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This paper shows that among isolated galaxies, lower-mass galaxies with lopsided 21-cm hydrogen profiles have higher specific star formation rates, a correlation predicted by cosmological simulations and pointing to stellar feedback as a dr

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2026-08-01 20:10 UTC pith:2DUVEZQC

load-bearing objection Solid reference catalog of isolated galaxies with HI asymmetry measurements; the EAGLE-like sSFR trend is plausible but the S/N robustness test is missing. the 3 major comments →

arxiv 2607.16700 v1 pith:2DUVEZQC submitted 2026-07-18 astro-ph.GA

Asymmetries in spatially unresolved 21-cm emission line profiles of isolated galaxies

Aditya Manuwal (1) , H. M. Hern\'andez-Toledo (1) , J. A. V\'azquez-Mata (1) , Diana Serrato Barrajas (1) , Aldo Rodr\'iguez-Puebla (1) , Vladimir \'Avila-Reese (1) , A. R. Calette (1) ((1) Universidad Nacional Aut\'onoma de M\'exico , Instituto de Astronom\'ia
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A.P. 70-264 04510 CDMX M\'exico)
This is my paper
classification astro-ph.GA
keywords galaxies: ISMradio lines: ISMgalaxies: interactionsgalaxies: evolutionmethods: data analysisHI asymmetryisolated galaxies21-cm line
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to build reliable reference samples of truly isolated galaxies with robust measurements of 21-cm line asymmetry, and to use them to identify the internal processes that distort neutral hydrogen disks. It assembles two samples of isolated galaxies from the UNAM-KIAS and AMIGA catalogs, applying careful beam-coverage, signal-to-noise, and velocity-resolution cuts, and measures a lopsidedness parameter A_l for each galaxy. Its central finding is a positive correlation between A_l and specific star formation rate for galaxies below about 10^10.3 solar masses, matching predictions from cosmological simulations for central galaxies; the paper interprets this as stellar feedback stirring the gas. If this is right, the released catalog becomes a standard control sample for environmental studies, and the low-mass correlation provides an observational handle on feedback-regulated gas disruption in isolated galaxies.

Core claim

The paper claims that in isolated galaxies, the lopsidedness of the integrated 21-cm profile (A_l, the fractional difference between the fluxes on the two velocity sides of the line) is a clean tracer of internal disturbance, and that its dominant driver depends on stellar mass. Based on 153 galaxies from UNAM-KIAS and 236 from AMIGA, it reports that A_l is independent of stellar mass, morphology, bar presence, HI fraction, and recent merger history, but that below M* ~ 10^10.3 Msun the most asymmetric galaxies have systematically higher specific star formation rates than their symmetric counterparts. The same behavior has been predicted for central galaxies in a large cosmological hydrodyna

What carries the argument

The key object is the lopsidedness measure A_l, computed from the fluxes on the low- and high-velocity halves of the 21-cm profile about its systemic velocity, which ranges from 0 (perfect symmetry) to 1. The analysis also relies on a beam-coverage selection using the HI size-mass relation to ensure that the single-dish beam captures most of the neutral gas, and on signal-to-noise and velocity-channel cuts designed to keep noise from inflating A_l. The A_l measure carries the entire asymmetry analysis: its convergence properties under noise determine which galaxies can be trusted and therefore what trends can be claimed.

Load-bearing premise

The claim that the S/N=10 cutoff yields reliable asymmetry measurements for the statistics used in this paper; the paper's own appendix shows that full convergence within 20% requires S/N about 60 over much of the asymmetry range, so if noise inflates A_l preferentially in low-mass, high-sSFR galaxies, the central correlation could be a noise artifact.

