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arxiv: 2604.14225 · v2 · submitted 2026-04-14 · 🌌 astro-ph.HE · gr-qc

Consistent Treatment of Muons in Binary Neutron Star Mergers

Henrique Gieg , Ramon Jaeger , Maximiliano Ujevic , Tim Dietrich This is my paper

Pith reviewed 2026-05-10 14:34 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords binary neutron star mergersmuonsnumerical relativityneutrino transportejectanucleosynthesisweak interactions
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The pith

Binary neutron star merger simulations that include muons produce ejecta masses reduced by at most 17 percent with other remnant properties differing by less than 6 percent.

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

The paper runs numerical relativity simulations of binary neutron star mergers that incorporate muons and muonic weak reactions using a gray truncated moments neutrino scheme. It compares these runs to otherwise identical simulations without muons and finds close agreement in remnant evolution, disk properties, and most outflow characteristics. The main difference appears as a modest reduction in the total ejected mass. This outcome indicates that muons do not produce the large changes in nucleosynthetic yields or electromagnetic signals reported in some earlier work.

Core claim

In simulations of binary neutron star mergers that account for muons using a gray truncated moments neutrino scheme and a two-timescales equilibration method, the presence of muons leads to at most a 17 percent reduction in ejecta mass while average electron fractions, asymptotic velocities, and temperatures differ by less than 6 percent from non-muonic cases. The overall evolution of the remnant, disk, and outflows remains largely consistent across two baseline baryonic equations of state.

What carries the argument

The gray energy-independent truncated moments neutrino scheme combined with a novel two-timescales approach for matter-radiation equilibration, applied to newly computed muonic reaction rates within the full kinematics framework.

If this is right

  • Nucleosynthetic yields from merger ejecta change only modestly when muons are included.
  • Electromagnetic counterparts such as kilonovae are expected to show only small variations from non-muonic predictions.
  • The gray neutrino treatment appears sufficient to capture the dominant effects of muons on remnant and outflow evolution.
  • Results hold for both baseline equations of state examined, suggesting the outcome is not strongly EOS-dependent.

Where Pith is reading between the lines

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

  • Simpler non-muonic models may remain adequate for many large-scale studies of merger nucleosynthesis and light curves.
  • Energy-dependent neutrino transport could be tested next to confirm that the modest muon impact survives higher resolution of reaction thresholds.
  • The small ejecta reduction could still matter for precise abundance pattern comparisons with observed heavy-element signatures.
  • Muon effects might differ in other high-density environments such as core-collapse supernovae where densities and timescales vary.

Load-bearing premise

The gray energy-independent neutrino scheme together with the two-timescales equilibration approach fully captures the relevant weak interaction physics and equilibration dynamics in the presence of muons.

What would settle it

A comparison simulation using an energy-dependent neutrino transport method that resolves muon production thresholds and reaction kinematics in detail would reveal whether the small differences in ejecta mass and composition persist.

Figures

Figures reproduced from arXiv: 2604.14225 by Henrique Gieg, Maximiliano Ujevic, Ramon Jaeger, Tim Dietrich.

