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REVIEW 3 major objections 5 minor 38 references

Combining (post-)Newtonian ideas with quasi-equilibrium (QE) sequence analysis for black hole-neutron star (BHNS) gravitational wave events

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Pith's one-line read Quasi-equilibrium models of GW200115-like binaries show the neutron star overflowing its Roche lobe, and thus starting mass transfer, before the binary reaches the innermost stable circular orbit.

desk verdict A useful set of QE sequences for GW200105/GW200115, but the third-fate claim rests on a Newtonian Roche-lobe comparison that contradicts the paper's own κ-based mass-shedding estimate, so the central conclusion is not yet established. read the letter →

arxiv 2507.09175 v1 pith:YNFLQEFO submitted 2025-07-12 gr-qc astro-ph.HE

Antonio Lanza , Samuel D. Tootle , Andrea Lapi This is my paper · ORCID
classification gr-qcastro-ph.HE PACS 04.25.D04.30.-w97.60.Jd97.80.-d
keywords blackhole–neutronstarbinariesquasi-equilibriumsequencesRochelobeoverflowinnermoststablecircularorbitmasstransferGW200115FUKAinitialdataneutrontidaldisruption
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Black hole–neutron star binaries whose masses and spins match the gravitational-wave events GW200105 and GW200115 are modelled as quasi-equilibrium sequences with the FUKA initial-data code, and the location of the innermost stable circular orbit is compared with two independent estimates of where the neutron star begins shedding mass. In most configurations the ISCO lies outside the mass-shedding radius, matching the standard picture that the neutron star plunges without yielding an electromagnetic counterpart. For the most probable GW200115 parameters ($q=0.4167$, black hole 3.6 solar masses, neutron star 1.5 solar masses), however, the neutron star's proper radius at the last converged separation exceeds both the Eggleton formula [30] and a second-post-Newtonian Roche lobe radius [32], while the ISCO sits at a slightly smaller separation. The authors therefore suggest that mass transfer can begin before the ISCO and, if it develops catastrophically, would suppress electromagnetic emission, a third possible fate beyond plunge and tidal disruption that could explain events like GW200115.

What carries the argument

The argument pivots on comparing the proper circumferential radius of the neutron star extracted from a FUKA quasi-equilibrium solution with two Roche lobe radii: the Eggleton formula [30] and a second-post-Newtonian formula [32], together with the Newtonian effective potential (Eq. 40) that locates the $L_1$ point. The ISCO of each sequence is found as the minimum of the binding energy, fitted as a quadratic in the orbital angular velocity, and the mass-shedding radius is estimated from the Newtonian formula (Eq. 38) with the elongation factor $1/\kappa$ supplied by a mass-shedding indicator [26]. The $q=0.4167$ sequence is singled out because at its last converged separation the comparison reverses: $R_{NS} > R_{LE}$ and $R_{NS} > R_{LPN}$ while $r_{ISCO}$ is only slightly smaller.

What would settle it

Evolve the $q=0.4167$ configuration from its last converged FUKA initial data (separation $d=24.3$ solar masses, the TNTYST equation of state [23], spins −0.2 and +0.2) with a full general-relativistic hydrodynamics code and check whether mass transfer begins before the orbit reaches the ISCO and whether an accretion disk or electromagnetic counterpart forms; a cheaper check is to recompute the Roche condition from the actual deformed stellar surface rather than a sphere.

Watch

Extended reading notes

Core claim

The central claim is that a neutron star in a black hole–neutron star binary can fill and overflow its Roche lobe at a separation larger than the ISCO, so that mass transfer precedes the final plunge. In the sequence matching GW200115 (mass ratio $q=0.4167$, black hole mass 3.6 solar masses, neutron star mass 1.5 solar masses, dimensionless spins −0.2 and +0.2), the last converged solution at $d=24.3$ solar masses gives a neutron star proper radius $R_{NS}=7.76$ solar masses, larger than the standard Roche lobe radius [30] of 7.44 solar masses and the second-post-Newtonian radius [32] of 6.90 solar masses, while the fitted ISCO is at the smaller separation $r_{ISCO}=23.34$ solar masses. The paper concludes that the neutron star is filling its Roche lobe before reaching the last stable orbit, and that if the ensuing mass transfer is catastrophic—on the model of the runaway instability seen in self-gravitating disks—no electromagnetic counterpart would be expected. This is presented as a third fate of the neutron star, beyond the usual plunge and tidal-disruption outcomes.

