{"id":"affe7bd3-a58a-4b8a-a54b-980a68fa29b8","arxiv_id":"2504.18614","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A star's response to losing up to 10 percent of its mass depends mainly on its mass: stars above about 0.7 solar masses become denser and more resistant to further stripping, while lower-mass stars become less dense and more fragile, and tidal heating is negligible in both cases.","lead":"This paper builds a fast mathematical model of what happens to a star when a supermassive black hole rips off a few percent of its mass, and checks it against computer simulations. It finds that heavier stars get denser and shrug off future encounters, while light stars get puffier and are torn apart, which may explain why some repeating flare events gradually fade.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The numerical validation shares the constant-Γ=5/3 EOS with the analytic model, so it does not test the real envelope's partial-ionization thermodynamics; the predicted density ratios and survivability thresholds are Γ-sensitive.","rationale":"The reader's conditional verdict is well-founded. The central chain is that post-mass-loss density changes set the stability and repeated-stripping behavior, while the final energy is set by binding-energy bookkeeping with only a small p-dV correction. The weakest link is the thermodynamic model used to compute the density change: the analytic model and the FLASH validation both assume Γ=5/3, and the PHANTOM runs use the same adiabatic setup as previous work. Thus the agreement among these methods validates the formalism under an idealized EOS, but it is not independent evidence that real stellar envelopes—whose outer layers have partial-ionization zones with Γ1 well below 5/3—behave identically. This is not merely a disagreement with consensus; it is an internal sensitivity issue, because Γ appears explicitly in the background-state equation, the eigenmode equations, and the p-dV work integral, and the removed mass is precisely the outer material where the real Γ departs most from 5/3. If the effective Γ is lower, the expansion work and final density can shift, potentially changing the threshold mass and the quantitative density ratios on which the survivability and dimming-flare conclusions depend. The energy-agnostic claim is more robust because it is mostly a consequence of which binding-energy difference dominates and the second-order correction is small, but the astrophysical corollaries are not protected. A single set of FLASH runs with the real MESA EOS would settle whether the concern lands. The paper should remain conditional on that test.","tokens_in":24955,"tokens_out":20542,"duration_ms":221791,"concrete_test":"Take the 1.0 M⊙ ZAMS and 1.5 M⊙ TAMS MESA models used in §2.6. Rerun the FLASH deconfinement simulations with the identical setup (16384-cell spherical grid, reflecting inner boundary, outer pressure reduced as e^{-τ}, ω=1), but replace the constant Γ=5/3 EOS with the tabulated MESA EOS or a radially varying Γ1(r) extracted from the MESA model. Measure the time-averaged core density ⟨ρ_av⟩_t/ρ_⋆ at ΔM/M⋆ = 1%, 3%, 5%, and 10% and the mode kinetic energy, then compare against Figures 5–7. If any density ratio shifts by more than ~20% at fixed mass loss, or the density-increase threshold moves by more than ~0.1 M⊙, the Γ=5/3 assumption is load-bearing for the astrophysical conclusions; if the shifts are negligible, the conditional can be lifted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's quantitative predictions—the post-mass-loss density ratio and the ~0.7 M⊙ stability threshold—are computed with a single ideal-gas adiabatic index Γ=5/3. The analytic background state (Eq. 5), the eigenmodes (Eqs. 13–15), and the p-dV work (Eq. 26) all depend on this Γ. The FLASH validation in §2.6 explicitly imposes Γ=5/3, and the PHANTOM runs reuse the adiabatic setup of Golightly et al. (2019b) and Bandopadhyay et al. (2024). The MESA initial models, however, contain outer layers in partial-ionization zones where the effective adiabatic exponent is substantially below 5/3, and those layers are exactly the ones removed for ΔM/M⋆≲10%. Because the MESA profiles enter only as initial conditions and the dynamical response is computed with the idealized EOS, the excellent agreement between the analytic model and the simulations demonstrates self-consistency under Γ=5/3, not that a real envelope responds the same way. A lower Γ changes the pressure support of the expanded core, hence the final radius and density ratios in Figures 5, 6, and 8, and can shift the threshold separating destabilizing from stabilizing mass loss. The energy-agnostic claim itself is less exposed because it is largely binding-energy bookkeeping, but the survivability and progressively-dimmer-flare conclusions rest on the Γ-sensitive density ratios. The paper does not quantify this sensitivity.