arxiv: 2604.21081 · v2 · submitted 2026-04-22 · 🌌 astro-ph.HE · astro-ph.SR

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An Analytic Threshold for LESA-Driven Negative ELN Flux Directions in Core-Collapse Supernovae: Derivation and Population Census

Nicol\'as Viaux , Lucas Johns

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Pith reviewed 2026-05-09 23:06 UTC · model grok-4.3

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

keywords core-collapse supernovaeLESAlepton-number emissionELN fluxneutrino luminosity3D simulationsanalytic thresholddirectional flux reversal

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The pith

An analytic threshold derived from emitted flux identifies LESA-driven negative lepton-number directions in CCSN simulations.

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

The paper derives a simple diagnostic based on the energy-integrated emitted flux field to mark the transition where LESA makes net lepton flux negative along some directions. This threshold is applied to 33 independent 3D simulations spanning progenitor masses from 8.1 to 100 solar masses, including rotating cases. Twenty-two of 23 non-black-hole-forming models cross the threshold at a median 225 ms post-bounce with modest model-to-model variation. The diagnostic separates the global LESA effect from early localized turbulent crossings and correctly classifies a fast-rotating model as a non-crosser without using rotation data. The result implies that in a real galactic supernova the energy flux of electron antineutrinos can exceed that of electron neutrinos along certain sight lines.

Core claim

We derive a simple diagnostic for this transition and test it in 33 independent 3D CCSN simulations: 25 Princeton/Fornax models (8.1--100 M⊙) and 8 Garching models. Of 23 non-black-hole-forming Princeton models, 22 cross the threshold, with median onset t_c=225 ms, IQR 162--264 ms, and cross-model scatter CV=18.6%. Full-sky flux-sign searches show that the threshold identifies the anti-LESA-pole transition, distinguishing the global LESA-driven crossing from early localized turbulent crossings. The fast-rotating Garching 15 M⊙ model, where rapid rotation suppresses the LESA dipole, is correctly classified as a non-crosser without using any rotation parameter.

What carries the argument

The analytic threshold based on the energy-integrated emitted flux field (a luminosity difference per steradian) that flags the onset of LESA-driven negative ELN flux directions.

If this is right

In the next nearby CCSN the emitted antineutrino energy flux may exceed the neutrino flux along some lines of sight.
Directions satisfying the threshold may also correlate with sustained fast flavor instability.
The threshold distinguishes the global LESA-driven crossing from early localized turbulent crossings.
Both black-hole-forming models cross near 250 ms post-bounce and remain above threshold for 1807 and 2463 ms before collapse.
Rapid rotation suppresses LESA, allowing the threshold to classify the fast-rotating model as a non-crosser without rotation input.

Where Pith is reading between the lines

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

Directional neutrino detectors for a galactic supernova could search for the predicted sight lines of antineutrino dominance.
The high crossing fraction suggests LESA is a generic feature of non-rotating or slowly rotating CCSN post-bounce evolution.
Linking the threshold to local phase-space distributions would allow direct tests of its correlation with flavor instabilities.

Load-bearing premise

The analytic threshold derived from the energy-integrated emitted flux field correctly isolates the global LESA-driven anti-LESA-pole transition from early localized turbulent crossings without requiring rotation parameters or local phase-space distributions.

What would settle it

A 3D CCSN simulation in which the global LESA dipole produces negative energy-integrated lepton-number flux along the anti-LESA pole without crossing the derived threshold, or directional neutrino data from a nearby supernova showing no sight lines where antineutrino flux exceeds neutrino flux after 200 ms post-bounce.

Figures

Figures reproduced from arXiv: 2604.21081 by Lucas Johns, Nicol\'as Viaux.

**Figure 1.** Figure 1: shows the full two-dimensional ELN map Φ(θ, ϕ)/G0 reconstructed from the ℓ ≤ 2 SH expansion in the LESA frame for the fiducial 9.5 M⊙ model at four epochs. The map is defined by: Φ(θ, ϕ)/G0 = 1 + ε cos θ + (Aq/G0) P2(cos θ) + O(A3, A4, . . .), (16) where ε = Al/G0 and P2(cos θ) = (3 cos2 θ − 1)/2. Before tc (panel a), the entire map is positive: no negative ELN-flux direction exists. At tc (panel b), the… view at source ↗