Load-bearing premise

The assumption that carries the conclusion is that a Newtonian or second-post-Newtonian Roche-lobe radius, computed by treating the deformed neutron star as a sphere in an effective potential, correctly marks the true general-relativistic mass-shedding threshold; the paper itself labels this comparison 'only indicative' in Section V.

Editorial extensions

If this is right

  • For GW200115-compatible parameters, a missing electromagnetic counterpart can be explained by catastrophic mass transfer before the ISCO, not only by plunge.
  • The $q=0.4167$ sequence is a concrete initial-data target for dynamical simulations that could confirm the onset of a runaway-type instability.
  • Mass transfer before the ISCO changes the mass ratio and angular momentum of the binary, so its subsequent inspiral would follow a different quasi-equilibrium track than the standard plunge picture.
  • The same Roche-lobe-versus-ISCO comparison can be applied to other black hole–neutron star candidates, for instance GW230529-like lower-mass-gap binaries, to predict whether they should show electromagnetic emission.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If a single full evolution validates the Roche-lobe screen, the same cheap comparison could map out large black hole–neutron star parameter spaces without solving for full initial data at every point.
  • The third fate is likely sensitive to the neutron star equation of state: a softer equation of state makes the star more compact and could push Roche filling inside the ISCO, so the prediction is testable with future events of different inferred compactness.
  • Because the paper compares a proper circumferential radius with spherical Newtonian and second-post-Newtonian Roche radii, a fully relativistic Roche criterion might shift the critical mass ratio; checking this would clarify how general the third fate is.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper constructs quasi-equilibrium (QE) initial-data sequences for black hole-neutron star (BHNS) binaries with component masses and spins compatible with the gravitational-wave events GW200105 and GW200115, using the FUKA framework and the Togashi equation of state. For each sequence the authors locate the ISCO by minimizing the binding energy and estimate the mass-shedding radius using the Kyutoku et al. formula with a kappa-based elongation factor. They then add a Newtonian and post-Newtonian Roche-lobe analysis, comparing the neutron star proper radius to the Eggleton and 2PN Roche-lobe radii. For the GW200115-compatible configuration with q=0.4167, they find that at the last converged separation d=24.3 solar masses the proper radius R_NS=7.76 solar masses exceeds both Roche-lobe estimates, while the extrapolated ISCO radius is r_ISCO=23.34 solar masses. The paper interprets this as evidence that the neutron star may fill its Roche lobe before reaching ISCO, proposing a third fate beyond plunge or tidal disruption: catastrophic mass transfer that suppresses electromagnetic emission.

Significance. If established, the proposed third fate would be a new physical channel for BHNS mergers and would affect how GW200115-like events with no electromagnetic counterparts are interpreted. The paper also provides a systematic set of QE-sequence data (ISCO fits, mass-shedding radii, kappa values, and Roche-lobe radii) for many mass-ratio and spin combinations, which is a useful resource, and it includes a resolution study supporting the numerical accuracy of the sequences. However, the central third-fate conclusion rests on a Newtonian/2PN Roche-lobe comparison that is not reconciled with the paper's own kappa-based mass-shedding diagnostic, and on an extrapolated ISCO value with no uncertainty estimate. As presented, the claim is therefore provisional rather than established.

