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Improved upper limits on the 21-cm signal power spectrum at $z=17.0$ and $z=20.3$ from an optimal field observed with NenuFAR

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Four nights of NenuFAR observations of a carefully chosen field produce the deepest 21-cm power spectrum upper limits yet from the Cosmic Dawn, more than an order of magnitude below all previous limits at these redshifts.

desk verdict A careful, genuinely improved upper-limit paper from NenuFAR whose headline numbers are solid, though the quoted limits inherit a real but not fatal caveat about the ML-GPR signal model. read the letter →

arxiv 2507.10533 v2 pith:BWIEX55D submitted 2025-07-14 astro-ph.CO astro-ph.IM

S. Munshi , F. G. Mertens , J. K. Chege , L. V. E. Koopmans , A. R. Offringa , B. Semelin , R. Barkana , J. Dhandha
show 14 more authors
A. Fialkov R. Mériot S. Sikder A. Bracco S. A. Brackenhoff E. Ceccotti R. Ghara S. Ghosh I. Hothi M. Mevius P. Ocvirk A. K. Shaw S. Yatawatta P. Zarka
This is my paper
classification astro-ph.COastro-ph.IM
keywords 21-cmcosmologyCosmicDawnpowerspectrumupperlimitsNenuFARradiointerferometryforegroundsubtractionGaussianprocessregressionEDGESexoticmodels
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

This paper reports the deepest upper limits so far on the 21-cm signal power spectrum from the Cosmic Dawn, using four nights of NenuFAR observations of the NT04 field: a 2σ limit of $\Delta^2_{21} < 4.6\times10^5\,\mathrm{mK}^2$ at $k = 0.038\,h\,\mathrm{cMpc}^{-1}$ at $z=20.3$, and $\Delta^2_{21} < 5.0\times10^6\,\mathrm{mK}^2$ at $k = 0.041\,h\,\mathrm{cMpc}^{-1}$ at $z=17.0$. The $z=20.3$ result improves on all previous Cosmic Dawn power spectrum limits by more than an order of magnitude, and reduces the excess variance over the earlier north celestial pole analysis by roughly a factor of 50. The authors attribute the improvement to selecting an optimal field that minimizes sidelobe leakage from bright off-axis sources, plus pipeline upgrades in A-team and 3C source subtraction, RFI mitigation in the uv plane, and an elevation cut that confines foregrounds to low line-of-sight modes. Comparing the limits with simulated exotic 21-cm signals, the $z=20.3$ limit begins to exclude only the most extreme models (those predicting global signals stronger than the EDGES detection); an order-of-magnitude deeper limit would start to constrain EDGES-compatible signals. The paper argues that the excess variance in the $z=20.3$ bin is largely incoherent across nights, so continued integration could push the limits substantially deeper.

What carries the argument

The argument rests on a multi-stage calibration and foreground-removal pipeline. First, direction-dependent calibration with adaptive solution intervals subtracts the bright A-team sources (Cas A, Cyg A, and others) as they move through NenuFAR's primary-beam grating lobes, using apparent sky models built from a simulated primary beam. A more conservative 3C-source subtraction avoids overfitting on the short baselines used for the power spectrum, and clustered target-field sources are subtracted down to the confusion limit. Two data-selection steps then confine foregrounds: five uv cells around the $u=0$ line (where stationary RFI accumulates for a non-NCP phase centre) are flagged, and only time ranges with phase-centre elevation above $50^\circ$ are kept, which keeps the full-sky horizon line shallow. Finally, machine-learning-enhanced Gaussian process regression (ML-GPR) models the residual data as the sum of foreground, 21-cm signal, excess, and noise Gaussian processes: the foreground kernels are RBF, the excess uses two Matern 3/2 kernels, and the 21-cm kernel is a variational autoencoder (VAE) trained on 21cmFAST simulations, with its variance left free so that boosted exotic-model signals can in principle be absorbed. The GPR is run on each spectral window separately, and the residual power spectrum is estimated from an ensemble of 1000 posterior hyperparameter samples.

What would settle it

A decisive test is to inject a synthetic 21-cm signal with a deliberately short frequency coherence scale (outside the VAE latent space) into the real calibrated visibility cubes and run the GPR; if the recovered power is biased low by more than 2σ in any k-bin used for the limits, the quoted upper limits do not hold for that signal class.

