{"id":"d99aa398-fc95-4b31-a080-59cd48569b2c","arxiv_id":"2607.07120","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":7,"one_line_summary":"Future CE+ET detectors may detect lensed BNS kilonovae at ~0.5/yr via pointed follow-up of known galaxy lenses, while lensed sGRBs and afterglows remain rare or undetectable with current-generation facilities.","lead":"This paper predicts how often future gravitational-wave detectors and telescopes would jointly detect gravitationally lensed binary neutron star mergers and their light signals. It matters because such rare lensed events could independently measure the Hubble constant and test whether gravitational waves travel at exactly the speed of light.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"Kilonova rates depend on an EOS→compactness→ejecta-mass→luminosity chain where the single SLy EOS choice and GW170817-fixed opacities introduce unquantified systematic uncertainty in f_KN.","rationale":"The reader's identification of the population synthesis model as the weakest assumption is correct, and I have sharpened it to the specific EOS→compactness→ejecta-mass→luminosity chain that controls the kilonova rates. However, this concern does not change the verdict from CONDITIONAL. The paper is already transparent about large uncertainties (error bars span factors of ~2, and Section 5 explicitly discusses the η_gamma, SMNS, and population model uncertainties). The rates are best interpreted as order-of-magnitude forecasts, which is consistent with a CONDITIONAL verdict. The additional issues I identified (EOS sensitivity, missing duty cycle correction, unspecified P_match in Eq. 17) are real but do not rise to the level of invalidating the methodology or the qualitative conclusions. The pointed-lens strategy is a genuine operational contribution, and the relative ranking of detectability across bands and messengers (kilonovae most promising, sGRBs rare, afterglows mainly in X-ray) is likely robust to these uncertainties. The paper would be strengthened by quantifying EOS sensitivity and explicitly applying the duty cycle correction, but these are improvements rather than fatal flaws.","tokens_in":30378,"tokens_out":7374,"duration_ms":391153,"concrete_test":"Re-run the pipeline with two additional EOS choices (e.g., APR4 and DD2, spanning the plausible NS radius range ~11–13 km) while keeping all other parameters fixed. Recompute f_KN for the F158 band. If f_KN shifts by more than 30% relative to the SLy result, the kilonova rate predictions are EOS-sensitive and the single-EOS assumption materially affects the central claim. Separately, multiply all Table 1 rates by 0.72 (double-image) / 0.85³ (triple) to quantify the duty-cycle correction that was discussed but not applied.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader correctly identifies the population synthesis model as the primary load-bearing assumption. I would sharpen this to a specific link in the chain: the kilonova detection rates depend on f_KN, which depends on the kilonova luminosity function, which depends on ejecta masses computed via the Krüger & Foucart (2020) fitting formulas (Eqs. A1–A3). These formulas take NS compactness C_{1,2} as input, and compactness is derived from the SLy equation of state (M_TOV = 2.06 M⊙, Section 2). This is a single EOS choice; alternative EOSs (e.g., APR4 with smaller radii, DD2 with larger radii) would yield different compactness for the same component masses, shifting the ejecta mass distribution and thus f_KN. The paper does not quantify this EOS sensitivity. Additionally, the opacity and energy normalization parameters (κ_low = 44.7, ε₀ = 183.4×10¹⁸, etc., Section 2.2) are fixed to GW170817 values and assumed universal across the BNS population, which is a strong assumption given that GW170817 may be atypical. A further concrete issue: the duty cycle correction (~20–30% reduction, Section 2.1) is discussed but not applied to the rates in Table 1 — the note to Table 1 lists it as an 'additional uncertainty' rather than a correction already incorporated, so all quoted rates are systematically overestimated by this factor. These effects compound: EOS uncertainty could shift f_KN by tens of percent, the opacity assumption could bias the luminosity function, and the missing duty cycle correction inflates all rates by ~25%. Combined, the kilonova rate predictions