Figure 1
Figure 1. Figure 1: Evolution of diagnostic quantities for the SFHo (upper panels) and DD2 (lower panels) runs. For a better visualiza￾tion, a moving-average with window size of 0.2 ms is applied. Left column: maximum rest-mass density for the 5-ν (black thick line) and 3-ν (red dashed line). Middle column: maximum temperature. Right column: neutrino luminosities of all species for the 3 (dashed lines) and 5-ν (thick lines) c… view at source ↗
Figure 2
Figure 2. Figure 2: Snapshots of the electron fraction for the SFHo (upper panels) and DD2 (lower panels) in the polar plane and orbital plane. The left (right) half represents 5-ν (3-ν) runs at t − tmrg = {2.5, 10, 20} ms from left to right columns. Black lines are isodensity contours from {1011 , 1012 , 1013 , 1014} g cm−3 . Regardless of the baryonic baseline, in both the muonic and electronic runs we note early electroniz… view at source ↗
Figure 3
Figure 3. Figure 3: Snapshots of the muon fraction Yµ (left half) and relative difference with respect to equilibrium |δYµ/Yµ|, Eq.(6), (right half) in the polar plane and orbital plane for the SFHo 5-ν (upper panels) and DD2 5-ν (lower panels) runs at t − tmrg = {2.5, 10, 20} ms from left to right columns. Green-dotted lines mark constant densities {1012 , 1013 , 1014} g cm−3 . at t − tmrg ≥ 10 ms (see [PITH_FULL_IMAGE:figu… view at source ↗
Figure 4
Figure 4. Figure 4: Diagnostics for the muonic content. Upper panel: evolution of normalized total muon number (thick lines) and mass-averaged deviation from equilibrium (dotted) for our 5- ν runs SFHo (blue) and DD2 (red). Lower panels: from top to bottom, we present radial averages of rest-mass density, temperature and muon density at different times along the post-merger for SFHo (left column) and DD2 (right column). for t… view at source ↗
Figure 5
Figure 5. Figure 5: Mass-normalized distributions of ejecta properties up to t−tmrg ≈ 20 ms: electron fraction (left column), asymptotic velocity (middle column) and temperature (right column) for our SFHo (upper panels) and DD2 (lower panels) runs. Note that at the extraction sphere (r ≈ 300 km), and there Yµ = 10−4 . this work. Consequently, we expect that nucleosynthetic yields and the associated kilonova signal to not be … view at source ↗
read the original abstract

We present a set of numerical-relativity binary neutron star merger simulations incorporating muons and muonic reactions for two baseline baryonic equations-of-state. In order to investigate the possible impact of muons and muonic weak reactions, we treat neutrinos with a gray (energy-independent) truncated moments scheme and an implicit-explicit time integrator. Newly computed neutrino rates are employed within the full kinematics approach for a set of relevant reactions, and pair-processes are modeled via opacities computed using reaction kernels, that allow a consistent treatment of neutrino interaction rates. We find that equilibration between matter and radiation is successfully captured by a novel two timescales approach. Of astrophysical interest is the general agreement between our muonic and non-muonic results regarding the remnant evolution, disk and outflow properties. Average electron fractions, asymptotic velocities and temperatures are different by less than $\sim 6\%$, while the main impact of muons is a reduction in ejecta masses by at most $\sim 17\%$. Therefore, based on our findings, accounting for the presence of muons and muonic reactions might result much less severe consequences regarding nucleosynthetic yields and electromagnetic counterparts than previously reported in the literature.

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

3 major / 2 minor

Summary. The paper reports numerical-relativity simulations of binary neutron star mergers that incorporate muons and muonic weak reactions for two baryonic equations of state. Neutrinos are evolved with a gray truncated-moments scheme and an implicit-explicit integrator; reaction rates use full kinematics and pair processes are treated via reaction kernels. A novel two-timescales equilibration method is introduced. The central result is that muonic and non-muonic runs differ by less than ~6% in average electron fraction, asymptotic velocity and temperature, with ejecta mass reduced by at most ~17%, implying substantially milder effects on nucleosynthetic yields and electromagnetic counterparts than reported in earlier literature.

Significance. If the modest differences are robust, the work would indicate that muons do not drive the large changes in Y_e and ejecta previously attributed to them, thereby reducing the expected impact on r-process yields and kilonova light curves. The manuscript receives credit for the consistent full-kinematics treatment of rates, the use of reaction kernels for pair processes, and the introduction of the two-timescales equilibration approach that successfully captures matter-radiation coupling in the reported runs.

major comments (3)
  1. [Methods (neutrino transport and rates)] The central claim that muons produce only modest changes rests on the gray (energy-independent) truncated-moments neutrino scheme described in the methods section. Because muonic opacities and pair processes possess distinct energy thresholds and kinematics from electronic channels, the gray closure can suppress spectral differences that prior spectral or Monte-Carlo treatments captured; without a controlled energy-binned comparison or reproduction of a previous setup, the reduced impact may be an artifact of the transport approximation rather than a physical result.
  2. [Results (remnant, disk and outflow properties)] No convergence tests with respect to spatial resolution, neutrino moment truncation order, or the two-timescales equilibration parameters are reported. Consequently the quantitative statements (differences <6% in Y_e, velocity, temperature; ≤17% in ejecta mass) lack error bars or robustness measures, leaving open whether the reported percentages are numerically converged or statistically significant.
  3. [Discussion and conclusions] The assertion that consequences for nucleosynthesis and electromagnetic counterparts are 'much less severe' than in the literature is not accompanied by a direct side-by-side comparison that isolates the neutrino-scheme difference from the inclusion of muons. A controlled run with the same gray scheme but without muons versus a spectral run from the literature would be required to substantiate the claim.
minor comments (2)
  1. [Abstract and §4] The abstract and results sections would benefit from explicit statements of the two baseline EOS employed and the precise definition of 'ejecta mass' (e.g., unbound material above a given density or velocity threshold).
  2. [Methods] Notation for the reaction kernels and the two-timescales equilibration parameters should be introduced with a short equation or table to avoid ambiguity when readers compare to other implementations.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive report. We address each major comment below, proposing revisions to strengthen the manuscript while maintaining scientific accuracy.

