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XRISM Spectroscopy of Variable Accretion-driven Disk Winds in NGC 4151: When, Where, and How Fast Outflows are Launched

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The fastest winds in NGC 4151 are transient, appearing about 10,000 seconds after X-ray flares and in low-flux hard states, which places their launch site within roughly 60 gravitational radii of the black hole and favors magnetic driving.

desk verdict A careful and genuinely useful variability-selected XRISM study of NGC 4151's winds, but the headline '10 ks response' is a window width, not a measured lag, and the compact 60 r_g conclusion is correspondingly shaky. read the letter →

arxiv 2608.11315 v1 pith:M3SCKIPY submitted 2026-08-11 astro-ph.HE

Xin Xiang , Jon Miller , Missagh Mehdipour , Ehud Behar , W. Niel Brandt , Laura Brenneman , Luigi Gallo , Elias Kammoun
show 7 more authors
Peter Kosec Liyi Gu Doyee Byun Richard Mushotzky Stephane Paltani Elisa Costantini Abderahmen Zoghbi
This is my paper · ORCID
classification astro-ph.HE
keywords activegalacticnucleiAGNwindsultra-fastoutflowsX-rayspectroscopyNGC4151blackholeaccretionabsorptionmeasuredistributionvariable
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 14 XRISM observations of the nearby Seyfert galaxy NGC 4151, this paper asks when, where, and how its accretion-disk winds are launched. It finds that slow “warm absorber” winds are always present, but the fastest outflow phases—very fast and ultra-fast outflows—are strongest in the 10,000-second window immediately after X-ray flares and in low-flux, spectrally hard states. That 10 ks response implies a compact launching region, at most about 60 gravitational radii from the black hole. The absorption measure distribution and the large outflow momentum rates indicate that these fast winds are magnetically driven and locally clumpy, with radiation pressure playing a secondary role.

What carries the argument

The load-bearing instrument is the set of seven variability-selected spectra: four time windows (Flare, Postflare, After, Hard-dip) and three hardness–intensity states (High-Soft, Low-Soft, Low-Hard). The timing device is the Postflare window—a fixed 10 ks interval immediately after each flare, retained only while the count rate stays below the flare peak. Comparing wind strength across these windows converts the 10 ks delay into a causal light-crossing scale of about $60\,GM/c^2$, which is the compactness argument for the launch site. The absorption measure distribution, parameterized as $\log N_{\rm H} = m\log\xi + b$, then connects the observed column–ionization trend to a large-scale density profile and to the magnetocentrifugal wind picture.

What would settle it

Compare wind absorption strength in post-flare windows of different lengths: if a 20–30 ks post-flare window shows equally strong or stronger UFO absorption, the 10 ks timescale is an artifact of window choice rather than a physical response. Alternatively, a lag analysis with time bins much shorter than 520 s would show whether the Fe K absorption indeed peaks 10 ks after continuum flares.

Watch

Extended reading notes

Core claim

The central discovery is that the fast wind in NGC 4151 is not a steady structure but a transient, flare-triggered one. In spectra selected for the 10 ks after flare peaks, the wind shows its richest structure: two warm absorbers, one very fast outflow, and two ultra-fast outflows, with the fastest component detected only there and in low-flux hard states. The 10 ks delay maps to a light-crossing scale of roughly $60\,GM/c^2$, among the shortest flare–wind response timescales reported in an AGN, so the absorbing gas must be close to the corona that produces the flare. The paper argues from the AMD slope, close to the $n(r)\propto r^{-1.5}$ expectation of a magnetocentrifugal wind, and from momentum rates exceeding the radiation momentum supply, that magnetic driving dominates, while local clumpiness may be shaped by radiation pressure.

Load-bearing premise

The headline 10 ks response time is defined by a fixed post-flare window chosen by the authors; if the true physical delay between flare and wind strengthening is not 10 ks, or if the appearance of absorption tracks line-of-sight coverage rather than a causal response, the compact $\sim 60\,GM/c^2$ launch radius and the timing conclusions change.

