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A spectral stacking analysis to search for faint outflow signatures in z~6 quasars

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Stacking 26 z∼6 quasar spectra reveals a tentative broad-line outflow component, strongest for a 12-source sub-sample at 1.2–2.5σ.

desk verdict A careful full-sample stacking analysis whose sub-sample outflow claim is undermined by selecting the sub-sample on the same wing flux later used as the detection. read the letter →

arxiv 1908.11395 v1 pith:3AF7JBRB submitted 2019-08-29 astro-ph.GA

F. Stanley , J. B. Jolly , S. König , K. K. Knudsen (Department of Space , Earth , Environment , Chalmers University of Technology) This is my paper · ORCID
classification astro-ph.GA PACS 98.54.Aj98.62.Nx
keywords galaxyevolutionquasarsathighredshiftgalacticoutflows[CII]158μmlinespectralstackingALMAobservationsAGNfeedbacksubmillimetergalaxies
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

The paper asks whether fast gas outflows — a key feedback channel in galaxy evolution — are already at work in quasar host galaxies when the universe was under a billion years old (z ≈ 6). Individual [C II] 158 μm spectra of 26 ALMA-observed quasars show no outflow component, so the authors stack both extracted spectra and full spectral cubes to bring up faint broad-line wings. They find a tentative broad component in the full-sample stack (1.1–1.5σ, FWHM > 700 km/s) and a stronger one in the stack of a 12-source sub-sample (1.2–2.5σ, FWHM > 775 km/s) selected by ranking 10,000 random sub-samples. If the signal is real, roughly half of these early quasars are driving gas out of their hosts at a mean rate of about 45 solar masses per year; the authors state that the significance is below the usual detection threshold and that deeper observations are required to confirm it.

What carries the argument

The machinery is spectral-line stacking with velocity re-binning, applied both to extracted spectra (1-D) and to full spectral cubes pixel-by-pixel (3-D), and combined with a sub-sample ranking scheme. Because the [C II] lines have different intrinsic widths, each line is re-binned so that every FWHM spans the same number of channels, normalized to the narrowest line (270 km/s); this prevents width variations from manufacturing an artificial broad component, but ties the recovered broad-line width to the main-line width. Stacks are made with three weightings — uniform, inverse-variance (1/σ²_rms), and peak-flux normalized (1/S_peak) — and the broad-component significance is the summed residual within ±800 km/s after subtracting a single-component fit. The sub-sample selector draws 10,000 random sub-samples of 3–25 sources, grades each by the integrated flux in channels at twice the FWHM from line center over radii 0.2–3″, and ranks sources by their accumulated grades to define the 12-source "max sub-sample".

What would settle it

Run the full sub-sample selection on 10,000 noise-only mock samples built from the observed single-component lines: if the same ranking procedure produces "max sub-samples" with 1.2–2.5σ broad-component excesses as often as the real data do, the reported signal is a selection-noise artifact. A direct check is to observe the 12 sources with deeper ALMA integrations, where a confirmed broad component with FWHM > 775 km/s in one or more individual spectra would settle whether the outflow is real.

Watch

Extended reading notes

Core claim

The paper's central claim is that stacking archival ALMA [C II] observations of 26 quasars at z ≈ 6 yields a broad emission component in the stacked line that individual spectra do not show, and that this component is most prominent for a sub-sample of 12 sources. In the 3-D stacks, where emission within about 2″ of the quasar is included, the excess over a single-Gaussian fit is 1.1–1.5σ for the full sample and 1.2–2.5σ for the "max sub-sample", with the broad component characterized by FWHM > 775 km/s and an integrated flux above 1.2 Jy km/s; the complementary "min sub-sample" shows no broad component. The authors interpret the excess as high-velocity outflowing gas, estimate a mean outflow rate of 45 ± 21 solar masses per year at a radius of 11.5 kpc, and present mock tests arguing that the stacking method itself does not generate the feature; they also state clearly that the detection is tentative, that the broad component could in principle be a gas flow between interacting galaxies rather than an outflow, and that deeper ALMA observations are required to confirm the component in individual spectra.

