{"id":"1bba5bae-b62d-4978-891d-86fb40cd3eef","arxiv_id":"2501.10659","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"In DHOST scalar-tensor theories with partial Vainshtein screening, gravitomagnetic tidal Love numbers deviate from general relativity by roughly ten times the parameter alpha_H, with the deviation growing with multipole and compactness and requiring a third parameter beyond alpha_H and beta_1 in…","lead":"This paper computes the gravitomagnetic tidal Love numbers of relativistic stars in modified-gravity theories (DHOST) where scalar-field screening is only partial inside matter, finding deviations from general relativity that grow with multipole order and compactness.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline quantitative claim inherits a known convention ambiguity: gravitomagnetic Love numbers computed in the irrotational-fluid convention (Sec. III, after Eq.","rationale":"The paper's derivation is coherent and the technical machinery is credible: the TOV background is handled through the known degenerate-system reduction, the odd-parity master equation is derived in a standard way, and the numerical implementation for energy polytropes with n>1 is consistent with the smooth-matching requirement. The q-dependence at larger compactness is a legitimate demonstration that alpha_H and beta_1 do not capture the strong-field behavior of this model family. However, the main quantitative statement is framed as relative deviations from GR, and those deviations are computed in one specific fluid convention. The paper cites Ref. [50] at the point where the convention is chosen but does not argue that the irrotational-fluid prescription describes the observable response of a non-rotating body. Since the gravitomagnetic response itself is subdominant in gravitational-wave phase, the paper's significance rests on the robustness of the reported Love-number differences. That robustness is not yet established. The correct response is conditional acceptance: the convention issue should be resolved, either by showing that the two prescriptions agree for the DHOST calculation or by recomputing in the U=0 convention and reframing the detectability claim accordingly. This is not a rejection of the derivation, which appears sound, but a precise limitation on the headline claim.","tokens_in":17112,"tokens_out":7668,"duration_ms":93641,"concrete_test":"Recompute the l=2,3,4 gravitomagnetic Love numbers with the U=0 convention for the same DHOST backgrounds and for GR: in Eq. (60), impose U=0 rather than U=-(rho+p)h0 from Eq. (58), set h1=0 in the static limit, solve for h0 with the center boundary condition h0 ~ r^{l+1}, and extract k_l via Eq. (70). Compare these values with Figs. 1-3 and the scaling (79). If the GR baseline vanishes and/or the DHOST k_l values change substantially, the relative-difference and detectability claims are convention-dependent; if the two conventions produce the same k_l for both GR and DHOST, the concern is resolved.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central results, including the abstract's detectability claim and the scaling (79), are obtained from Eq. (64) after explicitly adopting the irrotational-fluid convention of Refs. [5,48] instead of the U=0 choice (Sec. III, Eq. (54) and following). Ref. [50], which the paper itself cites, demonstrates that magnetic-type Love numbers of non-rotating perfect-fluid bodies are convention-dependent: the U=0 frame gives a different baseline, which in GR vanishes, whereas the irrotational prescription gives nonzero values. The paper does not justify that U=-(rho+p)h0, which follows from Eq. (58) for nonzero frequency and is then imposed in the zero-frequency limit, is the physically relevant response of a non-rotating star to an external odd-parity tidal field. Because the Love number is extracted by matching the internal solution to the external solution via Eq. (70), changing the fluid convention modifies the source term in Eq. (60) and hence the surface value of kappa(r)=rh0'/h0. The GR subtraction in Fig. 2 and the stated ~O(10) alpha_H, beta_1 relative deviations are therefore tied to this convention. A nonzero GR baseline is essential for the relative-difference claim; if the physical convention instead gives a vanishing baseline, the reported ratios and the detectability statement require reformulation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies gravitomagnetic (odd-parity) tidal Love numbers of nonrotating relativistic stars in quadratic DHOST theories with partial Vainshtein screening. It reviews the TOV background, derives an odd-parity master equation and a zero-frequency second-order equation for the metric perturbation h0 (Eqs. (63)-(66)), and then integrates this equation numerically for energy-polytrope stars in the concrete DHOST model of Eqs. (74)-(75). The main numerical findings are that the relative deviations of the Love numbers from their GR values are roughly O(10) × αH, β1, that these deviations grow with multipole order and compactness, and that a third parameter q produces effects not captured by αH and β1 once the weak-field regime is left. The paper concludes that αH and β1 alone are insufficient to characterize the strong-field tidal response.","tokens_in":17228,"tokens_out":33281,"duration_ms":323888,"significance":"If the convention issue discussed below is properly addressed, the paper would provide