{"id":"d6b4a5c4-c28c-4876-b1a2-9201260f607f","arxiv_id":"1908.08057","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Lensed extragalactic foregrounds create a percent-level bias in CMB lensing estimators that is significant for upcoming Simons Observatory measurements and can be reduced by modified estimators.","lead":"Extragalactic foregrounds in CMB temperature maps are themselves gravitationally lensed, and this foreground lensing produces a percent-level bias in CMB lensing measurements. The paper quantifies this bias for Simons Observatory-like experiments and shows it is significant for CMB lensing cross-correlations with LSST galaxies.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Percent-level bias amplitude rests on approximating the effective foreground source distribution Wf(χS,L) by dCf/dχ at ℓ=3000 (Sec. III B, Eq. 11); this L-dependent, estimator-weighted kernel is untested and could shift the bias by order unity.","rationale":"The paper's central claim is a quantitative prediction: lensed foregrounds produce a bias of order one percent in CMB lensing auto- and cross-spectra for a Simons Observatory-like experiment. The derivation chain is otherwise solid: the response functions are cross-checked with first-order lensing simulations, the secondary-bias cancellation is derived explicitly, and the code is public. The least secure input is the effective foreground source distribution Wf(χS,L), because the bias is directly proportional to the cross-correlation C^{κfκCMB}_L, and that cross-correlation is computed using a simplified approximation for Wf. The exact expression in Eq. (11) contains the estimator weights F and the lensing multipole L, but Sec. III.B replaces it with a shape proportional to dCf/dχ at ℓ=3000. This is not just an external uncertainty in foreground models; it is an internal simplification whose magnitude is unquantified within the paper. The reader's verdict was already CONDITIONAL with this same assumption flagged as weakest. I agree with that identification and do not think the verdict should change, because the paper is transparent about the approximation and the qualitative conclusion—that a correlated lensed-foreground bias exists and can be non-negligible—is well supported. However, the exact percent-level amplitude should be verified with the proposed recomputation before the quantitative headline is relied upon.","tokens_in":20108,"tokens_out":14863,"duration_ms":154719,"concrete_test":"In the public repository, evaluate Wf(χS,L) exactly from Eq. (11) for L = 100, 300, 1000 and for each foreground (CIB, tSZ, kSZ late, radio PS), using the same F weights, N_L, and dCf/dχS models; recompute C^{κfκCMB}_L and the QE/shear/magnification biases. Compare to the paper's ℓ=3000 approximation in Figs. 3, 5, 6, and 8. If any foreground bias changes by more than ~30%, or if the summed bias crosses the grey statistical-uncertainty bands, the headline percent-level amplitude is not yet robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline quantitative claim—a percent-level bias comparable to SO statistical errors—depends on the amplitude of C^{κfκCMB}_L, which is set by the effective foreground source distribution Wf(χS,L). Equations (10)-(11) define the exact Wf as N_L ∫ d²ℓ/(2π)² F_{ℓ,L−ℓ} f^{f,z}_{ℓ,L−ℓ}, i.e. it is estimator-weighted, L-dependent, and involves dCf/dχS at each ℓ entering the reconstruction. Section III.B replaces this with Wf(χS,L) ∝ dCf/dχS at ℓ=3000, dropping the F/N_L weighting and all L-dependence. The estimator integrals run over ℓ=30–3500, and for L≈100–1000 the low-ℓ leg of the response samples dCf/dχS at ℓ values well below 3000, where foreground source redshifts are typically lower. Because C^{κfκCMB}_L is a weighted line-of-sight integral of these kernels, an order-unity error in the effective source redshift distribution directly shifts the bias δC/C = 2Rf_L C^{κfκCMB}_L / C^{κCMBκCMB}_L (Eq. 19). The paper itself states (Sec. V) that the source-distribution uncertainty should be quantified. Since the claimed 'highly significant' cross-correlation bias is only ~1% against ~0.6% errors, a factor ~2 shift would change the conclusion. This is the load-bearing soft spot.