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arxiv: 2604.15567 · v1 · submitted 2026-04-16 · 🌌 astro-ph.GA

Recognition: unknown

The ubiquity of turbulence in the expanding kinematics of the ionized shells of Galactic planetary nebulae

Francisco Ruiz-Escobedo , Michael G. Richer , Jos\'e Alberto L\'opez

Authors on Pith no claims yet

Pith reviewed 2026-05-10 09:53 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords planetary nebulaeturbulenceresidual velocitiesionized shellskinematic analysisemission line profilescentral starsGalactic nebulae
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The pith

Turbulence is present throughout the ionized shells of all 105 planetary nebulae examined, appearing as transonic or slightly supersonic residual velocities.

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

The paper decomposes high-dispersion emission-line spectra from 105 Galactic planetary nebulae to isolate residual velocities after accounting for the overall expansion and other structural motions. It reports that these residuals, taken as turbulence, occur in every object and fall in the transonic to mildly supersonic range for the ionized gas, with a tendency for higher values in more highly ionized species that trace inner zones. No broad correlations appear with morphology, expansion speed, ionization level, or binary nature of the central star, though nebulae around hydrogen-poor Wolf-Rayet stars show distinctly larger residuals. A reader would care because the result places turbulence as a common, early-acting ingredient in how these shells expand and dissipate energy rather than an occasional or secondary effect.

Core claim

The analysis of residual velocities from a sample of 105 Galactic planetary nebulae reveals that turbulence is pervasive, with values either transonic or slightly supersonic in the ionized environment. Comparisons across ions show higher residual velocities for higher ionization species by 5-10 km s^{-1}, indicating larger turbulent structures in inner zones. No clear correlations exist with morphology, global expansion velocities, ionization degree, or binary cores, except for higher values in PNe with H-poor [WR]-type central stars. Turbulence is thus characterized as a localized, random, dissipative process in the inner sections of the shell that may affect its early evolution.

What carries the argument

The residual velocity obtained by decomposing emission line profiles into their structural contributors, which isolates the turbulent component from ordered expansion in the plasma.

If this is right

  • Turbulence occurs in every planetary nebula in the sample and can influence early shell evolution.
  • Inner shell zones show stronger turbulence, as higher-ionization lines consistently yield larger residual velocities.
  • PNe with hydrogen-poor [WR]-type central stars exhibit higher residual velocities than those with hydrogen-rich stars.
  • Turbulence acts as a localized random dissipative process without clear ties to most global nebular parameters such as morphology or expansion velocity.

Where Pith is reading between the lines

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

  • If the inner turbulence is dissipative, it may seed small-scale instabilities that later contribute to the observed morphological complexity of mature planetary nebulae.
  • Current hydrodynamic models of planetary nebula formation may need to incorporate an early turbulent energy source rather than treating turbulence as a later addition.
  • The absence of correlation with binary central stars suggests that any shaping by companions operates separately from this turbulent component.
  • Repeating the residual-velocity analysis on a sample of much younger or more distant planetary nebulae could test whether the turbulent signature strengthens or weakens with age.

Load-bearing premise

That decomposing the emission line profiles into structural contributors accurately isolates turbulence rather than other unresolved kinematic effects, instrumental artifacts, or fitting choices.

What would settle it

High-spatial-resolution spectroscopy or interferometry of a planetary nebula that measures small-scale velocity dispersions matching only thermal broadening plus ordered expansion, with no detectable excess random component.

Figures

Figures reproduced from arXiv: 2604.15567 by Francisco Ruiz-Escobedo, Jos\'e Alberto L\'opez, Michael G. Richer.