Load-bearing premise

The "max sub-sample" is chosen by ranking sources on the integrated flux in the line-free channels of the very stacks being measured, and the quoted 1.2–2.5σ significance does not correct for the 10,000 random sub-samples searched — if that ranking metric selects noise rather than genuine outflow emission, the sub-sample detection collapses.

Editorial extensions

If this is right

  • A broad component with FWHM > 775 km/s and 1.2–2.5σ excess appears in the stacked [C II] line of the 12-source sub-sample for all three weighting schemes, and removing any one source leaves the fitted parameters within 20% of their original values.
  • The wing emission is spatially extended to about 2″ (roughly 11.5 kpc) and disappears when only the central pixel is stacked, which explains why an earlier central-pixel-only stacking search found nothing.
  • For the sub-sample, the implied mean outflow rate is 45 ± 21 solar masses per year at outflow velocities of roughly 337–713 km/s, within the range measured for outflows in lower-redshift AGN.
  • Mock tests indicate the stacking method is not fabricating the feature: with no injected broad component, fewer than 17% of stacked mock iterations show excess above 0.4σ, while with a weak injected component about 75% of iterations recover a 1–2σ excess.
  • Because outflow orientation is random, the true outflow fraction may exceed the detected one: the paper's Monte-Carlo test recovers a >2σ stacked signal in only 27–50% of iterations even when every source carries a broad component with FWHM above 1000 km/s.

Reading between the lines

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

  • Because the sub-sample ranking uses the same line-free-channel flux that later counts as the detection, the quoted significance should carry a trials correction for the 10,000 sub-samples searched; repeating the full ranking on noise-only mocks would calibrate the true false-alarm rate and would likely lower the reported significance.
  • The ranking tool could be reused as a pre-selection step: shallow ALMA data on a larger quasar sample could flag the most promising outflow hosts, so that deeper and more expensive multi-tracer follow-up (CO, [O III], X-ray) is spent on the sources most likely to show outflows.
  • The velocity re-binning makes the recovered broad-line width proportional to the main-line FWHM, so the absolute velocity scale of the outflow is model-dependent; re-stacking a line-width-matched subset without re-binning, or fitting a joint narrow-plus-broad model directly, would test that dependence.
  • If individual confirmations follow, these outflow rates would provide one of the earliest empirical anchors for AGN feedback prescriptions in simulations of galaxy formation in the first billion years of cosmic time.
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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

4 major / 5 minor

Summary. The manuscript presents a spectral-stacking search for broad [C II] outflow components in 26 z~6 quasars observed with ALMA. After velocity-rebinning the [C II] lines to a common width and stacking both extracted 1-D spectra and full 3-D cubes under three weighting schemes, the authors find no outflow signature in individual sources. The full-sample 3-D stack shows excess emission over a single-component fit at 1.1-1.5 sigma, while the 1-D stack from smaller regions shows only 0.4-0.7 sigma. The authors then develop a sub-sampling procedure in which 10,000 random sub-samples are stacked and ranked by the integrated flux in channels at about twice the FWHM of the main line; the 12 sources with the highest ranks form the 'max sub-sample.' The 3-D stack of this sub-sample shows a broad component with FWHM > 775 km/s and excess significance of 1.2-2.5 sigma, from which they estimate an outflow rate of 45 +/- 21 solar masses per year. Mock tests presented in Section 5.3 and Appendix A show that the stacking method can recover injected broad components and that the false-detection rate for a fixed stack is below 17 percent above 0.4 sigma. The authors conclude with evidence suggesting outflows in a sub-sample of 12 of 26 quasars, while stressing that deeper ALMA observations are needed for confirmation.

Significance. If the sub-sample detection were robust, this would be one of the first systematic constraints on fast outflows in z~6 quasar hosts and would support the use of spectral stacking, especially 3-D stacking over extended regions, as a tool for searching for faint broad components. The paper has clear strengths: the archive recalibration is described in detail; the authors explicitly frame the detections as tentative and below conventional thresholds; the comparison with central-pixel-only stacking (Decarli et al. 2018) usefully demonstrates that extended emission matters; and the mock tests, while not covering the selection step, show that the basic stacking and fitting pipeline does not routinely create spurious broad components. However, the central positive claim for the sub-sample is not statistically established because the sub-sample is selected on the same wing flux that is then reported as the detection, without a trials correction.

