arxiv: 2605.06807 · v1 · submitted 2026-05-07 · 🌌 astro-ph.SR · astro-ph.GA· astro-ph.HE

Recognition: no theorem link

The impact of envelope binding energies on the merger rate density of binary compact objects

Cecilia Sgalletta , Guglielmo Costa , Giuliano Iorio , Kendall Shepherd , Francesco Addari , Alessandro A. Trani , Michela Mapelli , Ugo N. di Carlo

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Andrea Lapi Alessandro Bressan Mario Spera

Authors on Pith no claims yet

Pith reviewed 2026-05-11 00:55 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.GAastro-ph.HE

keywords common envelopeenvelope binding energybinary population synthesiscompact object mergersmerger rate densitystellar evolutionPARSEC tracks

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The pith

Envelope binding energies from detailed stellar models change predicted compact binary merger rates by more than an order of magnitude.

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

The paper computes envelope binding energies using an extensive grid of PARSEC v2.0 stellar evolution tracks for hydrogen-rich and helium stars across wide ranges of mass and metallicity. These binding energies prove highly sensitive to internal energy contributions for hydrogen-rich stars and to core-boundary definitions for helium stars. When the new prescriptions replace standard fitting formulas inside the SEVN binary population synthesis code, the predicted merger rate densities of compact objects shift by more than an order of magnitude. The work therefore stresses that population-synthesis results must remain consistent with the underlying stellar evolution assumptions rather than relying on extrapolated empirical fits.

Core claim

Envelope binding energies derived directly from PARSEC v2.0 tracks, when inserted into the SEVN population synthesis code, produce merger rate densities for compact binaries that differ by more than an order of magnitude from earlier models that used fitting formulas. Internal energy sources dominate the variation for hydrogen-rich stars while core-boundary choice dominates for pure-helium stars, with larger deviations appearing at higher masses and metallicities.

What carries the argument

Envelope binding energy prescriptions computed from PARSEC v2.0 stellar tracks, which set the energy cost of ejecting the common envelope in binary evolution.

If this is right

For hydrogen-rich stars, different internal energy sources alter envelope binding energies by more than an order of magnitude.
For pure-helium stars, the core-envelope boundary definition becomes the dominant source of variation in binding energy.
Envelope binding energies from different stellar tracks deviate by several orders of magnitude, especially at high masses and metallicities.
Inserting the new binding energies into SEVN shifts predicted compact-object merger rate densities by more than an order of magnitude relative to prior fitting-formula models.
Fitting formulas should not be extrapolated outside the stellar-parameter range where they were calibrated.

Where Pith is reading between the lines

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

Revised merger rates would alter expected event counts for ground-based gravitational-wave detectors.
Population synthesis codes should adopt self-consistent binding energies whenever the stellar model is updated.
Extending the grid to include rotation or binary interaction effects during the pre-common-envelope phase could further modify the rates.
Direct comparison across multiple stellar codes would quantify the systematic uncertainty still present in the binding energies.

Load-bearing premise

That the PARSEC v2.0 internal-energy contributions and core-boundary definitions accurately represent real stellar structure.

What would settle it

Recomputing envelope binding energies with an independent stellar evolution code such as MESA for the same initial masses and metallicities and checking whether the order-of-magnitude spread in merger rates remains.

Figures

Figures reproduced from arXiv: 2605.06807 by Alessandro A. Trani, Alessandro Bressan, Andrea Lapi, Cecilia Sgalletta, Francesco Addari, Giuliano Iorio, Guglielmo Costa, Kendall Shepherd, Mario Spera, Michela Mapelli, Ugo N. di Carlo.

**Figure 1.** Figure 1: Binding energy EH evaluated from parsec as a function of the radius R for different stellar masses. The rows from top to bottom show EG, EB and EH, respectively. Different columns represent different metallicities, from left to right: Z = 10−11, 0.0001, and 0.01. The black star markers indicate the formation of the He core. Different line styles show the results assuming different XH,0 thresholds to define… view at source ↗

**Figure 2.** Figure 2: Binding energies EB evolution with radius for different stellar masses. The color code shows the mass fraction of the outer convective envelope fCE. Diamonds indicate the beginning of He burning; squares show the end of the core He burning phase. Different columns represent different metallicities, from left to right: Z = 0.0001, 0.001 and 0.01. Here, we assume XH,0 = 10−3 . the star has already become a W… view at source ↗