one of the first quantitative studies of tidal response in theories with partial Vainshtein breaking. The reduction of the odd-parity perturbation system to a single zero-frequency equation for h0 is a useful technical step, and the systematic scan over αH, β1, q, and compactness gives a concrete picture of how modified-gravity parameters enter the tidal response. The paper is also honest about the technical difficulty of the even-parity sector. However, the headline quantitative claim is formulated in terms of gravitomagnetic Love numbers, which are known to be convention-dependent for nonrotating bodies; the manuscript does not establish that the chosen irrotational-fluid convention corresponds to an observable tidal response. No code, data files, or numerical accuracy estimates are provided, which limits reproducibility of the quantitative results.","major_comments":[{"comment":"The gravitomagnetic Love numbers are computed in the irrotational-fluid prescription, in which the zero-frequency limit is taken after imposing U = -(ρ+p)h0 from Eq. (58). Ref. [50], cited by the paper at Eq. (54), shows that magnetic-type Love numbers of nonrotating bodies are convention-dependent within the odd-parity sector: if one instead sets U = 0 from the beginning, the source term in Eq. (60) becomes r^2(ρ+p)h0 rather than zero, and the GR baseline can be different (vanishing in some conventions). The relative differences in Fig. 2 and the estimate (79) are normalized by the nonzero GR baseline in the irrotational convention, so the central quantitative claim and the abstract's detectability statement are tied to this convention. The manuscript does not justify that the irrotational-fluid choice is the physically relevant response of a nonrotating star to an external odd-parity tidal field, nor does it show that the U = 0 convention yields the same conclusions. Please provide such a justification or reformulate the claims as convention-dependent and soften the abstract accordingly.","section":"Sec. III, Eq. (54) and following; Figs. 2 and Eq. (79)"},{"comment":"The central reduction from the master equation (63) to the zero-frequency equation for h0 is stated with the phrase \"it can be shown\" and is not demonstrated. This equation, together with the definitions of P and Q in Eqs. (65)-(66), generates all numerical results in the paper; a reader cannot verify the handling of the boundary/source terms in Eq. (60) without rederiving the reduction by hand. Please include the derivation in an appendix or as a supplementary calculation.","section":"Sec. III, Eq. (64)"}],"minor_comments":[{"comment":"The numerical results are produced with NDSolve, but no error tolerances, convergence tests, or data files are reported. For a quantitative claim such as Eq. (79), an accuracy statement or a release of the numerical data would make the results reproducible and easier to assess.","section":"Sec. V"},{"comment":"The abstract says that partial breaking of Vainshtein screening can be detected through the tidal response, but the paper itself notes that the even-parity (gravitoelectric) Love numbers have a larger contribution to the gravitational-wave phase than the odd-parity ones computed here. This wording overstates what the odd-parity calculation alone establishes.","section":"Abstract and Sec. VI"},{"comment":"There are a few typographical issues, for example \"suitable νc does not necessarily exit\" should read \"exist,\" and the section heading in the conclusions is missing a period. These do not affect the physics.","section":"Sec. II C"}],"recommendation":"major_revision","confidential_remarks":"The technical framework appears sound as far as the equations can be checked from the text; the main obstacle is the magnetic-Love-number convention, which is a known subtlety and is explicitly flagged by Ref. [50]. If the authors can either justify the irrotational-fluid convention as the physically relevant one or clearly restrict the claims to that convention, I would support publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the first calculation of gravitomagnetic tidal Love numbers for relativistic stars in DHOST theories with partial Vainshtein screening. The derivation of the odd-parity master equation and the zero-frequency reduction is a natural but nontrivial extension of the Landry–Poisson machinery, and the paper is honest about its scope and limitations. The numerical work is careful within its chosen setup: energy polytropes with n > 1, smooth matching, and a clear parameter scan. The q-dependence at high compactness is a real result that supports the claim that alpha_H and beta_1 alone do not characterize strong-field deviations. Credit where due: the paper ships no code or data, but the equations are laid out in enough detail that re-implementation is feasible for a specialist.\n\nThe soft spots are mostly what the reader flagged. The convention issue is load-bearing: the paper adopts the irrotational-fluid prescription of Refs. [5,48] and does not justify why that prescription gives the observable tidal response, despite citing Ref. [50] which shows the magnetic Love numbers are convention-dependent. If the physical convention is the U=0 one, the GR baseline changes and the relative-difference plots need rethinking. The zero-frequency reduction from the master equation to Eq. (64) is stated with \"it can be shown\" and the intermediate steps are skipped; that is a derivation gap, not necessarily an error, but a referee should ask for the details. Also, restricting to n>1 polytropes is a practical choice but leaves open whether the scaling survives realistic equations of state. The abstract's detectability claim is too strong given both the convention ambiguity and the subdominant contribution of gravitomagnetic tides to inspiral phase; the conclusions are more careful than the abstract.