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper quantifies a new systematic for CMB lensing reconstruction: the lensing of extragalactic foregrounds by the same large-scale structure that lenses the CMB. The authors derive analytic expressions for the response of the standard quadratic, shear, and magnification estimators to foreground lensing (Eq. 14), the resulting primary, secondary, and 4-point biases in the lensing auto-spectrum (Eqs. 19-22), and the cross-correlation bias (Eq. 17). Using foreground power spectra and redshift distributions from the literature, a Simons Observatory-like single-frequency 143 GHz configuration, and the LSST gold sample, they find percent-level biases comparable to the statistical errors in the auto-spectrum and larger than the expected cross-correlation errors. They validate the analytic expressions against 8060-map Gaussian simulations, provide a public code repository, and propose bias-hardening estimators.","tokens_in":20412,"tokens_out":5285,"duration_ms":49885,"significance":"If the amplitude estimate is reliable, this is an important first quantification of a systematic that has been noted but not computed, and it is directly relevant to AdvACT, SPT-3G, Simons Observatory, and CMB-S4. The analytic derivation is careful, the exact cancellation of the secondary bias at low L is a clean result, and the extensive simulation cross-checks plus public code are clear strengths. The main limitation is that the bias amplitude inherits the uncertainty in the approximate effective foreground source distribution, which the paper itself flags as needing quantification; consequently the quantitative headline is not yet fully robust.","major_comments":[{"comment":"The exact effective foreground source distribution Wf(χS,L) defined in Eq. (11) is estimator-weighted and L-dependent, but the numerical results replace it with Wf ∝ dCf(ℓ=3000)/dχS, dropping the F/N_L weighting and all L dependence. Since the bias in Eq. (19) is linear in the resulting C^{κf κCMB}_L, an order-unity error in the effective source redshift distribution would change the percent-level claim and the 'highly significant' LSST cross-correlation conclusion. The paper itself states in Sec. V that quantifying the uncertainty in the foreground source distributions is needed, but no such quantification is provided. Please evaluate Eq. (11) exactly for representative L values, or propagate explicit uncertainties from the adopted source models, and report how the bias changes.","section":"Sec. III B (Eq. 11) and Sec. V"},{"comment":"The single-convergence approximation, where each foreground map is lensed as a whole by one convergence field κf, is stated in Sec. IV and in the Conclusions to be 'sufficient' and believed to be comparable to the redshift-distribution uncertainty, but no test is given. Because each redshift slice of a foreground is lensed by a different convergence, and because the estimator weights in Eq. (11) depend on the source distribution, this assumption directly affects the same C^{κf κCMB}_L that sets the headline amplitude. Please test the approximation, for example by splitting a foreground into two or more redshift slices and recomputing the bias.","section":"Sec. IV and Sec. V"},{"comment":"The simulation validation uses foreground convergence maps κf generated from the same approximate Wf used in the analytic calculation (App. B, Eqs. B1-B3). The agreement between simulation and analytic curves therefore validates the algebra of the response and bias formulae, but it does not validate the Wf approximation itself. The paper should make this explicit and, more importantly, the approximate input should be tested against exact or observationally calibrated source distributions.","section":"App. B and Figs. 4, 6"}],"minor_comments":[{"comment":"The sentence 'For the CMB S3 experiment we consider, and assuming lmax T = 3500, most of the CMB lensing signal-to-noise comes from temperature multipoles ℓ ~ 3000' is given without support; a quantitative statement of the signal-to-noise contribution would strengthen the justification for evaluating dCf/dχ at ℓ=3000.","section":"Sec. III B"},{"comment":"The second line of Eq. (C10) contains an undefined weight w'_{L,ℓ}; the primary-bias term should presumably involve (Σ_ℓ w_{L,ℓ} R^f_{L,ℓ})(Σ_ℓ w_{L,ℓ}) or simply (Σ_ℓ w_{L,ℓ} R^f_{L,ℓ}) since the estimator has unit CMB response. Please clarify or correct.","section":"App. C (Eq. C10)"},{"comment":"The grey shaded areas are described as 'statistical uncertainty on the amplitude' with fsky and Lmax,κ specified; stating clearly whether this includes cosmic variance of the CMB lensing field and of the tracer, and how the bandpower errors are combined, would help the reader.","section":"Figs. 5 and 6 captions"},{"comment":"The term 'lensed foreground bias-hardening' is used in the abstract and in Sec. V; the hyphenation makes it read as if 'lensed