**Figure 3.** Figure 3: Evolution of the envelope binding energy for a sample of stars with MZAMS = 10 M⊙ (top left), 35 M⊙ (top right), 60 M⊙ (bottom left) and 100 M⊙ (bottom right). All the stars have metallicity Z = 10−11. The x-axis is the stellar age normalized to tmax, where tmax is defined as the time at which the star reaches its maximum radial expansion (Z ≤ 0.0001) or becomes a Wolf-Rayet (Z = 0.01). The tracks are trun… view at source ↗

**Figure 4.** Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 7.** Figure 7: Merger efficiency η for BBHs (top), BHNS(middle) and BNSs(bottom) as a function of metallicity Z. The solid lines represent the results assuming the parsec envelope binding energies (EB) computed with XH,0 = XHe,0 = 10−3 . The other linestyles assume different λ prescriptions: dashed lines for Claeys et al. (2014), dotted lines for Klencki et al. (2021). The different colors show results for different α p… view at source ↗

**Figure 8.** Figure 8: Merger rate density of BBHs (left), BHNS (center) and BNSs (right) for different λ prescriptions and α parameters. The solid lines show the results adopting the λ self-consistent with the parsec tracks, derived from EB and XH,0 = XHe,0 = 10−3 . The dashed lines assume the λ prescription by Claeys et al. (2014), the dotted lines assume the prescription by Klencki et al. (2021). The different colors show the… view at source ↗

**Figure 9.** Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗

read the original abstract

The common envelope (CE) phase plays a key role in the formation of binary compact object systems. Its final outcome strongly depends on the envelope binding energy, but this quantity is often estimated using fitting formulas that are not fully consistent with the underlying stellar evolution models adopted in population-synthesis codes. Here, we investigate envelope binding energies across the most extensive stellar grid considered to date. Our stellar tracks, evolved with PARSEC v2.0, include hydrogen (H) -rich stars with metallicities ranging from $Z = 10^{-11}$ (Population III stars) to $Z = 0.03$, and initial masses between 2 and 2000 M$_\odot$, as well as pure-helium stars with masses from 0.36 to 350 M$_\odot$. We examine the sensitivity of the envelope binding energies to the selected core-envelope boundary definition and to different internal energy source contributions. For H-rich stars, we find that internal energy sources can alter the envelope binding energy by more than an order of magnitude, whereas the core boundary criteria play a secondary role. In contrast, for pure helium stars, the core-boundary criterion becomes the dominant factor. The envelope binding energies derived from different stellar tracks can show deviations of several orders of magnitude, with larger differences for more massive stars and higher metallicities.Finally, by implementing our new envelope binding energy prescriptions into the binary population synthesis code SEVN, we show that the predicted merger rate densities of compact binaries can differ by more than an order of magnitude compared to previous models. Our results highlight the importance of using envelope binding energies that are consistent with the underlying stellar evolution models and caution against extrapolating empirical fits beyond the considered parameter space.

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.

Desk Editor's Note private letter to a colleague

PARSEC-derived binding energies shift SEVN merger rates by more than an order of magnitude, but the size of that shift may be specific to PARSEC's physics choices.

read the letter

The key point is that new envelope binding energies from a large PARSEC v2.0 grid, when inserted into SEVN, move the predicted merger rate densities of compact binaries by more than a factor of ten compared with older fitting formulas. The paper also maps how those energies respond to core-boundary definitions and internal-energy terms across a wide parameter space that includes population III stars and very massive objects up to 2000 solar masses, plus a separate helium-star grid. For hydrogen-rich stars the internal energy contribution dominates the variation, while for helium stars the core boundary matters more. They then carry the new prescriptions straight into the population code and show the rate impact. That direct hand-off from stellar tracks to rates is the concrete advance here. The grid size and the sensitivity tests are done at a scale that earlier work did not reach, and the result replaces inconsistent empirical fits with values tied to the same models used downstream. The main soft spot is the absence of any cross-check against another stellar evolution code. The abstract already demonstrates that modest changes inside PARSEC alone can move binding energies by more than a dex, so swapping the entire code for MESA or similar would likely produce shifts of comparable size. Without that comparison it is difficult to judge whether the reported rate excursion is a general consequence of using self-consistent energies or an artifact of PARSEC's treatment of convection, overshooting, and thermal energy. Readers who run or rely on binary population synthesis for gravitational-wave forecasts will get the most from the numbers. The paper is worth a serious referee because the quantitative link between binding-energy choices and rate densities is new and the methods are described clearly enough to evaluate, even if later work will need to test robustness across codes.

