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Cosmology from LOFAR Two-metre Sky Survey Data Release 2: Cross-correlations with luminous red galaxies from eBOSS

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The baryon acoustic oscillation scale is recoverable from a radio-continuum survey when cross-correlated with optical galaxies.

desk verdict A solid first BAO measurement from radio-optical cross-correlation, but the headline significance is uncalibrated and the assumed LoTSS redshift distribution carries unpropagated uncertainty. read the letter →

arxiv 2504.20722 v1 pith:HF7CYIKW submitted 2025-04-29 astro-ph.CO

Jinglan Zheng , Prabhakar Tiwari , Gong-Bo Zhao , Dominik J. Schwarz , David Bacon , Stefano Camera , Caroline Heneka , Catherine Hale
show 2 more authors
Szymon J. Nakoneczny Morteza Pashapour-Ahmadabadi
This is my paper · ORCID
classification astro-ph.CO
keywords baryonacousticoscillationsradiocontinuumsurveysLoTSSDR2eBOSSluminousredgalaxiesangularpowerspectrumgalaxybiaslarge-scalestructurecross-correlation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using 4.4 million radio sources from LoTSS DR2 and 174,816 eBOSS luminous red galaxies, the paper measures the angular cross-power spectrum between the two populations and searches for the baryon acoustic oscillation (BAO) feature, the frozen sound horizon of the early universe that serves as a standard ruler. It reports the first BAO evidence in a radio-continuum and optical survey cross-correlation, with an isotropic dilation parameter $\alpha = 0.968^{+0.060}_{-0.095}$ at $z_{\rm eff}=0.72$ from four redshift slices. The same data yield the linear clustering bias of LoTSS radio sources, $b_C = 2.64 \pm 0.20$ for a constant-bias model and $b_D = 1.80 \pm 0.13$ for a model where bias evolves inversely with the linear growth factor. If correct, the result opens a distance measurement that needs no individual radio-source redshifts, only a statistical redshift distribution.

What carries the argument

The central object is the angular power spectrum $C_\ell$ of the LoTSS--eBOSS cross-correlation and the eBOSS auto-correlation, measured with a pseudo-$C_\ell$ estimator and modelled via the Limber projection of the matter power spectrum. The BAO analysis uses the template $C_\ell = B(\ell)\,\alpha^{-2}\,C^{\rm BAO}_{\ell/\alpha} + A(\ell)$, where $\alpha = [D_A(z)/r_d]_{\rm obs}/[D_A(z)/r_d]_{\rm fid}$ is the dilation parameter, $r_d$ is the sound horizon, and the polynomial $A(\ell)$ marginalises over the broadband shape. The redshift distribution of LoTSS sources is taken from the LOFAR Deep Fields, the eBOSS redshift distribution comes directly from the spectroscopic catalogue, and 1000 lognormal mock catalogues provide the covariance matrix and pipeline validation.

What would settle it

Measure spectroscopic redshifts for a flux-limited LoTSS DR2 sample over the eBOSS overlap region with the same cuts (S/N $>7.5$, $S_{144}>1.5$ mJy) and compare the resulting $p(z)$ with the LOFAR Deep Fields distribution; a mismatch large enough to move the model $C_\ell$ by more than the mock covariance would invalidate the quoted bias and $\alpha$ errors. Alternatively, re-run the BAO fit with $p(z)$ varied within its Deep Fields uncertainty and check whether $\alpha$ moves by more than its quoted 68\% interval.

Watch

Extended reading notes

Core claim

The paper's central claim is that the BAO feature survives projection in the angular cross-correlation between unresolved radio-continuum sources and galaxies with spectroscopic redshifts, and that this signal can be used to measure the angular diameter distance and the radio-source bias. The cross-correlation is detected at 7.8--9.2$\sigma$ per redshift bin and 14.7$\sigma$ when the four bins are combined; the BAO preference over a no-wiggle model reaches $\Delta\chi^2_{\rm nw}=16.28$ for the four-bin combination. Because the fitted parameter is non-Gaussian, the paper quotes 68\% intervals rather than Gaussian errors and reports the first evidence for BAO in this tracer combination rather than a definitive detection. The measured bias values are consistent with companion analyses in configuration space and with a LoTSS--CMB lensing cross-correlation, supporting the interpretation that the selected radio sources are mainly active galactic nuclei above the 1.5 mJy flux limit.

