{"id":"ccbfc07d-1885-4640-9e45-0d0eef460a69","arxiv_id":"2610.39402","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Bound supernova axion-like particles that cross the neutron star are absorbed within minutes, reducing the reheating signal by orders of magnitude and moving ALP-photon coupling limits upward.","lead":"This paper shows that axion-like particles orbiting a newborn neutron star are absorbed by the star long before they decay, so they reheat old neutron stars far less than a recent proposal assumed. The resulting limits on the particles' photon coupling are hundreds of times weaker, although a smaller excluded window survives.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"Quantitative high-mass window is computed from PNS evolutions that omit the ALP energy-loss sink, which the authors find reaches 91% of the neutrino luminosity; self-consistency could move the window edges.","rationale":"The paper's central qualitative claim is robust: a bound ALP on a star-crossing orbit crosses the star an enormous number of times, and the cold-star absorption margins exceed the decay time by more than five orders of magnitude across the scanned equations of state, rates, and orbits. That part of the argument does not depend on the PNS evolution details. The load-bearing uncertainty is therefore not the cold-star absorption but the quantitative surviving population and the resulting g_aγγ window. The reader's weakest assumption already identified the PNS evolution, including ALP energy loss, and the paper's own Sec. II D quantifies the problem at 91% of the neutrino luminosity near 100 MeV. Because the claimed window extends to 196 MeV (and 260 MeV with pion conversion), a large fraction of the window is computed in a regime where the back-reaction of the very ALPs being studied on the PNS thermal evolution cannot be neglected. This is an acknowledged limitation rather than a hidden error, and the authors correctly call for full supernova profiles and a self-consistent treatment. However, no such calculation or independent simulation is provided, so the precise window edges and margins remain conditional. The final-radius dependence identified by the reader is a second important uncertainty and reinforces the same conditional verdict, but the ALP energy-loss back-reaction is the more pointed concern because it is an internal consistency issue rather than an external parameter variation. The recommended verdict therefore stays CONDITIONAL, with no change from the reader's assessment.","tokens_in":33776,"tokens_out":9946,"duration_ms":77951,"concrete_test":"Add the local, redshifted ALP energy-loss rate as an extra sink in the matter-energy equation, Eq. (22), and rerun the GM3 and FSU2R evolutions at m_a = 10, 30, 100 and 200 MeV with g_ap = 2.7e-10 GeV^-1. Then repeat the orbit sampling and survival sum of Sec. IV and compare R_L and the 7.7-196 MeV window edges with Fig. 4 and Table I. If at 100-200 MeV the surviving heating shifts by more than the combined Monte Carlo and evolution-band errors, the reported high-mass window and margin are not yet settled; if it does not shift materially, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"At the high-mass end of the claimed surviving window the calculation is not self-consistent. The PNS evolutions solve Eqs. (21)-(22) without any ALP energy-loss term, yet in Sec. II D the authors compute that at m_a ≈ 100 MeV the escaped ALPs carry up to 60% of the neutrino energy and L_a reaches 91% of L_nu (sentence b215). That energy must come out of the same thermal and lepton reservoir that sets T(r,t), n_B(r,t) and Y_p(r,t), so the profiles used to produce and absorb the bound ALPs are not the profiles that would accompany the ALP population being modeled. Since the surviving fraction is set mainly by where ALPs are born and by how the contracting PNS radius pulls periapses inward, a faster, ALP-cooled evolution can shift the birth-region shape and the surviving-orbit distribution. This directly affects the upper part of the 7.7-196 MeV window and its margin of 43; the lower edge near 10 MeV is less exposed because the ALP energy loss is small there. The authors acknowledge this and list a self-consistent evolution as a next step, so the issue is not hidden, but the headline numerical window is nevertheless computed without it. The qualitative claim that star-crossing orbits are absorbed long before decay is unaffected; the concern is about the quantitative limits that are the paper's main deliverable.