The reviewed record of science sign in
Pith

arxiv: 2607.06067 · v1 · pith:BOBPIXW4 · submitted 2026-07-07 · astro-ph.HE · astro-ph.SR

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

Tian Huang , Xizhen Lu , Guoliang L\"u , Chunhua Zhu , Sufen Guo , Helei Liu , Zhuowen Li , Zhijun Wang
show 3 more authors
Lei Li Wei-Min Gu Nurzada Beissen
This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-07-08 17:26 UTCglm-5.2pith:BOBPIXW4record.jsonopen to challenge →

classification astro-ph.HE astro-ph.SR
keywords evolutionmasstriplebinaryblackdrivesframeworkgw190706
0
0 comments X

The pith

Triple Stars Can Forge Black Holes in the 'Forbidden' Mass Gap

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Some LIGO gravitational-wave detections contain black holes weighing 45–130 solar masses — a range where pair-instability supernovae should destroy stars entirely, leaving no remnant. This paper proposes that isolated hierarchical triple stars (three stars orbiting each other in a stable configuration) can bypass this destruction. In the proposed channel, two stars in a very tight inner orbit undergo tidal synchronization that drives chemically homogeneous evolution (CHE), bypassing the giant-phase expansion that normally leads to problematic mass transfer. These stars collapse directly into black holes. When the third, outer star later expands into a giant, it engulfs the inner binary in a triple common envelope (TCE) phase, shrinking the inner orbit enough to force the two black holes to merge promptly. Because the inner black holes are equal-mass and spin-aligned, the merger produces no gravitational recoil kick, so the merged remnant stays bound to the third star's collapsing core. The result is a binary containing one massive second-generation black hole sitting squarely in the PISN mass gap, paired with a smaller first-generation black hole. The paper traces a specific evolutionary track reproducing GW190706 (primary ~72.8 solar masses, secondary ~39.3 solar masses, effective spin ~0.45) and computes a volumetric merger rate of ~0.011 Gpc⁻³ yr⁻¹ at z≈0.68, accounting for roughly 22% of the empirically inferred rate for this sub-population.

Core claim

The paper constructs a complete evolutionary chain from a coplanar hierarchical triple of ~109 solar-mass stars at low metallicity (Z=0.001) through CHE of the inner binary, direct collapse via failed supernovae, a TCE phase driven by the tertiary's giant expansion, and prompt inner-binary merger, arriving at a final BBH system whose masses (72.8 + 39.3 solar masses) and effective spin (χ_eff ≈ 0.45) match GW190706. The rate calculation, built from empirically motivated initial-parameter distributions and a triple-star fraction of 0.73, yields a birth probability P_sys ≈ 1.41×10⁻⁹ per massive star, translating to ~22% of the observed mass-gap merger rate.

What carries the argument

Chemically homogeneous evolution (CHE) in the tidally locked inner binary; the triple common envelope (TCE) phase computed via the SCATTER angular-momentum-conservation formalism; the zero-recoil condition from equal-mass, spin-aligned inner mergers; and the direct-collapse (failed supernova) channel for forming first-generation black holes without natal kicks.

If this is right

  • If this channel is real, a subset of PISN mass-gap BBH mergers should show high positive effective spins (~0.4–0.7) from second-generation remnant spin, distinguishable from cluster-formed hierarchical mergers which would show more isotropic spin orientations.
  • The channel predicts a correlation between mass-gap primary mass and effective spin: the 2g remnant spin of ~0.686 is inherited from the inner merger, so systems near the center of the gap should cluster around χ_eff ≈ 0.45 when paired with a non-spinning 1g companion.
  • Future space-based detectors could potentially detect the tertiary companion's gravitational signature or residual eccentricity in pre-merger systems, providing a direct test of the triple-origin hypothesis.
  • The 22% rate contribution leaves room for complementary channels (cluster dynamics, AGN disks) to produce the remaining mass-gap events, making this a partial rather than exclusive explanation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The channel's predictability hinges on the inner binary having a mass ratio of exactly unity after early over-contact equilibration. If real systems retain q < 1, the gravitational recoil from the inner merger would be nonzero, potentially unbinding the system and reducing the rate well below 22%.
  • The SCATTER formalism is calibrated on post-CE binaries, not on triple systems with the extreme mass ratios and configurations studied here. If its orbital-shrinkage predictions are off by even a modest factor, the inner BBH may not merge promptly (t_GW > 1 yr threshold), breaking the chain.
  • The assumption of zero natal spin for 1g black holes (from efficient Tayler-Spruit angular momentum transport) is load-bearing for the χ_eff prediction. If 1g BHs retain even modest spins, the effective-spin signature would shift, potentially weakening the match with GW190706.
  • The delay-time approximation (neglecting delays beyond ~10 Myr) may underestimate or overestimate the rate at z≈0.68 depending on the true cosmic metallicity distribution at that redshift.

Load-bearing premise

The entire channel depends on the SCATTER triple common-envelope formalism, an angular-momentum-conservation prescription with fitted parameters (η, A, B, δ) calibrated on a limited sample of post-CE binaries. If this formalism misestimates the post-CE orbital shrinkage by even a factor of a few, the inner binary either fails to merge promptly or the system is disrupted, invalidating both the rate prediction and the GW190706 evolutionary track.

What would settle it

If future GW catalogs show that PISN mass-gap events with high positive χ_eff are rarer than ~22% of the sub-population rate, or if their spin-orbit misalignments are inconsistent with the strictly coplanar, spin-aligned topology this channel requires, the triple-CHE-TCE pathway would be constrained to a smaller contribution or ruled out as the dominant channel.

Figures

Figures reproduced from arXiv: 2607.06067 by Chunhua Zhu, Guoliang L\"u, Helei Liu, Lei Li, Nurzada Beissen, Sufen Guo, Tian Huang, Wei-Min Gu, Xizhen Lu, Zhijun Wang, Zhuowen Li.