could shift by factors of ~1.5–2 in either direction.","agreement_with_reader":"agree"},"referee_report":{"model":"glm-5.2","summary":"This manuscript estimates detection rates of strongly lensed electromagnetic counterparts (sGRBs, kilonovae, afterglows) associated with lensed binary neutron star (BNS) gravitational-wave events detectable by third-generation detectors (Cosmic Explorer and Einstein Telescope). The authors extend prior work (Ma et al. 2023) by using a binary population synthesis model to generate diverse BNS parameters rather than fixing all systems to GW170817-like values. Ejecta masses and jet energies are derived from component masses via fitted numerical-relation formulas, kilonova light curves are modeled with an anisotropic multi-component model, and afterglows are computed with AfterglowPy. A complementary pointed follow-up strategy targeting pre-identified galaxy-scale lens candidates is introduced. The main findings are: (1) lensed sGRBs are rare (~0.1/yr even with 10x Fermi-GBM sensitivity); (2) the identifiable lensed-host fraction is 0.15–0.30; (3) RST-like infrared facilities could detect lensed kilonovae at ~0.45–0.55/yr; (4) lensed afterglows are detectable mainly in X-rays with ATHENA (~0.5–5 events per decade). The methodology is internally consistent and validated against Colombo et al. (2022) and Yu et al. (2021).","tokens_in":30848,"tokens_out":1523,"duration_ms":231647,"significance":"The paper provides a timely and detailed forecast for lensed multi-messenger BNS science in the third-generation GW era. The use of a population synthesis model to sample BNS component masses—rather than assuming all systems resemble GW170817—is a genuine improvement over Ma et al. (2023) and makes the predicted kilonova and afterglow luminosity functions more representative. The pointed follow-up strategy targeting pre-identified lens candidates is a practical and well-motivated complement to wide-field ToO searches. The falsifiable, quantitative rate predictions for specific telescope/detector combinations (Table 1, Figures 4 and 8) are useful for observational planning. The validation against independent published rates (Colombo et al. 2022; Yu et al. 2021) lends credibility to the pipeline.","major_comments":[{"comment":"Section 2.1 discusses a duty-cycle correction of ~20–30% for GW detector downtime but this correction does not appear to be applied to the rates in Table 1. The note to Table 1 lists duty cycle as an 'additional uncertainty' rather than a correction already incorporated. If the quoted rates in Table 1 and the abstract do not include this factor, they are systematically overestimated by ~20–30%. The authors should clarify whether the duty-cycle correction is included in all quoted rates, and if not, either apply it or state explicitly that rates are upper limits assuming 100% duty cycle.","section":null},{"comment":"Section 2.2 and Appendix A.1: The kilonova luminosity function depends on ejecta masses computed via the Krüger & Foucart (2020) fits (Eqs. A1–A3), which require NS compactness derived from the SLy EOS (M_TOV = 2.06 M⊙). This is a single EOS choice. Alternative EOSs (e.g., APR4, DD2) would yield different compactness for the same component masses, shifting ejecta masses and thus f_KN and the final detection rates. The paper does not quantify this sensitivity. The authors should at minimum provide an estimate of how much f_KN or the kilonova detection rate changes under a different EOS choice, or discuss the range of uncertainty this introduces.","section":null},{"comment":"Section 2.2: The opacity and energy normalization parameters (κ_low = 44.7, κ_high = 0.43, κ_wind = 33.5, κ_vis = 47.8, ε₀ = 183.4×10¹⁸) are fixed to GW170817-fitted values and assumed universal across the BNS population. Given that the authors themselves note GW170817 'likely ranks among the most luminous kilonovae,' fixing these parameters to GW170817 may bias the luminosity function. The authors should discuss whether these parameters are expected to vary with ejecta composition (which depends on mass ratio and remnant lifetime) and how sensitive the final rates are to this assumption.","section":null}],"minor_comments":[{"comment":"Section 2.2: The text lists 'κ_low = 44.7 cm²/g' and then 'κ_low = 0.43 cm²/g' for high-elevation opacity. The second should be κ_high. This is a