major comments (4)
  1. [Section 5.2 and Table 5] The sub-sample detection is selected on the same line-free flux that is later reported as the detection. The ranking metric is the integrated flux in channels at 2 x FWHM from the line center of stacked random sub-samples, and the same type of wing excess is then used to compute the significance in Table 5 after subtracting the one-component fit. With typical narrow-line FWHM values of 300-400 km/s, the 'line-free' channels at +/-2 x FWHM are at roughly +/-600-800 km/s, where the claimed broad component with FWHM > 775 km/s has substantial flux; the selection and detection metrics are therefore not independent. The quoted 1.2-2.5 sigma is the maximum over 10,000 random sub-samples rather than a single pre-defined stack, so the relevant null distribution is that of the maximum significance over the full search, not the single-stack noise distribution. I request a trials-corrected significance, for example by running the full sub-sampling and ranking procedure on noise-only mock data and measuring the distribution of the maximum excess, or an independent validation of the selected sub-sample.
  2. [Section 5.3 and Appendix A] The mock tests validate the stacking of a fixed, pre-defined sample but do not exercise the sub-sample selection loop of Section 5.2. The statement that fewer than 17 percent of noise-only iterations produce an excess above 0.4 sigma refers to a fixed full-sample stack, not to the procedure that generates 10,000 candidate sub-samples, grades each by its integrated wing flux, and retains the maximum. The false-positive rate of the maximization procedure is expected to be much larger than that of a single stack, so the Appendix A thresholds cannot be used to support the significance quoted for the max sub-sample. I recommend adding a noise-only mock version of the complete Section 5.2 pipeline, including the random sub-sampling, grading, ranking, and re-fitting, and reporting the false-detection rate of the resulting 'max sub-sample' as a function of significance.
  3. [Section 5.2 and Figure 5] The manuscript itself notes in the Figure 5 caption that the max sub-sample 'does seem to prefer higher rms values.' This is concerning because higher-rms spectra contribute noisier stacked wings, so a selection that prefers high rms can produce an apparent broad-wing excess that is purely a noise-selection effect. The authors should quantify this: for example, compare the rms distribution of the selected 12 sources with that of random 12-source draws, and check in the mock samples whether the ranking metric correlates with individual-source rms. Without such a test, the sub-sample selection may be selecting noisy realizations rather than outflows, and the physical interpretation in Section 6.2 is not supported.
  4. [Section 5.2 and Section 6] The outflow mass-rate estimate of 45 +/- 21 solar masses per year is derived from the broad-component parameters of the max sub-sample, whose statistical significance is not established and whose fitted parameters vary strongly with weighting scheme (e.g., Table 4 gives broad FWHM values from 775 +/- 116 to 1427 +/- 408 km/s depending on weight). The derived rate should be presented as an explicitly conditional estimate, or removed from the results and placed in a clearly marked 'if confirmed' discussion, until the selection and significance issues are resolved. As written, the number could be read as a measurement rather than as an upper-limit illustration.
minor comments (5)
  1. [Abstract and Conclusions] The abstract states that the full-sample detection is only 1.1-1.5 sigma and 'tentative,' but the conclusions state 'we find evidence suggesting the presence of outflows in a sub-sample of 12 out of 26 sources.' Given that the sub-sample significance is not trials-corrected, the conclusions should be reworded to emphasize the tentative nature more strongly, for example by saying the sub-sample stack shows an excess whose significance requires confirmation with a corrected null test.
  2. [Section 3, first paragraph] There is a typo in the sentence about flux calibration: 'Consequently, the the fluxes extrapolated for the sources' should read 'Consequently, the fluxes extrapolated for the sources.' Also, in Table 1 the column header 'wether or not we detect' should be 'whether or not we detect.'
  3. [Section 5.3] The sentence 'We find excess emission due to a broad component with only a weak significance of < 3 sigma, with 75% of iterations having an excess emission of 1-2 sigma' is ambiguous because it mixes a threshold and a range. It would be clearer to state the full distribution, for example '75% of iterations have a detected excess in the 1-2 sigma range and the remaining iterations have lower or higher significance, with none above 3 sigma.'
  4. [Appendix A, Figure A.1 caption] The phrase 'only < 17% of the time do we retrieve excess emission between > 0.4 sigma' uses contradictory inequalities. The text should state the fraction of iterations with excess significance in the specified range, such as 'only 14-17% of iterations have an excess significance > 0.4 sigma and < 2 sigma.'
  5. [Section 6.1, mock tests] The discussion of the test of stacking without velocity rebinning is a good control, but it would benefit from stating explicitly that the 2-5% false-positive rate above 2 sigma applies to simple (non-rebinned) stacking and that the rebinned method used in the main analysis has a different (lower) false-positive rate in that test.