Figure 1
Figure 1. Figure 1: FIG. 1: The complete evolutionary pathway of GW190706, from the zero-age main sequence (ZAMS) to the final [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

4 major / 7 minor

Summary. The manuscript proposes an isolated hierarchical triple stellar evolution channel to produce binary black hole (BBH) mergers with one component in the pair-instability supernova (PISN) mass gap. The channel combines tidally driven chemically homogeneous evolution (CHE) in a tight inner binary with a subsequent triple common envelope (TCE) phase computed via the SCATTER formalism. A specific evolutionary track is shown to reproduce the observed properties of GW190706 (m1≈72.8 M☉, m2≈39.3 M☉, χeff≈0.45). A volumetric merger rate of ~0.011 Gpc⁻³ yr⁻¹ is derived, claimed to account for ~22% of the empirical rate for this sub-population at z≈0.68.

Significance. The question of how black holes in the PISN mass gap form is actively debated, and an isolated triple channel is a legitimate and interesting contribution to this discussion. The paper provides a concrete, step-by-step evolutionary pathway and a falsifiable rate prediction. The combination of CHE (which naturally produces aligned-spin, equal-mass inner binaries with zero recoil) with a TCE-driven inspiral is a physically motivated mechanism. However, the significance of the rate claim is limited by the unvalidated nature of the SCATTER formalism for triples and the unjustified survival fraction, both of which are load-bearing for the quantitative prediction.

major comments (4)
  1. §II.B, Eqs. (4)–(9): The SCATTER formalism is the load-bearing physical ingredient of the entire channel. The post-TCE inner-orbit shrinkage (Eq. 9) determines whether t_GW ≤ 1 yr (Eq. 18), which is the criterion for a prompt inner-binary merger. SCATTER was calibrated on post-CE binaries (Di Stefano et al. 2023, ref [77]), not on triple systems. The extension to triples assumes that the envelope mass partitioning between inner and outer orbits follows the Roche-lobe approximation in Eq. (8), but no 3D hydrodynamic validation of this assumption is cited. If the post-TCE inner orbit is larger than predicted by a factor of ~2–3, t_GW will exceed the tertiary helium-star lifetime (~0.1–1 Myr), the inner binary will not merge promptly, and no 2g+1g system forms. The manuscript should explicitly acknowledge this uncertainty and, at minimum, provide a sensitivity analysis showing how the rate和
  2. §III.C, Eq. (21): The survival fraction f_surv = 0.5 is introduced without justification ('Adopting a fiducial survival fraction of f_surv = 0.5 to account for dynamical disruption'). This parameter enters linearly into the final rate. More critically, it is unclear what f_surv is meant to capture: dynamical disruption, the fraction of systems satisfying t_GW ≤ 1 yr, or both? If it includes the latter, the rate calculation becomes partially circular, because P_sys is already computed from narrow parameter windows (§III.B) chosen because they produce the desired outcome, and f_surv then implicitly absorbs the unknown SCATTER success fraction. The paper should either compute this fraction from the simulations or provide a clear physical justification for the adopted value, with an exploration of how the rate scales with it.
  3. §III.C, Eq. (21): The quantity ⟨M⟩ in Eq. (21) is never defined. It presumably represents the mean stellar mass for IMF normalization, but its value is not stated. Since the rate is linear in 1/⟨M⟩, this omission makes the rate calculation unreproducible. Please define ⟨M⟩ and state its value.
  4. §III, §III.C: There is an internal inconsistency in the event count. §III states that after excluding events with negative χ_eff, 'the remaining sources, notably GW230824 and GW190706' are well-explained (implying N≈2). Yet in §III.C, Eq. (22), N_obs = 6 is used to compute the empirical rate R_obs ≈ 0.050 Gpc⁻³ yr⁻¹. Additionally, GW230824 does not appear in the initial sample of six events listed in §III (GW230107, GW230928, GW230820, GW190706, GW190620, GW170729). Please clarify which events are used for the rate baseline and reconcile the filtering described in §III with the N_obs = 6 used in Eq. (22).
minor comments (7)
  1. Figure 1 is difficult to parse: the orbital separation and mass labels overlap, and the time axis is non-linear with unmarked jumps (e.g., from 3.644 to 3.772 to 24.609 Myr). A cleaner version with a logarithmic time axis or separate panels would help.
  2. §III.A: The statement that ω_spin/ω_crit ≈ 1.21 triggers CHE should cite the specific threshold criterion used (e.g., from Li et al. 2025, ref [71]) and note its uncertainty.
  3. §III.A: The paper states the tertiary helium core 'also experiences violent episodic mass loss via PPISNe before undergoing a FSNe.' The pre-SN mass of the tertiary core and the resulting BH mass (39.3 M☉) should be traced explicitly, as is done for the inner binary components.
  4. §III.B: The outer period range ΔP_out ∈ [400, 1200] days is stated, but the GW190706 fiducial system has a_out = 3600 R☉, which for ~109 M☉ total mass corresponds to P_out ≈ 1400 days — outside this range. Please reconcile.
  5. Abstract and §IV: 'GW230107, GW230820, and GW230928' are cited as GWTC-4 events but no reference is given for these beyond the GWTC-4 catalog (ref [12]). If these are preliminary, this should be noted.
  6. §II.E, Eq. (14): The SFRD parameters a=0.015, b=2.7, c=2.9, d=5.6 are attributed to Madau & Dickinson (2014) and Madau & Fragos (2017) but the values differ between those references. Please clarify which parameter set is used.
  7. Several typographical issues: 'Merge' in the title should be 'Mergers'; 'A V AILABLE' in the Data Available section; inconsistent spacing in equations.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee raises four major points: (1) the SCATTER formalism lacks hydrodynamic validation for triples and a sensitivity analysis is needed; (2) the survival fraction f_surv=0.5 is unjustified and its physical meaning unclear; (3) ⟨M⟩ in Eq. (21) is undefined; (4) an internal inconsistency exists in the event count and event list between §III and §III.C. We agree that points (3) and (4) require correction, and that points (1) and (2) warrant additional discussion and sensitivity analysis. We do not claim that the current rate prediction is robust to order-unity uncertainties in the SCATTER formalism, and we will revise the manuscript to make this explicit.

read point-by-point responses

  1. Referee: SCATTER formalism is load-bearing, calibrated on post-CE binaries not triples, no 3D hydrodynamic validation cited. If post-TCE inner orbit is larger by factor 2-3, t_GW exceeds tertiary helium-star lifetime and no 2g+1g system forms. Should acknowledge uncertainty and provide sensitivity analysis.