typo.","section":null},{"comment":"Figure 1 caption: The x-axis label reads 'mF158' but the figure shows distributions for three bands (F106, F158, F213). The label should be generic (e.g., 'm_AB') or the caption should clarify that the x-axis applies to all three bands.","section":null},{"comment":"Section 2.3, Eq. (12): The variable 'a' is defined as a(θ, θ_v) but the subscript notation is inconsistent with Eq. (13) where 'a' appears without arguments. Minor notational cleanup needed.","section":null},{"comment":"Table 1: The 'Relative fraction' column header could be more explicit (e.g., 'Lensed fraction among all detectable lensed BNS GW events'). The current phrasing is slightly ambiguous.","section":null},{"comment":"Section 4.5: The Vega-to-AB conversion (Eq. 18) uses 1090 Jy as the Vega flux in F158. A reference or derivation for this zero-point value would be helpful for reproducibility.","section":null},{"comment":"Section 2.4: The 10-hour response time is justified but the statement that a 1-hour response would enhance rates by a factor of ~2–3 is stated without derivation. A brief justification or reference would strengthen this claim.","section":null},{"comment":"The abstract states rates as '~0.45^{+0.81}_{-0.34}' etc. The large asymmetric error bars (upper errors nearly 2x the central value) suggest a highly skewed posterior from the merger rate uncertainty. A brief note in the abstract or at first mention in Section 4.4 explaining the source of this asymmetry would aid interpretation.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The paper is a solid contribution suitable for a gravitational-wave or multi-messenger astronomy journal. The three major comments are addressable without re-running the full pipeline: the duty-cycle issue is a clarification/correction, and the EOS and opacity sensitivity can be addressed with a limited sensitivity test or a thorough discussion. The reader's stress-test concern about the population synthesis model being load-bearing is valid but the authors already acknowledge this limitation in Section 5. The EOS sensitivity is the most substantive unaddressed issue and should be explicitly discussed."},"author_rebuttal":null,"desk_editor":{"model":"glm-5.2","letter":"The main thing to know: this paper builds a forward-modeling pipeline that takes a binary population synthesis model, computes ejecta masses and jet energies for each mock BNS system, and feeds those into kilonova/afterglow/sGRB light curves to predict detection rates for strongly lensed multi-messenger events with CE and ET. The key improvement over Ma et al. (2023) is replacing the single GW170817 template with a population that varies component masses, ejecta properties, and jet energies. They also switch from SIE to an EPL lens profile. These are real improvements, and the validation against Colombo et al. (2022) for unlensed afterglow rates and Yu et al. (2021) for sGRB rates is good practice. The pointed-lens follow-up strategy—targeting pre-identified galaxy-scale lens candidates rather than tiling the full GW localization region—is a useful operational contribution that could genuinely improve per-lens sensitivity for faint counterparts. The headline numbers (kilonova rates of ~0.45–0.55/yr with RST, sGRBs rare even with 10x Fermi-GBM sensitivity, X-ray afterglows at 0.5–5 per decade with ATHENA) are reasonable order-of-magnitude forecasts. Now the soft spots. The stress-test note flags a concrete issue I confirmed: the duty-cycle correction (~20–30% reduction from detector downtime) is discussed in Section 2.1 but is not applied to the rates in Table 1. The table note lists it as an 'additional uncertainty' rather than incorporating it, so all quoted rates are systematically high by roughly that factor. This is fixable but should be corrected before publication. The EOS concern is also valid but less severe than it sounds. The kilonova luminosities do depend on a chain: SLy EOS → NS compactness → ejecta mass (via Krüger & Foucart fits) → luminosity. A different EOS would shift compactness and thus ejecta masses. But the paper already acknowledges that GW170817 may be atypically luminous, and the population spread in component masses partially absorbs this. The bigger unquantified systematic is the radiation efficiency η_γ, which the authors set to [0.1, 0.3] while noting the observed range spans 0.007–0.97. They flag