Referee Report

2 major / 3 minor

Summary. The manuscript computes envelope binding energies E_bind from an extensive grid of PARSEC v2.0 stellar tracks (H-rich stars: 2–2000 M⊙, Z=10^{-11}–0.03; pure-He stars: 0.36–350 M⊙). It quantifies sensitivity to core-envelope boundary definitions and internal-energy contributions, finding >1 dex variations from internal energies in H-rich stars and dominant core-boundary effects in He stars. New prescriptions derived from these tracks are inserted into the SEVN binary population-synthesis code, yielding compact-object merger rate densities that differ by more than an order of magnitude from earlier models that used analytic fitting formulae.

Significance. If the PARSEC-derived binding energies prove representative, the work demonstrates that inconsistency between stellar-evolution models and population-synthesis codes can shift predicted merger rates by >1 dex, directly affecting gravitational-wave source forecasts. The broad parameter space, explicit sensitivity tests, and self-consistent (rather than extrapolated) prescriptions constitute a clear methodological advance over prior fitting-formula approaches.

major comments (2)

[§4] §4 (SEVN implementation and rate-density results): The headline claim that merger rate densities shift by more than an order of magnitude rests on the assumption that PARSEC v2.0 binding energies are representative of modern stellar structure. The manuscript already shows that internal-energy terms alone move E_bind by >1 dex inside PARSEC; the same magnitude of variation is expected when swapping the entire stellar code (e.g., to MESA). No binding-energy tables or rate comparisons from a second code are provided, so it is impossible to determine whether the reported rate excursion is a general consequence of self-consistent energies or an artifact of PARSEC’s specific convection, overshooting, and thermal-energy treatment. A quantitative cross-code comparison is required to support the central claim.
[§3] §3 (binding-energy results): While the paper reports deviations of several orders of magnitude in E_bind for massive stars at higher metallicities, the propagation of these variations through SEVN is presented only as a single-point comparison to “previous models.” No Monte-Carlo error budget or sensitivity run that varies the binding-energy prescription within the observed PARSEC scatter is shown, leaving the robustness of the >1 dex rate shift unquantified.

minor comments (3)

[Figures] Figure captions and legends should explicitly state which internal-energy contributions (thermal, ionization, etc.) are included in each curve; current labels are ambiguous for readers unfamiliar with the exact PARSEC implementation.
[§3] The fitting formulae for the new E_bind prescriptions are introduced without an explicit functional form or table of coefficients in the main text; these should be provided (or clearly referenced to an appendix) so that other codes can adopt them directly.
[§2] A brief discussion of how the adopted core-boundary criteria compare with those used in the original SEVN stellar tracks would help readers assess internal consistency.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important aspects of robustness and generality that we address below. We have revised the manuscript to incorporate clarifications and additional discussion where feasible.

read point-by-point responses

Referee: [§4] §4 (SEVN implementation and rate-density results): The headline claim that merger rate densities shift by more than an order of magnitude rests on the assumption that PARSEC v2.0 binding energies are representative of modern stellar structure. The manuscript already shows that internal-energy terms alone move E_bind by >1 dex inside PARSEC; the same magnitude of variation is expected when swapping the entire stellar code (e.g., to MESA). No binding-energy tables or rate comparisons from a second code are provided, so it is impossible to determine whether the reported rate excursion is a general consequence of self-consistent energies or an artifact of PARSEC’s specific convection, overshooting, and thermal-energy treatment. A quantitative cross-code comparison is required to support the central claim.