    Authors: We agree that the SCATTER formalism has not been validated against 3D hydrodynamic simulations of triple common envelopes, and that this is a genuine uncertainty affecting the rate prediction. We will add an explicit caveat in §II.B acknowledging this limitation. Regarding the sensitivity analysis: the referee's concern is well-taken. The critical question is whether the post-TCE inner orbit a_in,f is small enough that t_GW ≤ 1 yr (Eq. 18). In our fiducial track, a_in,f ≈ 13.5 R☉ yields t_GW ≈ 0.05 yr, which is well below the 1 yr threshold. If a_in,f were larger by a factor of 2-3, t_GW would scale as a^4 (Eq. 18), giving t_GW ≈ 0.8-6.4 yr. At the lower end (factor ~2), the system would still satisfy t_GW ≤ 1 yr; at factor ~3, it would not. We will include a sensitivity analysis showing how the rate scales with a multiplicative factor on a_in,f, demonstrating that the channel survives for moderate (~2x) overestimates of the post-TCE inner orbit but fails for larger ones. We will also note that 3D hydrodynamic simulations of TCE phases are needed to resolve this uncertainty definitively. revision: yes

  2. Referee: f_surv = 0.5 introduced without justification. Unclear what it captures: dynamical disruption, fraction satisfying t_GW ≤ 1 yr, or both? If it includes the latter, rate calculation becomes partially circular since P_sys is already computed from narrow parameter windows. Should compute from simulations or provide physical justification with exploration of rate scaling.

    Authors: The referee is correct that f_surv = 0.5 is insufficiently justified and that its physical scope is ambiguous. To clarify: f_surv is intended to account for dynamical disruption of the triple system during the TCE phase and subsequent evolution — i.e., systems that are disrupted by natal kicks, dynamical instabilities, or envelope ejection that unbinds the inner binary. It is not intended to absorb the fraction of systems satisfying t_GW ≤ 1 yr, which is already implicitly encoded in the narrow parameter windows of §III.B. However, we acknowledge that this distinction is not clearly stated in the manuscript, and the referee is right that the current presentation risks circularity. We will revise the text to explicitly define f_surv as the fraction of systems surviving dynamical disruption (excluding the t_GW criterion), and we will add a rate scaling showing R_triple ∝ f_surv for f_surv ∈ [0.1, 1.0]. We note honestly that we cannot compute f_surv from first principles without a full population synthesis of TCE outcomes, which is beyond the scope of this paper. We will adopt f_surv = 0.5 as a fiducial value but present the rate as scaling linearly with this parameter. revision: yes

  3. Referee: ⟨M⟩ in Eq. (21) is never defined. Presumably mean stellar mass for IMF normalization, but value not stated. Rate is linear in 1/⟨M⟩, making calculation unreproducible. Please define and state its value.

    Authors: The referee is correct. ⟨M⟩ represents the mean stellar mass obtained by integrating the Kroupa IMF over the standard mass range [0.1, 150] M☉. Using the IMF P(M) ∝ M^{-2.3} for M > 0.5 M☉ (with the full Kroupa piecewise form below that), we compute ⟨M⟩ ≈ 0.35 M☉. We will add this definition and value to the manuscript, and we will show the explicit substitution so that the rate calculation is reproducible. We thank the referee for catching this omission. revision: yes

  4. Referee: Internal inconsistency in event count. §III says after excluding negative χ_eff events, 'remaining sources, notably GW230824 and GW190706' are well-explained (implying N≈2). But §III.C Eq. (22) uses N_obs=6. Also GW230824 does not appear in the initial sample of six events listed in §III. Clarify which events are used for rate baseline and reconcile filtering with N_obs=6.

    Authors: The referee has identified a genuine inconsistency in our manuscript, and we thank them for catching it. The issue is twofold. First, GW230824 was erroneously mentioned in §III as a well-explained event; it does not appear in our initial sample of six events (GW230107, GW230928, GW230820, GW190706, GW190620, GW170729) and should not have been referenced. This is an error we will correct. Second, there is a logical inconsistency between the filtering described in §III (which excludes negative-χ_eff events, leaving fewer than six) and the use of N_obs = 6 in Eq. (22). The intent was to use all six events as the observational baseline for the empirical rate, while noting that our model specifically explains the subset with positive χ_eff (such as GW190706). However, this logic is not clearly presented. We will revise §III and §III.C to either (a) use N_obs = 6 as the total population baseline and explicitly state that our channel accounts for a subset, or (b) recompute R_obs using only the positive-χ_eff subset. We will adopt option (a) for consistency with the 22% comparison, but will clarify the distinction between the full baseline and the subset our model targets. revision: yes

Circularity Check

0 steps flagged

No significant circularity found; the rate calculation and GW190706 match are fitting/assumption-laden but not self-reducing

full rationale

The paper's derivation chain does not exhibit structural circularity. (1) The GW190706 match: initial conditions (M1=M2=109.2 M☉, M3=108.7 M☉, specific orbital separations) are tuned to reproduce GW190706, but the output masses (~72.8 and 39.3 M☉) and spin (χeff≈0.45) emerge from stellar evolution physics (winds, PPISN, failed SNe, NR fitting formulas), not from the initial conditions by definition. This is fitting, not circularity. (2) The rate calculation (Eq. 21): P_sys is computed from parameter windows (M1∈[107,140] M☉, Pin∈[1.2,2.0] days, etc.) that are defined by the physical requirement of producing gap BHs, and the probabilities within those windows come from externally observed distributions (IMF from Kroupa, period/mass-ratio distributions from Moe & Di Stefano 2017). The rate is then compared to an independently derived empirical baseline (R_obs from GWTC-4 catalog events). This is standard population synthesis methodology, not circular: the windows are defined by physics, the probabilities by observation, and the comparison is to external data. (3) The SCATTER formalism (Eqs. 4–9) is cited from Di Stefano et al. 2023/2026 (refs [76,77]), who are not co-authors of this paper — this is an external prescription, not a self-citation. The η parameter (Eq. 6) is fitted to post-CE binaries and extrapolated to triples, which is an unvalidated extrapolation (a correctness risk), but not circularity since the fit target (binary CE outcomes) differs from the prediction target (triple CE outcomes). (4) The self-citation to Li et al. [71] for CHE parameters is load-bearing, but that work has independent content (its own stellar evolution models) and does not define its inputs in terms of the present paper's results. The f_surv=0.5 is a free assumption, not a fitted-then-predicted quantity. Overall, the central claims have independent content and the derivation does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