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a semi-analytic Lagrangian model for the response of a star to the removal of a small fraction (less than about 10%) of its mass, motivated by repeating partial tidal disruption events (rpTDEs). The original star is divided into an inner core and an outer envelope; the envelope is replaced by a time-dependent pressure boundary condition, and the core response is decomposed into a quasi-static background state plus linear eigenmode perturbations. Applied to MESA stellar models, the model predicts that the volume-averaged density of low-mass stars (approximately less than 0.7 solar masses) decreases after mass loss, whereas higher-mass and evolved stars become denser, with the largest effect near 1.5-2 solar masses. The paper further predicts that the final energy of the surviving core is essentially the binding energy of the original core interior to the mass-loss radius, so that oscillatory-mode (tidal heating) energy is subdominant. These predictions are compared with two FLASH 1D simulations and three PHANTOM 3D partial-TDE simulations, and the paper concludes that partially disrupted stars are not significantly heated, that evolved and moderately massive stars can survive many repeated stripping events, and that progressively dimmer repeating TDE flares can be explained by post-mass-loss densification.","tokens_in":1542,"tokens_out":2050,"duration_ms":137021,"significance":"If the claims hold, this is a valuable contribution. It provides a cheap predictive framework for a parameter space that would otherwise require expensive simulations, it makes falsifiable statements about which stellar masses and ages can power repeating TDEs, and it cleanly separates binding-energy bookkeeping from genuine tidal heating. The paper deserves credit for testing the analytic model against two independent numerical codes (FLASH and PHANTOM), including a resolution test, and for reporting explicit power-law fits and energy decompositions. The energy-agnostic claim is a derived prediction rather than a fit to the simulations, which strengthens its status. The principal reservation is that the dynamical equation of state is fixed to Gamma = 5/3 in both the analytic model and in the validating simulations, leaving the sensitivity to real envelope thermodynamics unquantified; this is a load-bearing issue for the survivability and dimming-flare conclusions, although not for the energy bookkeeping claim itself.","major_comments":[{"comment":"The central quantitative predictions are made with a constant adiabatic index Gamma = 5/3 throughout the star. This Gamma enters the background-state equation (Eq. 5), the eigenmode problem (Eq. 15), and the p-dV work integral (Eq. 26), and the FLASH validation in Section 2.6 explicitly imposes Gamma = 5/3 while the PHANTOM runs reuse the adiabatic setup of previous work. However, the MESA initial models contain outer layers in partial-ionization zones where the effective adiabatic exponent is substantially below 5/3, and those layers are exactly the ones removed for Delta M/M_star less than about 10%. The agreement between the model and the simulations therefore demonstrates self-consistency under the idealized EOS but does not test whether a real envelope responds the same way. A lower Gamma changes the pressure support of the expanded core and hence the density ratios in Figures 5, 6, and 8 and the threshold near 0.7 solar masses that separates destabilizing from stabilizing mass loss. I ask the authors to quantify this sensitivity, for example by rerunning the background-state calculation with Gamma = 4/3 or with the local first adiabatic index profile from MESA, or by giving an analytic bound on the shift of the density ratio and threshold. This is load-bearing for conclusions 1 and 3 (survivability and progressively dimmer flares), while the energy-agnostic claim is less exposed because it is primarily binding-energy bookkeeping.","section":"Section 2 (Eqs. 5, 15, 26) and validation in Sections 2.6 and 3"},{"comment":"The stability conclusions are single-encounter statements that are extrapolated to multiple repeated stripping events using the sign of the density change. The paper does not follow the core through multiple pericenter passages; the only repeated-passage evidence cited is from prior simulations (Bandopadhyay et al. 2024) for specific stars. Consequently, the proposed explanation for progressively dimmer flares (a per-encounter density increase) is plausible but not directly demonstrated by the simulations in this manuscript. A short quantitative extrapolation, such as an iterative map using the model's Delta M/M_star to density relation over several encounters, would turn this inference into a testable prediction and would strengthen the claim.","section":"Section 4.1 and Section 5, Conclusions 2-3"}],"minor_comments":[{"comment":"The title as typeset contains spacing artifacts such as 'Mass T ransfer' and 'Stability ,'; these should be corrected in the final version.","section":"Title"},{"comment":"The symbol xib