Authors: We agree that a cross-code comparison would help establish whether the magnitude of the rate shift is universal across modern stellar evolution codes. Our central result, however, is more limited in scope: it demonstrates that replacing analytic fitting formulae with binding energies self-consistently extracted from PARSEC v2.0 tracks inside SEVN produces merger-rate densities that differ by more than an order of magnitude from those in the existing literature. PARSEC v2.0 is a widely used, state-of-the-art code, and the internal variations we already quantify (>1 dex from internal-energy terms alone) illustrate the sensitivity even within a single model. We have added explicit language in the revised §4 and the conclusions stating that the quantitative values are specific to the PARSEC implementation and that other codes (e.g., MESA) may yield different numerical results, while the qualitative importance of self-consistency remains. A full cross-code study lies beyond the present work. revision: partial
Referee: [§3] §3 (binding-energy results): While the paper reports deviations of several orders of magnitude in E_bind for massive stars at higher metallicities, the propagation of these variations through SEVN is presented only as a single-point comparison to “previous models.” No Monte-Carlo error budget or sensitivity run that varies the binding-energy prescription within the observed PARSEC scatter is shown, leaving the robustness of the >1 dex rate shift unquantified.

Authors: We acknowledge that a dedicated sensitivity study would strengthen the robustness statement. The submitted manuscript presents the primary comparison using our fiducial PARSEC-derived prescription. Because the E_bind variations already documented in §3 exceed 1 dex for the stellar masses and metallicities that dominate the merger-rate integral, the order-of-magnitude shift relative to previous analytic prescriptions is driven by differences that are substantially larger than the internal PARSEC scatter. We have expanded the discussion in the revised §4 to make this explicit, noting that even if the binding energy were varied within the full range of core-boundary and internal-energy choices explored in the PARSEC grid, the resulting rate densities would still differ from the literature values by at least several times and typically by an order of magnitude. A full Monte-Carlo propagation over all possible combinations is computationally intensive and is noted as desirable future work. revision: partial

standing simulated objections not resolved

Quantitative cross-code comparison of binding-energy tables and resulting merger-rate densities using an independent stellar-evolution code such as MESA

Circularity Check

0 steps flagged

No significant circularity; binding energies derived from independent PARSEC v2.0 tracks and inserted into SEVN

full rationale

The paper computes envelope binding energies directly from PARSEC v2.0 stellar evolution grids (external code) across wide ranges of mass, metallicity, and internal-energy assumptions. These values are then supplied as prescriptions to the SEVN population-synthesis code to obtain merger-rate densities, which are compared against earlier models that used inconsistent fitting formulae. No step reduces by construction to its own inputs: the rate output is not a re-expression of the PARSEC-derived E_bind values, no parameter is fitted on a subset and then relabeled a prediction, and no load-bearing uniqueness theorem or ansatz is imported solely via self-citation. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the PARSEC v2.0 stellar models being an adequate physical description; no new free parameters are introduced by the authors themselves, but the stellar code contains many internal choices whose impact is only partially explored.

axioms (1)

domain assumption PARSEC v2.0 accurately captures the internal energy sources and core-envelope boundaries for the full mass and metallicity range examined
The abstract states that internal energy sources alter binding energies by more than an order of magnitude, but does not provide independent validation against other stellar codes.

pith-pipeline@v0.9.0 · 5667 in / 1438 out tokens · 29088 ms · 2026-05-11T00:55:43.835128+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

91 extracted references · 1 canonical work pages · 1 internal anchor

[1]

D., Acernese, F., et al

Abbott, R., Abbott, T. D., Acernese, F., et al. 2023, Phys. Rev. X, 13, 011048

2023
[2]

Andrews, B. H. & Martini, P. 2013, ApJ, 765, 140 Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935, 167 Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M., et al. 2018, AJ, 156, 123 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33

2013
[3]

S., Fragos, T., Zevin, M., et al

Bavera, S. S., Fragos, T., Zevin, M., et al. 2021, A&A, 647, A153

2021
[4]

2002, ApJ, 572, 407

Belczynski, K., Kalogera, V ., & Bulik, T. 2002, ApJ, 572, 407

2002
[5]

E., et al

Belczynski, K., Klencki, J., Fields, C. E., et al. 2020, A&A, 636, A104 Article number, page 10 of 13 C. Sgalletta et al.: Envelope binding energies and merger rate densities 10 8 10 6 10 4 10 7 10 5 [M 1] BBHs = 0.5 = 1 = 3 = 5 10 8 10 6 10 4 10 7 10 5 [M 1] BHNS This work Claeys+14 Klencki+21 10 3 10 2 Z 10 8 10 6 10 4 10 7 10 5 [M 1] BNSs Fig. 7.Merger...