What would settle it

Take the released sample, keep only the galaxies with S/N above 60 (or apply a noise-debiasing correction), and recompute the median sSFR for the most versus least asymmetric quartiles below 10^10.3 Msun. If the positive offset disappears, the central claim fails; if it remains, the claim is confirmed. Alternatively, compare the A_l distribution of low-mass galaxies with high sSFR to a matched sample of low-sSFR galaxies at the same S/N.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • If correct, the 389-galaxy catalog provides a reference set of isolated HI sources for comparing against galaxies in groups and clusters, where external perturbations are supposed to elevate asymmetry.
  • The low-mass sSFR-A_l correlation implies that stellar feedback can leave a measurable imprint on the global HI profile, not just on resolved kinematics.
  • The correlation gives modelers a direct test: galaxy formation simulations that predict the strength of feedback-driven outflows should reproduce the amplitude and mass dependence of the A_l-sSFR trend.
  • The null results (independence from bars, morphology, merger stage) simplify the interpretation of asymmetry in isolated systems: those properties do not need to be controlled for in environmental comparisons.
  • The paper's finding that isolated galaxies have higher HI fractions and lower star formation efficiencies than typical late-type centrals means that environmental references must use isolated samples, not field averages.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the noise inflation at low S/N preferentially affects the lowest-mass galaxies (which also tend to have the highest sSFR), part of the reported correlation could be an artifact; re-analyzing with the S/N>60 subsample would settle this.
  • The beam-coverage cut, while correct on average, may exclude the most extended HI disks; if those disks are also the most asymmetric, the absolute A_l distribution in the released catalog could be biased low, affecting any quantitative comparison with simulations.
  • A natural extension would be to measure A_l for galaxies in the same mass range but in richer environments using the same pipeline; the difference in the sSFR-A_l slope between environments would directly isolate the external vs internal contribution.
  • If the correlation holds, it suggests that a simple proxy — sSFR — could be used to predict which isolated galaxies are likely to show lopsided HI, useful for target selection with future high-resolution radio facilities.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper compiles new samples of isolated galaxies from the UNAM-KIAS and AMIGA catalogs with H I 21-cm line profiles from five single-dish surveys (H I-MaNGA, NIBLES, KLUN, ALFALFA, xGASS). Quality cuts include near-complete beam coverage using the Wang et al. (2016) size–mass relation, S/N>10, at least 20 velocity channels, and m_r<15.2, yielding 153 and 236 galaxies respectively. The authors measure the lopsidedness A_l using the Busy-function edge method of Manuwal et al. (2022), and derive ancillary stellar, gas, morphological, merger, and halo properties for the released catalog. The main physical claims are that isolated galaxies are predominantly late-type, star-forming, H I-rich, low-SFE systems, that bar fractions resemble normal spirals, that merger fractions are unexpectedly high, and—the headline result—that more H I-asymmetric galaxies have higher sSFRs below M*~10^10.3 Msun, in agreement with EAGLE predictions for centrals.

Significance. If the central trend is robust, the paper delivers a valuable reference catalog for environmental studies of H I asymmetry and provides observational support for stellar-feedback-driven asymmetries in low-mass isolated galaxies. The catalog construction is careful: cross-matching across five surveys, explicit beam-coverage cuts, channel-resolution requirements, and public release of measurements and ancillary properties are clear strengths. The convergence tests in Appendix A are also a useful addition to the literature. However, the headline sSFR–asymmetry correlation rests on A_l values measured at S/N=10, and the paper’s own Appendix A shows that this threshold is only reliable for A_l≳0.05–0.06. Because low-mass, high-sSFR galaxies are plausibly closer to the S/N cut, a direct S/N-robustness check is needed before the EAGLE-agreement claim can be considered established.