read point-by-point responses

  1. Referee: The central claim that muons produce only modest changes rests on the gray (energy-independent) truncated-moments neutrino scheme described in the methods section. Because muonic opacities and pair processes possess distinct energy thresholds and kinematics from electronic channels, the gray closure can suppress spectral differences that prior spectral or Monte-Carlo treatments captured; without a controlled energy-binned comparison or reproduction of a previous setup, the reduced impact may be an artifact of the transport approximation rather than a physical result.

    Authors: We agree that the gray approximation represents a limitation that could mask energy-dependent spectral effects, particularly given the distinct thresholds for muonic processes. Our study deliberately employs a consistent gray truncated-moments framework for both muonic and non-muonic runs to enable a controlled comparison within the same numerical setup. In the revised manuscript, we will expand the Methods and Discussion sections to explicitly discuss the gray scheme's limitations, its validity range for merger conditions, and how it may affect quantitative differences relative to spectral treatments in the literature. revision: partial

  2. Referee: No convergence tests with respect to spatial resolution, neutrino moment truncation order, or the two-timescales equilibration parameters are reported. Consequently the quantitative statements (differences <6% in Y_e, velocity, temperature; ≤17% in ejecta mass) lack error bars or robustness measures, leaving open whether the reported percentages are numerically converged or statistically significant.

    Authors: We acknowledge that explicit convergence tests were not included in the original submission. The simulations used resolutions standard in the field for similar gray-moment runs, and the two-timescales method was validated through equilibration behavior in the reported data. In the revised manuscript, we will add a dedicated subsection on numerical robustness, including resolution comparisons where available from our simulation suite and sensitivity checks on equilibration parameters, along with estimated uncertainties on the reported percentage differences. revision: yes

  3. Referee: The assertion that consequences for nucleosynthesis and electromagnetic counterparts are 'much less severe' than in the literature is not accompanied by a direct side-by-side comparison that isolates the neutrino-scheme difference from the inclusion of muons. A controlled run with the same gray scheme but without muons versus a spectral run from the literature would be required to substantiate the claim.

    Authors: We recognize that isolating the neutrino transport scheme from the inclusion of muons would require additional controlled simulations matching prior setups exactly, which is beyond the scope of the current work due to computational cost. Our conclusions are drawn from differences observed within our consistent gray framework compared to published results using varied methods. In the revised version, we will moderate the language in the Discussion and Conclusions to 'potentially less severe' and add explicit caveats about scheme differences, while retaining the core finding of modest changes under our treatment. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results from direct simulation comparisons

full rationale

The paper reports outcomes from explicit numerical-relativity runs that compare muonic versus non-muonic cases under a fixed gray truncated-moments neutrino scheme and two-timescales equilibration. Quantities such as average Y_e, velocities, temperatures, and ejecta masses are measured directly from the evolved hydrodynamics and neutrino transport; no parameter is fitted to a target observable and then re-labeled as a prediction, nor is any central claim reduced by definition or by a self-citation chain to its own inputs. The text presents the two-timescales method as a numerical implementation whose success is verified by the same runs, not presupposed. Because the reported differences are simulation outputs rather than algebraic identities or fitted renamings, the derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the gray neutrino approximation, the two-timescales equilibration method, and the two chosen baseline equations of state; no new particles or forces are introduced.

axioms (2)
  • domain assumption Gray (energy-independent) truncated moments scheme suffices for neutrino transport in this regime
    Explicitly adopted for the simulations
  • ad hoc to paper Novel two-timescales approach accurately captures matter-radiation equilibration
    Introduced in the paper to handle the muonic case

pith-pipeline@v0.9.0 · 5512 in / 1322 out tokens · 39314 ms · 2026-05-10T14:34:28.426953+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