Editorial extensions

If this is right

  • Fast winds in sub-Eddington Seyferts are intermittent rather than persistent: feedback-level kinetic power, around 0.3–0.5% of $L_{\rm Edd}$, is reached only occasionally, not continuously.
  • The 10 ks flare–wind response places the fast wind within roughly 60 gravitational radii, so high-cadence monitoring of similar AGN can directly resolve the causal chain from coronal flare to wind enhancement.
  • The persistent warm absorbers are best understood as failed or circulating winds, energetically weak, while the UFOs dominate the kinetic power and remain the plausible feedback channel.
  • The AMD slope and momentum-rate arguments favor magnetically driven, locally clumpy winds, suggesting MHD disk-wind models rather than pure radiation-pressure driving as the primary framework.
  • The intrinsic “hot” obscurer tracks the global spectral state, implying that the observed “softer when brighter” behavior is partly shaped by obscuration variability, not only by continuum changes.
  • Future time-dependent photoionization modeling and lag analyses could distinguish whether the post-flare visibility of the fast wind reflects physical launching, recombination, or line-of-sight motion of clumpy gas.

Reading between the lines

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

  • If the 10 ks delay is truly causal, a lag search between the hard-band continuum and the Fe K absorption lines should recover the same timescale at much finer time resolution than the 520 s bins used here.
  • The CINDICITY coordinate, defined as the first principal component of the hardness–intensity diagram, could be ported to other AGN and instruments to compare wind visibility states across sources.
  • Coordinated radio and X-ray monitoring could test whether the flare–post-flare cycle that launches the fast wind also couples to jet ejection, given the preference of VFOs for harder, lower-flux states.
  • The paper leaves open whether the blue-shifted Fe K excess is wind emission or the blue wing of relativistic disk reflection; a self-consistent reflection fit to the event-resolved spectra would settle that degeneracy.
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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 / 4 minor

Summary. The paper analyzes 14 XRISM/Resolve observations of NGC 4151 (0.9 Ms total exposure) by constructing seven spectra selected either by local variability phase (Flare, Postflare, After, Hard-Dip) or by global hardness/intensity state (HS, LS, LH). Using photoionization models in SPEX, the authors identify two persistent warm-absorber zones and transient very-fast and ultra-fast outflow components. The central claims are that the fast winds are strongest roughly 10 ks after flares and in low-flux, hard states; that this 10 ks timescale corresponds to a compact scale of about 60 r_g, locating the wind near the corona; and that the absorption measure distribution and outflow momentum rates favor magnetic driving with local clumpiness. The paper also introduces a new HID-based scalar, CINDICITY, and reports extensive statistical testing, including component-removal significance, AIC comparisons, constant-column tests, and Spearman correlation scans.

Significance. If confirmed, the paper would provide one of the shortest flare-wind response timescales reported in an AGN and would directly constrain where fast disk winds are launched. The dataset is unique: 14 high-resolution XRISM/Resolve observations of a single bright Seyfert galaxy, analyzed with a consistent multi-zone photoionization framework. The statistical treatment is a genuine strength: component-removal tests with AIC, constant-column variability tests, and systematic Spearman scans go well beyond simple line detection. The AMD slope and the momentum-rate argument are largely independent of the timing interpretation and support a magnetically driven, clumpy fast wind. However, the headline '10 ks response' is inherited from the bin width of the Postflare selection window rather than from a measured lag, and the constant-column test for the fastest UFO component is statistically inconclusive. These issues directly affect the 'when' and 'where' conclusions, so the paper's significance as written is lower than its abstract claims.