Watch

Extended reading notes

Core claim

The paper's central claim is that a better-chosen target field and a refocused calibration pipeline allow NenuFAR to set the deepest 21-cm power spectrum upper limits yet obtained from the Cosmic Dawn. After calibration-based sky-model subtraction and Gaussian-process-regression foreground removal, the noise-bias-subtracted residual power spectrum gives a best 2σ upper limit of $\Delta^2_{21} < 4.6\times10^5\,\mathrm{mK}^2$ at $k = 0.038\,h\,\mathrm{cMpc}^{-1}$ in the $z=20.3$ bin, and $\Delta^2_{21} < 5.0\times10^6\,\mathrm{mK}^2$ at $k = 0.041\,h\,\mathrm{cMpc}^{-1}$ in the $z=17.0$ bin. The $z=20.3$ limit improves on all previous Cosmic Dawn power spectrum limits by more than an order of magnitude and on the earlier NenuFAR NCP analysis by roughly a factor of 50. The paper further claims that these limits begin to exclude the most extreme exotic-model 21-cm signals invoked to explain the EDGES absorption feature, and that the remaining excess variance in the $z=20.3$ bin is largely incoherent across nights, so continued integration should deepen the limits substantially.

Load-bearing premise

The GPR foreground removal assumes that none of the true 21-cm signal is absorbed by the foreground or excess kernels, meaning the signal's frequency coherence is always large enough and its shape close enough to the trained VAE to stay in the signal kernel; if part of the signal leaks into the excess or foreground components, the quoted 2σ limits would be too low.

Editorial extensions

If this is right

  • The $z=20.3$ limit is more than an order of magnitude below all previous Cosmic Dawn power spectrum limits, and roughly 50 times below the earlier NenuFAR NCP analysis at the same redshift.
  • These limits begin to exclude the most extreme exotic-model 21-cm signals — those predicting a global absorption signal stronger than the EDGES detection.
  • An order-of-magnitude deeper limit, which the paper argues is attainable because the $z=20.3$ excess variance integrates down incoherently across nights, would probe models with signal strengths comparable to EDGES.
  • The $z=17.0$ result is the deepest limit at that redshift, but it is dominated by coherent RFI-related excess variance, so longer integrations alone will not improve it much without additional RFI mitigation.

Reading between the lines

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

  • Beyond the paper: if the $z=20.3$ excess variance stays incoherent over hundreds of hours, the 2σ limit should scale roughly as the inverse square root of integration time, bringing the EDGES-compatible model range within reach of the ~500 hours of NT04 data already collected.
  • Beyond the paper: the GPR verification tests only injected signals drawn from the VAE latent space; a test with signals of deliberately short frequency coherence would directly probe whether the Matern excess kernels can absorb part of the true 21-cm signal.
  • Beyond the paper: the elevation-cut strategy suggests that future Cosmic Dawn surveys could optimise their LST scheduling to keep the phase centre high, effectively trading integration time for foreground confinement.
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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 / 3 minor

Summary. The paper reports 2σ upper limits on the 21-cm power spectrum during the Cosmic Dawn using four nights of NenuFAR observations of a newly selected NT04 field, analyzed in two spectral windows centered at z=20.3 and z=17.0. The analysis pipeline includes improved A-team and 3C source subtraction, uv-plane RFI flagging, an elevation cut to confine the foreground wedge, and machine-learning Gaussian process regression (ML-GPR, the same framework as M24) for residual foreground removal. After GPR, the authors obtain noise-bias-subtracted residual power spectra and set upper limits of Δ²21 < 4.6×10^5 mK² at k=0.038 h/cMpc for z=20.3 and Δ²21 < 5.0×10^6 mK² at k=0.041 h/cMpc for z=17.0, claiming these are the deepest Cosmic Dawn limits at these redshifts. They also present signal injection tests, an analysis of the coherence of the excess variance, and a comparison of the z=20.3 limits against simulated exotic 21-cm models.