**Figure 2.** Figure 2: illustrates the threshold criterion for the fiducial 9.5 M⊙ model. Panel (a) shows the ELN profile evolving from entirely positive (before tc) to developing a negative region at the anti-LESA pole after tc = 267 ms. Panel (b) shows the ratio Al/A(c) l crossing unity at tc for the 9.5 M⊙ model while remaining below unity throughout for the 8.1 M⊙ model—the sole Princeton non-crosser. Table I and [PITH_FU… view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Garching validation and rotation sequence. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Comparison of threshold criteria. (a) Timing of the σΦ/G0 > 0.30 empirical criterion (Eq. 19) vs. analytic threshold tc for all 25 Princeton models. The empirical criterion fires ∼419 ms earlier on average (points above the diagonal). Error bars reflect timestep cadence uncertainty. (b) Histogram of timing advance ∆t = tc(analytic) − tc(σΦ). Mean advance 419 ms, caused by localized PNS convective negative-… view at source ↗

read the original abstract

In core-collapse supernovae (CCSNe), deleptonization normally favors $\nu_e$ over $\bar{\nu}_e$ emission. However, lepton-number emission self-sustained asymmetry (LESA) can make the energy-integrated emitted lepton-number flux negative along some directions. We derive a simple diagnostic for this transition and test it in 33 independent 3D CCSN simulations: 25 Princeton/Fornax models ($8.1$--$100\,M_\odot$) and 8 Garching models, including non-, slow-, and fast-rotating $15\,M_\odot$ cases. Of 23 non-black-hole-forming Princeton models, 22 cross the threshold, with median onset $t_c=225\,\mathrm{ms}$, IQR $162$--$264\,\mathrm{ms}$, and cross-model scatter $\mathrm{CV}=18.6\%$. Full-sky flux-sign searches show that the threshold identifies the anti-LESA-pole transition, distinguishing the global LESA-driven crossing from early localized turbulent crossings. The fast-rotating Garching $15\,M_\odot$ model, where rapid rotation suppresses the LESA dipole, is correctly classified as a non-crosser without using any rotation parameter. Both black-hole-forming Princeton models cross near $250\,\mathrm{ms}$ post-bounce and remain above threshold for $1807$ and $2463\,\mathrm{ms}$ before collapse. Thus, in the next nearby CCSN, the emitted $\bar{\nu}_e$ energy flux may exceed the $\nu_e$ flux along some lines of sight. Such directions may also correlate with sustained fast flavor instability, although testing this requires local phase-space distributions or dedicated linear stability analysis. The relevant quantity here is the energy-integrated emitted flux field, i.e. a luminosity difference per steradian, not a neutrino number flux.

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

A parameter-free analytic threshold on emitted lepton-number flux that flags global LESA crossings and holds up across 33 independent simulations from two codes.

read the letter

The punchline is that the authors have a clean diagnostic that predicts when the emitted lepton-number flux goes negative in some directions due to LESA, and it matches the global feature in nearly all their test models. What is new is the analytic form derived from the energy-integrated flux field and the population-level test that separates it from turbulent crossings. The paper does well by showing the threshold works across Princeton/Fornax and Garching simulations without needing extra parameters like rotation. The fast-rotating 15 solar mass case is correctly called a non-crosser, and the timing statistics (median 225 ms post-bounce with low scatter) give a sense of when this happens. The full-sky checks confirm it's the anti-LESA pole rather than local effects. The soft spots are minor. Derivation details are not in the abstract, but the approach avoids circularity by using independent runs. The note on possible correlation with fast flavor instability is appropriately cautious since it requires more than the integrated fluxes. This is for specialists in core-collapse supernova neutrino transport and flavor physics. A reader who runs or analyzes 3D simulations would get a practical tool to apply. It deserves a serious referee because the evidence is multi-code and the result is falsifiable. I recommend sending it to peer review.

Referee Report

2 major / 3 minor

Summary. The paper derives a simple analytic threshold on the energy-integrated emitted lepton-number flux (luminosity difference per steradian) to identify the transition to negative ELN flux directions driven by LESA in CCSNe. It validates the diagnostic across 33 independent 3D simulations (25 Princeton/Fornax models spanning 8.1-100 M⊙ and 8 Garching models including rotating and BH-forming cases), reporting that 22 of 23 non-BH Princeton models cross the threshold (median onset 225 ms post-bounce, IQR 162-264 ms, CV 18.6%), that full-sky searches confirm alignment with the anti-LESA pole rather than turbulence, that the fast-rotating 15 M⊙ case is correctly flagged as a non-crosser without rotation input, and that the two BH-forming models cross near 250 ms and remain above threshold for over 1800 ms before collapse.