major comments (3)
  1. [§3.1, §4.2, §5] The central claim that the fastest winds respond on a ~10 ks timescale is not supported by a lag measurement. In §3.1, the Postflare window is defined as a fixed 10 ks interval immediately following a ±5 ks flare interval and is retained only if the count rate stays below the flare peak; the After window is an analogous 10 ks interval starting 10 ks later. The '10 ks' is therefore the width of the selection window, and the Postflare spectrum actually samples roughly 5–15 ks after the flare peak, not a measured delay. The abstract states that 'Ten kiloseconds is among the shortest flare–wind response timescales reported in an AGN', and §3.5/§4.2 use the same 10 ks as a light-crossing scale of 60 r_g to locate the wind near the coronal region. These claims require a measured or modeled lag. §4.3 itself states that recombination, changing illumination, and line-of-sight motion 'cannot be separated from the spectra alone' and defers to 'a dedicated variability and lag analysis.' The comparison with the After window makes a delayed response plausible, but the specific 10 ks value is an analysis choice. Please either perform a cross-correlation/lag analysis or a time-resolved spectral series with variable bin sizes, or reframe the 10 ks as the adopted sampling window and an upper limit, and adjust the 'when'/'where' conclusions accordingly.
  2. [§3.3.4, Table 2] The constant-column test does not support the claim that the fastest UFO (pion#5) is transient. In Table 2, the fixed-column model for pion#5 gives ΔC = −19 with ΔAIC = 2, meaning the model with a single column density in all seven windows is statistically indistinguishable from the variable-column final model. The text acknowledges ΔC = −19 but dismisses it because pion#5 is not independently detected in four spectra. However, the component-removal significance in individual windows and the constant-column test answer different questions; as reported, the data do not prefer a variable column for pion#5. This weakens the §3.3.3 statement that the fastest UFO 'appears' in the Postflare spectrum and is absent before and after. The transient-wind claim for the postflare enhancement should rest on the VFO and pion#4, whose ΔAIC values are large, or the pion#5 test should be repeated with a model that allows a constant column plus a variable additional component.
  3. [Table 3, §3.3.2] Several parameters in Table 3 are frozen or at hard limits, and this affects an interpretive comparison. In particular, the VFO component pion#3 has σv = 1000 km/s with zero positive error in the Flare, Postflare, After, and Hard-Dip windows, and logξ and v_z are frozen in the HS and LS columns (Table 3 note: 'Some values are at the imposed hard limit if it has errors of zero'). Section 3.3.2 contrasts the 'relatively high velocity broadening' of the VFO in Postflare (σv ~ 1000 km/s) with the lower broadening in LH (σv ~ 300 km/s), but the Postflare value is pegged at its upper boundary. Please report which parameters are at physical versus numerical limits, list the actual boundary values, and test whether the broadening difference persists when the boundary is relaxed; also clarify how frozen parameters are counted in the degrees of freedom of the component-removal and AIC tests in Appendix A.
minor comments (4)
  1. [§3.1, Figure 8] Because the Flare interval is defined as ±5 ks around the peak and the Postflare window begins immediately after the flare, the effective sampling is 5–15 ks after the peak; stating this explicitly in the text and in the Figure 8/15 labels would prevent readers from equating the 10 ks bin width with a measured delay.
  2. [Appendix B, Appendix C] CINDICITY is constructed from the same count-rate and hardness variables used to define the HS/LS/LH regions, so the Spearman correlations between CINDICITY and L_bol (ρ = 0.79) and N_H,hot (ρ = −0.96) in Appendix C are partly built in by construction; the text should state this caveat or use an independent coordinate for validation.
  3. [§3.2] The blackbody peak temperature is given as 'kT = 2×16.8 eV'; if this is not a typographical artifact, please define the combination and provide the fixed value in a single consistent notation, since the current rendering is confusing.
  4. [Table 3] The 'Expected C-values' row repeats 399±28 for all seven windows; please specify how this expectation was computed and whether it is the same global value for each window or should differ with exposure and binning.

Circularity Check

1 steps flagged · score 4.0 of 10

The '10 ks response' is the predefined width of the Postflare bin, not a measured lag; the 60 r_g launch radius is derived from that bin width.

  1. self definitional [Section 3.1 (event-type definitions) and Section 3.5 (compact limiting scale); also abstract and Section 4.2]
    "Initial post-flare intervals—Postflares: For every flare interval, we defined the initial post-flare interval as the 10 ks period immediately following the end of the flare. ... For reference, a 10 ks light-crossing time corresponds to 60 r_g for NGC 4151. If the Postflare VFOs and UFOs are located on this compact limiting scale, the ionization parameter implies densities ..."