8 free parameters · 5 axioms · 0 invented entities

The paper introduces no new particles, forces, or physical entities. It combines existing physical prescriptions (CHE, TCE/SCATTER, MOBSE) within the TSE code. The main burden is carried by free parameters (8 listed) and domain assumptions (5 listed), particularly the unvalidated SCATTER triple CE formalism and the hand-tuned initial conditions for the GW190706 track.

free parameters (8)
  • Metallicity Z=0.001 = 0.001
    Fixed to a single low value to minimize wind mass loss; no metallicity distribution is sampled despite the cosmic integration framework.
  • Inner binary mass ratio q_in=1 = 1.0
    Assumed exactly unity 'to facilitate modeling' (§III.A); the system is initialized post-mass-transfer equilibration.
  • SCATTER η parameters A, B = A=0.95, B=0.6
    Angular momentum transfer efficiency parameters fitted to post-CE binaries [77]; not independently derived.
  • SCATTER δ = 3
    Envelope mass distribution parameter, adopted as typical without sensitivity analysis in this paper.
  • Survival fraction fsurv = 0.5
    Adopted to account for dynamical disruption with no derivation or justification (§III.C).
  • Initial conditions for GW190706 track = M1=M2=109.2 M☉, M3=108.7 M☉, ain=36.1 R☉, aout=3600 R☉
    Hand-set to reproduce GW190706; no parameter space exploration shown.
  • Radiative mass loss fraction = 0.05
    5% of total mass lost in BBH merger, adopted from [114].
  • SFRD parameters a,b,c,d = 0.015, 2.7, 2.9, 5.6
    Cosmic SFR fitting parameters from Madau & Dickinson, used as inputs.
axioms (5)
  • domain assumption Tidal synchronization in binaries with Pin<2 days drives CHE that fully bypasses giant expansion
    §II.A; adopted from Marchant et al. 2016 and Li et al. 2025. The threshold ωspin/ωcrit>1 is checked but the CHE outcome is assumed.
  • domain assumption 1g black holes from isolated stellar evolution have zero natal spin (χ1=χ2=0)
    §II.D; adopted from Fuller & Ma 2019 via Tayler-Spruit dynamo angular momentum transport.
  • domain assumption The SCATTER formalism correctly models triple common envelope orbital decay
    §II.B; the SCATTER mechanism [76,77] is a recently proposed prescription, not validated against 3D hydrodynamic simulations of triple CE.
  • domain assumption Stars with ZAMS mass ≳40 M☉ at Z=0.001 undergo direct collapse with ffb=1 (no natal kick)
    §II.C; adopted from Heger et al. 2003. Metallicity dependence of this threshold is not discussed.
  • standard math The Mardling & Aarseth stability criterion (Eq. 1) is sufficient for triple stability throughout evolution
    §II; empirical criterion widely used but derived for point-mass systems, not evolving stars with mass loss.

pith-pipeline@v1.1.0-glm · 25141 in / 3355 out tokens · 375172 ms · 2026-07-08T17:26:38.583913+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

116 extracted references · 116 canonical work pages · 100 internal anchors

  1. [1]

    The Nucleosynthetic Signature of Population III

    A. Heger and S. E. Woosley, The Nucleosynthetic Signature of Population III, ApJ567, 532 (2002), arXiv:astro-ph/0107037 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  2. [2]

    Mind the gap: The location of the lower edge of the pair instability supernovae black hole mass gap

    R. Farmer, M. Renzo, S. E. de Mink, P. Marchant, and S. Justham, Mind the Gap: The Location of the Lower Edge of the Pair-instability Supernova Black Hole Mass Gap, ApJ887, 53 (2019), arXiv:1910.12874 [astro- ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  3. [3]

    Umeda and K

    H. Umeda and K. Nomoto, Nucleosynthesis of Zinc and Iron Peak Elements in Population III Type II Super- 10 novae: Comparison with Abundances of Very Metal Poor Halo Stars, ApJ565, 385 (2002), arXiv:astro- ph/0103241 [astro-ph]

    work page arXiv 2002

  4. [4]

    Stellar Yields of Rotating First Stars. II. Pair Instability Supernovae and Comparison with Observations

    K. Takahashi, T. Yoshida, and H. Umeda, Stellar Yields of Rotating First Stars. II. Pair-instability Su- pernovae and Comparison with Observations, ApJ857, 111 (2018), arXiv:1803.06630 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  5. [5]

    W. Aoki, N. Tominaga, T. C. Beers, S. Honda, and Y. S. Lee, A chemical signature of first-generation very massive stars, Science345, 912 (2014)

    work page 2014

  6. [6]

    Q.-F. Xing, G. Zhao, Z.-W. Liu, A. Heger, Z.-W. Han, W. Aoki, Y.-Q. Chen, M. N. Ishigaki, H.-N. Li, and J.-K. Zhao, A metal-poor star with abundances from a pair-instability supernova, Nature618, 712 (2023)

    work page 2023

  7. [7]

    T. Abel, G. L. Bryan, and M. L. Norman, The Forma- tion of the First Star in the Universe, Science295, 93 (2002), arXiv:astro-ph/0112088 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  8. [8]

    The First Stars

    V. Bromm and R. B. Larson, The First Stars, ARA&A 42, 79 (2004), arXiv:astro-ph/0311019 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  9. [9]