Load-bearing premise

The paper assumes that the wide-area LoTSS DR2 redshift distribution equals the LOFAR Deep Fields redshift distribution, and it does not propagate any uncertainty in that choice into the quoted errors; if the true wide-area $p(z)$ differs, the fitted bias and the BAO template will shift.

Editorial extensions

If this is right

  • Radio-continuum surveys with a known statistical redshift distribution can measure $D_A(z)$ through BAO without per-source spectroscopic redshifts.
  • Combining more redshift bins, or overlaying future optical surveys over LoTSS, should tighten $\alpha$ and test dark energy at $z\sim0.7$--$1$.
  • The fitted bias $b_C=2.64\pm0.20$ calibrates LoTSS radio sources as tracers of large-scale structure for later cross-correlation and intensity-mapping analyses.
  • When LoTSS covers 80\% of the northern sky, the same cross-correlation analysis should turn the current BAO evidence into a statistically robust detection.
  • The consistency of the evolving-bias measurement with companion angular-correlation and CMB lensing results strengthens the case that radio sources at this flux limit trace the same underlying matter distribution as optical LRGs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the wide-area LoTSS redshift distribution differs from the LOFAR Deep Fields distribution, the fitted bias will shift and the quoted $\alpha$ errors will be underestimated; a spectroscopic redshift sample of LoTSS sources would settle this directly.
  • The combination of cross- and auto-correlation in one bin yields a more skewed $\alpha$ distribution, suggesting that the added nuisance parameters trade bias for variance; testing with more independent redshift bins would reveal whether this behaviour persists.
  • Because the 1.5 mJy flux cut selects mainly AGN-dominated radio sources, $b_C\approx2.6$ at $z\approx0.7$ is effectively a prediction for the linear bias of radio-loud AGN at those redshifts, testable with X-ray-selected or optically selected AGN samples.
  • A natural next step is to apply the same template to the upcoming full LoTSS survey in combination with DESI or Euclid galaxies: the projection smoothing that currently suppresses the BAO signal would be mitigated by thinner effective redshift slices and a larger overlapping area.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper cross-correlates LoTSS DR2 radio sources with eBOSS LRGs in harmonic space, using pymaster to measure the angular cross- and auto-power spectra and pyccl to model them. From the cross-correlation alone in one redshift bin the authors report the BAO dilation parameter α = 1.01 ± 0.11 at z_eff = 0.63, and from four combined bins they report α = 0.968 +0.060/−0.095 at z_eff = 0.72. They also measure the LoTSS linear bias, b_C = 2.64 ± 0.20 for a constant-bias model and b_D = 1.80 ± 0.13 for an evolving-bias model, together with per-bin biases. The analysis is validated with 1000 FLASK mocks, a Hartlap-corrected covariance, jackknife resampling, and a no-wiggle null test. The paper's headline claims are a 14.7σ detection of the cross-correlation and a 4σ detection of BAO in the four-bin cross-correlation, which it presents as the first BAO evidence from a radio-continuum and optical survey cross-correlation.

Significance. If the central claims hold, this is the first BAO detection in a radio-continuum × optical cross-correlation and would demonstrate that the BAO standard ruler can be recovered without per-source radio redshifts. The pipeline work is a genuine strength: the covariance is built from 1000 correlated FLASK mocks, the inverse covariance is Hartlap-corrected, the model choice is tested on mocks, and jackknife tests are reported. The bias measurements are also useful and show good consistency with the configuration-space results of H24 and the CMB-lensing results of N24. The main risk is that the 4σ BAO significance is not statistically calibrated, and the redshift-distribution assumption for LoTSS is not propagated into the error budget. These two issues affect exactly the two headline numbers—the detection significance and the bias/α uncertainties—so they must be addressed before the paper can be accepted as a reliable measurement.