  1. [1]

    P., Abbott, R., Abbott, T

    Abbott, B. P., et al. 2017a, Astrophys. J. Lett., 848, L12, doi: 10.3847/2041-8213/aa91c9 —. 2017b, Phys. Rev. Lett., 119, 161101, doi: 10.1103/PhysRevLett.119.161101 Alford, M. G., Brodie, L., Foucart, F., & Haber, A

    work page doi:10.3847/2041-8213/aa91c9 2041

  2. [2]

    A., et al

    https://arxiv.org/abs/2603.06788 Arcavi, I., et al. 2017, Nature, 551, 64, doi: 10.1038/nature24291 Arcones, A., & Thielemann, F.-K. 2023, Astron. Astrophys. Rev., 31, 1, doi: 10.1007/s00159-022-00146-x Ardevol-Pulpillo, R., Janka, H. T., Just, O., & Bauswein, A. 2019, Mon. Not. Roy. Astron. Soc., 485, 4754, doi: 10.1093/mnras/stz613 Barnes, J., & Kasen, ...

    work page doi:10.1038/nature24291 2017

  3. [3]

    2020, Gen

    https://arxiv.org/abs/2412.04570 Ciolfi, R. 2020, Gen. Rel. Grav., 52, 59, doi: 10.1007/s10714-020-02714-x Coulter, D. A., et al. 2017, Science, doi: 10.1126/science.aap9811 Daszuta, B., Bernuzzi, S., Jacobi, M., et al

    work page doi:10.1007/s10714-020-02714-x 2020

  4. [4]

    2015a, Phys

    https://arxiv.org/abs/2602.18290 Dietrich, T., Bernuzzi, S., Ujevic, M., & Br¨ ugmann, B. 2015a, Phys. Rev., D91, 124041, doi: 10.1103/PhysRevD.91.124041 Dietrich, T., Moldenhauer, N., Johnson-McDaniel, N. K., et al. 2015b, Phys. Rev., D92, 124007, doi: 10.1103/PhysRevD.92.124007 Drout, M. R., et al. 2017, Science, 358, 1570, doi: 10.1126/science.aaq0049 ...

    work page doi:10.1103/physrevd.91.124041 2017

  5. [5]

    1998, Astrophys

    https://arxiv.org/abs/2506.18995 Hannestad, S., & Raffelt, G. 1998, Astrophys. J., 507, 339, doi: 10.1086/306303 Harten, A., Lax, P. D., & Leer, B. v. 1983, SIAM Review, 25, 35, doi: 10.1137/1025002 Hempel, M., & Schaffner-Bielich, J. 2010, Nucl. Phys., A837, 210, doi: 10.1016/j.nuclphysa.2010.02.010 Hilditch, D., Bernuzzi, S., Thierfelder, M., et al. 201...

    work page doi:10.1086/306303 1998

  6. [6]

    https://arxiv.org/abs/2304.09168 Neuweiler, A., Dietrich, T., Br¨ ugmann, B., et al

    work page arXiv

  7. [7]

    2026, Phys

    https://arxiv.org/abs/2407.20946 Neuweiler, A., et al. 2026, Phys. Rev. D, 113, 043038, doi: 10.1103/mxlf-8sbm Ng, H. H.-Y., Cheong, P. C.-K., Lam, A. T.-L., & Li, T. G. F. 2024, Astrophys. J. Suppl., 272, 9, doi: 10.3847/1538-4365/ad2fbd Ng, H. H.-Y., Musolino, C., Tootle, S. D., & Rezzolla, L. 2025, Astrophys. J. Lett., 985, L36, doi: 10.3847/2041-8213/...

    work page doi:10.1103/mxlf-8sbm 2026

  8. [8]

    B., & Lightman, A

    https://arxiv.org/abs/astro-ph/9509006 Rybicki, G. B., & Lightman, A. P. 1986, Radiative Processes in Astrophysics Schianchi, F., Gieg, H., Nedora, V., et al. 2024, Phys. Rev. D, 109, 044012, doi: 10.1103/PhysRevD.109.044012 Sekiguchi, Y. 2010, Class.Quant.Grav., 27, 114107, doi: 10.1088/0264-9381/27/11/114107 Shibata, M., Kiuchi, K., Sekiguchi, Y.-i., & ...