Figure 1
Figure 1. Figure 1: illustrates the acquisition and format of the data in the SPM Calalogue, as well as the process of fitting the line profiles. The SPM Catalogue contains bidimensional spectra (FITS format). We extract one dimensional spectra using iraf’s6 splot task (Tody 1986, 1993; Fitzpatrick et al. 2025). We extracted the spectra at the spatial coordinate of the central star, or at the spatial centre for objects with n… view at source ↗
Figure 2
Figure 2. Figure 2: Top panel: We plot the velocity splitting for the [N ii] 𝜆6548 line as a function of that of the [N ii] 𝜆6583 line. The green dashed lines indicate the 5% and 95% percentiles of the distribution of differences in the velocity splitting for the two lines, ±1 km s−1 , which we adopt as the uncertainty associated with all velocity splittings. Bottom panel: We present the residual velocities in the [N ii] 𝜆654… view at source ↗
Figure 4
Figure 4. Figure 4: We plot the residual velocities for the receding side of the nebular shell as a function of residual velocity of the approaching side in the four emission lines. There is a good correlation between the residual velocity measured in a given object and line. The green diagonal dashed lines indicate our estimate of the total uncertainty of the residual velocities (§2.4, [PITH_FULL_IMAGE:figures/full_fig_p005… view at source ↗
Figure 3
Figure 3. Figure 3: We present pairwise scatter plots of the velocity splitting for the [N ii], [O iii] and He ii lines. In all panels, the more highly ionized line is on the vertical axis. The green diagonal dashed lines represent the uncertainty about equality, represented by the black dot-dashed line ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: These pairwise scatter plots compare the residual velocities in the [N ii], [O iii] and He ii lines. The green diagonal dashed lines indicate the uncertainty range about unity for residual velocities and the black dot-dashed indicates equal values. In all panels, the more highly ionized line is plotted on the vertical axis. The points clearly scatter above the uncertainty range, indicating that the residua… view at source ↗
Figure 6
Figure 6. Figure 6: We plot the residual velocity in each line as a function of the velocity splitting in the same line. We include the data for the blue- and redshifted sides of the nebular shell, shown in different colours. The diagonal dot-dashed line indicates the locus of identical values. Clearly, there is no correlation between the residual velocity and the velocity splitting in any line. As was found in [PITH_FULL_IM… view at source ↗
Figure 8
Figure 8. Figure 8: We present the eCDFs compariing the velocity splitting (top panel) and the residual velocities (bottom panel) for PNe with bubble (solid lines) and elliptical (dashed lines) morphologies. In all lines, the velocity splittings of the PNe with bubble morphology are larger than those of PNe with elliptical morphology, though the difference is not significant for [O iii] 𝜆5007. There are significant difference… view at source ↗
read the original abstract

We present an analysis of the residual velocities from a sample of 105 Galactic planetary nebulae (PNe), the largest done to date on this subject. The analysis has been carried out with long-slit, high dispersion echelle spectra. The data were drawn from the San Pedro M\'artir Kinematic Catalogue of Galactic Planetary Nebulae. The residual velocity is identified with turbulence in the plasma and is derived by decomposing the emission line profiles into their structural contributors. Turbulence seems pervasive throughout all the PNe in the sample. We find the values for the residual velocities in the sample to be either transonic or slightly supersonic in the ionized environment. When residual velocities of [N II], [O III] and He II in the same PNe are compared, there is a tendency for the residual velocities of the higher ionized ion to be larger by about 5-10 km s$^{-1}$, indicating that the turbulent structure is larger in the inner zones of the PN. We find in general no clear correlation between the residual velocities and other nebular parameters such as morphology, global expansion velocities, ionization degree and binary cores. The only exception is the case of PNe with H-poor ([WR]-type) central stars, where we confirm previous results that have consistently shown higher residual velocities for this group of PNe as compared to those with H-rich central star atmospheres. Turbulence seems to be a localised, random, dissipative process occurring in the inner sections of the shell and may affect its early evolution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript analyzes residual velocities extracted from long-slit, high-dispersion echelle spectra of 105 Galactic planetary nebulae drawn from the San Pedro Mártir Kinematic Catalogue. By decomposing [N II], [O III], and He II emission-line profiles into structural contributors, the authors equate the residuals with turbulence and conclude that it is ubiquitous, with values transonic to slightly supersonic, systematically larger (by 5–10 km s⁻¹) for higher-ionization species, and elevated in PNe with [WR]-type central stars; they find no clear correlations with morphology, global expansion velocity, or ionization degree and interpret turbulence as a localized, random, dissipative process in the inner shell that may influence early evolution.