    The paper's headline claim that the fastest winds strengthen '10 ks after the peak of flares' and the derived 'where' conclusion of a compact ~60 r_g launch site are built on a fixed bin width, not on a measured time lag. The Postflare window is defined by construction as a 10 ks interval immediately following the ±5 ks flare window, so the '10 ks response' is the predefined width of the bin (sampling roughly 5–15 ks after the peak), not a delay estimated from the data. Section 3.5 then takes this same predefined 10 ks as a 'causal timescale' and converts it to r = cΔt = 60 r_g, making the compact radius an arithmetic consequence of the bin definition.

full rationale

The central derivations that are independent of the timing claim—the column-density variability tests against constant-column models, the AMD slopes, and the momentum-rate comparisons—are self-contained and do not reduce to their inputs. The circularity burden is concentrated in the 'when' and 'where' narrative. The 10 ks value is introduced in Section 3.1 as the analyst-defined length of the Postflare window, and the abstract and Section 4.2 then treat it as a measured flare–wind response timescale. The 60 r_g compact scale in Section 3.5 is simply the light-crossing distance of that predefined bin width, so the 'most compact causal limiting scale' is not an independent result. However, the paper explicitly acknowledges the degeneracy in Section 4.3 and frames the causal interpretation as one of several possibilities, which reduces the severity. No load-bearing self-citation chain or uniqueness-imported-from-authors pattern is present; citations to Paper I and other prior work are for modeling conventions and external context. The AMD and momentum arguments for magnetic driving rest on the fitted spectral parameters and standard formulae, not on the 10 ks bin. Overall, the paper has one significant self-definitional step affecting the headline timescale and the compact-radius inference, while the bulk of the spectral analysis remains independently grounded.

Assumptions & free parameters 8 free parameters · 8 assumptions · 1 invented entities

The central claims rest on a large set of fitted wind and continuum parameters, plus assumptions about photoionization equilibrium, fixed solar abundances, fixed covering fraction, source geometry, and event-window definitions. The only new invented construct is CINDICITY, a data-defined index with no external calibration.

