{"id":"bd98c583-7be9-49d5-9bce-197c9d36a724","arxiv_id":"2608.01408","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"DECIGO and BBO could detect continuous gravitational waves from strange star - strange planet systems across a broad mass, distance, and eccentricity parameter space.","lead":"This paper calculates that future space-based gravitational wave detectors DECIGO and BBO could detect continuous gravitational waves from hypothetical systems consisting of a strange quark star and an orbiting strange planet. If such systems exist, these detectors would provide a new way to test the strange quark matter hypothesis.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (8) drops the 2π factor in the orbital chirp; recheck S/N tables, but the broad-detectability claim is unlikely to fail.","rationale":"The reader identified the existence and abundance of SS-SP systems as the weakest assumption. That is the physical premise, but it is explicitly conditional and not an internal error. My stress-test found a more concrete, manuscript-level issue: the orbital evolution equations in Section 2 appear to drop a factor 2^{8/3}. This is the type of mistake that can affect numerical S/N values, merger-time estimates, and the exact boundaries of the detectable parameter space. However, it does not threaten the core claim that DECIGO/BBO could detect such systems across a broad parameter space: the corrected evolution makes many low-frequency signals stronger (conservative underestimates), and the cases where it could overestimate S/N are all far above threshold. A focused recomputation is warranted, but the ACCEPT verdict can remain unless that recomputation reveals a boundary shift that removes a substantial part of the claimed parameter space.","tokens_in":16925,"tokens_out":40168,"duration_ms":351677,"concrete_test":"Recompute Table 2 and the Figs. 4–5 boundaries with Eq. (8) replaced by df_orb/dt = (96/5)(2π)^{8/3}(G M_c)^{5/3}/c^5 f_orb^{11/3} F(e), and the analogous corrected de/dt, or equivalently rerun LEGWORK's built-in Peters-Mathews evolution without any manuscript-side factor. If the S/N values and the m_2–f_orb detection contours change by less than roughly a factor of 2 in the regions highlighted by the paper, the central claim stands as accepted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The evolution equation for the orbital frequency, Eq. (8), is written as df_orb/dt = (96/5π)(G M_c)^{5/3}/c^5 (π f_orb)^{11/3} F(e). Starting from the standard Peters-Mathews result for the angular frequency, dΩ/dt = (96/5)(G M_c)^{5/3}/c^5 Ω^{11/3} F(e), with Ω = 2π f_orb, the coefficient in terms of f_orb should be (96/5)(2π)^{8/3}, not (96/5)π^{8/3}. The displayed equation is therefore too small by a factor 2^{8/3} ≈ 6.35. The same missing factor appears in Eq. (9) for de/dt. This is an internal inconsistency with Eq. (1), where f_orb is explicitly the cyclic orbital frequency. If the code implements Eq. (8) as printed, merger times and the frequency drift over T_obs are miscalculated. For systems with t_merge >> T_obs, the effect is to shrink the effective frequency band, making S/N conservative; for close, massive, high-eccentricity systems where t_merge < T_obs, the code would overestimate the usable evolution time and hence S/N. The central qualitative claim—that DECIGO/BBO can detect SS-SP systems over a broad parameter space—is probably unaffected, because the largest S/N values remain far above threshold and the marginal boundaries shift only mildly. But the numerical tables and contour maps should be recomputed before quoting precise detectability limits.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies continuous gravitational-wave emission from binaries consisting of a strange star (1.4 or 2.0 solar masses) and a strange planet (1e-10 to 1e-3 solar masses) in the pre-inspiral, close-orbit phase, under the Bodmer-Witten SQM hypothesis. Using Peters-Mathews orbital evolution and the LEGWORK package with DECIGO/BBO noise curves, the authors compute harmonic-resolved amplitude spectral densities and S/N for circular and eccentric orbits over a grid of masses, separations (periastron distances 4.75e7 to 5.6e10 cm), eccentricities (0, 0.5, 0.95), and distances (0.1-1000 kpc). They conclude that for T_obs = 4 yr, both DECIGO and BBO can detect such systems over a broad parameter space, and that eccentricity enhances detectability while extending detectable systems to lower orbital frequencies. They also discuss formation scenarios and implications for the SQM hypothesis.","tokens_in":17345,"tokens_out":10797,"duration_ms":102852,"significance":"If correct, the calculation provides a concrete, falsifiable observational channel for testing the SQM hypothesis in the mHz-dHz band, complementary to ground-based inspiral searches and electromagnetic observations. The modeling uses standard, published Peters-Mathews equations and the public LEGWORK code; no parameters are fitted to data, and the predicted S/N values and detection contours