major comments (3)
  1. [Sec. 3.1.3, Eq. (3); Appendix A, Figs. A3–A4; Sec. 4.6, Fig. 12] The S/N=10 threshold is load-bearing for the headline sSFR–A_l trend. Appendix A shows that full-range 20% convergence of A_l requires S/N≈60, and that at S/N=10 only A_l≳0.05–0.06 is reliable. If low-mass galaxies in the sample have lower S/N near the cut (plausible for fainter, more distant or H I-poor objects), noise will preferentially inflate their A_l and push them into the upper quartile used in Fig. 12, potentially manufacturing the positive sSFR correlation at M*<10^10.3 Msun. The current manuscript reports neither S/N distributions per mass bin nor a high-S/N subsample test for Fig. 12. I request (i) S/N versus M* plots, (ii) a rerun of the Fig. 12 quartile analysis restricted to S/N≥20 and S/N≥30, and (iii) explicit discussion of how many low-mass galaxies have A_l below the reliable threshold. This is directly testable with the released catalog and is essential to the abstrac
  2. [Sec. 4.6, Fig. 12] The quartile split in Fig. 12 is presented without error bars, without confidence intervals on the medians, and without stating the minimum number of galaxies per mass bin. The two panels show UNAM-KIAS and AMIGA separately, but 59 galaxies are shared between the samples (Sec. 3.1.4), so the panels are not fully independent; it is not stated whether the trend in Fig. 12 persists if shared objects are removed from one sample. Given that Fig. 12 is the main observational result, the authors should add bootstrap confidence intervals, report significance tests (e.g., KS or permutation) per mass bin, and show the trend for the independent subsamples. Without these, the visual separation in the low-mass bins is not yet quantitatively established.
  3. [Sec. 4.6 and Sec. 6] The interpretation that the low-mass sSFR–A_l correlation is caused by stellar-feedback-driven outflows relies on the EAGLE analysis of Manuwal et al. (2022), which uses the same A_l definition and the same edge-finding method as the present paper. This is a methodological lineage rather than circular reasoning, but the agreement is less independent than it might appear. The paper should state explicitly that the EAGLE prediction is generated with the same asymmetry pipeline, and should note that the observational trend is also consistent with other mechanisms that raise both sSFR and H I asymmetry (e.g., recent gas accretion) before settling on feedback. A brief acknowledgment of this degeneracy would make the conclusion appropriately cautious.
minor comments (4)
  1. [Fig. 12 caption] The caption says 'orange curve shows the median asymmetry' but the plotted quantity is median sSFR. Please correct to 'median sSFR'.
  2. [Throughout] The text uses 'Hiline' as a single word in many places; this is typographically inconsistent (e.g., 'H I line' or 'H I-line' would be clearer). Also, 'eagle' appears lowercase in the abstract and text; consider using 'EAGLE' consistently.
  3. [Appendix A, Fig. A4] The description of the color coding mentions green points for v_eff=10 km/s at v_res=1.2, 2.6, 5.5 and orange for v_res=1.4, but in the figure the color legend is not fully self-explanatory. A short caption expansion would help the reader follow which survey each resolution combination represents.
  4. [Sec. 5, Eq. (14)] The conversion A_l = |A_fr−1|/(A_fr+1) is correct, but the text refers to 'the asymmetry measure' without noting that A_fr in the original papers uses the ratio of integrated fluxes defined in different ways (e.g., high/low vs. low/high). Please state explicitly that the convention is consistent with Eq. (2) so that readers can verify the conversion.

Circularity Check

0 steps flagged

No significant circularity: self-citations are methodological lineage, and the EAGLE comparison is an independent test rather than a fitted input.

full rationale

The paper's derivation chain is observational: it assembles isolated-galaxy samples from UNAM-KIAS and AMIGA, retrieves single-dish HI spectra, measures the lopsidedness A_l (Eq. 1), applies S/N and velocity-channel cuts, and compares the sSFR of A_l quartiles to the EAGLE prediction from Manuwal et al. (2022). No parameter is fitted to reproduce the headline sSFR–asymmetry trend. The A_l definition and edge-finding method come from Manuwal et al. (2022), and the same measure is used in the EAGLE comparison; this is methodological consistency, not a circular reduction, because the observed A_l values are independent data and the EAGLE prediction is an external simulation output. The S/N=10 threshold is acknowledged in Appendix A and Sec. 3.1.3 to give only ~20% convergence for A_l ≳ 0.05 and to require S/N≈60 for full-range convergence; the paper justifies the lower cut partly with a cited expectation that very symmetric profiles are rare (Watts et al. 2020b; Glowacki et al. 2022; Manuwal et al. 2022). That is a robustness/correctness concern, not a logical equivalence: the observed sSFR–A_l relation is not constructed from that expectation, and the paper discloses the limitation. No uniqueness theorem is imported from the authors' prior work, and no ansatz is disguised as externally established fact. The self-citations are dense but load-bearing only as methodology and as an independent simulation comparison, so the central claim retains independent empirical content.