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"This paper revisits the bounds on the ALP-photon coupling derived by Bose et al. (Ref. [8]) from the decay-photon heating of old neutron stars (NSs) by axion-like particles produced in a core-collapse supernova and gravitationally bound to the newborn star. The authors argue that Ref. [8] neglected absorption of the bound population, and they compute this absorption by inverse nucleon bremsstrahlung (with pp and np channels, three rate models, 19 cold equations of state) in their own protoneutron-star (PNS) evolutions, following each ALP along general-relativistic orbits through the contracting PNS. Their main results are: (i) a bound ALP on a star-crossing orbit is absorbed in 0.1-400 s, against decay times above 1e8 s, so every such orbit is removed; (ii) the survivors are ALPs born outside the final star on nearly circular orbits, carrying 9e-9 to 6e-5 of the no-absorption heating; (iii) for PSR J2144-3933 a window survives at m_a ~ 7.7-196 MeV, with the lower edge of the photon coupling 280-700 times higher than in Ref. [8], extending to 260 MeV with pion conversion and the Delta(1232) resonance; and (iv) the window depends at comparable levels on the bremsstrahlung rate and on the final-star radius.","tokens_in":34227,"tokens_out":15804,"duration_ms":95933,"significance":"The qualitative mechanism is robust and the paper demonstrates it convincingly. The absorption-timescale hierarchy (<=400 s versus >=1e8 s decay times) holds across 19 equations of state, three bremsstrahlung rates, and twelve PNS evolutions, and the rate evaluation is carefully checked: agreement with published limits, detailed balance to 5e-4, and an explicit spin-isospin sum that settles the sign of the np interference term. The paper is also commendably candid about its limitations. Because the main deliverable is quantitative, the surviving exclusion window, the self-consistency of the PNS evolution at high ALP mass (Sec. II D) is the key uncertainty: near 100 MeV the authors find the ALP luminosity reaching 91% of the neutrino luminosity, yet Eqs. (21)-(22) contain no ALP energy-loss term. The window's upper edge should therefore be treated as provisional until this back-reaction is included or bracketed. The phenomenological status of the window is also conditional on the tuning of the induced photon coupling and on a recast of existing gamma-ray limits, both of which the authors acknowledge.","major_comments":[{"comment":"The central quantitative claim, the surviving window at 7.7-196 MeV (7.7-260 MeV with pion conversion), is computed from PNS evolutions whose energy equation contains no ALP energy-loss term. The paper's own estimate of that term (Sec. II D: at m_a ~ 100 MeV, L_a reaches 91% of the neutrino luminosity and the ALPs carry up to 60% of the neutrino energy over 10 s) shows that on the upper half of the window the ALP channel is not a small correction but the dominant cooling channel. That energy is drawn from the same thermal and lepton reservoir that sets T(r,t), n_B(r,t) and Y_p(r,t), so the profiles used to produce, absorb and orbit-average the bound ALPs are not the profiles that would accompany the modeled ALP population at those masses. Because the surviving fraction is set by the birth-region shape and by how the contracting radius pulls periapses inward, a faster, ALP-cooled evolution can shift the survival fraction and hence the upper window edge. The authors acknowledge this and list a self-consistent evolution as a next step, but the headline window is still reported without it. I request that the back-reaction be included, or at least bracketed by a controlled sensitivity test (for example, an evolution with the ALP luminosity added as a sink term to Eq. (22) for masses where L_a is comparable to or larger than L_nu), with the resulting shift in the window edge quantified.","section":"Sec. II D, Eqs. (21)-(22); Secs. IV-V","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The phenomenological status of the surviving window is not yet established, and the abstract's statement that PSR J2144-3933 'still excludes a window' is stronger than what the paper currently supports. The window masses lie well below the photon coupling induced by ALP-pion mixing, Eq. (4), so the window exists only with a tuned direct coupling that cancels the induced one (to one part in 14-46 at 10 MeV and one part in 3e4-6e5 at 100 MeV), and the authors state that the supernova gamma-ray limits of Refs. [1, 17] may already cover the window and have not been recast. Since the paper's main deliverable is the weakened exclusion window, I ask that the recast of these gamma-ray limits (or a conservative estimate of their coverage) be included, so the reader can see whether the window is phenomenologically open under the same production model rather than only under a tuning assumption.","section":"Secs. V-VI","authors_acknowledge":"The limits of Ref. [1] have not been recast to this coupling, and a recast of both sets of gamma-ray limits with the production rate used here is needed to de- cide.","authors_acknowledge_p":0.86}],"minor_comments":[{"comment":"The headline edges (7.7-196 MeV) are quoted more precisely than the underlying model spread warrants: the authors themselves find the window spanning 3.9-251 MeV at R = 11.5 km and 7.6-187 MeV at R = 13.5 