    One Hundred First Stars : Protostellar Evolution and the Final Masses

    S. Hirano, T. Hosokawa, N. Yoshida, H. Umeda, K. Omukai, G. Chiaki, and H. W. Yorke, One Hun- dred First Stars: Protostellar Evolution and the Final Masses, ApJ781, 60 (2014), arXiv:1308.4456 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  10. [10]

    B. P. Abbott, R. Abbott, T. D. Abbott, LIGO Scientific Collaboration, and Virgo Collaboration, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett.116, 061102 (2016), arXiv:1602.03837 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  11. [11]

    GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run

    R. Abbott, T. D. Abbott, F. Acernese, M. E. Zucker, J. Zweizig, LIGO Scientific Collaboration, VIRGO Collaboration, and KAGRA Collaboration, GWTC- 3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Ob- serving Run, Physical Review X13, 041039 (2023), arXiv:2111.03606 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  12. [12]

    The LIGO Scientific Collaboration, the Virgo Col- laboration, the KAGRA Collaboration, A. G. Abac, I. Abouelfettouh, F. Acernese, K. Ackley, C. Adam- cewicz, S. Adhicary, D. Adhikari, N. Adhikari, R. X. Ad- hikari, V. K. Adkins, S. Afroz, A. Agapito, D. Agarwal, M. Agathos, N. Aggarwal, and S. Aggarwal, GWTC- 4.0: Updating the Gravitational-Wave Transient...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  13. [13]

    B. P. Abbott, R. Abbott, T. D. Abbott, LIGO Scientific Collaboration, and Virgo Collaboration, GW190521: A Binary Black Hole Merger with a Total Mass of 150 M⊙, Phys. Rev. Lett.125, 101102 (2020), arXiv:2009.01075 [gr-qc]

    work page arXiv 2020

  14. [14]

    The Effect of Pair-Instability Mass Loss on Black Hole Mergers

    K. Belczynski, A. Heger, W. Gladysz, A. J. Ruiter, S. Woosley, G. Wiktorowicz, H.-Y. Chen, T. Bu- lik, R. O’Shaughnessy, D. E. Holz, C. L. Fryer, and E. Berti, The effect of pair-instability mass loss on black- hole mergers, A&A594, A97 (2016), arXiv:1607.03116 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  15. [15]

    S. E. Woosley, Pulsational Pair-instability Supernovae, ApJ836, 244 (2017), arXiv:1608.08939 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  16. [16]

    The evolutionary roads leading to low effective spins, high black hole masses, and O1/O2 rates of LIGO/Virgo binary black holes

    K. Belczynski, J. Klencki, C. E. Fields, A. Ole- jak, E. Berti, G. Meynet, C. L. Fryer, D. E. Holz, R. O’Shaughnessy, D. A. Brown, T. Bulik, S. C. Leung, K. Nomoto, P. Madau, R. Hirschi, E. Kaiser, S. Jones, S. Mondal, M. Chruslinska, P. Drozda, D. Gerosa, Z. Doctor, M. Giersz, S. Ekstrom, C. Georgy, A. Askar, V. Baibhav, D. Wysocki, T. Natan, W. M. Farr,...

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  17. [17]

    Formation of GW190521 from stellar evolution: the impact of the hydrogen-rich envelope, dredge-up and $^{12}$C($\alpha$, $\gamma$)$^{16}$O rate on the pair-instability black hole mass gap

    G. Costa, A. Bressan, M. Mapelli, P. Marigo, G. Io- rio, and M. Spera, Formation of GW190521 from stel- lar evolution: the impact of the hydrogen-rich enve- lope, dredge-up, and 12C(α,γ) 16O rate on the pair- instability black hole mass gap, MNRAS501, 4514 (2021), arXiv:2010.02242 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  18. [18]

    Predictions for the hydrogen-free ejecta of pulsational pair-instability supernovae

    M. Renzo, R. Farmer, S. Justham, Y. G¨ otberg, S. E. de Mink, E. Zapartas, P. Marchant, and N. Smith, Predictions for the hydrogen-free ejecta of pulsational pair-instability supernovae, A&A640, A56 (2020), arXiv:2002.05077 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  19. [19]

    Populating the upper black hole mass gap through stellar collisions in young star clusters

    K. Kremer, M. Spera, D. Becker, S. Chatterjee, U. N. Di Carlo, G. Fragione, C. L. Rodriguez, C. S. Ye, and F. A. Rasio, Populating the Upper Black Hole Mass Gap through Stellar Collisions in Young Star Clusters, ApJ 903, 45 (2020), arXiv:2006.10771 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  20. [20]

    U. N. Di Carlo, M. Mapelli, Y. Bouffanais, N. Giacobbo, F. Santoliquido, A. Bressan, M. Spera, and F. Haardt, Binary black holes in the pair instability mass gap, MN- RAS497, 1043 (2020), arXiv:1911.01434 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  21. [21]

    C. L. Rodriguez, M. Zevin, P. Amaro-Seoane, S. Chat- terjee, K. Kremer, F. A. Rasio, and C. S. Ye, Black holes: The next generation—repeated mergers in dense star clusters and their gravitational-wave properties, Phys. Rev. D100, 043027 (2019), arXiv:1906.10260 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  22. [22]

    Black hole growth through hierarchical black hole mergers in dense star clusters: implications for gravitational wave detections

    F. Antonini, M. Gieles, and A. Gualandris, Black hole growth through hierarchical black hole mergers in dense star clusters: implications for gravitational wave de- tections, MNRAS486, 5008 (2019), arXiv:1811.03640 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  23. [23]

    Y. Yang, I. Bartos, V. Gayathri, K. E. S. Ford, Z. Haiman, S. Klimenko, B. Kocsis, S. M´ arka, Z. M´ arka, B. McKernan, and R. O’Shaughnessy, Hierarchical Black Hole Mergers in Active Galactic Nuclei, Phys. Rev. Lett.123, 181101 (2019), arXiv:1906.09281 [astro- ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  24. [24]