Axiom & Free-Parameter Ledger

3 free parameters · 7 axioms · 0 invented entities

The paper is an observational catalog; it introduces no new particles, forces, or conserved quantities. Its central claims rest on a chain of external empirical relations and hand-chosen thresholds: the Wang+16 HI size–mass relation for beam coverage, the Manuwal+22 edge/asymmetry measurement, the Tinker+21 halo masses, the GSWLC-X2 SED calibration, and the Nevin+23 merger classifier. None of these is fitted to the paper's own conclusions, but each could bias the sample if wrong.

free parameters (3)
  • S/N cut = 10
    Choice of signal-to-noise threshold for sample inclusion; Appendix A shows S/N≈60 needed for convergence over the full A_l range, so this is a hand-chosen compromise.
  • Intrinsic disk thickness q = 0.2
    Fixed value used to convert b/a to inclination in Eq. (9); affects inclination corrections across the sample.
  • Beam coverage factor = 1
    Exclusion threshold D_beam/D_HI,pred <1 based on mean Wang+16 size–mass relation; controls which galaxies are considered fully covered.
axioms (7)
  • domain assumption The Wang et al. (2016) HI size–mass relation and self-similar HI profiles hold for isolated galaxies and predict total HI diameter from catalog M_HI.
    Used to define the beam coverage cut in Sec. 3.1.2; if the relation fails for low-mass or extended disks, the sample is biased.
  • domain assumption Busy-function-fitted profile edges from Manuwal et al. (2022) approximate the noiseless line edges of observed single-dish spectra.
    Required to compute A_l and W95 in Sec. 3.1.3; biased edges would bias all asymmetry measurements.
  • domain assumption Unresolved HI profile asymmetry, measured by A_l, is a statistically unbiased population-level tracer of intrinsic HI asymmetry for randomly oriented galaxies.
    Acknowledged limitation in Sec. 3.1.3/4.2: a symmetric line does not imply a symmetric galaxy, and population comparisons are assumed valid.
  • domain assumption The Tinker (2021) group catalog provides accurate halo masses and central/satellite assignments for isolated galaxies at z<0.08.
    Used for halo masses and central status in Sec. 3.2.6; errors propagate into the accretion-rate inference.
  • domain assumption GSWLC-X2 SED-based stellar masses and SFRs remain on a consistent scale after cross-calibration relations from Durbala et al. (2020), Chang et al. (2015), and Siudek et al. (2024).
    Homogenization of M* and SFR in Sec. 3.2.1 affects mass cuts and the sSFR–asymmetry trend.
  • standard math Standard frequentist statistics (KS, Mood's median, Spearman rank, bootstrap) are appropriate for the sample sizes and selection.
    Many p-values are marginal (0.02–0.08) and multiple comparisons are not formally corrected; interpretations rely on these tests.
  • domain assumption The Nevin et al. (2023) LDA merger classifier with a probability threshold of 0.9 reliably separates mergers from non-mergers at the population level.
    Used for merger fractions in Sec. 3.2.5; the authors note it was not trained on flybys, so merger/flies classification is uncertain.

pith-pipeline@v1.3.0-alltime-deepseek · 44719 in / 14475 out tokens · 126872 ms · 2026-08-01T20:10:54.959296+00:00 · methodology

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Cite this review

Pith. "Pith review of Asymmetries in spatially unresolved 21-cm emission line profiles of isolated galaxies." pith.science (2026). https://pith.science/paper/2DUVEZQC

@misc{pith2026260716700,
  author       = {Pith},
  title        = {Pith review of: Asymmetries in spatially unresolved 21-cm emission line profiles of isolated galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2DUVEZQC}},
  note         = {Machine review of arXiv:2607.16700}
}
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read the original abstract