are direct outputs of the assumed model. The paper is also explicit that non-detection would not falsify SQM because other observational channels remain. The main limitations are the speculative existence of SS-SP systems and several parameter choices that bracket the claimed 'broad parameter space.' These do not undermine the logical structure but need to be made precise and, in places, corrected.","major_comments":[{"comment":"Equations (8) and (9) lose a factor 2^{8/3}. With Ω = 2π f_orb, the standard Peters-Mathews equation dΩ/dt = (96/5)(G M_c)^{5/3}/c^5 Ω^{11/3} F(e) becomes df_orb/dt = (96/5)(2π)^{8/3}(G M_c)^{5/3}/c^5 f_orb^{11/3} F(e); the printed form (96/5π)(π f_orb)^{11/3} is smaller by a factor 2^{8/3} ≈ 6.35. The same error affects Eq. (9). Because Eq. (7) uses the initial/final frequencies obtained from these evolution equations, the numerical tables and contours depend on this factor unless the public LEGWORK routine uses the correct form. Please correct the equations and explicitly confirm which form the code implements; if the code implements the printed equations, all S/N values, Table 2, and Figures 3–5 must be recomputed.","section":"§2, Eqs. (8)–(9)"},{"comment":"The code description sets t_evo = min(T_obs, t_merge − t_before), with t_before = 1 s for circular orbits and t_before = 0.1 yr for eccentric orbits. The eccentric value is asserted without derivation. This parameter matters precisely in the close, massive, high-eccentricity corner where t_merge can become comparable to or shorter than T_obs; Figures 4–5 extend to r_p = 4.75×10^7 cm, where this regime occurs. Please justify the choice (e.g., where the point-particle/continuous-wave approximation breaks down before merger) and demonstrate robustness of the S/N ≥ 5 boundaries to the choice, for instance over t_before ≈ 0.01–1 yr.","section":"§4.1, tevo definition"},{"comment":"The adopted orbital-separation upper bound r_p = 5.6×10^10 cm is the tidal disruption radius of a normal-matter planet with ρ̄ = 30 g cm^{-3}, not of a strange planet (r_td ≈ 2.37×10^6 cm for SQM-density matter). The text gives no physical reason why a strange planet could not reside at larger periastron distances. Because Figures 4–5 use this value as the low-frequency edge of the parameter grid, the stated detectable parameter space is partly determined by this normal-matter bound. Please either justify the bound from SS-SP formation physics or extend the grid and state how the detection boundaries change.","section":"§3, r_p range"}],"minor_comments":[{"comment":"The parameter list in the text says D_L = {0.1, 10, 1000} kpc, while Figure 3's caption and Table 2 use D_L = {0.1, 1, 10} kpc. These should be aligned.","section":"§4.1"},{"comment":"The phrase 'S/N and ADS calculations' should be 'ASD calculations'; the acronym is defined earlier as amplitude spectral density.","section":"§4.1"},{"comment":"Equation (11) defines ASD_n = ⟨S/N_n⟩ sqrt(S_n(f_gw,n)). As written, this is not the usual amplitude spectral density and the relation to h_c,n is not transparent. Please state the normalization convention explicitly so that Figure 3 can be reproduced.","section":"§2, Eq. (11)"}],"recommendation":"major_revision","confidential_remarks":"I see no circularity or novelty-disclosure concern: the self-citations are contextual and the detectability conclusion does not reduce to them. The main risk is that Eqs. (8)–(9) as printed are incorrect and could be propagated into future work; a correction and a code check are essential. The parameter-space bounds and t_before also need more justification before the quantitative contours can be taken at face value. I expect the qualitative conclusion to survive these changes, since the largest S/N values are far above threshold and the public LEGWORK code very likely implements the correct Peters-Mathews equations."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a straightforward, honest feasibility study, and it does what it says. The genuinely new thing is the first systematic mapping of the continuous mHz-dHz gravitational-wave band from strange-star/strange-planet binaries for DECIGO and BBO, including eccentric orbits and planet masses up to 1e-3 solar masses. Prior work by the same group looked at lower-mass companions for LISA-like detectors; here the question is whether decihertz detectors could see these systems, and the answer is yes across a broad parameter space.\n\nThe methods are standard: Peters-Mathews formalism, LEGWORK for S/N, public PSDs for DECIGO and BBO with confusion noise. The paper uses the public code rather than reinventing the wheel, and it is explicit about the assumptions that go into the parameter grid. That is a real credit.\n\nThe soft spots are mostly the usual ones in feasibility studies. The upper bound on orbital separation is set by the tidal radius of a normal-matter planet, not a strange planet, so the explored parameter space is a somewhat arbitrary carve-out. The t_before choice for eccentric orbits is ad hoc. Neither of these breaks the central claim.