Circularity Check

1 steps flagged · score 6.0 of 10

Sub-sample detection is selected on the same wing flux later quoted as the 1.2–2.5 sigma excess, so that detection is forced by the selection criterion.

  1. fitted input called prediction [Section 5.2 (sub-sample selection) and Section 5.1 (significance estimate), Tables 4 and 5]
    "From the resulting stacked spectrum we select the “line-free” channels, defined to be at a distance of 2 × FWHM of the center of the main line component. These are channels were we can expect to see only emission due to an outflow component. We then integrate over these channels at different radii from the center, within the range of 0.2–3″in steps of 0.2″. The integrated flux density for each integration radius is saved as a grade for the sub-sample. ... For this we subtract the single component fit from the spectrum, and take the sum of the residuals within ±800 km/s."

    The sub-sample ranking is based on the integrated flux in the line-free channels (≥2×FWHM from line center), which is the same wing emission later used to compute the detection significance (residuals within ±800 km/s). For typical narrow-line FWHM of ~300–400 km/s, the 2×FWHM boundary is ~600–800 km/s, so the selection metric and the detection metric overlap almost exactly. Thus, selecting the 12 sources that maximize this quantity and then reporting the significance of that same quantity in the selected stack is selection on the dependent variable. The 1.2–2.5σ excess is a direct consequence of the selection criterion, not an independent measurement. The mock false-detection tests in Sect.

full rationale

The full-sample spectral stacking analysis (Sect. 5.1) is self-contained: the observed [C II] lines are rebinned, stacked with three weighting schemes, and fit with one- and two-component Gaussians; the resulting low-significance excess (0.4–1.5σ) is honestly reported, and the mock tests in Sect. 5.3/Appendix A provide a reasonable check for a fixed stack. No problematic self-citations appear; the in-prep Line Stacker tool (Jolly et al.) is described in the text and is not load-bearing. The circularity is concentrated in the sub-sample analysis (Sect. 5.2): the selection grade is the integrated flux in the line-free wing channels, and the reported detection significance is the residual sum over essentially the same velocity range. The max sub-sample is therefore built to maximize the very quantity later quoted as the detection, and the 1.2–2.5σ significance is not corrected for the 10,000 trials. The mock test used to argue against noise artifacts does not apply the sub-sample selection procedure, so it does not cover this selection-induced inflation. Hence the central claim of outflow evidence in the sub-sample reduces, by construction, to the selection criterion.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central detection claim rests on standard assumptions about [C II] as a gas tracer and Gaussian line profiles, plus a hand-chosen extraction radius and a paper-specific sub-sample selection criterion. The latter is the most fragile assumption and is not independently validated. The outflow mass and rate estimates add further modeling parameters, but those do not affect the detection itself.