The origin of asymmetry in the ${\rm H}\,{\scriptsize{\rm I}}$ of galaxies remains an elusive problem, largely due to the difficulties associated with distinguishing between its secular and external contributors. We have compiled a sample of local isolated galaxies from the UNAM-KIAS and the latest AMIGA samples with near-complete beam coverage and robust estimates of ${\rm H}\,{\scriptsize{\rm I}}$ line asymmetry. The ${\rm H}\,{\scriptsize{\rm I}}$ measurements are based on single-dish spectra sourced from five surveys: ${\rm H}\,{\scriptsize{\rm I}}$-MaNGA, NIBLES, KLUN, ALFALFA, and xGASS. Our galaxies tend to be late-type, star-forming centrals at all masses but exhibit slightly lower specific star formation rates (sSFRs) and higher ${\rm H}\,{\scriptsize{\rm I}}$ contents than expected. The latter is likely driven by lower star formation efficiency, weaker outflows, and additionally, higher accretion rate of gas onto the galaxy at $M_\star\lesssim 10^{10.3}\,\mathrm{M}_\odot$. AMIGA, however, shows systematically higher ${\rm H}\,{\scriptsize{\rm I}}$ masses than UNAM-KIAS, which we attribute to higher local densities probed by the latter. Furthermore, both samples show bar frequencies similar to normal spirals, indicating that the gravitational instabilities leading to bars predominantly stem from internal processes, as suggested by recent works. Our galaxies show unexpectedly high merger fractions, possibly due to sampling bias and/or the inability of the classification method to distinguish between flybys and encounters leading to coalescence. We also find higher sSFRs for asymmetric galaxies below $M_\star\sim 10^{10.3}\,\mathrm{M}_\odot$, in agreement with the predictions for centrals from the ${\scriptsize{\rm EAGLE}}$ simulation. We release the ${\rm H}\,{\scriptsize{\rm I}}$ measurements along with ancillary galaxy and halo properties for public use.

Figures

Figures reproduced from arXiv: 2607.16700 by 04510 CDMX, Aditya Manuwal (1), Aldo Rodr\'iguez-Puebla (1), A.P. 70-264, A. R. Calette (1) ((1) Universidad Nacional Aut\'onoma de M\'exico, Diana Serrato Barrajas (1), H. M. Hern\'andez-Toledo (1), Instituto de Astronom\'ia, J. A. V\'azquez-Mata (1), M\'exico), Vladimir \'Avila-Reese (1).