    Orbital Migration of Interacting Stellar Mass Black Holes in Disks around Supermassive Black Holes

    A. Secunda, J. Bellovary, M.-M. Mac Low, K. E. S. Ford, B. McKernan, N. W. C. Leigh, W. Lyra, and Z. S´ andor, Orbital Migration of Interacting Stellar Mass Black Holes in Disks around Supermassive Black Holes, ApJ878, 85 (2019), arXiv:1807.02859 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  25. [25]

    Hierarchical mergers of stellar-mass black holes and their gravitational-wave signatures

    D. Gerosa and M. Fishbach, Hierarchical mergers of stellar-mass black holes and their gravitational- wave signatures, Nature Astronomy5, 749 (2021), arXiv:2105.03439 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  26. [26]

    The first gravitational-wave source from the isolated evolution of two 40-100 Msun stars

    K. Belczynski, D. E. Holz, T. Bulik, and R. O’Shaughnessy, The first gravitational-wave source from the isolated evolution of two stars in the 40-100 solar mass range, Nature534, 512 (2016), arXiv:1602.04531 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  27. [27]

    L. A. C. van Son, S. E. De Mink, F. S. Broekgaarden, M. Renzo, S. Justham, E. Laplace, J. Mor´ an-Fraile, D. D. Hendriks, and R. Farmer, Polluting the Pair- instability Mass Gap for Binary Black Holes through Super-Eddington Accretion in Isolated Binaries, ApJ 897, 100 (2020), arXiv:2004.05187 [astro-ph.HE]. 11

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  28. [28]

    A new route towards merging massive black holes

    P. Marchant, N. Langer, P. Podsiadlowski, T. M. Tauris, and T. J. Moriya, A new route towards merging massive black holes, A&A588, A50 (2016), arXiv:1601.03718 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  29. [29]

    J. S. Vink, E. R. Higgins, A. A. C. Sander, and G. N. Sabhahit, Maximum black hole mass across cos- mic time, MNRAS504, 146 (2021), arXiv:2010.11730 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  30. [30]

    Formation of black holes in the pair-instability mass gap: Hydrodynamical simulations of a head-on massive star collision

    A. Ballone, G. Costa, M. Mapelli, M. MacLeod, S. Tor- niamenti, and J. M. Pacheco-Arias, Formation of black holes in the pair-instability mass gap: hydrodynamical simulations of a head-on massive star collision, MNRAS 519, 5191 (2023), arXiv:2204.03493 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  31. [31]

    R. A. Patton, M. H. Pinsonneault, and T. A. Thomp- son, The structure and evolution of a high-mass stellar merger in the hertzsprung gap, The Astrophysical Jour- nal987, 212 (2025)

    work page 2025

  32. [32]

    Livio and N

    M. Livio and N. Soker, The Common Envelope Phase in the Evolution of Binary Stars, ApJ329, 764 (1988)

    work page 1988

  33. [33]

    The Cosmic Evolution of Binary Black Holes in Young, Globular and Nuclear Star Clusters: Rates, Masses, Spins and Mixing Fractions

    M. Mapelli, Y. Bouffanais, F. Santoliquido, M. Arca Sedda, and M. C. Artale, The cosmic evolution of binary black holes in young, globular, and nuclear star clusters: rates, masses, spins, and mixing fractions, MNRAS511, 5797 (2022), arXiv:2109.06222 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  34. [34]

    B. M. Ziosi, M. Mapelli, M. Branchesi, and G. Tormen, Dynamics of stellar black holes in young star clusters with different metallicities - II. Black hole-black hole binaries, MNRAS441, 3703 (2014), arXiv:1404.7147 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  35. [35]

    U. N. Di Carlo, N. Giacobbo, M. Mapelli, M. Pasquato, M. Spera, L. Wang, and F. Haardt, Merging black holes in young star clusters, MNRAS487, 2947 (2019), arXiv:1901.00863 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  36. [36]

    Black hole mergers from an evolving population of globular clusters

    G. Fragione and B. Kocsis, Black Hole Mergers from an Evolving Population of Globular Clusters, Phys. Rev. Lett.121, 161103 (2018), arXiv:1806.02351 [astro- ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  37. [37]

    S. F. Portegies Zwart and S. L. W. McMillan, Black Hole Mergers in the Universe, ApJ528, L17 (2000), arXiv:astro-ph/9910061 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  38. [38]

    Black Hole Coagulation: Modeling Hierarchical Mergers in Black Hole Populations

    Z. Doctor, D. Wysocki, R. O’Shaughnessy, D. E. Holz, and B. Farr, Black Hole Coagulation: Modeling Hierar- chical Mergers in Black Hole Populations, ApJ893, 35 (2020), arXiv:1911.04424 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  39. [39]

    Hierarchical black hole mergers in young, globular and nuclear star clusters: the effect of metallicity, spin and cluster properties

    M. Mapelli, M. Dall’Amico, Y. Bouffanais, N. Gia- cobbo, M. Arca Sedda, M. C. Artale, A. Ballone, U. N. Di Carlo, G. Iorio, F. Santoliquido, and S. Tornia- menti, Hierarchical black hole mergers in young, glob- ular and nuclear star clusters: the effect of metallicity, spin and cluster properties, MNRAS505, 339 (2021), arXiv:2103.05016 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  40. [40]

    Rapid and Bright Stellar-mass Binary Black Hole Mergers in Active Galactic Nuclei

    I. Bartos, B. Kocsis, Z. Haiman, and S. M´ arka, Rapid and Bright Stellar-mass Binary Black Hole Merg- ers in Active Galactic Nuclei, ApJ835, 165 (2017), arXiv:1602.03831 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  41. [41]

    N. C. Stone, B. D. Metzger, and Z. Haiman, Assisted inspirals of stellar mass black holes embedded in AGN discs: solving the ‘final au problem’, MNRAS464, 946 (2017), arXiv:1602.04226 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  42. [42]

    J. M. Bellovary, M.-M. Mac Low, B. McKernan, and K. E. S. Ford, Migration Traps in Disks around Supermassive Black Holes, ApJ819, L17 (2016), arXiv:1511.00005 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  43. [43]