km, while the cold radii of the 19 RMF sets range from 11.9 to 13.4 km. Please quote the window edges together with the radius- and evolution-induced range, or state explicitly that the quoted edges are for the envelope minimum over the twelve evolutions.","section":"Table I; Fig. 3(b)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The absorption time is integrated over the core only (n_B > 0.08 fm^-3), so orbits whose periapsis lies in the crust are not covered by the quoted 0.1-400 s values. For such shallow orbits the statement that 'every ALP whose orbit enters the star is absorbed within minutes' should be qualified, or the crust contribution to tau_1 should be computed; the comparison with decay times above 1e8 s makes this a presentation issue rather than a threat to the qualitative claim.","section":"Sec. III, Eq. (34)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The initial PNS model contains unconstrained choices ('the mantle lepton fraction, the tanh form and its width are our choice'), and the eleven variants are valuable; the presentation would benefit from attributing the factor-2.6-4.7 spread in R_L among the variants (opacity, entropy, mantle location, equation of state), so that the reader can see which input choices dominate the quantitative spread.","section":"Sec. II D","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The referee's main concern is the ALP energy-loss back-reaction (major comment 1); the remaining issues are presentation or interpretation. The paper relies numerically on the companion preprint Ref. [8] for the benchmark g_ap, L_obs, and the NS list; if that preprint is not yet formally published, the editor may want its status confirmed before acceptance. On scope: the manuscript is numerical astro-particle phenomenology, and for a hep-th journal the phenomenological emphasis may be a consideration, although the basin-absorption physics is of general interest."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"Two things to know up front. The qualitative claim holds: a bound ALP whose orbit enters the cold star is absorbed by inverse nucleon bremsstrahlung in 0.1–400 s, while the decay times for the relevant couplings exceed 10^8 s, across all 19 equations of state and three rates. That margin is five orders of magnitude, so Ref. [8]'s neglect of reabsorption is a real gap, and the reheating limits they proposed lose most of their force. The quantitative part is more conditional: the surviving window at 7.7–196 MeV for J2144-3933 comes from PNS evolutions that omit the ALP energy-loss sink, which the authors themselves compute reaches 91% of the neutrino luminosity near 100 MeV (sentence b215). The high-mass edge of the window is softer than the low-mass edge.\n\nWhat is new is the absorption calculation itself. Earlier basin literature noted reabsorption qualitatively or for other particles (solar basins, KK gravitons); nobody had computed it for this system with actual orbits. The paper follows bound ALPs through a contracting PNS in GR, with adiabatic invariants, survival fractions of 9e-9 to 6e-5, and a careful treatment of light bending in the decay-photon capture. That is a substantial, self-contained calculation.\n\nThe paper earns credit for how it is done. The three bremsstrahlung rates are normalized to the same light-ALP supernova energy loss, so rate comparisons are honest. The numerical checks are real: detailed balance at 5e-4, the eight-dimensional integrals against the two-dimensional expression of Ref. [39], the orbit map against direct integration, and the np-interference sign settled by an explicit spin-isospin sum. Limitations are stated where they bite, not buried.\n\nSoft spots, in proportion. The stress-test concern is valid, and the authors concede it in Sec. II D: near 100 MeV the ALPs carry away up to 60% of the neutrino energy, so the thermal and lepton profiles used for production and absorption are not the profiles that would accompany the ALP population being modeled. A self-consistent evolution could move the upper window edge; this is flagged as a next step, but the headline window is computed without it. Second, the surviving window requires a direct photon coupling tuned to cancel the pion-mixing-induced coupling to one part in 10^4–10^5 at 100 MeV, and the authors themselves say the supernova gamma-ray limits may already cover the window. The practical constraint could be superseded before the heating argument matters. Third, no code or data is shipped, and the surviving heating comes from a small effective Monte Carlo sample (up to 39% in one evolution); taking the envelope minimum is conservative but not the same as an accurate central value.