major comments (3)
  1. [Section 4.2, Eq. (16), Table 1] The 4σ BAO detection significance reported in the abstract and conclusions is not calibrated. The statistic Δχ²_nw compares models that are not nested: in Eq. (12) the BAO wiggle amplitude is fixed by (P_lin − P_nw) with Σ_nl = 5.5 Mpc/h, and no free amplitude parameter can reduce the model to the no-wiggle template within the prior α ∈ [0.8, 1.2]. Wilks' theorem therefore does not apply, and the assumption that Δχ²_nw follows a χ²_1 distribution is unjustified. This concern is compounded by the paper's own KS test (Section 3.2), which reports D > 0.7 for all parametrisations, and by the statement in Section 4.2 that 'reporting detection significance in sigma levels may not be appropriate'. The abstract nevertheless headlines 4σ. I ask the authors to calibrate the null distribution of Δχ²_nw using the 1000 mocks (for example, by generating null mocks from the no-wiggle template) or to rephrase the claim as an uncalibrated preference, not a detection significance.
  2. [Section 2.3, Fig. 3, Eqs. (8)–(9)] The LoTSS wide-area redshift distribution is assumed to equal the LOFAR Deep Fields p(z) from H24, without propagating any uncertainty. This p(z) enters the theoretical C_ℓ, the input spectra of the FLASK mocks, the covariance matrix, and the fits for both α and the bias parameters b_C and b_D. If the wide-field LoTSS DR2 population differs from the deep-field population—for example because of the S/N > 7.5 and 1.5 mJy cuts—the fitted bias b_C = 2.64 ± 0.20 and b_D = 1.80 ± 0.13 shift by an unknown amount, and the BAO template also changes. The paper should at least test robustness to alternative p(z) estimates (e.g., from N24 or from DR1-based analyses) and, ideally, marginalise over p(z) shape parameters; without this, the quoted statistical errors on the bias are not the full error budget.
  3. [Section 3.2, Table A.1, Section 4.2] The α constraints rest on a posterior that the KS test finds strongly non-Gaussian (D > 0.7 for every tested parametrisation), yet Table 1 reports 68% intervals and the text uses them to claim consistency with other BAO surveys in Fig. 12. The model-selection rule in Section 3.2—choose the parametrisation whose mock mean is closest to 1 and whose 68% CI is narrowest—is not a standard model-comparison criterion, and with D > 0.7 the interval endpoints are not Gaussian error bars. Several entries in Table A.1 have 68% intervals hitting the prior edge at 1.2, which suggests the criterion may be sensitive to prior truncation. I ask the authors to present the full α posterior (or a calibrated credible interval validated on the mocks) and to state explicitly what the quoted intervals mean; as written, the precision of the headline α = 0.968 +0.060/−0.095 is not yet established.
minor comments (5)
  1. [Section 4.2] The sentence 'by combining four redshift bins, the errors are reduced by 2%' is inconsistent with Table 1, where the upper error drops from 0.11 to 0.060; please correct the percentage or the wording.
  2. [Section 3.2] The KS-test statistic D > 0.7 is reported, but the sample size and the corresponding p-value are not; please add these so the reader can judge how severely non-Gaussian the posterior is.
  3. [Table 1] The conversion from α to DA(z_eff)/r_d uses Eq. (11), but the fiducial DA/r_d value is not quoted; please include it for reproducibility.
  4. [Fig. 12] The figure mixes angular α measurements with 3D α_⊥ measurements from other surveys; the text notes this in one sentence, but the figure legend should state it more prominently to avoid misinterpretation.
  5. [Section 2.3] The phrase 'the theoretical input must remain consistent' is unclear; please rephrase to specify which theoretical input is meant and why consistency is required.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: alpha and bias are direct fits to data with externally sourced templates and marginalised nuisance parameters.