Significance. If the quoted limits are robust, this is an important advance for 21-cm cosmology at Cosmic Dawn: the z=20.3 limit improves on previous NenuFAR/NCP results by more than an order of magnitude and begins to approach predictions of extreme EDGES-inspired models. The paper is thorough in its calibration description, uses a conservative approach by not subtracting the excess variance, and provides a useful analysis of the temporal coherence of the excess. The public pipelines (Nenuflow, pspipe), explicit calibration parameters, and signal injection tests are strengths. However, the central claim of 'deepest upper limits' is conditional on the ML-GPR model not absorbing the 21-cm signal, and the current injection tests only probe signals drawn from the same VAE latent space used in the GPR model, leaving the most important failure mode untested.

major comments (3)
  1. [§5.1–5.2 (Eqs. 1–3, Table 3, Fig. 13)] The central claim of deepest upper limits rests on the residual power spectrum after ML-GPR subtraction, in which the 21-cm component is modelled by a VAE kernel trained on 21cmFAST while two Matern 3/2 excess kernels (Kex1, Kex2; Table 3) absorb short-coherence power. A real 21-cm signal whose spectral shape lies outside the VAE latent space—e.g. a flatter or steeper power-spectrum slope than any 21cmFAST realization, or a narrow spectral feature—would be attributed to Kex or the foreground component and subtracted, biasing the residual power spectrum low. The injection tests in §5.2 draw injected signals from the same VAE latent space (x1, x2 ∈ [−2, 2]) used by the GPR signal kernel, so they cannot detect this failure mode; the tests also cover only the central part of the prior range [−4, 4] and already show 1.33% of z-scores below −2. Because the quoted z=20.3 limit at k=0.038 (4.6×10^5 mK²) is only about 2.2 times the measured residual (2.1×10^5 mK²), even a modest downward bias would invalidate the limit as an upper bound on the true 21-cm signal. I ask for out-of-sample injection tests with signals not representable by the VAE (e.g. power-law spectra of varying slope, narrow band features, or the 21cmSPACE/LICORICE models used in §7.1) and a quantification of the resulting bias at the k bins of Table 4.
  2. [§2.2] The field (NT04) and the four nights were selected after the fact using criteria directly tied to the measured power spectra: the field was identified as optimal from a survey using power spectra after subtraction of brightest sources as a metric, and the four nights were chosen 'based on superior RFI statistics' (Table 1, Fig. 2). This selection on the dependent variable can bias the quoted upper limits downward relative to a pre-defined observing strategy. To support the claim that these are the deepest limits to date, the authors should either present the corresponding limits for all four nights without selection, report limits for the full survey of fields, or quantify the selection bias (e.g. by bootstrap over the six survey fields/nights).
  3. [§5.1, Table 3] The 21-cm hyperparameters are unconstrained (x1, x2) and σ²21 has only an upper limit (< −3.208 for Z20, < −2.749 for Z17), which the text correctly interprets as no detection. However, the upper limits are not constructed from the fitted 21-cm component but from the total residual power after subtracting the posterior-mean foreground. The uncertainty on the residual therefore depends on the assumed GPR model; if the model is misspecified, the ensemble of 1000 posterior samples provides underestimates of the true systematic uncertainty. The paper should state this explicitly and, if possible, quantify the model-marginalized uncertainty, e.g. by varying the choice of excess kernels or priors and recomputing the limits.
minor comments (3)
  1. [References] The reference 'Bennett A., Simth F., 1962' contains a typo in the second author's name; it should be 'Smith'.
  2. [§2.2] The field-selection criteria are deferred to Mertens et al. (in prep.), which makes it difficult for the reader to assess the selection bias discussed above; please include the relevant selection metrics or a summary in an appendix.
  3. [Fig. 13] The caption of the left panel says the z-scores are shown as a function of 'injected signal variances', but the x-axis appears to be k; please clarify the meaning of the axis and the color/line coding.

Circularity Check

1 steps flagged · score 2.0 of 10

Upper limits are data-driven residuals; the only self-referential element is the injection-test loop, which draws test signals from the same VAE latent space used in the GPR signal kernel.

