{"id":"e9d8ecd4-d127-4a2a-8404-9d5b3e076fb6","arxiv_id":"1908.02969","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Numerical simulations show the gravitational wave strain from a 1 solar mass unstable disc in a tidal disruption event is about 4e-24, two orders below analytic estimates, and only a speculative extrapolation to 10-100 solar mass discs may be detectable by LISA.","lead":"This paper estimates gravitational waves from lopsided, unstable gas discs that form after a star is torn apart by a black hole. It finds the signal is about a hundred times weaker than the simplest analytic guess, so only unusually heavy stars disrupted very deeply might be visible to LISA.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The measured strain depends on an unreported seeded m=1 perturbation; the efficiency factor xi≈1e-2 is likely set by the seed, so the extrapolation to higher-mass discs lacks support.","rationale":"The paper provides a clear SPH setup, a resolution study, and an honest comparison with Kiuchi et al. (2011); the basic peak-strain measurement for this single simulation is probably reproducible. However, the central numerical claim is calibrated by an unreported initial perturbation. The m=1 mode's quadrupole radiation is second order in mode amplitude (a pure m=1 density perturbation has zero overlap with the quadrupole moment, and a rigid m=1 shift changes M_xx−M_yy only at order ε^2). Hence xi is not a dimensionless constant of the PPI but a function of the saturation amplitude, which may depend on the seed amplitude and the run duration. The paper's forward-looking LISA detectability claim for 10–100 M_sun discs depends on assuming xi is universal; this is exactly the weakest point, and the unreported seed makes it even harder to evaluate than the reader's formulation suggests. The reader's verdict (CONDITIONAL) remains appropriate, so I do not change the verdict, but I flag a more fundamental reason the conditionality cannot be resolved from the current manuscript: without the seed amplitude, the measured xi is not an independent physical result.","tokens_in":12811,"tokens_out":17320,"duration_ms":178842,"concrete_test":"Rerun the PHANTOM simulation of Section 4 with the same physical parameters but with the initial m=1 density perturbation amplitude reduced by a factor of 2 and increased by a factor of 2 (and, if feasible, with no seed at all, relying on numerical noise). Measure the peak strain h_PPI and the saturation amplitude ε of the m=1 mode in each case. If h_PPI scales with the seed amplitude or its square (e.g., h_PPI ∝ ε^2) rather than converging to a constant as the seed is reduced, then the reported xi≈10^-2 is seed-dependent and cannot be extrapolated to higher-mass tori. Also report the seed amplitude and the mode amplitude at saturation to allow this scaling to be checked analytically.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4 states that the m=1 PPI mode is initiated by adding an m=1 density perturbation, but the amplitude of this seed is never reported. This matters because a pure m=1 density perturbation does not produce a time-varying quadrupole at first order: for a density component ∝ cos(φ−Ω_p t), the quadrupole integrals ∫ δρ r^2 cos 2φ dV and ∫ δρ r^2 sin 2φ dV vanish after azimuthal integration. The GW emission from an m=1 mode is therefore a second-order effect, scaling as ε^2 times the point-mass estimate, where ε is the mode amplitude at saturation. The measured efficiency xi ≈ 10^-2 is thus plausibly ε^2 for this one simulation, not a universal property of PPI-unstable TDE discs. Since the seed amplitude is unreported, one cannot determine whether ε is set by the physics of saturation or by the initial conditions; consequently the numerical strain measurement is not reproducible and the assumption in Section 4.1 that xi≈10^-2 holds for M_d=10 and 100 M_sun and for β≠5 is unsupported. The resolution test (Section 4.2) only demonstrates convergence with particle number, not independence of the seeded perturbation or of the run duration relative to the mode's linear growth phase.