full rationale

The central results are derived by fitting measured LoTSS DR2 x eBOSS angular power spectra to standard BAO and bias templates. In Eq. (10), C_ell = B(ell)/alpha^2 C_BAO(ell/alpha) + A(ell), alpha is a free dilation parameter and B and A are broadband nuisance terms, so the BAO dilation measurement is not constructed from its own target value. The linear bias is measured by setting the LoTSS bias to unity in the theoretical template (Section 2.3: 'we take a theoretical bias of 1 and do not assume any LoTSS bias in the theoretical model') and fitting it to the data. The LoTSS p(z) is imported from H24's external LOFAR Deep Fields analysis, and the b(z) from Tiwari et al. (2022) is used only as an input to mocks and is explicitly marginalised as broadband shape for BAO; neither is defined in terms of the fitted alpha or b_C, and both are independently falsifiable empirical inputs. The mock catalogues supply covariance and validate the pipeline, but do not encode the measured values. The paper's own caveats (Sect. 3.2: 'D > 0.7 for all tested parameterisations'; Sect. 4.2: 'reporting detection significance in sigma levels may not be appropriate') concern non-Gaussianity and the calibration of the null distribution for the 4-sigma claim; these are statistical-correctness limitations, not circular reductions. No equation in the paper reduces the claimed prediction to a fitted input by construction.

Assumptions & free parameters 8 free parameters · 8 assumptions · 0 invented entities

The analysis introduces no new physical entities. It relies on standard cosmology assumptions plus several analyst choices and data-driven inputs: the LoTSS redshift distribution, the eBOSS bias calibration, the flux and S/N cuts, the multipole window, the fixed nonlinear damping scale, and the broadband nuisance polynomials. The most consequential input is the LoTSS p(z) from LOFAR Deep Fields, which is treated as exact. The free parameters listed are either fitted targets, marginalized shape parameters, or hand-set analysis choices that shape the reported errors.

free parameters (8)
  • BAO dilation parameter alpha = alpha = 0.968 (+0.060/-0.095) 4-bin; alpha = 1.01 ± 0.11 single bin
    The central fitted parameter; it rescales the BAO template relative to the fiducial angular diameter distance. This is the measured target, not an ad hoc input.
  • LoTSS linear bias b_C or b_D = b_C = 2.64 ± 0.20; b_D = 1.80 ± 0.13
    Bias parameters in the cross-power spectrum fit for the constant-bias and evolving-bias models. These are the other central measured quantities.
  • BAO broadband nuisance coefficients B0, a1, a2, a3 = not reported (marginalized)
    Polynomial broadband terms in Eq. A.1 are fitted per spectrum to marginalize over bias, RSD, projection, and other smooth contributions. They absorb much of the signal, so alpha constraints rely on the residual BAO wiggle shape.
  • eBOSS auto-spectrum shot-noise amplitude = not reported
    The shot-noise floor for the eBOSS auto-correlation is inferred by fitting the flat high-ell tail of the measured C_ell, following the Garcia-Garcia et al. 2021 upgrading method.
  • LoTSS sample flux and S/N thresholds = S_144MHz > 1.5 mJy; S/N > 7.5
    Hand-chosen selection limits adopted from H24 and N24 to ensure catalogue completeness and suppress systematics. They also determine the AGN-dominated source population that sets the measured bias.
  • Redshift bin width and multipole window = Delta z = 0.06; 50 < ell < 500; Delta ell = 16
    Analysis choices made so that BAO wiggles are resolved in projection and the Limber approximation is valid. They were validated on mocks.
  • Nonlinear BAO damping Sigma_nl = 5.5 Mpc/h (fixed)
    Fixed to the eBOSS LRG value from Bautista et al. 2018. The authors tested 2 to 8 Mpc/h and report little impact on the cross-correlation.
  • Multi-component source fraction in radio mocks = up to 25 percent
    A hand-set fraction of the LoTSS mock sources is split into double or triple components to mimic resolved radio morphology, based on the LoTSS DR1 value-added catalogue fraction.
assumptions (8)
  • domain assumption The LoTSS DR2 wide-field redshift distribution p(z) is represented by the LOFAR Deep Fields distribution.
    Sect. 2.3 and Fig. 3: p(z) from Duncan et al. 2021 and H24 is used as fixed input for the theoretical C_ell and mock generation. If the wide-field distribution differs, the inferred bias shifts, and this uncertainty is not propagated.
  • domain assumption eBOSS LRG bias b(z) is calibrated from EZmock simulations.
    Sect. 2.3: b(z) for eBOSS is obtained from Pg(k)/Pm(k) of 1000 EZmocks and used to fix the eBOSS bias in the cross-correlation fit. A wrong eBOSS bias transfers into the measured LoTSS bias.
  • domain assumption Galaxy bias is linear, deterministic, and scale-independent: delta_g = b(z) delta_m.
    Eq. 6 and the window function in Eq. 9 assume a simple bias relation. Scale dependence and stochasticity are not modeled, although the broadband polynomial terms partly absorb them in the BAO fit.
  • domain assumption Shot noise between the two surveys is uncorrelated.
    Sect. 2.2.1 and 2.2.2: the cross-power spectrum needs no shot-noise subtraction because systematics between independent surveys are assumed uncorrelated. Shared calibration errors or source confusion would violate this assumption.
  • domain assumption FLASK lognormal mocks provide an unbiased covariance and pipeline validation.
    Sect. 3: 1000 correlated lognormal mocks are used for the covariance and model selection. The authors note the results are within 1 percent of Gaussian covariance at ell > 50, but lognormal mocks cannot capture unknown survey-specific systematics.
  • standard math Limber approximation is accurate for this analysis.
    Sect. 2.2.2: the spherical Bessel function is replaced by a delta function at kr = ell + 1/2. The approximation is validated against CAMB without Limber on mocks, so this is standard and low risk.
  • domain assumption The no-wiggle test statistic Delta chi^2_nw is approximately chi-square distributed with one degree of freedom.
    Sect. 4.2: p-values are derived from Delta chi^2_nw = 5.02, 7.27, and 16.28, while the alpha posterior is non-Gaussian with KS D > 0.7. This assumption may overstate the BAO detection significance.
  • standard math Hartlap correction makes the inverse mock covariance unbiased.
    Sect. 3.1: the inverse covariance from N = 1000 mocks is rescaled by (N-1)/(N-p-1), a standard correction for noise in covariance estimation.