this themselves as a factor-of-5+ uncertainty. The opacity parameters fixed to GW170817 values are a stronger assumption than the EOS choice, since those directly set the kilonova luminosity function shape. None of these are fatal—the pipeline is sound and the assumptions are stated—but the paper would benefit from at least a paragraph quantifying how sensitive the kilonova rates are to the EOS and opacity choices, even if just through a single alternative-EOS test run. Overall: this is a competent, methodologically transparent paper that advances the lensed multi-messenger forecasting literature. The predictions should be read as order-of-magnitude estimates, which the authors mostly frame correctly. It deserves a serious referee who can push on the EOS/opacity sensitivity question and catch the duty-cycle correction.","headline":"Solid forward-modeling pipeline for lensed BNS multi-messenger rates; quantitative predictions are order-of-magnitude estimates with unquantified EOS and opacity systematics, plus a missing duty-cycle correction in Table 1.","tokens_in":31503,"tokens_out":735,"would_cite":true,"duration_ms":111989,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"glm-5.2","headline":"Lensed kilonovae from neutron star mergers detectable ~once per year","keywords":[],"falsifier":"If next-generation gravitational-wave detectors observe that the binary neutron star mass distribution or merger rate density evolution at high redshift differs substantially from the alpha10.kb_beta0.9 model predictions, the ejecta mass and jet energy distributions—and thus the kilonova and afterglow luminosity functions—would shift, potentially changing the predicted lensed detection rates by factors of several in either direction.","tokens_in":30563,"feed_emoji":"🔭","tokens_out":1213,"duration_ms":145954,"temperature":0.7,"pith_summary":"This paper estimates how often the various electromagnetic signals from binary neutron star mergers—short gamma-ray bursts, kilonovae, and afterglows—would be seen in gravitationally lensed form by next-generation gravitational-wave detectors and their electromagnetic follow-up telescopes. The central mechanism is a pointed observation strategy: rather than scanning the entire gravitational-wave localization region, astronomers would target pre-identified galaxy-scale lens candidates within that region, cross-matching the gravitational-wave trigger against existing lens catalogs. The paper finds that lensed kilonovae are the most promising signal, detectable at roughly half an event per year with a Roman-Space-Telescope-like infrared facility, while lensed short gamma-ray bursts remain rare even with substantially improved gamma-ray sensitivity, and lensed afterglows are detectable mainly in X-rays at a rate of perhaps one event every few years with a future facility like ATHENA. The rates depend on a population synthesis model for binary neutron star component masses and merger rate evolution, which sets the distribution of ejecta masses, jet energies, and thus the luminosities of the electromagnetic counterparts.","feed_headline":"Lensed kilonovae from neutron star mergers detectable ~once per year","feed_subtitle":"A pointed strategy targeting known galaxy-scale lens candidates could make lensed kilonovae the first routinely detectable multi-messenger引力","key_machinery":"The rate estimation chain runs from a binary population synthesis model (alpha10.kb_beta0.9) generating 10^7 mock BNS mergers with component masses and redshifts, through calibrated fits to numerical relativity simulations mapping those masses to ejecta masses and remnant disk masses, through a Blandford-Znajek jet-launching model setting sGRB and afterglow energies, through an elliptical power-law density lensing model (EPL with external shear) producing multiple images with magnification factors and time delays, to a Bayesian framework for identifying lensed host galaxies within gravitational-wave localization regions. Detection criteria combine gravitational-wave signal-to-noise ratios,电磁","core_discovery":"The paper's central result is a set of detection-rate estimates for lensed electromagnetic counterparts of binary neutron star mergers, showing that kilonovae are the most accessible signal (approximately 0.45–0.55 detections per year in near-infrared bands with a pointed lens-targeting strategy), while sGRBs and afterglows