\n\nOverall, the central derivation appears sound and the paper is a real contribution to the modified-gravity tidal literature. It deserves a serious referee, but the convention issue should be addressed head-on, either by justifying the irrotational choice or by presenting the results in a convention-independent way. I would recommend conditional acceptance after heavy revision, with the convention question and the derivation gap as the main demands.","headline":"First gravitomagnetic Love numbers for DHOST stars with partial Vainshtein breaking, but the headline scaling inherits a known convention ambiguity that needs a clear caveat; worth refereeing with major revision.","tokens_in":17919,"tokens_out":760,"would_cite":true,"duration_ms":10040,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.50.Kd","04.40.Dg"],"model":"deepseek-v4-flash","headline":"In DHOST scalar-tensor theories, partial failure of Vainshtein screening inside matter leaves a roughly ten-times-parameter imprint on the gravitomagnetic tidal Love numbers of relativistic stars, growing with multipole and compactness.","keywords":["gravitomagnetic tidal Love numbers","DHOST theories","Vainshtein screening","scalar-tensor gravity","neutron star tidal deformability","odd-parity perturbations","compact stars","modified gravity"],"falsifier":"Compute the same gravitomagnetic Love numbers with the alternative fluid convention ($U=0$ from the outset, as discussed in the paper); if the GR baseline becomes zero while the DHOST Love numbers remain nonzero, the paper's relative-deviation story is convention-driven rather than observable. Alternatively, a high-signal-to-noise gravitational-wave measurement of the tidal deformability of a compact binary that matches GR to much better than the predicted $\\mathcal{O}(10)\\,\\alpha_H,\\beta_1$ shift would rule out the large-deviation part of the parameter space.","tokens_in":16703,"feed_emoji":"🧲","tokens_out":12496,"duration_ms":114182,"temperature":0.7,"pith_summary":"The paper aims to show that the Vainshtein screening mechanism, though complete outside a star, is only partially effective inside matter in scalar-tensor theories beyond Horndeski, and that this internal leak is visible in the star's tidal response. It computes the gravitomagnetic (odd-parity) tidal Love numbers of static relativistic stars in a concrete class of DHOST theories and finds deviations from general relativity of order ten times the modified-gravity parameters $\\alpha_H$ and $\\beta_1$. The deviations increase with multipole order and with compactness, so more compact stars and higher multipoles should be better probes. The paper also argues that $\\alpha_H$ and $\\beta_1$ do not fully characterize the strong-field tidal response, since a third parameter of the model affects the Love numbers at large compactness.","feed_headline":"Star tides reveal a partial leak in gravity's screening shield","feed_subtitle":"Tides of neutron stars deviate from general relativity by about ten times the theory's screening parameters.","key_machinery":"The argument is carried by the zero-frequency odd-parity perturbation equation for the metric component $h_0$, Eq. (64): $h_0'' - (P/r)h_0' - (Q/r^2)h_0=0$, with $P=r(\\nu'/2+\\lambda'/2 - f_X X'/f)$ and $Q=e^\\lambda[\\ell(\\ell+1)-2(1-e^{-\\lambda})]-2P$, where primes denote radial derivatives and $f_X=\\partial f/\\partial X$. At the center the regular solution satisfies $\\kappa(0)=\\ell+1$ for $\\kappa=rh_0'/h_0$; integrating Eq. (71) to the surface and matching to the analytic GR exterior solution (67) yields the rescaled Love number $\\tilde{k}_\\ell$. Modified gravity enters in two ways: the background metric functions $\\nu,\\lambda$ carry the DHOST-modified stellar structure, and the new term $f_X X'/f$ modifies the perturbation equation itself relative to GR. The external solution reduces to Schwarzschild with $X=1/2$, so the screening outside the star is complete.","core_discovery":"The central result is that in quadratic DHOST theories with gravitational-wave speed equal to $c$, the gravitomagnetic Love numbers $\\tilde{k}_\\ell$ of an irrotational fluid star deviate from their GR values by roughly $(\\tilde{k}_\\ell-\\tilde{k}_\\ell^{\\rm GR})/\\tilde{k}_\\ell^{\\rm GR}\\sim -\\mathcal{O}(10)\\,\\alpha_H$, with $\\beta_1$ acting similarly; higher multipoles $\\ell$ and larger compactness $C=\\mu/R$ enlarge the relative difference, and positive (negative) $\\alpha_H,\\beta_1$ decrease (increase) $|\\tilde{k}_\\ell|$. The deviations have two sources: the modified interior metric of the star and the nonvanishing gradient $X'$ of the scalar kinetic term, which enters the perturbation equation directly. Outside the star the metric is exactly Schwarzschild, so complete Vainshtein screening hides the modification in the exterior; the signal lives in the interior tidal response. Away from the weak-field limit the two standard parameters are not enough: changing the model parameter $q$ at fixed $\\alpha_H,\\beta_1$ changes the Love numbers once the star is sufficiently compact.","pith_inferences":["Beyond the paper, the same calculation should be repeated with the alternative fluid convention (the one the paper cites but does not use); if that convention is the physical one, the GR baseline for gravitomagnetic Love numbers can change, possibly to zero, and the ten-times-parameter deviations would need re-evaluation.","Beyond the paper, the partial-screening effect should also shift the gravitoelectric (even-parity) Love numbers that dominate binary-inspiral phasing; the paper defers them for technical reasons, so a full observational test needs that sector.","Beyond the paper, extending the polytropic models to realistic neutron-star equations of state, including the low-index cases the paper excludes because of surface-matching discontinuities, would test whether the $\\sim\\mathcal{O}(10)\\,\\alpha_H,\\beta_1$ scaling is robust in astrophysical settings.","Beyond the paper, the $q$-dependence at large compactness implies that future tidal measurements should be fitted with at least three theory parameters (for example $\\alpha_H$, $\\beta_1$, and a shape parameter of the scalar interaction), not just the two standard ones."],"forward_implications":["For fixed DHOST parameters, the relative deviation of the gravitomagnetic Love number from GR grows with multipole order and compactness, so higher-multipole tidal moments and more compact stars give stronger tests of the theory.","Positive values of $\\alpha_H$ and $\\beta_1$ decrease $|\\tilde{k}_\\ell|$ and negative values increase it, by roughly the same order, so the sign of a measured Love-number shift can help orient the allowed parameter region.","The exterior metric in this theory class is Schwarzschild, so the partial-screening signal is carried by the tidal response itself rather than by the leading exterior geometry; Love numbers are the right observable.","Within the paper's adopted observational ranges for $\\alpha_H$ and $\\beta_1$, the predicted relative shifts are potentially of order unity, large enough to matter for gravitational-wave tidal measurements."],"supporting_citations":[{"why":"Supplies the irrotational-fluid definition and the relativistic tidal-property framework that the paper adopts for gravitomagnetic Love numbers.","marker":"[5]"},{"why":"Provides the zero-frequency Regge-Wheeler exterior solution and matching formula for the rescaled Love number $\\tilde{k}_\\ell$ used here.","marker":"[48]"},{"why":"Clarifies that gravitomagnetic Love numbers are convention-dependent, identifying the alternative $U=0$ convention that would change the GR baseline.","marker":"[50]"},{"why":"Gives the TOV system and degeneracy-based reduction procedure for DHOST backgrounds that the paper follows for the unperturbed stellar configuration.","marker":"[39]"},{"why":"Establishes the breaking of Vainshtein screening inside matter in scalar-tensor theories beyond Horndeski, the physical effect the paper probes.","marker":"[24]"},{"why":"Sets out the viable DHOST subclass after GW170817 and the condition $A_1=0$ that the paper imposes on the model.","marker":"[33]"},{"why":"Provides the observational constraints on $\\alpha_H$ and $\\beta_1$ that define the parameter region surveyed in the numerical results.","marker":"[35]"},{"why":"Introduces the effective-field-theory parametrization with $M^2$, $\\alpha_H$, and $\\beta_1$ that the paper uses throughout.","marker":"[44]"}],"fun_headline_variants":["Partial Vainshtein leak shows in star tides","Tidal numbers expose gravity's screening gap","Neutron star tides reveal screening leak","Gravity screening fails partially inside stars"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported size of the deviations rests on the choice of the irrotational-fluid, zero-frequency convention for gravitomagnetic Love numbers; if the alternative convention for the fluid motion is the physically observable one, the general-relativity baseline changes, possibly to zero, and the claimed ten-times-parameter shifts would not hold as stated.","fun_headline_variants_meta":{"raw":{"variants":["Partial Vainshtein leak shows in star tides","Tidal numbers expose gravity's screening gap","Neutron star tides reveal screening leak","Gravity screening fails partially inside stars"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000142,"raw_usage":{"total_tokens":1148,"prompt_tokens":908,"completion_tokens":240,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":524,"completion_tokens_details":{"reasoning_tokens":184}},"tokens_in":524,"tokens_out":240,"duration_ms":2896,"temperature":1.0,"reasoning_tokens":184,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T19:02:16.472108+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the same gravitomagnetic Love numbers with the alternative fluid convention ($U=0$ from the outset, as discussed in the paper); if the GR baseline becomes zero while the DHOST Love numbers remain nonzero, the paper's relative-deviation story is convention-driven rather than observable. Alternatively, a high-signal-to-noise gravitational-wave measurement of the tidal deformability of a compact binary that matches GR to much better than the predicted $\\mathcal{O}(10)\\,\\alpha_H,\\beta_1$ shift would rule out the large-deviation part of the parameter space.","supporting_citations":[],"review_version":1}