    work page doi:10.1103/physrevd.109.044012 1986

  9. [9]

    For theβ-reactions (a) – (f) in Table 1, we follow (Guo et al

    Spectral (energy-dependent) opacities and annihilation kernels are produced for all thermodynamical points (ρ,T,Y e,Y µ) in the EOS range at neutrino energies ϵ= [0.5,420] MeV, binned in 18 log 10 spaced intervals. For theβ-reactions (a) – (f) in Table 1, we follow (Guo et al. (2020)) in the full kinematics approach, i.e., considering self-consistent modi...

    work page 2020

  10. [10]

    emission ratesQ p,i, i.e. κp,i = Qp,i cBi(ην, T) ,(A1) where the black-body integral reads Bi(ην, T) = 4π (hc)3 T 3+iF2+i(ην),(A2) F2+i(ην) is the (2+i)th order Fermi integral, and the neutrino degeneracyην is set by thermal and chemical equilibrium with matter. For heavy-lepton neutrinos,η νx = 0 and the denominator of Eq. (A1) never vanishes. This, howe...

    work page 2025

  11. [11]

    opacityκ p,i for neutrinoνas κp,i = R dϵ ϵ 2+iκp(ϵ)feq ν (ϵ, T, ην)R dϵ ϵ 2+ifeq ν (ϵ, T, ην) = 4π (hc)3 1 Bi(T, ην) Z dϵ ϵ 2+iκp(ϵ)feq ν (ϵ, T, ην), (A7) which automatically satisfies the Kirchhoff’s law for number and energy emission rates Qp,i = Z dϵ ϵ 2+ijp(ϵ) =κ p,i cBi(T, ην),(A8) when detailed-balance Eq.(A5) is enforced. It is worth noting that th...

    work page 2018

  12. [12]

    This is the case for nucleon-nucleon bremsstrahlung (j), as the kernel depends on the sum of neutrino energies

    Otherwise, the vanishing of the product of distribution functions is guaranteed if the isotropic kernel is symmetric on the energies. This is the case for nucleon-nucleon bremsstrahlung (j), as the kernel depends on the sum of neutrino energies. For electron-positron pair annihilation (i), the kernel is not symmetric, but Kawaguchi et al. (2025a) show tha...

    work page 2011

  13. [13]

    emission ratesQ i and absorption opacitiesκ a,i, while scattering opacitiesκ s are always averaged with respect to the energy spectrum. B.EQUILIBRATION: THE TWO TIMESCALES APPROACH Given the (possibly) stiff coupling between matter and radiation fields, the usage of the fluid’s temperatureTand compositionY e (after the explicit substep) to determine inter...

    work page 2024

  14. [14]

    Once (ρ, T ∗, Y ∗ e , Y ∗ µ ) are obtained, we recompute opacities in the PT and T states accordingly, while neutrinos in the F state have opacities corrected as in Eq. (A12). Note that this correction follows the prescription of Foucart et al. (2016a), and is based on the approximateϵ 2 scaling of opacities in the elastic approach of, e.g., Ruffert et al...

    work page 1996

  15. [15]

    (C23)-(C24), to be evaluated at fixedY µ

    With this adaption, the partiall=eequilibrium system is of the form Eqs. (C23)-(C24), to be evaluated at fixedY µ. Likewise, the partial l=µsystem is obtained by changingY e →Y µ,η νe →η νµ, to be evaluated at fixedY e. It is also worth noting that in the cases of partial equilibrium, the temperatureT ∗(Y ∗ e , Y ∗ µ ) is obtained by solving Eq. (C24) for...

    work page 2025

  16. [16]

    Whereas, in the present work, this is not needed, as the opacities are finite by construction

    forτ νµ <1 (τ ¯νµ <1), andη νµ =η ¯νµ = 0 forY µ <5×10 −3. Whereas, in the present work, this is not needed, as the opacities are finite by construction. Thus, in their approach, the neutrino degeneracy approachesη ν →0 outside of the neutrinosphereτ ν <1, while corrections become negligible inside, whereτ ν ≥1. But, since opacities for gray schemes are t...

    work page 2020