free parameters (8)
  • Per-window pion zone N_H (five zones x seven windows) = 10^22.4 to 10^23.5 cm^-2 for detections; upper limits otherwise (Table 3)
    Column densities are freely fitted and are the primary variability tracers; all timing and energetics conclusions depend on their changes.
  • Per-window pion zone log xi (five zones x seven windows) = 2.5-3.8 (Table 3)
    Ionization parameters are free; they enter the AMD, r_max, density, and filling-factor estimates.
  • Per-window pion zone v_z and sigma_v (five zones x seven windows) = v_z -200 to -48,700 km/s; sigma_v 100-5,000 km/s (Table 3)
    Velocities define WA/VFO/UFO classes; the 10 ks flow-time and escape-speed arguments rely on them.
  • Continuum parameters per window: Gamma, DeltaGamma, E0, normalization = Gamma 1.68-1.77; DeltaGamma -0.47 to -0.26; E0 8.6-9.8 keV; norm 2.0-2.9e7 (Table 3)
    Continuum shape determines Lion and all derived radii and energetics.
  • Hot partial-coverer parameters per window: N_H, fcov, T = N_H 1.3-2.0e23 cm^-2; fcov 0.85-0.88; T 3-5 eV (Table 3)
    The obscurer affects the observed continuum and the 'softer when brighter' interpretation.
  • Absorber covering fraction fixed at fcov=0.5 = 0.5 (fixed)
    Set uniformly from the Tombesi et al. 2010 population study; mass and energy rates scale linearly with fcov.
  • Pion emission components: Omega_emis, v_z, sigma_v_gau (pion emis #2/#4, blue-emis) = Omega 0.04-0.38; v_z to -11,700 km/s; widths 0-2,040 km/s (Table 3)
    Free parameters used to infer re-emission geometry and filling factors.
  • Volume filling factor f_v (nominal = 1; corrected using f_v,min) = 1 nominal; f_v,min as low as 3.8e-4 for fast UFO
    Not directly fit; the minimum is computed from radius inequalities and applied to energetics.
assumptions (8)
  • domain assumption Photoionization equilibrium for all wind zones
    SPEX pion assumes steady-state photoionization; the paper estimates recombination times shorter than 10 ks, but this is still a model assumption. See Section 3.2.
  • ad hoc to paper Fixed solar abundances and fixed fcov=0.5 for absorption zones
    Adopted from Paper I for consistency; no abundance fitting is done, and fcov scales all mass and energy rates. See Section 3.2.
  • domain assumption Static FUV/UV blackbody component from HST STIS
    kT and area are fixed; the ionizing luminosity depends partly on this component, which is assumed non-varying on the timescales probed. See Sections 3.2 and 4.3.
  • domain assumption Line-of-sight stratification of pion absorbers from inner fast to outer slow zones
    The model ordering assumes nested absorbing layers; the attenuation of outer zones by inner zones follows from this ordering. See Section 3.2.
  • domain assumption Radial thickness and escape-velocity inequalities (Eqs. 2-4)
    r_max requires Delta-r <= r; r_min assumes the observed velocity reaches the local escape velocity; all filling factors and radii follow from these assumptions. See Section 3.5.
  • domain assumption AMD density-profile mapping n(r) proportional to r^-alpha with alpha = (1+2m)/(1+m)
    Interpreting the log N_H versus log xi slope as a radial density profile assumes a large-scale smooth wind; the small-scale clumpy alternative gives different effective indices. See Section 3.6.1.
  • domain assumption Black hole mass MBH = 3.4e7 M_sun from Bentz and Katz
    Converts the 10 ks timescale to 60 r_g; any mass error shifts all radii and compactness conclusions. See Section 1.
  • ad hoc to paper Event selections: Savitzky-Golay filter, 1-sigma thresholds, 10 ks flare/postflare windows, HID divisions at mean values
    The windows are algorithmically defined; the 10 ks response timescale is set by this definition rather than measured independently. See Section 3.1.
invented entities (1)
  • CINDICITY
    purpose: Single scalar combining count rate and hardness to track spectral state along the main axis of the hardness-intensity diagram
    Derived from the same time-resolved dataset and used as the independent variable in correlations; it has no external benchmark or falsifiable handle outside this paper.

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Pith. "Pith review of XRISM Spectroscopy of Variable Accretion-driven Disk Winds in NGC 4151: When, Where, and How Fast Outflows are Launched." pith.science (2026). https://pith.science/paper/M3SCKIPY

@misc{pith2026260811315,
  author       = {Pith},
  title        = {Pith review of: XRISM Spectroscopy of Variable Accretion-driven Disk Winds in NGC 4151: When, Where, and How Fast Outflows are Launched},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M3SCKIPY}},
  note         = {Machine review of arXiv:2608.11315}
}
abstract

X-ray observations probe the inner accretion flow within active galactic nuclei, revealing the highest gas column densities and fastest winds. The most diverse winds yet revealed with the Resolve calorimeter spectrometer aboard XRISM are found in NGC~4151, a nearby Seyfert-1 AGN that may qualify as a ``changing-look'' source (CLAGN). Herein, we report on wind variability in 14 XRISM observations of NGC~4151, summing to 0.9~Ms of exposure over a period of 395 days. We examined the dependence of key wind parameters on hardness and intensity selections, and as a function of time relative to flaring and dip events. The results suggest a globally organized but locally complex wind structure. Slow ``warm absorber'' components (WAs; $v_{\rm{out}} \sim 100-1000~\rm{km~s^{-1}}$) are always observed and likely represent failed winds at radius of $10^4 - 10^5 GM/c^2$, within the inner wall of the torus. In contrast, ``very fast'' and ``ultra-fast'' outflows (VFOs and UFOs; $v_{\rm{out}} \sim 10^3-10^4~\rm{km~s^{-1}}$, $v_{\rm{out}} \sim 0.033-0.33~c$) are strongest 10~ks after the peak of flares, and during periods with low flux. Ten kiloseconds is among the shortest flare--wind response timescales reported in an AGN, suggesting that the winds are observed close to the launching site. The absorption measure distribution (AMD) and the large outflow momentum rates suggest that the high-velocity flows visible in the Fe~K band are magnetically driven, while locally clumpy, likely owing to radiation pressure; one or both of these mechanisms may be enhanced following a flare and most visible during low-flux windows.