\n\nThe bigger issue is in the printed equations. Equation (8) for df_orb/dt and Eq. (9) for de/dt are missing a factor of 2^{8/3} relative to the standard Peters-Mathews result when written in terms of cyclic frequency. The code is LEGWORK, which almost certainly uses the correct factors, so the tables and figures are probably fine. But the displayed equations are wrong as written, and the authors need to fix them and confirm that the code output matches the corrected equations. If the code actually used the printed equations, the S/N values would be somewhat conservative for long-lived systems and possibly overestimated for the closest, highest-eccentricity cases, but the qualitative conclusion—that DECIGO/BBO can detect these systems over a large region of parameter space—would still hold.\n\nThe paper is worth a serious referee. It is not a breakthrough, but it is a clean, useful sensitivity study that connects GW astronomy to the strange quark matter hypothesis. Send it to review, with a request to correct the evolution equations and verify the code's consistency.","headline":"Straightforward feasibility study mapping the detectable parameter space for SS-SP binaries with DECIGO/BBO; printed evolution equations have a missing factor but the qualitative conclusion holds.","tokens_in":17881,"tokens_out":5011,"would_cite":true,"duration_ms":42972,"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":"If strange quark matter exists, DECIGO and BBO should hear the continuous gravitational waves of strange planets orbiting strange stars out to about 1000 kpc.","keywords":["strange quark matter","strange stars","strange planets","continuous gravitational waves","eccentric binaries","DECIGO","BBO","pulsars"],"falsifier":"Observe the continuous GW band with DECIGO or BBO for several years and find no signals from any known nearby pulsar with a low-mass companion at the predicted frequencies and S/N threshold; this would falsify the claim that SS–SP systems populate the surveyed parameter space. Conversely, a detected continuous GW source showing an unexpectedly high orbital-frequency cutoff would rule out an ordinary neutron star companion and support the strange-planet interpretation.","tokens_in":16839,"feed_emoji":"🛰️","tokens_out":5770,"duration_ms":55064,"temperature":0.7,"pith_summary":"Under the Bodmer–Witten hypothesis, strange quark matter could form objects ranging from planets to stars, and a strange star orbited by a strange planet would emit gravitational waves long before any inspiral. This paper calculates the continuous GW signal from such binaries at millihertz to decihertz frequencies using the Peters–Mathews harmonic formalism and compares it with the planned space-based detectors DECIGO and BBO. For a four-year observation, both detectors reach signal-to-noise ratios above 5 across broad regions of the physically motivated parameter space, including systems up to 1000 kpc away. If such systems exist, these detectors would offer a new, independent test of the strange quark matter hypothesis.","feed_headline":"Strange-matter planets would shine in DECIGO and BBO bands","feed_subtitle":"Continuous waves from quark-matter planets orbiting strange stars would test the SQM hypothesis out to 1000 kpc.","key_machinery":"The Peters–Mathews (1963) decomposition of GW emission from an eccentric binary into harmonics $n f_{\\rm orb}$, with the enhancement factor $F(e)$, together with the coupled evolution equations for orbital frequency and eccentricity under radiation reaction. The signal-to-noise ratio is computed by summing up to $n=1200$ harmonics using the LEGWORK code (Wagg et al. 2022) with DECIGO and BBO power spectral densities from Yagi & Seto (2011, 2017) and confusion noise following Sun et al. (2024). The tidal-disruption-radius argument sets the allowed orbital separations: a strange planet, with mean density $\\bar\\rho\\approx 4\\times10^{14}\\,{\\rm g\\,cm^{-3}}$, can survive down to $r_{\\rm td}\\approx","core_discovery":"The central claim is that strange star–strange planet (SS–SP) binaries in a long-lived close orbit, before the companion enters the inspiral phase, produce continuous GWs whose frequencies fall in the DECIGO/BBO band and that these signals are detectable with S/N $\\geq 5$ for wide ranges of planet mass, orbital frequency, eccentricity, and distance. Eccentricity is shown to enhance the signal substantially: for $e=0.95$ a planet of $10^{-7}\\,M_\\odot$ at 1 kpc reaches S/N about 3.4 for DECIGO and about 17.6 for BBO, while for $e=0$ the same system is undetectable. The detectable planet mass ranges from $7.6\\times10^{-10}\\,M_\\odot$ for a close, circular, nearby system to about $4.7\\times10^{-5","pith_inferences":["The same harmonic formalism could be used in reverse: the observed high-frequency cutoff of a continuous GW source would encode the companion's tidal disruption radius, and thus its mean density, providing a direct way to tell a strange-matter planet