free parameters (5)
  • Narrowest line FWHM normalization for velocity rebinning = 270 km/s
    All lines are re-binned so that the narrowest [C II] line (FWHM 270 km/s) is covered by the same number of channels; this choice sets the channel width of the stacked spectrum and may affect the broad component shape.
  • 3-D stacking extraction radius = 2 arcsec
    The stacked cube spectra are extracted within 2 arcsec (Sect. 5.1); significance drops to 0.4-0.7 sigma for smaller 1-D extraction regions, so the radius partially determines the reported detection significance.
  • Line-free channel definition for sub-sample grading = >= 2 x FWHM from line center
    Used in the random sub-sample ranking (Sect. 5.2); a different choice would change which sources are placed in the max sub-sample.
  • Outflow radius for mass outflow rate = 11.5 kpc (2 arcsec)
    Adopted as the radius of outflow emission to estimate the mass outflow rate; affects the derived rate, not the detection itself.
  • Outflow velocity definition = 0.5 x FWHM = 493 km/s
    Assumed to convert the broad component FWHM to a physical outflow velocity, following Cicone et al. (2015); a modeling choice, not a measured value.
assumptions (4)
  • domain assumption [C II] emission can trace outflows in high-redshift quasars
    The interpretation of the broad component as an outflow relies on [C II] tracing outflowing gas; the paper itself notes in Sect. 6.2.2 that it is unclear whether [C II] is a good outflow tracer.
  • domain assumption The outflow spectral signature is a single broad Gaussian component
    Stated in Sect. 5.2; real outflows may have asymmetric or one-sided profiles, which would not be fully captured by the fitting.
  • domain assumption The systemic velocity is set by the [C II] line center of the host galaxy
    The stack uses the [C II] redshift to align sources; if the line center is offset from the true systemic velocity, the broad component could be smeared or shifted.
  • ad hoc to paper Random sub-sampling and ranking of sources isolates outflow carriers
    The max sub-sample selection assumes the ranking grade (integrated line-free flux) is dominated by real outflow emission rather than noise; this is not validated by the mock tests in Sect. 5.3.

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Cite this review

Pith. "Pith review of A spectral stacking analysis to search for faint outflow signatures in z~6 quasars." pith.science (2026). https://pith.science/paper/3AF7JBRB

@misc{pith2026190811395,
  author       = {Pith},
  title        = {Pith review of: A spectral stacking analysis to search for faint outflow signatures in z~6 quasars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3AF7JBRB}},
  note         = {Machine review of arXiv:1908.11395}
}
read the original abstract

Outflows in quasars during the early epochs of galaxy evolution are an important part of the feedback mechanisms potentially affecting the evolution of the host galaxy. However, systematic observations of outflows are only now becoming possible with the advent of sensitive mm telescopes. In this study we use spectral stacking methods to search for faint high velocity outflow signal in a sample of [C II] detected, z ~ 6 quasars. We search for broad emission line signatures from high-velocity outflows for a sample of 26 z ~ 6 quasars observed with ALMA, with a detection of the [C II] line. The observed emission lines of the sources are dominated by the host galaxy, and outflow emission is not detected for the individual sources. We use a spectral line stacking analysis developed for interferometric data to search for outflow emission. We stack both extracted spectra and the full spectral cubes. We also investigate the possibility that only a sub-set of our sample contributes to the stacked outflow emission. We find only a tentative detection of a broad emission line component in the stacked spectra. When taking a region of about 2 arcsec around the source central position of the stacked cubes, the stacked line shows an excess emission due to a broad component of 1.1-1.5 sigma, but the significance drops to 0.4-0.7 sigma when stacking the extracted spectra from a smaller region. The broad component can be characterised by a line width of full width half max FWHM > 700 km/s. Furthermore, we find a sub-sample of 12 sources the stack of which maximises the broad component emission. The stack of this sub-sample shows an excess emission due to a broad component of 1.2-2.5 sigma. The stacked line of these sources has a broad component of FWHM > 775 km/s. Deeper ALMA observations are necessary to confirm the presence of a broad component in the individual spectra.

Figures

Figures reproduced from arXiv: 1908.11395 by the authors.

Figure 1
Figure 1. The AGN bolometric luminosity (Lbol) as a function of redshift (z) of our sample (red triangles). Also plotted are the known high redshift quasars from the compiled catalogue of Bañados et al. (2016), the catalogue of SDSS detections of Jiang et al. (2016) and the new detections of Mazzucchelli et al. (2017), from which the majority of our sample has been selected. used for the purpose of this paper. This final samp… view at source ↗
Figure 2
Figure 2. Example for an integrated intensity distribution (mo [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Results from our 1-D stacking analysis. (left) The stacked spectra of the full sample,(middle) the max sub-sample, and (right) the min-sub-sample, using weights of w = 1 (1st row), w = 1/σ2 rms (2nd row), and w = 1/S peak (3rd row). On the last row we give the number of sources per channel of the stacked line. extended emission, we perform a test. We repeat our stacking analysis as many times as the number of source… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: We have also looked into the stack of the sources excluded from the max sub-sample described above (right column of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 4
Figure 4. Figure 4: Results from our 3-D stacking analysis, for [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Here we show the distribution of the properties of the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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