  1. self definitional [Section 5.2 (Signal injection tests), with the VAE kernel defined in Section 5.1]
    "For each spectral window, the injection test is repeated for 25 different shapes of the signal sampled uniformly within the range x1,x2 ∈ [−2, 2] from the 2D latent space of the VAE. ... a variational auto-encoder (VAE) kernel trained on simulations of the 21-cm signal is used in order to describe the signal of interest."

    The injected test signals are drawn from the same 2D VAE latent space that defines the GPR 21-cm signal kernel. The injection test therefore verifies only that GPR can recover signals the model was explicitly built to describe; it cannot detect the failure mode where a true 21-cm signal with a spectral shape outside this latent space is absorbed by the foreground or excess (Kex1/Kex2) kernels and subtracted, biasing the residual power spectrum low. The recovery success is thus a self-consistency check rather than independent validation of the assumption that the quoted 2σ limits are valid upper limits on the true 21-cm signal. The paper acknowledges this assumption in footnote 29, but this does not remove the self-referential character of the injection-test evidence.

full rationale

The central upper limits are not fitted outputs of the 21-cm model: Section 6.2 sets them as 2σ above the noise-bias-subtracted residual power spectrum after GPR foreground subtraction, and Section 5.1/Table 3 show that the 21-cm hyperparameters x1 and x2 are unconstrained while σ²(21) reaches the lower prior boundary, indicating that the 21-cm signal is not detected. The residual power spectrum is therefore a data-driven quantity, not a prediction equivalent to the VAE input. The comparison against previous limits (M24 and other instruments) is external and does not reduce to the model inputs. The only notable self-referential element is the signal-injection validation: injected signals are sampled from the same VAE latent space that defines the GPR signal kernel, so the tests confirm internal consistency but do not independently validate the limits for out-of-latent-space signal shapes. Footnote 29 explicitly flags this assumption. This is a robustness limitation rather than a circular derivation of the headline limits, so the overall circularity score is low.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The free parameters are the fitted GPR hyperparameters and the hand-chosen processing thresholds that jointly determine the residual power spectrum from which the upper limits are derived. The axioms are the modeling assumptions about the signal shape, the excess variance, the primary beam, and the horizon line that the pipeline relies on. No new physical entities are introduced.

free parameters (7)
  • Kint hyperparameters (intrinsic foreground) = Z20: log10 σ²=0.104, l=27.2 MHz; Z17: log10 σ²=0.046, l=30.7 MHz
    Table 3: fitted with nested sampling in ML-GPR; controls the smooth foreground component subtracted before power spectrum estimation.
  • Kmix hyperparameters (mode-mixing foreground) = Z20: log10 σ²=-1.657, l=0.503 MHz; Z17: log10 σ²=-1.157, l=0.582 MHz
    Table 3: fitted; models off-axis foreground leakage into the wedge.
  • Kex1/Kex2 hyperparameters (excess variance) = Z20: log10 σ²=-4.586/-3.812, l=0.045/0.251 MHz; Z17: log10 σ²=-3.163/-2.159, l=0.057/0.561 MHz
    Table 3: fitted; excess components can absorb unresolved systematics and potentially part of the 21-cm signal.
  • 21-cm VAE hyperparameters (x1, x2, σ²21) = Z20 and Z17: x1, x2 unconstrained; σ²21 hits lower prior boundary (Z20 <10^-3.208, Z17 <10^-2.749)
    Table 3: free parameters in the GPR 21-cm kernel; unconstrained indicates no detection, but the kernel shape is assumed to span all plausible signals.
  • A-team and 3C flux thresholds = 2 Jy (A-team), 10 Jy (3C)
    Sec 3.2.1-3.2.2: chosen by hand to balance calibration S/N and overfitting; affects how much off-axis power is subtracted.
  • Elevation threshold and uv-cell flagging choices = Elevation >50 deg; five uv cells along u=0 and five near Cas A flagged
    Sec 4.2-4.3: ad hoc choices that reduce foreground and RFI power before GPR; changing them changes the residual power and limits.
  • Calibration and power-spectrum baseline cuts = Calibration >40λ, limits 10-40λ; 10 or 8 target clusters
    Sec 3.2.3 and 6.2: cuts inherited or chosen to avoid signal suppression; define the k range and quality of subtraction.
assumptions (6)
  • domain assumption The VAE trained on 21cmFAST simulations describes the shape of the true 21-cm power spectrum, including exotic boosted models.
    Sec 5.1 and Fig. 11; if the true signal shape lies outside the latent space, GPR can misattribute signal to foreground or excess components.
  • ad hoc to paper The excess variance components Kex1 and Kex2, modeled as Matern 3/2 kernels, are not part of the 21-cm signal.
    Sec 5.1 Eq. (2): separation by frequency coherence scale is assumed; injection tests in Sec 5.2 are the only empirical check.
  • domain assumption The full-sky horizon line equations of Munshi et al. (2025a) correctly describe the elevation-dependent foreground wedge.
    Sec 4.3 uses these equations to justify the 50-degree elevation cut; an error here would misplace the wedge boundary.
  • domain assumption The simulated NenuFAR primary beam from Nenupy is accurate enough for apparent sky models and calibration.
    Sec 3.2.1-3.2.2; the real beam is not integrated in EveryBeam, so gain solutions must absorb beam errors, affecting residuals.
  • domain assumption Thermal noise estimated from time-differenced Stokes V provides an unbiased estimate of the noise power spectrum.
    Sec 4.1; if Stokes V contains signal or correlated systematics, noise subtraction could bias the residual power.
  • standard math Flat ΛCDM cosmology with Planck 2015 parameters is used for redshift and k conversions.
    Sec 1; standard and well-justified, minor impact on limits.