2020
[6]

P., Broekgaarden, F

Boesky, A. P., Broekgaarden, F. S., & Berger, E. 2024, ApJ, 976, 24

2024
[7]

2020, ApJ, 898, 71

Breivik, K., Coughlin, S., Zevin, M., et al. 2020, ApJ, 898, 71

2020
[8]

2012, MNRAS, 427, 127

Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127

2012
[9]

G., Chiosi, C., & Bertelli, G

Bressan, A. G., Chiosi, C., & Bertelli, G. 1981, A&A, 102, 25

1981
[10]

S., Berger, E., Neijssel, C

Broekgaarden, F. S., Berger, E., Neijssel, C. J., et al. 2021, MNRAS, 508, 5028

2021
[11]

S., Berger, E., Stevenson, S., et al

Broekgaarden, F. S., Berger, E., Stevenson, S., et al. 2022, MNRAS, 516, 5737

2022
[12]

G., Steffen, M., Freytag, B., & Bonifacio, P

Caffau, E., Ludwig, H. G., Steffen, M., Freytag, B., & Bonifacio, P. 2011, Sol. Phys., 268, 255

2011
[13]

2018, MNRAS, 474, 2937

Chruslinska, M., Belczynski, K., Klencki, J., & Benacquista, M. 2018, MNRAS, 474, 2937

2018
[14]

& Nelemans, G

Chruslinska, M. & Nelemans, G. 2019, MNRAS, 488, 5300

2019
[15]

Claeys, J. S. W., Pols, O. R., Izzard, R. G., Vink, J., & Verbunt, F. W. M. 2014, A&A, 563, A83

2014
[16]

2021, 501, 4514

Costa, G., Bressan, A., Mapelli, M., et al. 2021, 501, 4514

2021
[17]

2019, MNRAS, 485, 4641

Costa, G., Girardi, L., Bressan, A., et al. 2019, MNRAS, 485, 4641

2019
[18]

G., Bressan, A., et al

Costa, G., Shepherd, K. G., Bressan, A., et al. 2025, A&A, 694, A193 De Marco, O., Passy, J.-C., Moe, M., et al. 2011, MNRAS, 411, 2277

2025
[19]

Dewi, J. D. M. & Tauris, T. M. 2000, A&A, 360, 1043 Di Stefano, R., Kruckow, M. U., Gao, Y ., Neunteufel, P. G., & Kobayashi, C. 2023, ApJ, 944, 87

2000
[20]

2023, MNRAS, 521, 4323

El-Badry, K., Rix, H.-W., Cendes, Y ., et al. 2023, MNRAS, 521, 4323

2023
[21]

J., Ramirez-Ruiz, E., et al

Fragos, T., Andrews, J. J., Ramirez-Ruiz, E., et al. 2019, ApJ, 883, L45

2019
[22]

L., Belczynski, K., Wiktorowicz, G., et al

Fryer, C. L., Belczynski, K., Wiktorowicz, G., et al. 2012, ApJ, 749, 91

2012
[23]

Gallegos-Garcia, M., Berry, C. P. L., Marchant, P., & Kalogera, V . 2021, ApJ, 922, 110

2021
[24]

F., Chen, X., & Han, Z

Ge, H., Webbink, R. F., Chen, X., & Han, Z. 2020, ApJ, 899, 132

2020
[25]

& Mapelli, M

Giacobbo, N. & Mapelli, M. 2018, MNRAS, 480, 2011

2018
[26]

& Mapelli, M

Giacobbo, N. & Mapelli, M. 2020, ApJ, 891, 141

2020
[27]

& Podsiadlowski, P

Han, Z. & Podsiadlowski, P. 2004, Monthly Notices of the Royal Astronomical Society, 350, 1301

2004
[28]

Han, Z., Podsiadlowski, P., Maxted, P. F. L., & Marsh, T. R. 2003, Monthly Notices of the Royal Astronomical Society, 341, 669

2003
[29]

Han, Z., Podsiadlowski, P., Maxted, P. F. L., Marsh, T. R., & Ivanova, N. 2002, Monthly Notices of the Royal Astronomical Society, 336, 449

2002
[30]

R., Millman, K

Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357

2020
[31]

& Mandel, I

Hirai, R. & Mandel, I. 2022, ApJ, 937, L42

2022
[32]

R., Lyne, A

Hobbs, G., Lorimer, D. R., Lyne, A. G., & Kramer, M. 2005, MNRAS, 360, 974

2005
[33]

Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90

2007
[34]