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Cite this review

Pith. "Pith review of Cosmology from LOFAR Two-metre Sky Survey Data Release 2: Cross-correlations with luminous red galaxies from eBOSS." pith.science (2026). https://pith.science/paper/HF7CYIKW

@misc{pith2026250420722,
  author       = {Pith},
  title        = {Pith review of: Cosmology from LOFAR Two-metre Sky Survey Data Release 2: Cross-correlations with luminous red galaxies from eBOSS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HF7CYIKW}},
  note         = {Machine review of arXiv:2504.20722}
}
abstract

We cross-correlated galaxies from the LOw-Frequency ARray (LOFAR) Two-metre Sky Survey (LoTSS) second data release (DR2) radio source with the extended Baryon Oscillation Spectroscopic Survey (eBOSS) luminous red galaxy (LRG) sample to extract the baryon acoustic oscillation (BAO) signal and constrain the linear clustering bias of radio sources in LoTSS DR2. In the LoTSS DR2 catalogue, employing a flux density limit of $1.5$ mJy at the central LoTSS frequency of 144 MHz and a signal-to-noise ratio (S/N) of $7.5$, additionally considering eBOSS LRGs with redshifts between 0.6 and 1, we measured both the angular LoTSS-eBOSS cross-power spectrum and the angular eBOSS auto-power spectrum. These measurements were performed across various eBOSS redshift tomographic bins with a width of $\Delta z=0.06$. By marginalising over the broadband shape of the angular power spectra, we searched for a BAO signal in cross-correlation with radio galaxies, and determine the linear clustering bias of LoTSS radio sources for a constant-bias and an evolving-bias model. Using the cross-correlation, we measured the isotropic BAO dilation parameter as $\alpha=1.01\pm 0.11$ at $z_{\rm eff}=0.63$. By combining four redshift slices at $z_{\rm eff}=0.63, 0.69, 0.75$, and $0.81$, we determined a more constrained value of $\alpha = 0.968^{+0.060}_{-0.095}$. For the entire redshift range of $z_{\rm eff}=0.715$, we measured $b_C = 2.64 \pm 0.20$ for the constant-bias model, $b(z)=b_C$, and then $b_D = 1.80 \pm 0.13$ for the evolving-bias model, $b(z) = b_D / D(z)$, with $D(z)$ denoting the growth rate of linear structures. Additionally, we measured the clustering bias for individual redshift bins.

Figures

Figures reproduced from arXiv: 2504.20722 by the authors.