\n\nThis paper is for axion/ALP phenomenologists and neutron-star cooling people. It deserves a serious referee: the qualitative correction to Ref. [8] is important on its own, and the quantitative part is honestly conditional rather than overstated.","headline":"Absorption kills most of the bound-ALP reheating limits from Ref. [8]; the surviving window is real but its high-mass end rests on PNS evolutions the authors admit omit the ALP energy loss.","tokens_in":34727,"tokens_out":3803,"would_cite":true,"duration_ms":30713,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["14.80.Va","97.60.Jd","97.60.Bw"],"model":"deepseek/deepseek-v4-flash","headline":"A neutron star absorbs its own bound axion-like particles in minutes, so the reheating limits on their photon coupling weaken, with lower edges rising 280–700 times.","keywords":["axion-like particles","neutron star reheating","inverse nucleon bremsstrahlung","gravitationally bound orbits","protoneutron star evolution","PSR J2144-3933","ALP-photon coupling","core-collapse supernova"],"falsifier":"Recompute the survival of bound ALPs on full supernova profiles that include accretion, convection and the ALP energy loss coupled back into the cooling: near $m_a = 100$ MeV that omitted loss reaches 91 percent of the neutrino luminosity, and a different contraction history or production region would move or close the surviving window at $m_a \\simeq 7.7$–$196$ MeV. A cheaper check is the cold-star radius of PSR J2144−3933, since the margin swings from 236 at $R = 11.5$ km to 45 at $R = 13.5$ km, fixing the window edges by roughly that factor.","tokens_in":35274,"feed_emoji":"⭐","tokens_out":18704,"duration_ms":113853,"temperature":0.7,"pith_summary":"Core-collapse supernovae produce axion-like particles (ALPs) coupled to protons, and the slowest of these stay gravitationally bound to the newborn neutron star. A prior proposal argued that these bound ALPs decay into photons over the star's life and reheat old, cold neutron stars, and used the absence of such heating in the coldest known star, PSR J2144−3933, to set strong limits on the ALP–photon coupling, while neglecting that the star itself could absorb the ALPs. This paper argues that absorption dominates: a bound ALP whose orbit enters the star crosses it about $6\\times 10^{18}$ times over the star's age, and inverse nucleon bremsstrahlung — absorption during a nucleon-nucleon scatter — removes such an ALP within 0.1 s to 7 minutes, long before it decays. Only ALPs born outside the final star on nearly circular orbits survive, carrying just $9\\times 10^{-9}$–$6\\times 10^{-5}$ of the previously counted heating, so the reheating limits weaken: the surviving excluded window at $m_a \\simeq 7.7$–$196$ MeV has its lower edge in the photon coupling raised 280–700 times. The result matters because it relocates the search: existing supernova gamma-ray limits may already cover the surviving window, and sharper temperature limits on old neutron stars are what would widen it.","feed_headline":"A neutron star swallows its bound axion cloud in minutes","feed_subtitle":"Only wide, star-skirting orbits survive, so older reheating limits on the photon coupling weaken by 280–700 times.","key_machinery":"The engine is inverse nucleon bremsstrahlung — the absorption process $aNN \\to NN$ in which a slow ALP is absorbed while two nucleons scatter — with a per-crossing optical depth far below one. What makes that tiny rate effective is the orbit: the paper follows each bound ALP as a general-relativistic trajectory with conserved energy and angular momentum and adiabatically invariant radial action, through the contracting protoneutron star slice by slice, and counts a particle as surviving only if its periapsis at 10 s clears the cold-star radius. The absorption rate itself is an eight-dimensional adaptive Monte Carlo integral over nucleon Fermi-Dirac distributions, with one-pion-exchange and $\\rho$-exchange matrix elements in both $pp$ and $np$ channels, normalized so emission and absorption obey detailed balance. Around this core the paper builds its own inputs: twelve protoneutron-star evolutions from a finite-temperature relativistic mean-field equation of state, nineteen cold-star equations of state, pion conversion and $\\Delta(1232)$ channels above $m_\\pi$, and light-bending-corrected photon capture, so the spread of the surviving window across all these variants is the paper's own measure of uncertainty.","core_discovery":"The paper's claim is that the bound cloud of supernova ALPs around a newborn neutron star is almost entirely eaten by the star it orbits. The authors compute the absorption of a massive ALP by inverse nucleon bremsstrahlung in cold neutron-star matter, follow each bound ALP along its general-relativistic orbit through the contracting protoneutron star, and find that any orbit whose periapsis dips inside the cold star is absorbed within 0.1 s to 7 minutes at $m_a = 10$–$200$ MeV, while the ALP lifetime for the relevant photon couplings is $10^8$ s or longer. A single crossing is nearly transparent; what makes absorption inevitable is repetition, since a bound orbit re-crosses the star about $6\\times 