R., Tout, C

Hurley, J. R., Tout, C. A., & Pols, O. R. 2002, MNRAS, 329, 897

2002
[35]

2017, MNRAS, 464, 4028

Iaconi, R., Reichardt, T., Staff, J., et al. 2017, MNRAS, 464, 4028

2017
[36]

& Livio, M

Iben, Jr., I. & Livio, M. 1993, PASP, 105, 1373

1993
[37]

& Tutukov, A

Iben, Jr., I. & Tutukov, A. V . 1984, ApJS, 54, 335

1984
[38]

2023, Monthly Notices of the Royal As- tronomical Society, 524, 426

Iorio, G., Mapelli, M., Costa, G., et al. 2023, Monthly Notices of the Royal As- tronomical Society, 524, 426

2023
[39]

2011, ApJ, 730, 76

Ivanova, N. 2011, ApJ, 730, 76

2011
[40]

& Chaichenets, S

Ivanova, N. & Chaichenets, S. 2011, ApJ, 731, L36

2011
[41]

2013, A&A Rev., 21, 59

Ivanova, N., Justham, S., Chen, X., et al. 2013, A&A Rev., 21, 59

2013
[42]

Ivanova, N., Justham, S., Nandez, J. L. A., & Lombardi, J. C. 2013, Science, 339, 433

2013
[43]

2020, Common Envelope Evolution, 2514- 3433 (IOP Publishing)

Ivanova, N., Justham, S., & Ricker, P. 2020, Common Envelope Evolution, 2514- 3433 (IOP Publishing)

2020
[44]

G., & Chruslinska, M

Klencki, J., Nelemans, G., Istrate, A. G., & Chruslinska, M. 2021, A&A, 645, A54

2021
[45]

2001, MNRAS, 322, 231

Kroupa, P. 2001, MNRAS, 322, 231

2001
[46]

U., Tauris, T

Kruckow, M. U., Tauris, T. M., Langer, N., Kramer, M., & Izzard, R. G. 2018, MNRAS, 481, 1908

2018
[47]

U., Tauris, T

Kruckow, M. U., Tauris, T. M., Langer, N., et al. 2016, A&A, 596, A58

2016
[48]

2017, ApJ, 838, 56

MacLeod, M., Antoni, A., Murguia-Berthier, A., Macias, P., & Ramirez-Ruiz, E. 2017, ApJ, 838, 56

2017
[49]

2020, Frontiers in Astronomy and Space Sciences, 7, 38

Mapelli, M. 2020, Frontiers in Astronomy and Space Sciences, 7, 38

2020
[50]

2021, in Handbook of Gravitational Wave Astronomy, ed

Mapelli, M. 2021, in Handbook of Gravitational Wave Astronomy, ed. C. Bambi, S. Katsanevas, & K. D. Kokkotas, 16

2021
[51]

& Giacobbo, N

Mapelli, M. & Giacobbo, N. 2018, MNRAS, 479, 4391

2018
[52]

2020, ApJ, 888, 76

Mapelli, M., Spera, M., Montanari, E., et al. 2020, ApJ, 888, 76

2020
[53]

Marchant, P., Pappas, K. M. W., Gallegos-Garcia, M., et al. 2021, A&A, 650, A107

2021
[54]

& Meyer-Hofmeister, E

Meyer, F. & Meyer-Hofmeister, E. 1979, A&A, 78, 167

1979
[55]

& Di Stefano, R

Moe, M. & Di Stefano, R. 2017, ApJS, 230, 15

2017
[56]

M., Schneider, F

Moreno, M. M., Schneider, F. R. N., Röpke, F. K., et al. 2022, A&A, 667, A72

2022
[57]

Nandez, J. L. A., Ivanova, N., & Lombardi, J. C. J. 2015, MNRAS, 450, L39

2015
[58]

J., Vigna-Gómez, A., Stevenson, S., et al

Neijssel, C. J., Vigna-Gómez, A., Stevenson, S., et al. 2019, MNRAS, 490, 3740

2019
[59]

& Tout, C

Nelemans, G. & Tout, C. A. 2005, MNRAS, 356, 753

2005
[60]

R., & Portegies Zwart, S

Nelemans, G., Verbunt, F., Yungelson, L. R., & Portegies Zwart, S. F. 2000, A&A, 360, 1011

2000
[61]

T., Costa, G., Girardi, L., et al

Nguyen, C. T., Costa, G., Girardi, L., et al. 2022, Astronomy & Astrophysics, 665, A126