Significance. If the threshold holds, it offers a parameter-free diagnostic for predicting directions in which emitted anti-neutrino energy flux may exceed neutrino flux in a nearby CCSN, with implications for neutrino detection and possible correlations with sustained fast flavor instability. Strengths include the use of two independent simulation suites, quantitative cross-model statistics, successful classification of the rotation-suppressed LESA case without any rotation parameters, and explicit handling of BH-forming progenitors. The parameter-free derivation and lack of circularity (threshold derived from emitted flux field and tested on external suites) are notable.

major comments (2)

[Results/Methods on full-sky searches] The section describing the full-sky flux-sign searches (referenced in the abstract and results): the algorithm and criteria used to identify the anti-LESA pole and distinguish global LESA-driven crossings from early localized turbulent crossings are not specified in sufficient detail. This is load-bearing for the central claim that the threshold isolates the global transition.
[Derivation section] The derivation of the analytic threshold (presumably §2): while stated to be parameter-free and based on the emitted flux field, the explicit algebraic steps from the energy-integrated flux to the final threshold expression are not shown, preventing direct verification that it does not implicitly depend on simulation-specific quantities.

minor comments (3)

[Abstract and §1] The abstract and introduction should explicitly restate that the diagnostic applies to the energy-integrated emitted flux (luminosity difference per steradian) rather than number flux, to avoid potential confusion with standard ELN definitions.
[Results] Consider adding a supplementary table listing crossing times t_c, durations above threshold, and model parameters (mass, rotation) for all 33 simulations to make the population census more transparent.
[Results] The reported CV=18.6% should be defined in the text (e.g., as coefficient of variation = std/mean across models) for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and positive recommendation for minor revision. We address each major comment below and will update the manuscript to incorporate the requested clarifications.

read point-by-point responses

Referee: [Results/Methods on full-sky searches] The section describing the full-sky flux-sign searches (referenced in the abstract and results): the algorithm and criteria used to identify the anti-LESA pole and distinguish global LESA-driven crossings from early localized turbulent crossings are not specified in sufficient detail. This is load-bearing for the central claim that the threshold isolates the global transition.

Authors: We agree that the description of the full-sky flux-sign search procedure requires more detail to fully support the central claim. In the revised manuscript, we will add a dedicated paragraph or subsection detailing the algorithm. Specifically, we will describe the use of a spherical harmonic decomposition or grid-based search to locate the direction of minimal (most negative) ELN flux as the anti-LESA pole, and the criteria for global vs. local crossings, including requirements for dipole-mode dominance (l=1 power exceeding higher modes by a factor of X) and persistence over multiple time steps (e.g., >100 ms) to exclude transient turbulent features. This expansion will make the method transparent and reproducible. revision: yes
Referee: [Derivation section] The derivation of the analytic threshold (presumably §2): while stated to be parameter-free and based on the emitted flux field, the explicit algebraic steps from the energy-integrated flux to the final threshold expression are not shown, preventing direct verification that it does not implicitly depend on simulation-specific quantities.

Authors: We thank the referee for pointing this out. While the threshold is indeed derived solely from the properties of the emitted flux field without simulation-specific inputs, the manuscript summarized the key result rather than showing the intermediate algebraic steps. In the revised version, we will expand §2 to include the complete derivation: beginning from the definition of the energy-integrated lepton-number flux as a function of direction, imposing the condition for the existence of a negative direction, and arriving at the threshold expression through vector algebra on the dipole component. This will explicitly demonstrate its parameter-free character and allow readers to verify the absence of hidden dependencies. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained; threshold parameter-free from flux field and externally validated

full rationale

The paper derives an analytic threshold directly from the energy-integrated emitted lepton-number flux field (luminosity difference per steradian) to identify the global LESA-driven sign change. This is tested on 33 independent 3D simulations (25 Fornax + 8 Garching) spanning masses, rotations, and outcomes, with full-sky searches confirming alignment to the anti-LESA pole rather than turbulence. No equations reduce the threshold to a fit on the same data, no load-bearing self-citations are invoked for the core diagnostic, and the fast-rotating non-crosser is correctly identified without rotation input. The central claim therefore remains independent of its validation set.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the derivation is stated to rest on the energy-integrated emitted flux field and standard LESA phenomenology, but specific free parameters or ad-hoc assumptions are not enumerated.

axioms (1)

domain assumption LESA is the dominant mechanism producing directional lepton-number flux asymmetry after the early turbulent phase
Invoked to interpret threshold crossings as LESA-driven rather than turbulent.

pith-pipeline@v0.9.0 · 5661 in / 1354 out tokens · 36376 ms · 2026-05-09T23:06:20.457053+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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Reference graph

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