    On stellar-mass black hole mergers in AGN disks detectable with LIGO

    B. McKernan, K. E. S. Ford, J. Bellovary, N. W. C. Leigh, Z. Haiman, B. Kocsis, W. Lyra, M.-M. Mac Low, B. Metzger, M. O’Dowd, S. Endlich, and D. J. Rosen, Constraining Stellar-mass Black Hole Mergers in AGN Disks Detectable with LIGO, ApJ866, 66 (2018), arXiv:1702.07818 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  44. [44]

    Formation and Evolution of Compact Object Binaries in AGN Disks

    H. Tagawa, Z. Haiman, and B. Kocsis, Formation and Evolution of Compact-object Binaries in AGN Disks, ApJ898, 25 (2020), arXiv:1912.08218 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  45. [45]

    Mass-gap Mergers in Active Galactic Nuclei

    H. Tagawa, B. Kocsis, Z. Haiman, I. Bartos, K. Omukai, and J. Samsing, Mass-gap Mergers in Active Galactic Nuclei, ApJ908, 194 (2021), arXiv:2012.00011 [astro- ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  46. [46]

    Very massive stars, pair-instability supernovae and intermediate-mass black holes with the SEVN code

    M. Spera and M. Mapelli, Very massive stars, pair- instability supernovae and intermediate-mass black holes with the sevn code, MNRAS470, 4739 (2017), arXiv:1706.06109 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  47. [47]

    Pulsational pair-instability supernovae in very close binaries

    P. Marchant, M. Renzo, R. Farmer, K. M. W. Pappas, R. E. Taam, S. E. de Mink, and V. Kalogera, Pulsational Pair-instability Supernovae in Very Close Binaries, ApJ 882, 36 (2019), arXiv:1810.13412 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  48. [48]

    H. Sana, S. E. de Mink, A. de Koter, N. Langer, C. J. Evans, M. Gieles, E. Gosset, R. G. Izzard, J.-B. Le Bouquin, and F. R. N. Schneider, Binary Interaction Dominates the Evolution of Massive Stars, Science337, 444 (2012), arXiv:1207.6397 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  49. [49]

    Stellar Multiplicity

    G. Duchˆ ene and A. Kraus, Stellar Multiplicity, ARA&A 51, 269 (2013), arXiv:1303.3028 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  50. [50]

    Southern Massive Stars at High Angular Resolution: Observational Campaign and Companion Detection

    H. Sana, J.-B. Le Bouquin, S. Lacour, J.-P. Berger, G. Duvert, L. Gauchet, B. Norris, J. Olofsson, D. Pickel, G. Zins, O. Absil, A. de Koter, K. Krat- ter, O. Schnurr, and H. Zinnecker, Southern Massive Stars at High Angular Resolution: Observational Cam- paign and Companion Detection, ApJS215, 15 (2014), arXiv:1409.6304 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  51. [51]

    H. A. Kobulnicky, D. C. Kiminki, M. J. Lundquist, J. Burke, J. Chapman, E. Keller, K. Lester, E. K. Rolen, E. Topel, A. Bhattacharjee, R. A. Smullen, C. A. Vargas ´Alvarez, J. C. Runnoe, D. A. Dale, and M. M. Brotherton, Toward Complete Statistics of Mas- sive Binary Stars: Penultimate Results from the Cygnus OB2 Radial Velocity Survey, ApJS213, 34 (2014)...

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  52. [52]

    Mind your Ps and Qs: the Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars

    M. Moe and R. Di Stefano, Mind Your Ps and Qs: The Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars, ApJS230, 15 (2017), arXiv:1606.05347 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  53. [53]

    Binary black hole mergers from field triples: properties, rates and the impact of stellar evolution

    F. Antonini, S. Toonen, and A. S. Hamers, Binary Black Hole Mergers from Field Triples: Properties, Rates, and the Impact of Stellar Evolution, ApJ841, 77 (2017), arXiv:1703.06614 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  54. [54]

    Black Hole and Neutron Star Binary Mergers in Triple Systems: Merger Fraction and Spin-Orbit Misalignment

    B. Liu and D. Lai, Black Hole and Neutron Star Binary Mergers in Triple Systems: Merger Fraction and Spin-Orbit Misalignment, ApJ863, 68 (2018), arXiv:1805.03202 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  55. [55]

    Black hole-neutron star mergers from triples

    G. Fragione and A. Loeb, Black hole-neutron star mergers from triples, MNRAS486, 4443 (2019), arXiv:1903.10511 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  56. [56]

    Massive Stellar Triples Leading to Sequential Binary Black-Hole Mergers in the Field

    A. Vigna-G´ omez, S. Toonen, E. Ramirez-Ruiz, N. W. C. Leigh, J. Riley, and C.-J. Haster, Massive Stellar Triples Leading to Sequential Binary Black Hole Mergers in the Field, ApJ907, L19 (2021), arXiv:2010.13669 [astro- ph.HE]. 12

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  57. [57]

    Stellar triples on the edge; Comprehensive overview of the evolution of destabilised triples leading to stellar and binary exotica

    S. Toonen, T. C. N. Boekholt, and S. Portegies Zwart, Stellar triples on the edge. Comprehensive overview of the evolution of destabilised triples leading to stellar and binary exotica, A&A661, A61 (2022), arXiv:2108.04272 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  58. [58]

    Evolution of massive stellar triples and implications for compact object binary formation

    J. Stegmann, F. Antonini, and M. Moe, Evolution of massive stellar triples and implications for compact object binary formation, MNRAS516, 1406 (2022), arXiv:2112.10786 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  59. [59]

    R. A. Mardling and S. J. Aarseth, Tidal interactions in star cluster simulations, MNRAS321, 398 (2001)

    work page 2001

  60. [60]

    Merging binary black holes formed through chemically homogeneous evolution in short-period stellar binaries

    I. Mandel and S. E. de Mink, Merging binary black holes formed through chemically homogeneous evolution in short-period stellar binaries, MNRAS458, 2634 (2016), arXiv:1601.00007 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  61. [61]