major comments (3)
  1. [IV.C-IV.D, Tables III-IV, Eqs. (38)-(40)] The central claim for q=0.4167 is not reconciled with the paper's own GR-informed mass-shedding diagnostic. At the last converged separation d=24.3 solar masses, Table III lists 1/kappa=1.46 (kappa about 0.68), far from the cusp value kappa to 0 that is the standard signature of mass shedding in QE sequences. Inserting this c_R into Eq. (38) with R_NS=7.76 solar masses and M_BH/M_NS=2.4 gives r_MS about 19.11 solar masses, which is smaller than the extrapolated r_ISCO=23.34 solar masses. The kappa-based estimate therefore predicts plunge before mass shedding, in direct conflict with the overflow conclusion drawn from Table IV. The paper reports both numbers without explaining why the Roche-lobe comparison should be preferred over the sequence's own deformation indicator; if the Roche-lobe comparison is correct, the paper must explain why kappa remains at about 0.68 at a configuration that is already overflowing. This tension is load-bearing for the third-fate claim.
  2. [IV.D and Section V, Eq. (40), Table IV] The overflow comparison compares a GR proper radius with Newtonian and 2PN Roche-lobe radii for spherical stars. R_NS is the proper circumferential radius of a deformed relativistic star, whereas R_LE (Eggleton) and R_LPN (Ratkovic et al.) are spherical approximations for point-mass binaries; the paper's own statements in Section V acknowledge this but do not quantify its effect. In particular, the Roche-lobe calculation uses the Newtonian potential Eq. (40) and ignores the tidal flattening that kappa measures. Without a GR-informed filling criterion (for example, comparing the effective-potential cusp from the FUKA solution with the stellar surface), the conclusion that the NS fills its Roche lobe before ISCO remains an unquantified approximation rather than a supported result.
  3. [IV.B, Eqs. (35)-(37), Table II] The ordering r_ISCO < d_min that underlies the 'before reaching ISCO' claim depends on an extrapolated value. For q=0.4167, d_ISCO=23.34 solar masses is obtained by fitting E_b(Omega) with a parabola and then inverting the relation M_infinity Omega = a/d + b, yet d_min=24.3 solar masses is the last converged point; the extrapolation distance is less than one solar mass. No error estimates, residual plots, or robustness checks are given for the fit parameters or for d_ISCO. Since the margin is small, modest extrapolation uncertainty could reverse the ordering and eliminate the third-fate scenario. Please quantify the uncertainty or extend the sequences, or soften the claim accordingly.
minor comments (5)
  1. [IV.D and Table IV] The sentence 'RN S > RLLE t' contains a typo; it should read R_NS > R_LE, and the table header should distinguish R_LP from R_LPN more clearly.
  2. [Abstract and Section I] The abstract and introduction contain grammatical errors, including 'we are suggestion a third fate' and 'will be smaller of ISCO'; a careful language edit is needed.
  3. [References] Reference [5] is malformed; the author list should be 'M. A. Abramowicz, M. Calvani, and L. Nobili'.
  4. [Tables III and VII] Table VII labels R_NS as the 'Areal radius' while Table III calls it the 'proper circumferential radius'; the same definition should be used consistently throughout.
  5. [Eq. (38)] Eq. (38) is typeset as 'rM S= 21/3cR'; the intended expression 2^{1/3} c_R (M_BH/M_NS)^{1/3} R_NS should be written unambiguously.

Circularity Check

0 steps flagged · score 0.0 of 10

No load-bearing circularity; the Roche-lobe overflow conclusion is an independent comparison against external formulas, not a reconstruction of its inputs.

full rationale

The paper's derivation chain is self-contained and benchmarked against external, non-fitted formulas. ISCO locations are extracted from the minimum of the binding energy along FUKA quasi-equilibrium sequences via the fits in Eqs. (35)-(37), and the mass-shedding radius uses the Kyutoku et al. formula, Eq. (38), with the c_R=1/kappa indicator from Eq. (39). The central overflow claim for q=0.4167 is a direct comparison of the proper neutron-star radius R_NS=7.76 M_sun from the QE solution with the Eggleton Roche-lobe radius R_LE=7.44 M_sun and the 2PN radius R_LPN=6.90 M_sun at the same separation d=24.3 M_sun (Table IV). Neither Roche-lobe radius is fitted to R_NS nor derived from kappa, so the inequality R_NS > R_LE is an independent diagnostic rather than a consistency relation. The self-citations present, namely the functional ansatz and spin-choice guidance from [16] (with overlapping author Tootle) and the runaway-instability papers [6],[8],[9] (with author Lanza), are not load-bearing: the quadratic ISCO fit is checked against the sequence data in Fig. 2, and the runaway-instability analogy is explicitly deferred to future time evolutions rather than used to establish the overflow. The paper itself flags the Roche-lobe comparison as 'only indicative' in Section V, and the tension between the kappa-based r_MS=19.11 M_sun and the Roche-lobe inference is a physical/interpretive limitation, not a case of an output equaling its input by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the FUKA QE framework, on Newtonian and post-Newtonian Roche-lobe estimates, and on fitting procedures. All numerical inputs, including EOS, spins and masses, are pulled from prior work or posterior ranges; the genuinely new additions are the sequence fits and the third-fate interpretation.