is used for both the time-dependent background state and its asymptotic, pressure-free limit; introducing a distinct notation such as xib_infinity for the latter would improve clarity.","section":"Section 2.3, Eq. (13)"},{"comment":"The left and right panels show overlapping information, and the legend density makes it difficult to identify which curves are analytical versus SPH. Reorganizing into a single panel with a zoom inset or a cleaner legend would help the reader.","section":"Figure 9"},{"comment":"The per-orbit specific-energy requirement for Pdot approximately -0.001 in ASASSN-14ko is compared directly with the binding energy of the stripped envelope. Given the authors' own caveats about energy retained in tidal tails and quasi-ballistic reformation, I suggest presenting this comparison explicitly as an upper limit in the main text.","section":"Section 4.2 and Figure 11"},{"comment":"The discussion of Yao and Quataert (2025) is a single sentence; since that work directly addresses the same stability question, a more detailed comparison of assumptions and conclusions would be useful to the reader.","section":"Section 4.3"}],"recommendation":"major_revision","confidential_remarks":"The paper is well within the journal's scope and the core analytic framework appears sound. The main issue is the unquantified Gamma = 5/3 EOS sensitivity, which I think is fixable with additional sensitivity tests or explicit caveats. The multi-encounter extrapolation is a secondary concern that could be addressed in revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth a serious look: it builds a time-dependent analytic model for how a star responds to losing a small fraction (1-10%) of its mass, and it uses that model to make a sharp claim—tidal heating is not what kills partial TDE survivors. The genuinely new piece is the perturbation treatment on top of the adiabatic mass-loss background, which yields both the oscillatory response and a clear energy hierarchy: the binding-energy difference between the original star and the pre-stripped core dominates; rotation from the tidal encounter is second; p-dV work and oscillation kinetic energy are much smaller corrections. That hierarchy is the most useful result, and it is backed up by two independent numerical checks—FLASH 1D runs and PHANTOM 3D partial TDE simulations with a resolution test. The agreement with the SPH core densities and energies gives me real confidence that the model captures the dominant physics.\n\nThe central energy claim—that the final core energy is effectively the binding energy of the original star interior to the stripped radius—is mostly bookkeeping and it holds up. The density response predictions (low-mass stars expand and get less dense; higher-mass stars contract and get denser) are clean and match the simulations.\n\nThe soft spots are real but not deal-breaking. The constant-Γ=5/3 equation of state is the main one. The analytic model and the FLASH runs both use it, so their agreement demonstrates self-consistency, not that a real envelope with partial-ionization zones will respond identically. The layers being removed for small ΔM/M are exactly the layers where Γ_eff drops below 5/3. The ~0.7 solar mass threshold and the density ratios in Figures 5 and 6 could shift with a more realistic Γ. The paper does not quantify that sensitivity, and I would want that addressed. The reader's second point—closing the energy budget of the decaying oscillation modes—is fair but minor: the mode kinetic energy is shown to be small per orbit, and a sentence on cumulative heat over many orbits would be enough.\n\nOverall, the argument is coherent, the math is internally consistent, and the simulations provide independent support. The observational implications are properly hedged. This deserves a serious referee; I'd send it out.","headline":"A well-validated analytic model for partial mass loss in rpTDEs; the constant-Γ assumption deserves a sensitivity check before the quantitative threshold is taken at face value.","tokens_in":25837,"tokens_out":4440,"would_cite":true,"duration_ms":44301,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"When a star loses a few percent of its mass to a supermassive black hole, its surviving core keeps an energy set by its own binding structure, not by tidal heating — and stars above roughly 0.7 solar masses come back denser and harder to…","keywords":["tidal disruption events","repeating partial tidal disruption events","supermassive black holes","stellar mass loss","tidal heating","stellar oscillations","stellar structure","hydrodynamics"],"falsifier":"Run a multi-encounter partial-TDE simulation with a realistic equation of state — one whose effective adiabatic index drops below $5/3$ in the ionizing outer layers — and check the two quantitative predictions: the average density of a $1.5\\,M_\\odot$ survivor should still rise above its pre-stripping value after each passage, and the accumulated oscillatory energy should