10^{18}$ times over the 333 Myr age of PSR J2144−3933. The survivors are therefore only ALPs born outside the final radius on nearly circular orbits, carrying $9\\times 10^{-9}$–$6\\times 10^{-5}$ of the previously counted heating. Recomputing the limits, PSR J2144−3933 still excludes a window at $m_a \\simeq 7.7$–$196$ MeV with the lower edge of the photon coupling raised 280–700 times, extended to $m_a \\simeq 7.7$–$260$ MeV when pion conversion and the $\\Delta(1232)$ resonance are included; the window's existence, but not its precise edges, survives across all twelve protoneutron-star evolutions, three bremsstrahlung rates and nineteen equations of state.","pith_inferences":["The robust part of the result is the mechanism itself: with roughly $10^{18}$ star crossings, absorption beats decay for any plausible per-crossing opacity, so the prior proposal's reheating signal survives only for orbits that never touch the star — future work should probably treat that qualitative conclusion as the durable output, not the precise window edges.","The most direct test the paper's own numbers suggest: a protoneutron-star evolution that couples the ALP energy loss back into the cooling, which near $m_a \\sim 100$ MeV reaches 91 percent of the neutrino luminosity, would most likely shrink or close the high-mass end of the surviving window.","The repeated-crossing argument transfers to other long-lived particles bound to neutron stars — dark photons, muon- or electron-coupled ALPs, Kaluza-Klein gravitons — with the absorption channel changing but the count of crossings the same, so bound-basin searches around neutron stars generally need an absorption cut before a decay-heating signal can be claimed.","A measured radius for PSR J2144−3933 would turn the window from a band smeared over evolutions into a sharper prediction, since the margin swings by a factor 3.7–5 between final radii of 11.5 and 13.5 km."],"forward_implications":["The reheating bounds on the ALP–photon coupling $g_{a\\gamma\\gamma}$ from old neutron stars are substantially weaker than the no-absorption calculation claimed: the surviving window for PSR J2144−3933 sits at $m_a \\simeq 7.7$–$196$ MeV with its lower edge raised 280–700 times, and the other windows move correspondingly.","Any use of the bound cloud — including the trapped-ALP gamma-ray limit for the Cas A neutron star that the prior proposal relied on — must be recomputed with absorption, since the Cas A star keeps no heating window at all in this treatment.","The surviving windows require a finely tuned cancellation: the photon coupling induced by ALP-pion mixing would exclude the proton coupling used here unless a direct coupling cancels it to one part in 14–46 at 10 MeV and one part in $3\\times 10^4$–$6\\times 10^5$ at 100 MeV.","The existing supernova gamma-ray limits from SN 1987A and from time-delayed photon searches may already cover the surviving windows; a recast at the same production rate is what decides.","Deeper temperature limits on old neutron stars, obtained with next-generation telescopes, would widen the excluded windows, because the margin grows as the product of luminosity and age falls."],"supporting_citations":[{"why":"The prior proposal that bound supernova ALPs reheat old neutron stars; its no-absorption limits, couplings and seven target stars are the baseline that absorption weakens.","marker":"[8]"},{"why":"The protoneutron-star evolution formalism — structure and neutrino transport equations, initial entropy and lepton profiles — on which the paper's twelve evolutions are built.","marker":"[4]"},{"why":"The improved axion emissivity model (one-pion and rho exchange, $g_A/2f_\\pi$ normalization) that defines the baseline bremsstrahlung rate and its normalization to the supernova energy loss of light ALPs.","marker":"[5]"},{"why":"The massive-axion nucleon-nucleon bremsstrahlung matrix elements used for the pp channel and the nondegenerate-matter check of the absorption integrals.","marker":"[39]"},{"why":"The heavy-baryon chiral perturbation theory amplitude with the $\\Delta(1232)$ resonance that supplies the pion-conversion and $aN \\to \\Delta$ absorption and production channels above $m_\\pi$.","marker":"[37]"},{"why":"The space-telescope nondetection of PSR J2144−3933 that supplies the temperature limit, distance and 333 Myr age anchoring the strongest surviving window.","marker":"[30]"},{"why":"Time-delayed gamma-ray limits for heavy QCD-coupled axions that may already cover the surviving windows, and the ALP-pion mixing that induces a photon coupling.","marker":"[17]"},{"why":"QCD axionlike-particle supernova limits: the induced photon coupling that would exclude the adopted proton coupling unless a direct coupling cancels it.","marker":"[40]"}],"fun_headline_variants":["Neutron star absorbs its bound axion cloud in minutes","Only star-skirting axions survive; the rest are absorbed in minutes","Bound axion cloud is