Figure 1
Figure 1. Footprint covered by the LoTSS DR2 (in orange) and eBOSS LRGs NGC(in blue), plotted against right ascension (RA) and declination (DEC). This visualisation highlights the significant overlap between the two surveys, which allows for a cross-correlation analysis. The mask applied on the LoTSS DR2 data (in pink shaded region with black edge) is also shown. . P p np/ P p wp, following the method of optimal inverse-varia… view at source ↗
Figure 2
Figure 2. Flowchart of this work. Left panel: Analysis (in light yellow region), representing the process of using real survey data to measure the angular power spectrum. Right panel: Modelling (in light blue region), which consists of generating mock catalogues and computing the theoretical angular power spectrum. The measured Cℓ , the theoretical prediction, and the covariance matrix (computed from 1000 mock catalogues) are… view at source ↗
Figure 3
Figure 3. Upper panel: Model prediction of the bias function b(z) for eBOSS and LoTSS DR2 surveys. The vertical dotted lines show the redshift range of eBOSS LRGs. Lower panel: Redshift distribution of LoTSS radio sources as inferred from the exquisite multi-wavelength coverage of LoTSS Deep Fields (see Duncan et al. 2021; Hale et al. 2024; Bhardwaj et al. 2024 for details). NDF represents the total number of galaxies in LOFA… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: eBOSS auto-angular power spectrum computed from mock and real catalogue in different redshift bins. Presented green curves are the mean Cℓ values of the 1000 mocks, the black dots with errorbars rep￾resent the measured Cℓ from the real catalogue. The errors are obtaine…
Figure 6
Figure 6. Figure 6: Correlation matrices for the eBOSS auto-correlation and LoTSS×eBOSS cross-correlation angular power spectrum measured from the mock catalogues in four redshift slices shown in the legend. In each block, the angular scale interval is ∆ℓ = 16 in the range of 50 < ℓ < 500…
Figure 7
Figure 7. Figure 7: Correlation matrix for the eBOSS auto-correlation and LoTSS×eBOSS cross-correlation angular power spectrum measured from the mock catalogues in the redshift range of 0.6 < z < 1. In each block, the angular scale interval is ∆ℓ = 16 in the range of 50 < ℓ < 500. and obs…
Figure 8
Figure 8. Figure 8: , the cross-correlation errors are large, and the BAO wig￾gles in the angular power spectrum are relatively weak. This situ￾ation can lead to slight overfitting of the parameter, where some noise fluctuations in the cross-correlation measurements might be misinterprete…
Figure 9
Figure 9. Figure 9: Best-fit cross angular power spectrum in the first redshift bin: 0.60 < z < 0.66, data measurements (green) compared with the fitting results (black), normalised with the no-wiggle Cℓs. 10 0 4 × 10 1 6 × 10 1 2 × 10 0 3 × 10 0 C / C , n w LoTSS × eBOSS + eBOSS × eBOSS …
Figure 11
Figure 11. Figure 11: Best-fit LoTSS × eBOSS cross angular power spectrum com￾bining four redshift bins, data measurements (green) compared with the fitting results (black), normalised with the no-wiggle Cℓs. The quantity χ 2 no-wiggle represents the chi-squared value ob￾tained from fittin…
Figure 10
Figure 10. Figure 10: Best-fit LoTSS × eBOSS + eBOSS auto angular power spec￾trum in the first redshift bin: 0.60 < z < 0.66, data measurements (green) compared with the fitting results (black), normalised with the no-wiggle Cℓs. 10 0 4 × 10 1 6 × 10 1 2 × 10 0 3 × 10 0 C / C , n w LoTSS ×…
Figure 12
Figure 12. Figure 12: BAO dilation parameter α i.e. the ratio of DA/rd to fiducial ones measured in this work (orange) compared to previous works. Pre￾sented are LoTSS × eBOSS in redshift bin 0.6 < z < 0.66 (orange star), LoTSS × eBOSS combining all redshift bins (orange triangular). Other…
Figure 13
Figure 13. Figure 13: Bias values measured in this work and compared with previous studies. The evolving bias model derived from this work (0.6 < z < 1) is shown as a dashed blue line with a shaded error band, while the evolving bias model from H24 is shown as a dot-dashed orange line with…

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