2022
[62]

T., Röpke, F

Ohlmann, S. T., Röpke, F. K., Pakmor, R., & Springel, V . 2016, ApJ, 816, L9 Özel, F., Psaltis, D., Arzoumanian, Z., Morsink, S., & Bauböck, M. 2016, ApJ, 832, 92 Özel, F., Psaltis, D., Narayan, R., & Santos Villarreal, A. 2012, ApJ, 757, 55

2016
[63]

1976, in IAU Symposium, V ol

Paczynski, B. 1976, in IAU Symposium, V ol. 73, Structure and Evolution of Close Binary Systems, ed. P. Eggleton, S. Mitton, & J. Whelan, 75

1976
[64]

L., et al

Passy, J.-C., De Marco, O., Fryer, C. L., et al. 2012, ApJ, 744, 52

2012
[65]

2024, ApJ, 969, 1

Picker, L., Hirai, R., & Mandel, I. 2024, ApJ, 969, 1

2024
[66]

2001, in Astronomical Society of the Pacific Conference Se- ries, V ol

Podsiadlowski, P. 2001, in Astronomical Society of the Pacific Conference Se- ries, V ol. 229, Evolution of Binary and Multiple Star Systems, ed. P. Podsiad- lowski, S. Rappaport, A. R. King, F. D’Antona, & L. Burderi, 239

2001
[67]

& Weiler, K

Politano, M. & Weiler, K. P. 2007, ApJ, 665, 663

2007
[68]

2023, MNRAS, 519, 1526

Popesso, P., Concas, A., Cresci, G., et al. 2023, MNRAS, 519, 1526

2023
[69]

Ricker, P. M. & Taam, R. E. 2012, ApJ, 746, 74

2012
[70]

W., et al

Riley, J., Agrawal, P., Barrett, J. W., et al. 2022, ApJS, 258, 34

2022
[71]

2015, The Astrophysical Journal Letters, 800, L10 Román-Garza, J., Bavera, S

Rodighiero, G., Brusa, M., Daddi, E., et al. 2015, The Astrophysical Journal Letters, 800, L10 Román-Garza, J., Bavera, S. S., Fragos, T., et al. 2021, ApJ, 912, L23 Röpke, F. K. & De Marco, O. 2023, Living Reviews in Computational Astro- physics, 9, 2

2015
[72]

E., de Koter, A., et al

Sana, H., de Mink, S. E., de Koter, A., et al. 2012, Science, 337, 444

2012
[73]

C., & Boco, L

Santoliquido, F., Mapelli, M., Artale, M. C., & Boco, L. 2022, MNRAS, 516, 3297

2022
[74]

T., Béthermin, M., Daddi, E., & Elbaz, D

Sargent, M. T., Béthermin, M., Daddi, E., & Elbaz, D. 2012, ApJ, 747, L31

2012
[75]

2015, A&A, 575, A74

Schreiber, C., Pannella, M., Elbaz, D., et al. 2015, A&A, 575, A74

2015
[76]

2023, MNRAS, 526, 2210

Sgalletta, C., Iorio, G., Mapelli, M., et al. 2023, MNRAS, 526, 2210

2023
[77]

2025, A&A, 698, A144

Sgalletta, C., Mapelli, M., Boco, L., et al. 2025, A&A, 698, A144

2025
[78]

G., Costa, G., Ugolini, C., et al

Shepherd, K. G., Costa, G., Ugolini, C., et al. 2025, A&A, 701, A126

2025
[79]

& Mapelli, M

Spera, M. & Mapelli, M. 2017, MNRAS, 470, 4739 Article number, page 11 of 13 A&A proofs:manuscript no. main 0.0 2.5 5.0 7.5 z 10 1 100 101 102 103 104 (z) [Gpc 3 yr 1] BBHs This work Claeys+14 Klencki+21 0.0 2.5 5.0 7.5 z BHNS = 0.5 = 1 = 3 = 5 0.0 2.5 5.0 7.5 z BNSs Fig. 8.Merger rate density of BBHs (left), BHNS (center) and BNSs (right) for differentλp...

2017
[80]

2019, MNRAS, 485, 889

Spera, M., Mapelli, M., Giacobbo, N., et al. 2019, MNRAS, 485, 889

2019

Showing first 80 references.