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Cite this review

Pith. "Pith review of Improved upper limits on the 21-cm signal power spectrum at $z=17.0$ and $z=20.3$ from an optimal field observed with NenuFAR." pith.science (2026). https://pith.science/paper/BWIEX55D

@misc{pith2026250710533,
  author       = {Pith},
  title        = {Pith review of: Improved upper limits on the 21-cm signal power spectrum at $z=17.0$ and $z=20.3$ from an optimal field observed with NenuFAR},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BWIEX55D}},
  note         = {Machine review of arXiv:2507.10533}
}
abstract

We report the deepest upper limits to date on the power spectrum of the 21-cm signal during the Cosmic Dawn (redshifts: $z>15$), using four nights of observations with NenuFAR. The limits are derived from two redshift bins, centred at $z=20.3$ and $z=17.0$, with integration times of 26.1 h and 23.6 h, from observations of an optimal target field chosen to minimise sidelobe leakage from bright sources. Our analysis incorporates improvements to the data processing pipeline, particularly in subtracting strong radio sources in the primary beam sidelobes and mitigating low-level radio frequency interference, yielding a 50-fold reduction in the excess variance compared to a previous analysis of the north celestial pole field. At $z=20.3$, we achieve a best $2\sigma$ upper limit of $\Delta^{2}_{21}<4.6 \times 10^5 \, \textrm{mK}^{2}$ at $k=0.038$ $h\, \mathrm{cMpc}^{-1}$, while at $z=17.0$, the best limit is $\Delta^{2}_{21}<5.0 \times 10^6 \, \textrm{mK}^{2}$ at $k=0.041$ $h\, \mathrm{cMpc}^{-1}$. These are the strongest constraints on the 21-cm power spectrum at the respective redshifts, with the limit at $z = 20.3$ being deeper by more than an order of magnitude over all previous Cosmic Dawn power spectrum limits. Comparison against simulated exotic 21-cm signals shows that while the $z=20.3$ limits begin to exclude the most extreme models predicting signals stronger than the EDGES detection, an order-of-magnitude improvement would constrain signals compatible with EDGES. A coherence analysis reveals that the excess variance is largely incoherent across nights for the $z=20.3$ redshift bin, suggesting that deeper integrations could yield significantly stronger constraints on the 21-cm signal from the Cosmic Dawn.

Figures

Figures reproduced from arXiv: 2507.10533 by the authors.