Figures

Figures reproduced from arXiv: 2608.11315 by the authors.

Figure 1
Figure 1. Top Panels: Trailed spectra. Middle Panels: full band (2.4–17.4 keV) lightcurves. Bottom Panels: hardness ratios (8.8–11.8 keV / 3.0–4.0 keV) [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. The Hardness-Intensity diagram: full band count rate versus Hard/Soft ratio. The red vertical and the blue horizontal lines mark the global mean of the hardness ratio and full-band count rates. The histogram shows the Time-bin Fraction of the local Event Types within each spectral region [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Upper panel: Spectra corresponding to time-selected phases (Flare, Postflare, After, and Hard-dip) with their best-fit models ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Transmission profiles of the individual “pion" components for spectra of time-selected phases, computed by dividing the final model by the model with the specified component removed. Note, the marginally significant components (1.5σ < D.S. < 3σ) include UFO1 in the fla…
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Transmission profiles of the individual “pion" components for spectra of HID-selected regions [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: The spectral and wind properties as a function of event type. The top left panel shows the mean count rate and hardness ratio. The top right panel shows the CINDICITY. The lower four panels show the wind column density (log NH), ionization parameter (log ξ), line-of-si…
Figure 9
Figure 9. Figure 9: Left panel: comparison of the escape-based lower limit to the launching radius, rmin/ cos2 θ, and the ionization-based upper limit, rmax, for each outflow component, in units of GM/c2 . The dashed line marks equality. Circles, triangles, and stars denote WAs, VFOs, and…
Figure 10
Figure 10. Figure 10: Upper panel: mass outflow rate, M /f ˙ v,min, as a function of event type. Lower panel: kinetic power, E˙ k/fv,min, as a function of event type. Circles, triangles, and stars denote WAs, VFOs, and UFOs, respectively. Filled markers show the nominal values assuming fv …
Figure 11
Figure 11. Figure 11: Hardness–intensity diagram for all time bins, colored by CINDICITY. The horizontal and vertical lines mark the boundaries used to define the global spectral states: High–Soft (HS), Low–Soft (LS), and Low–Hard (LH). Different symbols denote the time-selected intervals …
Figure 12
Figure 12. Figure 12: Top panel: bolometric luminosity, Lbol, as a function of CINDICITY. Bottom panel: intrinsic obscurer column density, NH,hot (black circles; left axis), and total wind column density, ΣNH,wind, for significant (D.S > 3σ) wind components (red squares; right axis), as a …
Figure 13
Figure 13. Figure 13: Outflow momentum rate versus radiation mo￾mentum flux, for all absorption components. Circles, trian￾gles, and stars denote WAs, VFOs, and UFOs, respectively. Filled markers show the nominal values assuming fv = 1, while the lighter markers show the values after apply…
Figure 14
Figure 14. Figure 14: Pairwise relations among the fitted properties of all significant absorption components (D.S. > 3σ) from the seven time-selected and HID-selected spectra analyzed in this work. Circles, triangles, and stars denote WAs, VFOs, and UFOs, respectively. Colored lines show …
Figure 15
Figure 15. Figure 15: Schematic illustration of the proposed wind geometry and visibility windows in NGC 4151. The WAs form an extended, partially failed or circulating component at large radii and are present in all selections, while the VFO and UFO phases are more transient and depend on…
Figure 16
Figure 16. Figure 16: Spearman rank-correlation matrix for the integrated quantities of the seven time-selected and HID-selected spectra analyzed in this work. Wind properties are calculated from significant components (D.S > 3σ). Each cell lists the correlation coefficient ρ (upper value)…
Figure 17
Figure 17. Figure 17: Spearman rank-correlation matrix for all significant (D.S > 3 σ) individual absorption components in seven time￾selected and HID-selected spectra analyzed in this work. Each cell lists the correlation coefficient ρ (upper value) and the corresponding two-sided p-value…

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