Figure 1
Figure 1. Figure 1: The relationships between H i lopsidedness and stellar mass for the isolated galaxies from UNAM-KIAS and AMIGA, shown in pink and blue, respectively. The curves are the medians and are only shown for mass bins with at least 10 points. The shaded regions show the bootstrapping errors on the medians. The open blue curve is for the AMIGA subsample without the galaxies in common with UNAM-KIAS (see the text). … view at source ↗
Figure 3
Figure 3. Figure 3: presents the optical morphology against 𝑀★, where the morphology has been parameterised to follow the T-type scheme in Nair & Abraham (2010). The morphology distributions on the right clearly show that nearly all the galaxies span 1 ≤ T-type ≤ 8 (i.e. Sa to Sdm), with a median of ≈ 4.5 for AMIGA and 5 for UNAM￾KIAS. Our KS and Mood’s tests show that this offset between the samples, albeit small, is signifi… view at source ↗
Figure 2
Figure 2. Figure 2: H i lopsidedness plotted against galaxy inclination. The asymmetry is generally independent of inclination for our isolated samples, except for a slight positive correlation at 𝑖 ≳ 40◦ for UNAM-KIAS. The asymmetries are broadly consistent between the samples at low inclinations, but UNAM￾KIAS shows slightly lower asymmetries at 60◦ ≲ 𝑖 ≲ 70◦ . UNAM-KIAS also shows a minor preference towards lower inclinati… view at source ↗
Figure 4
Figure 4. Figure 4: H i line asymmetry plotted against stellar morphology (T-type). The asymmetry is agnostic to morphology and consistent between the samples for a given T-type. from early- to late-types, and find that the two morphological groups are virtually identical in this respect. Both of these quantities are generally sensitive to inclination, but in opposite ways: 𝐴𝑙 becomes more reliable at high inclinations, where… view at source ↗
Figure 5
Figure 5. Figure 5: Spatial asymmetry of stars plotted against stellar mass. The top panel shows the results for the rotational asymmetry (𝐴) and the bottom panel for the shape asymmetry (𝐴𝑠), the latter being more sensitive to the outskirts of the galaxy (see the text). The stellar asymmetry is generally independent of stellar mass for both measures, but there is a mild positive relation in UNAM-KIAS for 𝑀★ ≳ 1010.2 M⊙. At f… view at source ↗
Figure 6
Figure 6. Figure 6: The relationship between spatial asymmetry of stars and H i line asymmetry. The top panel shows the results for the rotational asymmetry (𝐴), and the bottom panel shows it with the shape asymmetry (𝐴𝑠). H i line asymmetry is independent of optical asymmetry for UNAM-KIAS, but 𝐴 exhibits a weak positive correlation for AMIGA. not show any offset indicates that the two mainly differ in asymmetry levels at la… view at source ↗
Figure 8
Figure 8. Figure 8: Stellar-to-halo mass relations (SHMRs) for our samples. The brown curve is the relation for blue centrals by Rodríguez-Puebla et al. (2015) based on abundance matching. The olive curve is the relation for blue centrals derived by Mandelbaum et al. (2016) using weak lensing. The orange curve is the relation inferred from rotation curves of local spirals by Lapi et al. (2018). The black curve is the relation… view at source ↗
Figure 9
Figure 9. Figure 9: Star formation efficiency (SFE) based on H i mass at different stellar masses. For reference, we have added the means and 1𝜎 scatters for LTC calculated using the H i fractions and the SFMS in Calette et al. (2021) and Stephenson et al. (2024), respectively. The SFE is agnostic to stellar mass. UNAM-KIAS and AMIGA are biased towards lower SFEs than typical SF galaxies. The two are consistent in their media… view at source ↗
Figure 10
Figure 10. Figure 10: The relationship between H i lopsidedness and H i fraction for UNAM-KIAS (top) and AMIGA (bottom). The orange and green curves show the median values for the most and least asymmetric galaxies in each mass bin, respectively (see the text). H i fraction is generally independent of 𝐴𝑙 for both samples. are therefore not strongly influenced by stochastic fluctuations in star formation activity. We now invest… view at source ↗
Figure 11
Figure 11. Figure 11: Specific star formation rate vs stellar mass. The black curve shows the mean star-forming main sequence (SFMS) determined by Stephenson et al. (2024) for the central galaxies in SDSS. The dashed curves encompass ±0.25 dex around the SFMS and denote the main sequence region. Our isolated galaxies are generally on the main sequence but exhibit a bias towards sSFRs below the mean SFMS. UNAM-KIAS and AMIGA ar… view at source ↗
Figure 12
Figure 12. Figure 12: Specific star formation rates for the least and most H i asymmetric galaxies in UNAM-KIAS (top panel) and AMIGA (bottom). The orange curve shows the median asymmetry for upper quartile of 𝐴𝑙 within each mass bin, and the green curve shows it for the lower 𝐴𝑙 quartile. Asymmetric galaxies show higher sSFRs below 𝑀★ ∼ 1010.3 M⊙. formation and its connection to galaxy evolution. Observed samples of isolated … view at source ↗
Figure 13
Figure 13. Figure 13: Fraction of galaxies with bars at different masses. The error bars are the uncertainties on the fractions from bootstrapping. The top and bottom panels show the results for all kinds of bars and strong/prominent bars, respectively. The bar fraction tends to be higher for UNAM-KIAS in general, but is slightly lower for strong bars. turn-over value (see Erwin 2018 for a discussion). At higher masses, both g… view at source ↗
Figure 15
Figure 15. Figure 15: shows the merger statistics across stellar mass bins. These statistics are computed only for galaxies with merger information. We only plot the values for the bins with more than 10 objects. The top panel shows the fraction of galaxies affected by mergers. It seems that mergers have impacted ∼ 15 − 50 per cent of our samples at any given mass. The merger fractions of ≲ 0.5 broadly align with the qualitati… view at source ↗
Figure 16
Figure 16. Figure 16: Dependence of H i lopsidedness on mergers. The orange points show the galaxies that are probably affected by a merger (minor or major), and the green points are the galaxies do not appear to be affected by any merger. The asymmetry is independent of mergers in general. 5 COMPARISON AGAINST PREVIOUS SAMPLES Some samples of isolated H i sources have already been presented before this work. The most notewort… view at source ↗
Figure 17
Figure 17. Figure 17: H i line asymmetries in UNAM-KIAS and AMIGA compared against those in previously published samples of isolated galaxies in the literature: Haynes et al. (1998) (top), Matthews et al. (1998) (middle), and Espada et al. (2011) (bottom). These samples are shown as the black curves. The solid coloured curves show the asymmetries for our samples based on the peak method, which is the method adopted in the lite… view at source ↗

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