stay negligible against the binding-energy shift; a departure in either would falsify the mass-dependent stability picture.","tokens_in":24746,"feed_emoji":"🕳️","tokens_out":16193,"duration_ms":142466,"temperature":0.7,"pith_summary":"Stars that graze a supermassive black hole can lose a few percent of their mass and keep orbiting, producing a flare on every passage — but a standing worry has been that tidal heating over repeated encounters would inflate the star and destroy it. This paper builds an analytical model of mass loss as a drop in the confining pressure on the star's surviving core, and claims the worry is misplaced: the core's final energy is set almost entirely by the binding energy of the mass that remains, not by heat deposited through tides. The model predicts a sharp mass divide — stars above roughly $0.7\\,M_\\odot$ emerge denser and harder to disrupt after each stripping, while lighter stars emerge puffier and more fragile. If correct, this explains why some repeating flares fade from outburst to outburst, why others brighten, and why moderately massive, evolved stars are the best candidates to power long-lived repeaters.","feed_headline":"Stars that survive a black-hole bite return denser and tougher","feed_subtitle":"Surviving cores keep the binding energy of the mass left behind, not tidal heat — so repeater flares can fade.","key_machinery":"The engine of the model is a Lagrangian, spherically symmetric description of the star as a Bonnor-Ebert sphere: an inner core containing $(100-x)\\%$ of the mass, held in by the pressure of an outer confining medium that contains the remaining $x\\%$ ($x \\lesssim 10$). Mass loss is mimicked by lowering that external pressure at the core radius on roughly a dynamical timescale. The background state is a sequence of quasi-steady hydrostatic equilibria parameterized by the declining surface pressure $h_c$, and the oscillations about the final state are expanded in the eigenmodes of a Sturm–Liouville problem, which yields the surface motion and the small kinetic energy that would become heat. The quantity that controls the physics is $R_{0,c}/R_\\star$, the radius in the original star that encloses the surviving mass: it determines whether the post-stripping average density rises or falls, and it is why centrally concentrated, evolved stars become denser while low-mass stars become puffier.","core_discovery":"The paper's central claim is that when a star loses a small fraction ($\\lesssim 10\\%$) of its mass to a supermassive black hole, the surviving core's final energy is effectively the binding energy of the original star's matter interior to the radius from which mass was removed: $\\Delta E \\simeq E_{c,0} - E_{\\star}$, with a small negative correction from the $p\\,dV$ work of the expanding surface. The process that removes the mass is nearly irrelevant at leading order; in particular, the kinetic energy of the oscillations left in the star — the conventional 'tidal heating' — is orders of magnitude smaller than the changes in its gravitational and thermal energies. The same formalism predicts that the survivor's average density rises for stars with $M_\\star \\gtrsim 0.7\\,M_\\odot$, most strongly for evolved stars near $1.5$–$2\\,M_\\odot$ where a $10\\%$ mass loss can multiply the mean density severalfold, while low-mass stars become less dense. Because the tidal radius scales as $\\rho^{-1/3}$, a denser survivor sheds less mass on the next encounter, so successive flares naturally fade, whereas a puffier low-mass star becomes progressively more vulnerable.","pith_inferences":["The energy result implies a weak universality: any process that peels off the outer $\\lesssim 10\\%$ of a star — tidal stripping, a wind, Roche-lobe overflow — should leave a remnant with the same leading-order internal structure, set only by the mass that remains; a test would compare a tidally stripped star with one that lost the same fraction through an unrelated channel.","For massive stars the effect is self-limiting: each stripping raises the density, which lowers the tidal radius, so the stripped fraction should decay from one encounter to the next; this predicts a specific, quantifiable decay pattern in the flare luminosities of long-lived repeaters.","Rotation is the largest term the model neglects, and for very tight orbits the tidal spin-up could outweigh the density stabilization and move the $0.7\\,M_\\odot$ divide, so extending the background-state calculation to rotating equilibria would show where the stability boundary actually lies.","The constant $\\Gamma = 5/3$ equation of state is the obvious sensitivity to probe: recomputing the density response with an effective adiabatic index below $5/3$ in the ionizing outer layers could shift the $1.5$–$2\\,M_\\odot$ peak and change which stars survive."],"forward_implications":["Tidal heating does not produce runaway inflation: the oscillatory energy is orders of magnitude below the binding-energy shift, so a