free parameters (3)
  • b1, b2, b3 = per sequence, e.g., q=0.4167: -0.00155, -0.2886, 1.8542
    Coefficients of the quadratic fit to binding energy versus orbital angular velocity used to locate the ISCO minimum (Eq. 35).
  • a, b of Omega(d) fit = per sequence, e.g., q=0.4167: a=2.10, b=-0.0121
    Coefficients of the fit M_inf Omega = a/d + b used to convert Omega_ISCO to the separation d_ISCO (Eq. 37).
  • c_R = 1/kappa = varies from 1.13 to 2.05, e.g., 1.46 for q=0.4167
    Degree of tidal elongation extracted from the QE solution at the last converged separation and inserted into the Newtonian mass-shedding radius formula (Eqs. 38-39).
assumptions (5)
  • domain assumption Minimum of binding energy marks the ISCO of the QE sequence.
    Standard in numerical relativity initial data analysis; used to locate ISCO in Section IV B.
  • domain assumption Newtonian formula r_MS = 2^(1/3) c_R (MBH/MNS)^(1/3) R_NS provides a valid estimate of the mass-shedding radius in a GR context.
    Taken from Kyutoku et al. review [3] and applied to GR QE sequences with c_R derived from kappa.
  • domain assumption Newtonian effective potential (Eq. 40) and Eggleton/2PN Roche lobe radii describe the Roche lobe of the neutron star in a BHNS binary.
    The Roche-lobe overflow conclusion rests on comparing the GR stellar radius with these Newtonian and post-Newtonian approximations (Section IV D, Table IV).
  • domain assumption The Togashi (TNTYST) equation of state is representative for the neutron star models.
    A single cold tabulated EOS is used with no EOS variation across the sequences (Section II B).
  • domain assumption The fluid is in hydrostatic equilibrium along the QE sequence under the constant rotation velocity approximation.
    FUKA assumes an isentropic, quasi-equilibrium fluid and uses the CRV approximation to model spin (Section II B).

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Cite this review

Pith. "Pith review of Combining (post-)Newtonian ideas with quasi-equilibrium (QE) sequence analysis for black hole-neutron star (BHNS) gravitational wave events." pith.science (2026). https://pith.science/paper/YNFLQEFO

@misc{pith2026250709175,
  author       = {Pith},
  title        = {Pith review of: Combining (post-)Newtonian ideas with quasi-equilibrium (QE) sequence analysis for black hole-neutron star (BHNS) gravitational wave events},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YNFLQEFO}},
  note         = {Machine review of arXiv:2507.09175}
}
read the original abstract

In this paper we present quasi equilibrium models of black hole-neutron star (BHNS) binaries with mass and spin values compatible with parameter estimates derived from gravitational radiation events GW200105 and GW200115, events consistent with the merger of BHNSs. Using the FUKA initial data framework, we determine the location of ISCO (Innermost Stable Circular Orbit) and radius of mass shedding. In most of the cases studied here the innermost stable orbit is located at larger separations. This is consistent with the fact that for those two events no electromagnetic counterparts have been observed since it is believed that the NS will enter into the plunge phase in a short time once the separation of the components of the binary will be smaller of ISCO. In analogy with classical binaries, we have associated to these QE sequences a Newtonian and Post Newtonian Roche Lobe analysis to verify whether the NS is filling its Roche Lobe before approaching the ISCO. For selected configurations explored here, the location of ISCO and of the orbit at which mass shedding occurs are at separation smaller than the last converged solution of our sequences. Our analysis shows that in such cases the neutron star is filling its Roche lobe suggesting that mass transfer might occur well before encountering the last stable orbit, and this should happen in catastrophic way in order to prevent any electromagnetic emissions. If this is the case, we are suggestion a third fate of the neutron star beyond the plunge or tidal disruption ones.

Figures

Figures reproduced from arXiv: 2507.09175 by the authors.

Figure 1
Figure 1. FIG. 1. a) Binding energy [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Reduced Newtonian Effective Potential surfaces for four QE sequences with different mass ratios in a frame with [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Radii of reduced Newtonian Effective Potential surfaces for different separation compared with the relative positions [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Reduced Newtonian Effective Potential surfaces for four QE sequences with different mass ratios in a frame with [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Radii of reduced Newtonian Effective Potential surfaces for different separation compared with the relative positions [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]

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Works this paper leans on

38 extracted references · 34 canonical work pages

  1. [1]

    Asymptotic flatness Given Kadath utilizes a multi-domain approach with the outer domain utilizing a compactified coordinate sys- tem such that spatial infinity is mapped to a finite value, we can accurately impose asymptotic boundary condi- tions in a consistent manner. In this way, asymptotic flatness boundary conditions are enforce on the lapse, conform...

    work page

  2. [2]

    For initial data, it has become common practice to excise the surface of the black to avoid this

    Black-hole excision boundary conditions In numerical simulations the presence of a black hole introduces a singularity unless suitable boundary con- ditions are enforced. For initial data, it has become common practice to excise the surface of the black to avoid this. The excision region for conformally flat initial data is defined as the marginally outer...