    L. Li, C. Zhu, S. Guo, H. Liu, and G. L¨ u, The Ef- fects of Rotation, Metallicity, and Magnetic Field on the Islands of Failed Supernovae, ApJ952, 79 (2023), arXiv:2306.15879 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  62. [62]

    S.-C. Yoon, N. Langer, and C. Norman, Single star pro- genitors of long gamma-ray bursts. I. Model grids and redshift dependent GRB rate, A&A460, 199 (2006), arXiv:astro-ph/0606637 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  63. [63]

    S. E. de Mink, M. Cantiello, N. Langer, O. R. Pols, I. Brott, and S.-C. Yoon, Rotational mixing in massive binaries. Detached short-period systems, A&A497, 243 (2009), arXiv:0902.1751 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  64. [64]

    H. Wang, C. Zhu, H. Liu, S. Guo, and G. L¨ u, Evolu- tionary tracks of massive stars with different rotation and metallicity in neutrino H-R diagram, MNRAS526, 4335 (2023), arXiv:2310.02824 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  65. [65]

    Z. Li, X. Lu, G. L¨ u, C. Zhu, H. Liu, L. Lei, S. Guo, X. He, and N. Beissen, Formation of the dormant black holes with luminous companions from binary or triple systems, A&A706, A105 (2026), arXiv:2512.04774 [astro-ph.SR]

    work page arXiv 2026

  66. [66]

    Z. Li, C. Zhu, X. Lu, G. L¨ u, L. Li, H. Liu, S. Guo, and J. Yu, A Possible Formation Scenario of the Gaia BH1: Inner Binary Merger in Triple Systems, ApJ975, L8 (2024), arXiv:2410.10581 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  67. [67]

    Z. Li, X. Lu, G. L¨ u, C. Zhu, H. Liu, and J. Yu, A Possible Formation Scenario of the Gaia ID 3425577610762832384: Inner Binary Merger inside a Triple Common Envelope, ApJ979, L37 (2025), arXiv:2501.05139 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  68. [68]

    S. E. de Mink and I. Mandel, The chemically ho- mogeneous evolutionary channel for binary black hole mergers: rates and properties of gravitational-wave events detectable by advanced LIGO, MNRAS460, 3545 (2016), arXiv:1603.02291 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  69. [69]

    Chemically Homogeneous Evolution: A rapid population synthesis approach

    J. Riley, I. Mandel, P. Marchant, E. Butler, K. Nathaniel, C. Neijssel, S. Shortt, and A. Vigna- G´ omez, Chemically homogeneous evolution: a rapid population synthesis approach, MNRAS505, 663 (2021), arXiv:2010.00002 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  70. [70]

    Formation and Destiny of White Dwarf and Be Star Binaries

    C.-H. Zhu, G.-L. L¨ u, X.-Z. Lu, and J. He, Formation and Destiny of White Dwarf and Be Star Binaries, Research in Astronomy and Astrophysics23, 025021 (2023), arXiv:2304.02615 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  71. [71]

    L. Li, G. L¨ u, C. Zhu, S. Guo, H. Ge, W. Gu, Z. Li, and X. He, Explanation of the mass distribution of binary black hole mergers, Phys. Rev. D112, 103005 (2025), arXiv:2510.08231 [astro-ph.HE]

    work page arXiv 2025

  72. [72]

    P. P. Eggleton, Aproximations to the radii of Roche lobes., ApJ268, 368 (1983)

    work page 1983

  73. [73]

    J. R. Hurley, C. A. Tout, and O. R. Pols, Evolu- tion of binary stars and the effect of tides on binary populations, MNRAS329, 897 (2002), arXiv:astro- ph/0201220 [astro-ph]

    work page arXiv 2002

  74. [74]

    Common Envelope Evolution: Where we stand and how we can move forward

    N. Ivanova, S. Justham, X. Chen, O. De Marco, C. L. Fryer, E. Gaburov, H. Ge, E. Glebbeek, Z. Han, X.- D. Li, G. Lu, T. Marsh, P. Podsiadlowski, A. Potter, N. Soker, R. Taam, T. M. Tauris, E. P. J. van den Heuvel, and R. F. Webbink, Common envelope evo- lution: where we stand and how we can move for- ward, A&A Rev.21, 59 (2013), arXiv:1209.4302 [astro- ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  75. [75]

    The evolution of hierarchical triple star-systems

    S. Toonen, A. Hamers, and S. Portegies Zwart, The evolution of hierarchical triple star-systems, Compu- tational Astrophysics and Cosmology3, 6 (2016), arXiv:1612.06172 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  76. [76]

    Di Stefano, A

    R. Di Stefano, A. Khwaja, and C. Kobayashi, SCAT- TER common envelope formalism for triples, MNRAS 547, stag192 (2026), arXiv:2511.04857 [astro-ph.SR]

    work page arXiv 2026

  77. [77]

    SCATTER: A New Common Envelope Formalism

    R. Di Stefano, M. U. Kruckow, Y. Gao, P. G. Neunteufel, and C. Kobayashi, SCATTER: A New Common Envelope Formalism, ApJ944, 87 (2023), arXiv:2212.06770 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  78. [78]

    C. L. Fryer and V. Kalogera, Theoretical Black Hole Mass Distributions, ApJ554, 548 (2001), arXiv:astro- ph/9911312 [astro-ph]

    work page arXiv 2001

  79. [79]

    The mass spectrum of compact remnants from the PARSEC stellar evolution tracks

    M. Spera, M. Mapelli, and A. Bressan, The mass spectrum of compact remnants from the PARSEC stellar evolution tracks, MNRAS451, 4086 (2015), arXiv:1505.05201 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  80. [80]

    C. L. Fryer, K. Belczynski, G. Wiktorowicz, M. Do- minik, V. Kalogera, and D. E. Holz, Compact Rem- nant Mass Function: Dependence on the Explo- sion Mechanism and Metallicity, ApJ749, 91 (2012), arXiv:1110.1726 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

Showing first 80 references.