from an ordinary rocky or gaseous planet.","The predicted eccentricity boost suggests that searches with DECIGO/BBO should prioritize known pulsars with planetary-mass companions; even a non-detection would place upper limits on the abundance of strange planets and constrain the SQM hypothesis.","A distance reach of roughly 1000 kpc means a positive detection might come from Andromeda rather than the Milky Way, which would broaden the source volume but complicate electromagnetic follow-up.","Combining a GW detection with a prompt search for X-ray or radio bursts from tidal stripping could test whether the companion is genuinely quark matter rather than a low-mass white dwarf."],"forward_implications":["If SS–SP systems exist in the adopted parameter grid, DECIGO and BBO will detect continuous GWs from them within the Milky Way and out to about 1000 kpc, covering most Local Group galaxies such as M31.","Eccentric orbits raise the S/N by orders of magnitude and shift the detectable window to lower orbital frequencies, so the first detections may be highly eccentric systems formed by capture or SQM clump ejection.","Non-detection would not disprove the SQM hypothesis, because strange stars could still form through hadron–quark phase transitions in neutron star mergers or core-collapse supernovae and produce high-frequency GW signatures.","A detection would test the SQM hypothesis and help distinguish formation channels: strange planets ejected from newborn strange stars versus primordial strangelets captured by compact objects.","BBO's sensitivity advantage over DECIGO in roughly 0.07–0.9 Hz means it can probe planet masses down to about half the DECIGO lower limit in that band."],"supporting_citations":[{"why":"Provides the harmonic decomposition and enhancement factor used to compute GW power, strain, and evolution for eccentric binaries.","marker":"Peters & Mathews 1963"},{"why":"Supplies the LEGWORK code used to compute signal-to-noise ratios with full orbital evolution over the observational window.","marker":"Wagg et al. 2022"},{"why":"Provides the DECIGO and BBO power spectral densities used as the detector sensitivity curves.","marker":"Yagi & Seto 2011, 2017"},{"why":"Supplies the prescription for adding confusion noise to the detector power spectral densities.","marker":"Sun et al. 2024"},{"why":"Provides the strange-planet tidal disruption radius and mass–radius relation that define the allowed orbital separation and planet mass range.","marker":"Kuerban et al. 2020"},{"why":"Earlier work on high-frequency inspiral GWs from SS–SP systems that this paper extends to the long-lived continuous-wave phase.","marker":"Geng et al. 2015"},{"why":"The DECIGO mission design whose sensitivity curve and science case motivate the detectability analysis.","marker":"Kawamura et al. 2006"},{"why":"The BBO mission design whose sensitivity curve and science case motivate the detectability analysis.","marker":"Harry et al. 2006"}],"fun_headline_variants":["Continuous GWs from quark-matter binaries reach DECIGO","Quark-matter planets reveal themselves to DECIGO and BBO","Eccentric orbits amplify strange-matter GW signals","Future space detectors to spot strange quark stars and planets"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The central claim depends on strange star–strange planet systems actually existing with the assumed masses, separations, eccentricities, and distances; if such binaries never form or are extremely rare in the Milky Way and nearby galaxies, the predicted detections will not occur.","fun_headline_variants_meta":{"raw":{"variants":["Continuous GWs from quark-matter binaries reach DECIGO","Quark-matter planets reveal themselves to DECIGO and BBO","Eccentric orbits amplify strange-matter GW signals","Future space detectors to spot strange quark stars and planets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00022,"raw_usage":{"total_tokens":1331,"prompt_tokens":842,"completion_tokens":489,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":586,"completion_tokens_details":{"reasoning_tokens":420}},"tokens_in":586,"tokens_out":489,"duration_ms":4924,"temperature":1.0,"reasoning_tokens":420,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T00:12:19.583031+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Observe the continuous GW band with DECIGO or BBO for several years and find no signals from any known nearby pulsar with a low-mass companion at the predicted frequencies and S/N threshold; this would falsify the claim that SS–SP systems populate the surveyed parameter space. Conversely, a detected continuous GW source showing an unexpectedly high orbital-frequency cutoff would rule out an ordinary neutron star companion and support the strange-planet interpretation.","supporting_citations":[{"cited_title":"2024, A&A, 682, A177, doi: 10.1051/0004-6361/202347221","cited_arxiv_id":null,"evidence_quote":"Supplies the prescription for adding confusion noise to the detector power spectral densities."}],"review_version":1}