of such systems in the Milky Way. The mass of the black hole in binaries evolved through the non-interacting channel can potentially provide insights into the wind strength during the progenitors evolution.

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To Be or not to Be: the role of rotation in modeling Galactic Be X-ray Binaries

Be X-ray binaries (Be-XRBs) are one of the largest subclasses of high-mass X-ray binaries, comprised of a rapidly rotating Be star and neutron star companion in an eccentric orbit, intermittently accreting material from a decretion disk around the donor. Originating from binary stellar evolution, Be-XRBs are of significant interest to binary population synthesis (BPS) studies, encapsulating the physics of supernovae, common envelope, and mass transfer (MT). Using the state-of-the-art BPS code, POSYDON, which relies on pre-computed grids of detailed binary stellar evolution models, we investigate the Galactic Be-XRB population. POSYDON incorporates stellar rotation self-consistently during MT phases, enabling detailed examination of the rotational distribution of Be stars in multiple phases of evolution. Our fiducial BPS and Be-XRB model align well with the orbital properties of Galactic Be-XRBs, emphasizing the role of rotational constraints. Our modeling reveals a rapidly rotating population ($ω/ω_\mathrm{crit} \gtrsim 0.3$) of Be-XRB-like systems with a strong peak at intermediate rotation rates ($ω/ω_\mathrm{crit} \simeq 0.6$) in close alignment with observations. All Be-XRBs undergo a MT phase before the first compact object forms, with over half experiencing a second MT phase from a stripped helium companion (Case BB). Computing rotationally-limited MT efficiencies and applying them to our population, we derive a physically motivated MT efficiency distribution, finding that most Be-XRBs have undergone highly non-conservative MT ($\barβ_\mathrm{rot} \simeq 0.05$). Our study underscores the importance of detailed angular momentum modeling during MT in interpreting Be-XRB populations, emphasizing this population as a key probe for the stability and efficiency of MT in interacting binaries.

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Formation of Wind-Fed Black Hole High-mass X-ray Binaries: The Role of Roche-lobe-Overflow Post Black-Hole Formation

The three dynamically confirmed wind-fed black hole high-mass X-ray binaries (BH-HMXBs) are suggested to all contain a highly spinning black hole (BH). However, based on the theories of efficient angular momentum transport inside the stars, we expect that the first-born BHs in binary systems should have low spins, which is consistent with gravitational-wave observations. As a result, the origin of the high BH spins measured in wind-fed BH-HMXBs remains a mystery. In this paper, we conduct a binary population synthesis study on wind-fed BH-HMXBs at solar metallicity with the use of the newly developed code POSYDON, considering three scenarios for BH accretion: Eddington-limited, moderately super-Eddington, and fully conservative accretion. Taking into account the conditions for accretion-disk formation, we find that regardless of the accretion model, these systems are more likely to have already experienced a phase of Roche-lobe overflow after the BH formation. To account for the extreme BH spins, highly conservative accretion onto BHs is required, when assuming the accreted material carries the specific angular momentum at the innermost stable orbit. Besides, in our simulations we found that the systems with donor stars within the mass range of $10-20\,M_{\odot}$ are prevalent, posing a challenge in explaining simultaneously all observed properties of the BH-HMXB in our Galaxy, Cygnus X-1, and potentially hinting that the accretion efficiency onto non-degenerate stars, before the formation of the BH, is also more conservative than assumed in our simulations.

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