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates gravitational-wave (GW) emission from Papaloizou-Pringle unstable tori formed in tidal disruption events (TDEs). The authors first derive analytical estimates of the peak and characteristic strain using a point-mass quadrupole approximation for the stellar debris, obtaining h ~ 1e-22 beta m*^(1/3) for a 1 Msun star around a 1e6 Msun black hole, and conclude that the analytically estimated signal could exceed the LISA sensitivity curve for sufficiently large penetration factor beta. They then perform a 3D SPH simulation with the PHANTOM code of a 1 Msun, beta = 5 torus, seeding an m = 1 density perturbation to trigger the PPI. From the simulated waveforms they measure a peak strain of about 4e-24, roughly two orders of magnitude below the analytical estimate, and introduce an efficiency factor xi ~ 1e-2 that relates the numerical to the analytical strain. Assuming this xi also applies to other beta values and stellar masses, they conclude that PPI-unstable discs from deeply penetrating TDEs of 10-100 Msun stars may be detectable by LISA.","tokens_in":12955,"tokens_out":8958,"duration_ms":94779,"significance":"If the numerical measurement is robust, the paper provides a useful and nontrivial correction to the naive point-mass estimate: for a 1 Msun, beta = 5 torus, the expected GW strain is roughly 100 times smaller than the analytical prediction, placing the source below LISA's sensitivity. The analytical framework is clearly presented, the use of an independent SPH simulation to test the estimate is appropriate, and the paper explicitly lists important simplifications such as MRI quenching, partial mass participation in the instability, and disc spreading. The comparison between numerical and analytical strain is not circular, and the resolution test with increasing particle number is a genuine strength. However, the quantitative numerical result depends on an unreported seeded perturbation amplitude, and the extrapolation to higher-mass discs rests on the untested universality of xi. The central claim is therefore conditional rather than parameter-free, and the detectability conclusion for 10-100 Msun discs is not yet supported by the presented evidence.","major_comments":[{"comment":"The numerical experiment seeds the m = 1 mode by 'add[ing] m = 1 density perturbation', but the amplitude of this seed is never reported. For a rigidly rotating m = 1 density perturbation proportional to cos(phi - Omega_p t), the quadrupole integrals int delta-rho r^2 cos(2 phi) dV and int delta-rho r^2 sin(2 phi) dV vanish after azimuthal integration, so the leading-order GW emission from this mode is a second-order effect scaling as the square of the mode amplitude. Consequently, the measured efficiency xi ~ 1e-2 in Eq. (41) could be set by the chosen seed rather than by the saturation physics of the PPI, and the quoted peak strain h_PPI ~ 4e-24 is not reproducible from the information given in the paper. Please report the seed amplitude, test the dependence of the saturated mode amplitude and of xi on the seed amplitude, and clarify the relation between the seeded perturbation and the m = 1 mode found in Nealon et al. (2018).","section":"Section 4"},{"comment":"The extrapolation in Section 4.1, stated as 'If we assume that the same scaling factor holds also for different beta and for different stellar masses', is load-bearing for the main astrophysical conclusion in Section 6 that discs from TDEs of 10-100 Msun stars could be detectable by LISA, but it is presented as a pure assumption. xi is measured from a single simulation with M_d = 1 Msun, beta = 5, one torus geometry, and one seeded perturbation; no physical scaling argument or additional simulation is provided to justify applying the same factor to other masses, penetration factors, or disc structures. The detectability statement should either be supported by simulations at other masses and beta values, or by a physically motivated model of how xi depends on the disc parameters, or it should be explicitly downgraded to a conjecture.","section":"Section 4.1"},{"comment":"The resolution test in Fig. 4 demonstrates convergence with particle number, which is useful, but it does not directly address the two inputs on which the strain depends most strongly: the amplitude and form of the seeded m = 1 perturbation, and the time sampling of the linear growth and saturation phases. Convergence in particle number alone does not establish that the peak strain is a property of the PPI dynamics rather than of the initial conditions. A seed-amplitude study, together with a statement of the time step Delta t used in the second derivative in Eq. (40) and any smoothing applied to M_kl or to the waveform, is needed before h_PPI can be regarded as a robust numerical prediction.","section":"Section 4.2"}],"minor_comments":[{"comment":"The phrase 'momentum of inertia' should be 'moment of inertia'.","section":"Section 4"},{"comment":"In the text near Fig. 3, h_PPI is said to be computed from 'equation 19'; the strain is actually the quadrature sum defined in Eq. (18), so the cross-reference should be corrected.","section":"Sections 3.1 and 4.1"},{"comment":"Equations (A4) and (A5) as printed contain a dimensionally inconsistent expression, 'M_h r_1 = 10^-6 M_d r_2^2'; the intended relation is presumably M_h r_1^2 = (M_d/M_h) M_d r_2^2. Please fix the notation.","section":"Appendix A"},{"comment":"The PHANTOM code is used but no code reference is provided; please cite the appropriate PHANTOM paper (e.g. Price et al. 2018) along with the specific version or settings used.","section":"Section 4"},{"comment":"The caption states that beta increases from left to right, but it is not explicit which curve corresponds to which beta values for each mass, especially in relation to the red triangle marking the beta = 5 case. Please add the relevant beta values to the caption or legend.","section":"Figure 1"},{"comment":"Equation (36) introduces the dimensionless cross-section parameter d using r_- and r_+ without defining these quantities in the text; please define them explicitly.