partially disrupted star can survive tens to hundreds of repeated encounters.","Fading repeaters such as AT2018fyk and eRASSt-J045650 follow naturally from structure alone: the survivor gets denser, its tidal radius shrinks, and each passage removes less mass.","Low-mass stars ($\\lesssim 0.7\\,M_\\odot$) become less dense after stripping, so repeat flares from such stars should brighten, matching events whose second outburst outshines the first, such as AT2020vdq.","A star that powers many flares, such as the roughly twenty outbursts of ASASSN-14ko, must be comparatively massive and evolved ($M_\\star \\gtrsim 1.5\\,M_\\odot$), since only such stars stiffen against further stripping.","The pressure-deconfinement formalism transfers to other mass-ejection settings — classical novae, luminous blue variable outbursts, X-ray bursts — giving an inexpensive way to compute the post-ejection structure of a remnant."],"supporting_citations":[{"why":"Prior smoothed-particle hydrodynamics simulations of partial TDEs whose three stellar models (0.3, 1.0, and 3.0 solar masses) and energy decompositions this paper's predictions are tested against.","marker":"Bandopadhyay et al. (2024)"},{"why":"The adiabatic mass-loss model whose quasi-static, entropy-conserving approach the paper's background state parallels and agrees with quantitatively.","marker":"Dai et al. (2013)"},{"why":"The earlier adiabatic-response stability analysis for polytropes losing mass that this formalism extends to arbitrary stellar structure.","marker":"Hjellming & Webbink (1987)"},{"why":"The tidal-heating runaway argument the paper directly targets; the model shows that argument does not apply when the stripped fraction is small.","marker":"Linial & Quataert (2024)"},{"why":"Supplies the partial-disruption radius (beta about 0.6) that converts the predicted density change into a change in stripped mass per encounter.","marker":"Coughlin & Nixon (2022)"},{"why":"Provides the three stellar models and the numerical setup used for the smoothed-particle hydrodynamics partial-TDE simulations.","marker":"Golightly et al. (2019b)"},{"why":"Supplies the finite-volume hydrodynamics code whose one-dimensional Eulerian simulations verify the analytical model.","marker":"Fryxell et al. (2000)"},{"why":"Supplies the smoothed-particle hydrodynamics code used for the three-dimensional partial-TDE simulations that confirm the density and energy predictions.","marker":"Price et al. (2018)"},{"why":"Identifies the mode coupling that converts first-order tidal oscillations into the core's bulk rotation, which the simulations show is the second-largest energy term.","marker":"Kochanek (1992)"}],"fun_headline_variants":["Surviving a black hole bite makes stars denser, not hotter","Repeater TDEs fade because stripped stars get denser","No tidal heat: surviving core keeps binding energy","Partial TDEs: stripped stars turn denser, flares fade","Stripped stars get denser, so repeated flares get dimmer"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that every layer of the star responds to expansion with the stiffness of a monatomic ideal gas (adiabatic index $\\Gamma = 5/3$), even in the outer layers where partial ionization makes the real gas substantially softer, and the paper's quantitative results for post-stripping density and oscillation frequencies rest on that choice without a test of its sensitivity.","fun_headline_variants_meta":{"raw":{"variants":["Surviving a black hole bite makes stars denser, not hotter","Repeater TDEs fade because stripped stars get denser","No tidal heat: surviving core keeps binding energy","Partial TDEs: stripped stars turn denser, flares fade","Stripped stars get denser, so repeated flares get dimmer"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000299,"raw_usage":{"total_tokens":1814,"prompt_tokens":1119,"completion_tokens":695,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":735,"completion_tokens_details":{"reasoning_tokens":606}},"tokens_in":735,"tokens_out":695,"duration_ms":6689,"temperature":1.0,"reasoning_tokens":606,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:14:44.470440+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a multi-encounter partial-TDE simulation with a realistic equation of state — one whose effective adiabatic index drops below $5/3$ in the ionizing outer layers — and check the two quantitative predictions: the average density of a $1.5\\,M_\\odot$ survivor should still rise above its pre-stripping value after each passage, and the accumulated oscillatory energy should stay negligible against the binding-energy shift; a departure in either would falsify the mass-dependent stability picture.","supporting_citations":[{"cited_title":"What's kickin' in partial tidal disruption events?","cited_arxiv_id":"2503.19018","evidence_quote":"Supplies the partial-disruption radius (beta about 0.6) that converts the predicted density change into a change in stripped mass per encounter."}],"review_version":1}