Figure 1
Figure 1. The baseline coverage of observations of the NT04 field. The different colours correspond to the four different nights of observation. 19 antennas in a hexagonal configuration, called Mini-Arrays (MAs hereafter). Most of the MAs are distributed within a 400 m diameter dense core, with a few remote MAs located at distances of a few kilo￾metres from the core. We refer the reader to Zarka et al. (2012, 2015, 2020) for … view at source ↗
Figure 2
Figure 2. RFI flagging statistics at different stages of processing. Left: The flagged RFI percentage in the highest time and frequency resolution correlated data for the two spectral windows (rows) for the four nights (columns). Right: A scatter plot of NenuFAR MA locations showing the number of nights each MA has been identified and flagged (in Z20) based on bad solutions in the A-team subtraction step. 2.2 Field and night … view at source ↗
Figure 3
Figure 3. A flowchart describing the NenuFAR 21-cm cosmology processing pipeline. The green rectangles indicate the different data levels, and the blue regions correspond to the three main sections of the pipeline. across the 11.5 MHz frequency bandwidth. The top panel in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (13 more)
Figure 5
Figure 5. Figure 5: Comparison between calibration with a fixed and adaptive solution time interval. The top row shows the XX gain amplitudes for an example station, in the direction of Cyg A, during a 1 h portion of Night 1. The middle row shows a zoomed-in view of a single 8 min time se…
Figure 6
Figure 6. Figure 6: Cleaned images of the target field after DI correction, with the sky models from Night 1 overplotted. The two panels correspond to the two spectral windows. The overplotted white curves indicate the clusters of sources which are used as separate directions when the tar…
Figure 7
Figure 7. Figure 7: Wide-field dirty images before and after calibration-based sky model subtraction. The two columns correspond to the two spectral windows. The top and bottom rows show the images before and after sky model subtraction, respectively. The NenuFAR primary beam is simulated…
Figure 8
Figure 8. Figure 8: Power spectra estimated at different data levels. The two rows correspond to the two spectral windows. The first column corresponds to the L2 data. The second and third columns show the level of power subtracted in the off-axis source subtraction and target subtraction…
Figure 9
Figure 9. Figure 9: The signature of RFI in the data. The two columns correspond to the two spectral windows. The top row shows the frequency channel differenced noise in the 𝑢𝑣 plane. The grey dashed circles indicate the baseline cut. The bottom row shows the ratio of the power spectrum …
Figure 10
Figure 10. Figure 10: The ratio of power spectra estimated from the full data to that estimated from the LST range where the phase centre elevation is above 50◦ . The two columns correspond to the two spectral windows. The black dashed lines indicate the full-sky horizon limit, correspondi…
Figure 11
Figure 11. Figure 11: Power spectrum shapes captured by the 21-cm covariance kernel in ML-GPR. The normalised power spectra of the 1000 21cmFAST simulations for both redshifts are shown in grey curves. The normalised power spectra generated by the trained VAEs at a set of uniformly spaced …
Figure 12
Figure 12. Figure 12: Cylindrical power spectra, expressed as a ratio over the thermal noise power spectrum, before and after GPR-based foreground subtraction. The two rows correspond to the two spectral windows. and covariance of the foreground component can now be estimated E (ffg) = Kfg…
Figure 13
Figure 13. Figure 13: Results of the signal injection tests performed on GPR for each spectral window. The two rows correspond to the two redshift bins. The left panels show the distribution of the z-scores as a function of 𝑘 values and injected signal variances. The black crosses with the…
Figure 14
Figure 14. Figure 14: , we compare the cylindrical power spectrum from Z20 after calibration and sky model subtraction to that of the NCP field at the same stage. Since the NT04 field integration is ∼ 2.3 times longer than the NCP observation, to leave the difference in noise power out of …
Figure 16
Figure 16. Figure 16: Cosmic dawn power spectrum upper limits from different inter￾ferometers. The range of power spectra expected from standard models (blue shaded region) and an approximate range of power spectra expected from exotic models (grey shaded region) are indicated. The 𝑘 value…
Figure 17
Figure 17. Figure 17: Coherence of the excess variance across LSTs and nights in different regions of the 𝑘⊥, 𝑘∥ space. The different columns correspond to three regions: the main lobe, the sidelobes, and the EoR window. The top row shows the average data and noise power in the cylindrical…
Figure 18
Figure 18. Figure 18: Comparison of the upper limits derived in this analysis at 𝑧 = 20.3 against simulated exotic 21-cm signals. The left panel shows the power spectra of signals simulated using 21cmSPACE and the right panel shows the power spectra obtained from the LICORICE simulations. …

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.