are substantially harder—sGRBs requiring gamma-ray sensitivity more than ten times beyond current instruments for even one detection per decade, and afterglows being detectable primarily in X-rays at 0.5–5 events per decade. The pointed strategy targeting pre-identified galaxy-scale lens candidates yields an identifiable lensed-host fraction of 0.15–0.30, which the paper取","pith_inferences":["The pointed strategy's dependence on pre-existing lens catalogs means its effectiveness scales with survey completeness; Euclid, CSST, and Roman's wide-field lens surveys become enabling infrastructure for lensed multi-messenger astronomy, not just for their primary cosmology missions.","If the BNS mass distribution at high redshift differs systematically from the population synthesis model—say, due to metallicity-dependent evolution or a different channel contribution—the ejecta mass and jet energy distributions shift, and the kilonova rate could move by factors of several in either direction, making early high-redshift BNS detections critical for calibrating the model.","The dominance of double-image cases over triples and quadruples in the detection rates suggests that Einstein ring and cross configurations, while visually striking, contribute negligibly to the lensed multi-messenger event budget."],"forward_implications":["If the predicted kilonova detection rate of ~0.5/yr holds, a decade of operation with CE+ET and an RST-like facility could accumulate 5–15 lensed kilonova events, enabling time-delay cosmography with gravitational-wave sources as independent distance indicators.","The pointed lens-candidate strategy could be validated even before CE/ET operations begin by testing it on simulated or real O4-era lensed GW candidates, measuring the fraction of lensed hosts recoverable with current survey depths.","If supramassive neutron star remnants inject additional energy into kilonovae (as the paper notes but does not model), the kilonova detection rates could increase by a factor of two or more, making the infrared channel even more dominant.","The rarity of lensed sGRB detections (~0.1/yr even with 10x Fermi-GBM sensitivity) implies that gamma-ray follow-up of lensed BNS events is not a viable primary detection channel and should be treated as a bonus rather than a baseline strategy."],"fun_headline_variants":["Lensed kilonovae beat afterglows and short GRBs as top neutron star merger signal","Pointed galaxy-lens strategy makes lensed kilonovae the leading detectable counterpart","Near-infrared telescopes could catch lensed kilonovae from neutron star mergers yearly","Lensed afterglows and short GRBs trail kilonovae as detectable merger counterparts"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The entire rate estimation depends on a binary population synthesis model correctly predicting the distribution of neutron star masses, mass ratios, and merger rate evolution out to redshifts of about 2. If the true binary neutron star population at high redshift differs—for instance, having a different mass distribution or merger rate evolution—the predicted electromagnetic counterpart rates could shift by factors of several.","fun_headline_variants_meta":{"raw":{"variants":["Lensed kilonovae beat afterglows and short GRBs as top neutron star merger signal","Pointed galaxy-lens strategy makes lensed kilonovae the leading detectable counterpart","Near-infrared telescopes could catch lensed kilonovae from neutron star mergers yearly","Lensed afterglows and short GRBs trail kilonovae as detectable merger counterparts"]},"model":"glm-5.2","effort":"low","cost_usd":0.0,"raw_usage":{"total_tokens":862,"prompt_tokens":778,"completion_tokens":84,"prompt_tokens_details":null},"tokens_in":778,"tokens_out":84,"duration_ms":27349,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-09T19:40:50.421419+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"If next-generation gravitational-wave detectors observe that the binary neutron star mass distribution or merger rate density evolution at high redshift differs substantially from the alpha10.kb_beta0.9 model predictions, the ejecta mass and jet energy distributions—and thus the kilonova and afterglow luminosity functions—would shift, potentially changing the predicted lensed detection rates by factors of several in either direction.","supporting_citations":[],"review_version":1}