    work page

  3. [3]

    From the equation of hy- drostatic equilibrium Eqs

    On the surface of the neutron star The surface of the neutron star is defined as that sur- face in which H := ln (h) → 0. From the equation of hy- drostatic equilibrium Eqs. (20) the boundary condition of the surface of the neutron star becomes: V i ˜DiH = 0 . (29) D. Diagnostics To characterize the properties of the quasi-equilibrium sequences, we define...

    work page

  4. [4]

    Ferrari, L

    V. Ferrari, L. Gualtieri, and A. Maselli, Tidal interaction in compact binaries: A post-newtonian affine framework, Phys. Rev. D 85, 044045 (2012)

    work page 2012

  5. [5]

    N. L. Abramowicz M. A., Calvani M., Nature 302, 597 (1983)

    work page 1983

  6. [6]

    Lanza, Self-gravitating Thin Disks around Rapidly Rotating Black Holes, Astrophys

    A. Lanza, Self-gravitating Thin Disks around Rapidly Rotating Black Holes, Astrophys. J. 389, 141 (1992)

    work page 1992

  7. [7]

    Abbott et al

    R. Abbott et al. , Astrophys. J. L. 915, L5 (2021)

    work page 2021

  8. [8]

    A. G. Abac et al. , Astrophys. J. Lett. 970, L34 (2024)

    work page 2024

Show all 38 references
  1. [9]

    Kyutoku, M

    K. Kyutoku, M. Shibata, and K. Taniguchi, Coalescence of black hole–neutron star binaries, Living Rev. Relativ. 24 (2021)

    2021

  2. [10]

    Masuda and Y

    N. Masuda and Y. Eriguchi, Three-dimensional simula- tions of runaway instability of self-gravitating accretion disks, Astrophys. J. 489, 804 (1997)

    1997

  3. [11]

    Korobkin, E

    O. Korobkin, E. Abdikamalov, N. Stergioulas, E. Schnetter, B. Zink, S. Rosswog, and C. D. Ott, The runaway instability in general rel- ativistic accretion discs, MNRAS 431, 349 (2013), https://academic.oup.com/mnras/article- pdf/431/1/349/18241216/stt166.pdf

    2013

  4. [12]

    Blinnikov, A

    S. Blinnikov, A. Yudin, N. Kramarev, and M. Potashov, Stripping model for short gamma-ray bursts in neutron star mergers, Particles 5, 198 (2022)

    2022

  5. [13]

    Nishida and Y

    S. Nishida and Y. Eriguchi, A General Relativistic Toroid around a Black Hole, Astrophys. J. 427, 429 (1994)

    1994

  6. [14]

    The equations result- ing from the spectral representation are solved by using Newton-Raphson iterative method [15]

    for a more detailed discussion). The equations result- ing from the spectral representation are solved by using Newton-Raphson iterative method [15]. The libraries is modular and one has to specify which solver to use according to the nature of the binary con- sidered BBH, BNS...

  7. [15]

    For binary ID, a bi-spherical decomposition is used for the numerical space resulting in at least twelve domains to resolve the problem efficiently (see [15] and

    which make use of a novel multi-domain discretiza- tion which maps the physical space to an optimized nu- merical grid. For binary ID, a bi-spherical decomposition is used for the numerical space resulting in at least twelve domains to resolve the problem efficiently (see [15] and

  8. [16]

    Nishida, A

    S. Nishida, A. Lanza, Y. Eriguchi, and M. A. Abramow- icz, Runaway instability and gamma-ray bursts, MNRAS 278, L41 (1996)

    1996

  9. [17]

    M. A. Abramowicz, V. Karas, and A. Lanza, On the run- away instability of relativistic tori, Astron. & Astrophys. 331, 1143 (1998), arXiv:astro-ph/9712245 [astro-ph]

    1998 arXiv

  10. [18]

    Gourgoulhon, 3+1 formalism and bases of numerical relativity (2007), arXiv:gr-qc/0703035 [gr-qc]

    E. Gourgoulhon, 3+1 formalism and bases of numerical relativity (2007), arXiv:gr-qc/0703035 [gr-qc]

    2007 arXiv

  11. [19]

    Kramarev, A

    N. Kramarev, A. Kuranov, A. Yudin, and K. Postnov, Stripping of a Neutron Star in a Close Binary System in a Pair with a Black Hole, Astron. Lett. 50, 302 (2024), arXiv:2410.12541 [astro-ph.HE]

    2024 arXiv

  12. [20]