foreground' modifies 'bias-hardening'. Consider rewording as 'hardening against the lensed foreground bias'.","section":"Abstract and Sec. V"},{"comment":"The statement 'This bias is thus marginally significant in auto-correlation, and highly significant in cross-correlation' would benefit from repeating the quantitative numbers (e.g., percent-level bias versus 0.6% cross-correlation uncertainty and 1% auto-spectrum uncertainty) so that the conclusion does not depend on the figures alone.","section":"Sec. V"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the journal's scope and the analytic derivation appears sound. The central risk is that the quantitative headline is tied to an approximate foreground source distribution whose uncertainty is acknowledged but not quantified, and the simulations validate the algebra rather than the approximation. If the authors can demonstrate robustness of the amplitude to the Wf approximation, or at least quantify its uncertainty, I would support acceptance. The self-citation to Schaan, Ferraro, and Spergel (2018) is appropriate and not circular."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper does something new and does it carefully: it quantifies the bias to CMB lensing estimators from the fact that extragalactic foregrounds are themselves lensed by structure correlated with CMB lensing. That effect was discussed qualitatively before, but this is the first numerical estimate for the quadratic estimator, shear, and magnification estimators. The analytic decomposition into primary, secondary, and 4-point biases is clear; the exact cancellation of the secondary bias at low L is a nice result; and the simulation cross-checks with 8060 maps are appropriate. The code is public, and the authors are honest about their main approximations.\n\nThe soft spot is real and it is the load-bearing one: the bias amplitude depends on the effective foreground source distribution Wf(χS,L), defined in Eq. (11) as an estimator-weighted, L-dependent quantity. Section III.B replaces it with dCf/dχ at ℓ=3000, dropping the F/N_L weighting and all L-dependence. The stress-test note is right that this can shift the bias by order unity, because for L~100–1000 the low-ℓ leg of the response samples source redshifts well below ℓ=3000. For the cross-correlation, where the claimed bias is ~1% against ~0.6% statistical errors, a factor-of-two shift turns “highly significant” into “marginal.” This does not sink the paper: the effect is real, and the order of magnitude is probably right. But the percent-level numbers are estimates with order-unity uncertainty, not predictions. The authors basically say this in Section V, though it could have been more prominent.\n\nThe citation pattern is fine. The response formalism comes from Schaan, Ferraro, Spergel 2018, co-authored by one of the current authors; that is self-citation, not circularity. No parameters are fitted to the bias; inputs are foreground power spectra and redshift distributions from the literature.\n\nWho is this for? Anyone forecasting CMB lensing systematics for Simons Observatory or CMB-S4, and anyone working on foreground bias-hardening. It deserves a serious referee. The referee should ask for a concrete test of the Wf approximation—e.g., evaluating the exact estimator-weighted kernel at a few L values, or lensing a redshift-resolved foreground mock like Websky—before the quantitative claims are used to plan analyses.\n\nRecommendation: send it to peer review. It is a worthwhile contribution with a clear, honest statement of its main caveat.","headline":"A genuinely new, carefully quantified systematic in CMB lensing, with a real order-unity uncertainty that the authors openly admit; worth refereeing, but the headline percent-level numbers should be read as estimates, not predictions.","tokens_in":20945,"tokens_out":2651,"would_cite":true,"duration_ms":26808,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper shows that extragalactic foregrounds in CMB temperature maps are lensed by the same large-scale structure that lenses the CMB, so standard lensing reconstructions pick up a correlated foreground-lensing signal that biases them…","keywords":["CMB lensing","extragalactic foregrounds","lensed foreground bias","quadratic estimator","shear estimator","magnification estimator","cosmic infrared background","Sunyaev-Zeldovich effect"],"falsifier":"Build a realistic foreground map split into redshift slices, lens each slice by its own convergence field correlated with the CMB convergence, add it to a lensed CMB map, apply the