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the manuscript is a reasonable exploratory study and the concerns raised in the report are addressable in a revision. The main issue is that the quantitative conclusion rests on an unstated seed amplitude and on an untested universality assumption for xi, which is a load-bearing point rather than a cosmetic one. I recommend major revision rather than rejection. The citation list is appropriate and I see no novelty or scope concerns."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, what the paper actually adds: it gives the first estimate of the GW strain from a Papaloizou–Pringle unstable torus formed in a TDE, rather than from the disruption phase itself or from the self-gravitating supermassive-star collapse tori studied by Kiuchi et al. The authors run a 3D SPH simulation, seed the m=1 PPI mode, and compute the strain with the standard quadrupole formula. The headline number—strain around 4e-24 for a 1 Msun torus around a 1e6 Msun BH with beta=5—is two orders of magnitude below the point-mass analytic estimate, and the resolution study with up to 9e6 particles gives them some confidence in convergence. If correct, that is a useful calibration: the simple point-mass ansatz is optimistic for these systems.\n\nThe soft spot the stress test identified is real. The seeded m=1 perturbation amplitude is never reported. Because a pure m=1 density perturbation has no first-order quadrupole moment, the measured strain is a second-order effect, scaling with the square of the mode amplitude. So the efficiency factor xi ~ 1e-2 is plausibly just the squared saturation amplitude for this single run. Without the seed amplitude, there is no way to tell whether that saturation reflects the physics or is partly an artifact of the initial conditions. That makes the numerical measurement non-reproducible, and it makes the blanket extrapolation of xi to 10 and 100 Msun discs in section 4.1 unsupported. The paper says \"If we assume the same scaling factor holds\"—an honest hedge, but a big if.\n\nA smaller issue: the analytic frequency is evaluated at rp while the torus actually sits around 2rp. That shifts the signal in frequency space and matters for the LISA detectability curve. The authors know the torus location, so this is likely just an inconsistency, but it should be fixed.\n\nWhat is solid: the resolution test is decent, the comparison to Kiuchi et al. is thoughtful, and the appendix correctly shows the BH contribution is negligible for the mass ratios considered.\n\nBottom line: this is a genuine new result with a clean enough simulation, but the load-bearing extrapolation rests on an unreported seed amplitude. I would send it to peer review—a good referee can extract the useful numerical measurement and insist on the missing details. This is a solid stepping stone rather than a breakthrough, and the LISA detectability claim should be read as conditional.","headline":"A useful first measurement of GW strain from a PPI-unstable TDE torus, but the claimed efficiency factor rests on an unreported seeded mode and is extrapolated far beyond the one simulation.","tokens_in":13682,"tokens_out":4597,"would_cite":false,"duration_ms":50219,"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":"Unstable accretion discs from tidal disruption events emit gravitational waves roughly one hundred times weaker than analytic point-mass estimates.","keywords":["tidal disruption events","gravitational waves","accretion discs","Papaloizou-Pringle instability","LISA","smoothed particle hydrodynamics","black hole physics","gravitational wave detectability"],"falsifier":"Repeat the PPI simulation for 10 and 100 solar-mass tori and for $\\beta=10$ and $\\beta=20$, and compare the peak strain with the analytic point-mass estimate; if the suppression factor departs from $10^{-2}$ by more than a factor of a few, the extrapolated LISA detectability claim fails.","tokens_in":12522,"feed_emoji":"🛰️","tokens_out":17920,"duration_ms":155635,"temperature":0.7,"pith_summary":"This paper asks whether the gravitational waves emitted by a thick accretion disc formed after a tidal disruption event (TDE) could be detected by the space-based interferometer LISA. The starting point is a $1\\,M_\\odot$ torus around a non-rotating $10^6\\,M_\\odot$ black hole, produced by the disruption of a solar-type star with penetration factor $\\beta=5$ and known to be unstable to the Papaloizou-Pringle instability. The authors compare simple analytic point-mass estimates of the gravitational-wave strain with a 3D smoothed-particle-hydrodynamics simulation of the same torus. The numerically measured strain peaks at about $4\\times10^{-24}$, roughly two orders of magnitude below the analytic estimate of about $5\\times10^{-22}$, giving an efficiency factor $\\xi\\sim10^{-2}$. If that factor is universal, then PPI-unstable discs from deeply penetrating TDEs of 10 to 100 solar-mass stars could still be interesting sources for LISA.","feed_headline":"Shredded-star discs emit 100 times weaker gravitational waves than estimates","feed_subtitle":"A 3D simulation cuts the predicted strain by 100; heavier tori from deeper disruptions may still be visible to LISA.","key_machinery":"The load-bearing object is the disc's mass quadrupole, built from simulated particles as $M^{kl}=\\sum_a m_a x_a^k x_a^l$, whose second time derivative, computed by central differencing, feeds the two strain polarizations $h_+$ and $h_\\times$ through the quadrupole formula. The physical mechanism making the quadrupole time-dependent is the Papaloizou-Pringle instability, a global non-axisymmetric hydrodynamic instability in which an $m=1$ overdensity forms in the torus and orbits at close to the Keplerian frequency, so the gravitational-wave frequency is the Keplerian frequency of the original stellar orbit. The analytic point-mass estimate applies the standard quadrupole formula to a lump of mass moving at the pericenter Keplerian velocity, and the comparison between the two routes produces the efficiency factor $\\xi$ that carries the extrapolation to heavier discs.","core_discovery":"On its own terms, the central claim is that the point-mass approximation used for the stellar disruption phase badly overestimates the gravitational-wave strain from the later unstable-disc phase. For a $1\\,M_\\odot$ torus with $\\beta=5$ around a static $10^6\\,M_\\odot$ black hole, the numerically derived strain peaks at about $4\\times10^{-24}$ in the direction perpendicular to the stellar orbit, while the analytic point-mass estimate gives about $5\\times10^{-22}$; the ratio is $\\xi=h_{\\rm PPI}/h\\sim10^{-2}$. The paper attributes the reduction to the torus spreading out under the instability and to only part of the disc mass participating in the PPI mode. Assuming the same reduction factor holds for other penetration factors and stellar masses, the characteristic strain curves for 1, 10, and 100 solar-mass discs are shifted down by $10^{-2}$; the consequence is that only discs from deeply penetrating disruptions ($\\beta$ roughly beyond 15 for 10 solar masses and 45 for 100 solar masses) rise above LISA's sensitivity curve.","pith_inferences":["The paper leaves untested the universality of $\\xi$: repeating the measurement for $\\beta=10$ and $\\beta=20$ tori and for 10 and 100 solar-mass discs would show whether the LISA detectability forecast survives.","Since the $m=1$ mode is seeded by hand, the measured $\\xi$ may depend on the seed amplitude, which is not reported; growing the instability from noise would give a physically grounded value.","The factor-of-100 gap between point-mass and extended-disc estimates suggests that LISA search templates for TDE remnants should be built from simulated waveforms rather than rescaled point-mass signals.","Self-gravity is neglected in the simulation; it becomes relatively more important for 100 solar-mass discs, where it could either enhance clumping and emission or change the mode structure, making the highest-mass extrapolation the least secure."],"forward_implications":["The $1\\,M_\\odot$, $\\beta=5$ remnant simulated here would not be detected by LISA: its characteristic strain sits below the sensitivity curve even before the numerical suppression is applied.","If $\\xi\\sim10^{-2}$ applies to all masses, the 1 solar-mass case leaves LISA's reach at every $\\beta$, while 10 and 100 solar-mass tori remain detectable only for deeply penetrating disruptions ($\\beta\\gtrsim15$ and $\\beta\\gtrsim45$, respectively).","The gravitational-wave frequency stays near $10^{-3}$ to $10^{-2}\\,\\mathrm{Hz}$ for a $10^6\\,M_\\odot$ black hole, placing any detectable signal squarely in LISA's mHz band.","The simulated strain converges by 5 million particles, so the factor-of-100 suppression is not a resolution artefact.","The black hole contributes negligibly to the strain: its moment of inertia is between $10^{-6}$ and $10^{-4}$ times that of the disc for