swallowed by the neutron star within minutes","Absorption strips the axion cloud, weakening reheating limits 280–700 times","Axions born on star-crossing orbits die in minutes, skimming ones survive"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The quantified surviving populations and window edges rest on the protoneutron-star evolution and on the final radius of the cold star — the models are spherical, start at 0.1 s, and omit accretion, convection, and the ALPs' own energy loss (which near 100 MeV can reach 91 percent of the neutrino luminosity), and the radius alone shifts the J2144−3933 margin by a factor 3.7–5 — so if the contraction or the production region differs from these evolutions, the window edges move even though the absorption of every star-crossing orbit does not.","fun_headline_variants_meta":{"raw":{"variants":["Neutron star absorbs its bound axion cloud in minutes","Only star-skirting axions survive; the rest are absorbed in minutes","Bound axion cloud is swallowed by the neutron star within minutes","Absorption strips the axion cloud, weakening reheating limits 280–700 times","Axions born on star-crossing orbits die in minutes, skimming ones survive"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.000398,"raw_usage":{"cost":0.0003980704,"is_byok":false,"cost_details":{"upstream_inference_cost":0.0003980704,"upstream_inference_prompt_cost":3.51624e-05,"upstream_inference_completions_cost":0.000362908},"total_tokens":3374,"prompt_tokens":1380,"completion_tokens":1994,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":1242,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":1909}},"tokens_in":1380,"tokens_out":1994,"cost_source":"openrouter_usage","duration_ms":13819,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":1909,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-30T20:42:30.947546+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"Recompute the survival of bound ALPs on full supernova profiles that include accretion, convection and the ALP energy loss coupled back into the cooling: near $m_a = 100$ MeV that omitted loss reaches 91 percent of the neutrino luminosity, and a different contraction history or production region would move or close the surviving window at $m_a \\simeq 7.7$–$196$ MeV. A cheaper check is the cold-star radius of PSR J2144−3933, since the margin swings from 236 at $R = 11.5$ km to 45 at $R = 13.5$ km, fixing the window edges by roughly that factor.","supporting_citations":[{"cited_title":"The photon coupling Laγ =− 14 gaγγ aFµν ˜F µν gives the decay rate [41] Γa→γγ =τ −1a = g2aγγ m3a64π ,(3) withτ a the ALP lifetime","cited_arxiv_id":null,"evidence_quote":"The prior proposal that bound supernova ALPs reheat old neutron stars; its no-absorption limits, couplings and seven target stars are the baseline that absorption weakens."},{"cited_title":"Evolution of Protoneutron Stars","cited_arxiv_id":"astro-ph/9807040","evidence_quote":"The protoneutron-star evolution formalism — structure and neutrino transport equations, initial entropy and lepton profiles — on which the paper's twelve evolutions are built."},{"cited_title":"Improved axion emissivity from a supernova via nucleon-nucleon bremsstrahlung","cited_arxiv_id":"1906.11844","evidence_quote":"The improved axion emissivity model (one-pion and rho exchange, $g_A/2f_\\pi$ normalization) that defines the baseline bremsstrahlung rate and its normalization to the supernova energy loss of light ALPs."},{"cited_title":"Axion emission from supernova with axion-pion-nucleon contact interaction","cited_arxiv_id":"2110.01972","evidence_quote":"The massive-axion nucleon-nucleon bremsstrahlung matrix elements used for the pp channel and the nondegenerate-matter check of the absorption integrals."},{"cited_title":"Collider probes of axion-like particles","cited_arxiv_id":"1708.00443","evidence_quote":"The heavy-baryon chiral perturbation theory amplitude with the $\\Delta(1232)$ resonance that supplies the pion-conversion and $aN \\to \\Delta$ absorption and production channels above $m_\\pi$."},{"cited_title":"Dark Matter Heating vs. Rotochemical Heating in Old Neutron Stars","cited_arxiv_id":"1905.02991","evidence_quote":"The space-telescope nondetection of PSR J2144−3933 that supplies the temperature limit, distance and 333 Myr age anchoring the strongest surviving window."},{"cited_title":"New constraints for heavy axion-like particles from supernovae","cited_arxiv_id":"1009.5714","evidence_quote":"Time-delayed gamma-ray limits for heavy QCD-coupled axions that may already cover the surviving windows, and the ALP-pion mixing that induces a photon coupling."},{"cited_title":"Nucleon-Nucleon Bremsstrahlung emission of massive Axion","cited_arxiv_id":"hep-ph/0505090","evidence_quote":"QCD axionlike-particle supernova limits: the induced photon coupling that would exclude the adopted proton coupling unless a direct coupling cancels it."}],"review_version":1}