quadratic, shear, and magnification estimators, and compare the measured bias with this paper's single-effective-convergence prediction; a mismatch larger than the simulation error would falsify that approximation.","tokens_in":19891,"feed_emoji":"🌌","tokens_out":9773,"duration_ms":82108,"temperature":0.7,"pith_summary":"The paper establishes that extragalactic foregrounds in CMB temperature maps are themselves gravitationally lensed, and because this foreground lensing is correlated with CMB lensing, standard CMB lensing reconstruction measures a combination of both and is biased. For a next-generation stage-III 143 GHz temperature map with a 1.4 arcmin beam and 7 microK-arcmin white noise, the bias is about one percent of the CMB lensing auto-spectrum, comparable to the statistical uncertainty, and larger than the statistical error in cross-correlation with a deep galaxy sample. This matters because upcoming lensing measurements aim for percent-level precision, and the bias persists even for perfectly Gaussian foregrounds, so methods that only remove foreground non-Gaussianity do not cure it. The paper derives analytic bias formulas, confirms them in simulations, and proposes modified estimators that null the bias at some noise cost.","feed_headline":"Lensed foregrounds bias CMB lensing by a percent","feed_subtitle":"Even Gaussian foregrounds are lensed by the same structure as the CMB, so the bias rivals the statistical error","key_machinery":"The load-bearing object is the response function $R_L^f$, the ratio of a quadratic estimator's response to foreground lensing, built from the foreground power spectrum $C_\\ell^f$, to its response to CMB lensing, built from $C_\\ell^{\\rm CMB}$. Multiplying this response by the correlation $C_L^{\\kappa_f\\kappa_{\\rm CMB}}$ between foreground and CMB convergence gives the bias to the auto-spectrum, and by $C_L^{g\\kappa_f}$ gives the bias in cross-correlation with galaxies. The foreground lensing convergence is defined through an effective kernel $W^{\\kappa_f}(\\chi,L)$, constructed from the redshift distribution of the foreground power spectrum $\\mathrm{d}C_f/\\mathrm{d}\\chi_S$, evaluated at $\\ell=3000$ in this paper. A secondary bias term, given by a four-dimensional integral, cancels exactly in the limit $L,L_0\\ll\\ell$ and dominates at high lensing multipoles.","core_discovery":"The central claim is that CMB lensing quadratic estimators applied to a temperature map containing lensed extragalactic foregrounds reconstruct a weighted sum of CMB lensing and foreground lensing, and that the correlation between the two convergences converts this response into a bias. The paper computes this lensed foreground bias for the standard quadratic estimator, the shear estimator, and the magnification estimator, finding percent-level biases for a single-frequency 143 GHz stage-III experiment. The foreground lensing convergence itself is 5% to 85% as large as the CMB lensing convergence depending on the component, but the estimators' response to foreground lensing is only about a percent, which sets the bias size. In the CMB lensing auto-spectrum the bias is comparable to the statistical uncertainty, while in cross-correlation with a deep galaxy sample it exceeds the statistical error and is thus highly significant. The bias formulas include primary, secondary, and four-point terms; the secondary term cancels at low lensing multipoles and dominates at multipoles of a few thousand.","pith_inferences":["The bias depends directly on foreground redshift distributions, so measuring those distributions, for example by cross-correlating foreground maps with galaxy positions, could turn the predicted bias into a correctable template; the paper's statement that a 10% theory error is acceptable sets the required calibration.","The single-effective-convergence approximation could be checked with redshift-sliced foreground mocks; if slice-by-slice lensing matters, the bias formulas would need the full $\\mathrm{d}C_f/\\mathrm{d}\\chi_S$ integral rather than a single $\\ell=3000$ evaluation.","The same correlated-lensing logic should also bias CMB lensing cross-correlations with the foreground fields themselves, such as CIB or tSZ tracers, since those tracers share the foreground lensing convergence and would enter through the same response formulas.","The opposite signs of the shear and magnification responses suggest an internal consistency test on real data: the difference of the two estimators should flip sign where lensed foregrounds dominate, independently of any assumed