the masses considered."],"supporting_citations":[{"why":"This reference defines the instability whose $m=1$ mode drives the time-varying quadrupole.","marker":"Papaloizou & Pringle (1984)"},{"why":"This reference provides the TDE torus simulation that the paper extends and establishes the $m=1$ unstable mode and its Keplerian frequency.","marker":"Nealon et al. (2018)"},{"why":"This reference supplies the $\\beta=5$ initial conditions and the torus location near $2r_p$ used in the simulation.","marker":"Bonnerot et al. (2016)"},{"why":"This reference gives the point-mass analytic gravitational-wave estimates for TDEs that the paper adapts to the unstable-disc phase.","marker":"Kobayashi et al. (2004)"},{"why":"This reference provides the previous numerical-versus-analytic comparison for PPI tori, showing a one-order-of-magnitude gap that contrasts with the two-order gap found here.","marker":"Kiuchi et al. (2011)"},{"why":"This reference supplies the quadrupole-strain formula used for the analytic maximum amplitude.","marker":"Thorne (1987)"},{"why":"This reference defines the LISA sensitivity curve used to judge whether the predicted strains are detectable.","marker":"Amaro-Seoane et al. (2017)"},{"why":"This reference provides the definitions of characteristic strain and cycle counting used to turn raw strain into a detectability estimate.","marker":"Maggiore (2018)"},{"why":"This reference shows that magnetic fields can suppress or quench the PPI, motivating the paper's caveat that the signal may be reduced in magnetised discs.","marker":"Bugli et al. (2018)"}],"fun_headline_variants":["PPI discs emit 100x weaker gravitational waves than predicted","Simulation slashes gravitational wave signal from shredded-star discs","Unstable accretion discs: GW strain 100 times lower than analytic","Tidal disruption discs: numerical strain lags analytic by 100","Heavy tori from deep disruptions may still be seen by LISA despite 100x lower strain"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the suppression factor $\\xi\\sim10^{-2}$ measured in one $1\\,M_\\odot$, $\\beta=5$ simulation is universal; if $\\xi$ depends on disc mass, penetration factor, or the seeded perturbation's amplitude, the predicted LISA detectability for heavier discs does not follow.","fun_headline_variants_meta":{"raw":{"variants":["PPI discs emit 100x weaker gravitational waves than predicted","Simulation slashes gravitational wave signal from shredded-star discs","Unstable accretion discs: GW strain 100 times lower than analytic","Tidal disruption discs: numerical strain lags analytic by 100","Heavy tori from deep disruptions may still be seen by LISA despite 100x lower strain"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000531,"raw_usage":{"total_tokens":2588,"prompt_tokens":1005,"completion_tokens":1583,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":621,"completion_tokens_details":{"reasoning_tokens":1488}},"tokens_in":621,"tokens_out":1583,"duration_ms":12456,"temperature":1.0,"reasoning_tokens":1488,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:29:24.626582+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the PPI simulation for 10 and 100 solar-mass tori and for $\\beta=10$ and $\\beta=20$, and compare the peak strain with the analytic point-mass estimate; if the suppression factor departs from $10^{-2}$ by more than a factor of a few, the extrapolated LISA detectability claim fails.","supporting_citations":[{"cited_title":"J., Bonnerot C., Lodato G., 2018, @doi [ ] 10.1093/mnras/stx2871 , http://adsabs.harvard.edu/abs/2018MNRAS.474.1737N 474, 1737","cited_arxiv_id":null,"evidence_quote":"This reference provides the TDE torus simulation that the paper extends and establishes the $m=1$ unstable mode and its Keplerian frequency."},{"cited_title":"J., Font J","cited_arxiv_id":null,"evidence_quote":"This reference provides the previous numerical-versus-analytic comparison for PPI tori, showing a one-order-of-magnitude gap that contrasts with the two-order gap found here."},{"cited_title":"pp 330--458","cited_arxiv_id":null,"evidence_quote":"This reference supplies the quadrupole-strain formula used for the analytic maximum amplitude."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference defines the LISA sensitivity curve used to judge whether the predicted strains are detectable."},{"cited_title":"Volume 2: Astrophysics and Cosmology","cited_arxiv_id":null,"evidence_quote":"This reference provides the definitions of characteristic strain and cycle counting used to turn raw strain into a detectability estimate."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference shows that magnetic fields can suppress or quench the PPI, motivating the paper's caveat that the signal may be reduced in magnetised discs."}],"review_version":1}