    L. J. Papenfort, S. D. Tootle, P. Grandcl´ ement, E. R. Most, and L. Rezzolla, New public code for initial data of unequal-mass, spinning compact-object binaries, Phys. Rev. D 104, 024057 (2021)

    2021

  13. [21]

    Grandcl´ ement, Kadath: A spectral solver for theoret- ical physics, J

    P. Grandcl´ ement, Kadath: A spectral solver for theoret- ical physics, J. Comput. Phys. 229, 3334 (2010)

    2010

  14. [22]

    Topolski, S

    K. Topolski, S. Tootle, and L. Rezzolla, Black hole- neutron star binaries with high spins and large mass asymmetries: I. properties of quasi-equilibrium sequences (2024), arXiv:2409.06767 [gr-qc]

    2024 arXiv

  15. [23]

    Topolski, S

    K. Topolski, S. Tootle, and L. Rezzolla, Black hole - neu- tron star binaries with high spins and large mass asym- metries: Ii. properties of dynamical simulations (2024), arXiv:2409.06777 [gr-qc]

    2024 arXiv

  16. [24]

    G. B. Cook and H. P. Pfeiffer, Excision boundary con- ditions for black-hole initial data, Phys. Rev. D 70, 10.1103/physrevd.70.104016 (2004)

    2004 doi

  17. [25]

    T. W. Baumgarte and S. L. Shapiro, Numerical Relativ- ity: Solving Einstein ’s Equations on the Computer (Cam- bridge University Press, 2010)

    2010

  18. [26]

    T. W. Baumgarte and S. L. Shapiro, Numerical Relativ- ity: Starting from Scratch (Cambridge University Press, 2021)

    2021

  19. [27]

    However, in some cases the code does not converge for smaller separations and it is not possible to find a minimum of the binding energy

    and reference therein). However, in some cases the code does not converge for smaller separations and it is not possible to find a minimum of the binding energy. Following the suggestion in [16], we use the following functional ansatz to fit the computed data and extrapolate t...

  20. [28]

    Shibata, Relativistic formalism for computation of ir- rotational binary stars in quasiequilibrium states, Phys

    M. Shibata, Relativistic formalism for computation of ir- rotational binary stars in quasiequilibrium states, Phys. Rev. D 58, 10.1103/physrevd.58.024012 (1998)

    1998 doi

  21. [29]

    S. A. Teukolsky, Irrotational binary neutron stars in quasi-equilibrium in general relativity, Astrophys. J.504, 442–449 (1998)

    1998

  22. [30]

    Togashi, K

    H. Togashi, K. Nakazato, Y. Takehara, S. Yamamuro, H. Suzuki, and M. Takano, Nuclear equation of state for core-collapse supernova simulations with realistic nuclear forces, Nucl. Phys. A 961, 78–105 (2017)

    2017

  23. [31]

    Caudill, G

    M. Caudill, G. B. Cook, J. D. Grigsby, and H. P. Pfeiffer, Circular orbits and spin in black-hole initial data, Phys. Rev. D 74, 10.1103/physrevd.74.064011 (2006)

    2006 doi

  24. [32]

    Taniguchi, T

    K. Taniguchi, T. W. Baumgarte, J. A. Faber, and S. L. Shapiro, Relativistic black hole-neutron star binaries in quasiequilibrium: Effects of the black hole excision boundary condition, Phys. Rev. D 77, 044003 (2008)

    2008

  25. [33]

    W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes 3rd Edition: The Art of Sci- entific Computing , 3rd ed. (Cambridge University Press, USA, 2007)

    2007

  26. [34]

    Frank, A

    J. Frank, A. King, and D. Raine, Accretion Power in As- trophysics, 3rd ed. (Cambridge University Press, 2002)

    2002

  27. [35]

    Orbital mechanics & astrodynamics, available at https://orbital-mechanics.space/intro.html

  28. [36]

    P. P. Eggleton, Aproximations to the radii of roche lobes., Astrophys. J. 268, 368 (1983)

    1983

  29. [37]

    Paczy´ nski, Evolutionary processes in close binary sys- tems, Ann

    B. Paczy´ nski, Evolutionary processes in close binary sys- tems, Ann. Rev. Astr. Ap. 9, 183 (1971)

    1971

  30. [38]

    Ratkovic, M

    S. Ratkovic, M. Prakash, and J. M. Lattimer, Roche lobes in the second post-newtonian approximation (2005), arXiv:astro-ph/0512133 [astro-ph]

    2005 arXiv

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