foreground model."],"forward_implications":["For a stage-III single-frequency temperature experiment, the lensed foreground bias must be included in the error budget because it is comparable to the statistical uncertainty on the CMB lensing auto-spectrum.","In cross-correlation with a deep galaxy sample, the bias is larger than the statistical error, so ignoring it would produce a biased measurement of the galaxy-CMB lensing correlation.","The shear and magnification estimators have opposite-sign responses to foreground lensing, so comparing them provides a null test for the presence of lensed foreground bias.","Mitigation methods that rely on foreground non-Gaussianity, such as standard bias hardening or the shear estimator alone, do not remove this bias; reducing the foreground level in the map, scale cuts, or the lensed-foreground bias-hardened estimators are needed.","At lensing multipoles of a few thousand the secondary bias dominates, so small-scale lensing measurements from temperature need special treatment."],"supporting_citations":[{"why":"First suggested that lensed foregrounds would bias CMB lensing through their correlation with CMB lensing.","marker":"[41]"},{"why":"Derives the effective foreground lensing kernel and the response of quadratic estimators to lensed contaminants, the basis of the bias calculation.","marker":"[42]"},{"why":"Supplies the foreground auto- and cross-power spectra at 143 GHz used for the numerical estimates.","marker":"[52]"},{"why":"Defines the shear and magnification estimators and their noise properties, including the L~3000 noise spike seen in the bias plots.","marker":"[33]"},{"why":"Derives the minimum-variance quadratic estimator used as the baseline for the response and bias formulas.","marker":"[46]"},{"why":"Provides the CIB halo model and luminosity functions used for the CIB redshift distribution.","marker":"[54]"},{"why":"Provides the thermal Sunyaev-Zel'dovich halo model used for the tSZ redshift distribution.","marker":"[57]"},{"why":"Provides the late-time kSZ redshift distribution used in the effective foreground lensing kernel.","marker":"[58]"},{"why":"Provides the radio point-source redshift distribution used for the radio foreground component.","marker":"[60]"}],"fun_headline_variants":["Lensed foregrounds add percent-level bias to CMB lensing","CMB lensing bias from lensed foregrounds rivals noise","Foreground lensing biases CMB lensing by ~1%","New bias in CMB lensing from lensed foregrounds","Percent-level bias in CMB lensing from foregrounds"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes each foreground component is lensed as a whole by a single effective convergence field built from its adopted redshift distribution, and it assumes those foreground redshift distributions and power spectra are accurate; if they are not, the percent-level bias estimate changes.","fun_headline_variants_meta":{"raw":{"variants":["Lensed foregrounds add percent-level bias to CMB lensing","CMB lensing bias from lensed foregrounds rivals noise","Foreground lensing biases CMB lensing by ~1%","New bias in CMB lensing from lensed foregrounds","Percent-level bias in CMB lensing from foregrounds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00024,"raw_usage":{"total_tokens":1522,"prompt_tokens":956,"completion_tokens":566,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":572,"completion_tokens_details":{"reasoning_tokens":479}},"tokens_in":572,"tokens_out":566,"duration_ms":5041,"temperature":1.0,"reasoning_tokens":479,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:50:36.505117+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build a realistic foreground map split into redshift slices, lens each slice by its own convergence field correlated with the CMB convergence, add it to a lensed CMB map, apply the quadratic, shear, and magnification estimators, and compare the measured bias with this paper's single-effective-convergence prediction; a mismatch larger than the simulation error would falsify that approximation.","supporting_citations":[{"cited_title":"Lensing Studies with Diffuse Backgrounds","cited_arxiv_id":"astro-ph/0309301","evidence_quote":"First suggested that lensed foregrounds would bias CMB lensing through their correlation with CMB lensing."},{"cited_title":"Modeling the evolution of infrared galaxies : clustering of galaxies in the Cosmic Infrared Background","cited_arxiv_id":"1110.0395","evidence_quote":"Provides the CIB halo model and luminosity functions used for the CIB redshift distribution."}],"review_version":1}