Significance. If the decomposition reliably isolates turbulent dispersion, the study would supply the largest empirical sample to date on small-scale kinematics in PNe, offering quantitative constraints on the role of turbulence in shell expansion and providing a potential explanation for observed velocity discrepancies in evolutionary models. The reported ion-to-ion trend and the [WR] exception would add useful observational anchors for hydrodynamical simulations of PN formation.

major comments (2)
  1. [Methods (decomposition procedure)] The central claim that residual velocities after profile decomposition represent turbulence (rather than unresolved expansion gradients, projection effects along the slit, or non-Gaussian components) is load-bearing for every subsequent conclusion. The manuscript must supply a quantitative error budget and explicit tests (e.g., Monte Carlo realizations of shell geometry or comparison with high-resolution imaging) showing that the reported 5–10 km s⁻¹ ion-to-ion differences and the transonic/supersonic regime survive these alternatives.
  2. [Results section] The statement of “no clear correlation” with morphology, expansion velocity, ionization degree, and binary cores is used to argue that turbulence is largely independent of global parameters. The manuscript should report the actual correlation coefficients, p-values, or rank statistics for the 105-object sample so that the strength (or absence) of these null results can be evaluated.
minor comments (3)
  1. Define the sound speed adopted for the “transonic/slightly supersonic” classification and state the assumed electron temperature range; this is needed to convert the numerical residual velocities into Mach numbers.
  2. The abstract claims the sample is “the largest done to date”; the introduction should briefly tabulate or cite the sizes of previous residual-velocity studies for context.
  3. Ensure that all velocity values in figures, tables, and text carry consistent units (km s⁻¹) and that error bars or uncertainties are shown for the residual-velocity measurements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. We address each of the major comments below and outline the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [Methods (decomposition procedure)] The central claim that residual velocities after profile decomposition represent turbulence (rather than unresolved expansion gradients, projection effects along the slit, or non-Gaussian components) is load-bearing for every subsequent conclusion. The manuscript must supply a quantitative error budget and explicit tests (e.g., Monte Carlo realizations of shell geometry or comparison with high-resolution imaging) showing that the reported 5–10 km s⁻¹ ion-to-ion differences and the transonic/supersonic regime survive these alternatives.

    Authors: We recognize the importance of rigorously validating that the residual velocities primarily reflect turbulence rather than other kinematic effects. While our decomposition method follows established procedures in the literature for separating bulk expansion, thermal broadening, and instrumental contributions, we agree that an explicit error analysis is needed. In the revised manuscript, we will add a quantitative error budget in the Methods section, estimating the potential contributions from unresolved expansion gradients and projection effects based on typical shell geometries. Additionally, we will conduct Monte Carlo simulations for a representative subsample of PNe that have high-resolution imaging data available, to assess the impact on the derived residuals. These tests will confirm that the 5–10 km s⁻¹ differences between ions and the transonic to slightly supersonic regime remain robust. revision: yes

  2. Referee: [Results section] The statement of “no clear correlation” with morphology, expansion velocity, ionization degree, and binary cores is used to argue that turbulence is largely independent of global parameters. The manuscript should report the actual correlation coefficients, p-values, or rank statistics for the 105-object sample so that the strength (or absence) of these null results can be evaluated.

    Authors: We concur that including statistical measures will better support our claim of no clear correlations. In the revised Results section, we will present Spearman rank-order correlation coefficients and corresponding p-values for the residual velocities versus morphology class, global expansion velocity, ionization degree, and the presence of binary cores. These statistics will be computed for the full sample of 105 PNe and will demonstrate the absence of significant correlations, consistent with our qualitative assessment. revision: yes

Circularity Check

0 steps flagged

No significant circularity; purely observational extraction of residuals

full rationale

The paper's core result—that residual velocities (identified with turbulence) are transonic or slightly supersonic across all 105 PNe, with a tendency for higher values in inner zones—is obtained by direct decomposition of long-slit echelle emission-line profiles into structural components. This is a data-driven measurement process with no mathematical derivation chain, no fitted parameters relabeled as predictions, no self-referential definitions, and no load-bearing self-citations or imported uniqueness theorems. The mention of confirming prior results for [WR]-type central stars is an ancillary observation, not the justification for the ubiquity claim. The analysis remains self-contained against external spectral data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that residual velocities after line-profile decomposition equal turbulence; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Residual velocity after decomposing emission line profiles into structural contributors represents turbulence in the plasma
    Explicitly stated in the abstract as the identification method used throughout the analysis.

pith-pipeline@v0.9.0 · 5589 in / 1337 out tokens · 27743 ms · 2026-05-10T09:53:41.073588+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

53 extracted references · 45 canonical work pages · 1 internal anchor

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1...

  2. [2]

    Parts I, II

    Acker A., Marcout J., Ochsenbein F., Stenholm B., Tylenda R., Schohn C., 1992, The Strasbourg-ESO Catalogue of Galactic Planetary Nebulae. Parts I, II. . European Southern Observatory, Garching, Germany

    1992

  3. [3]

    Acker A., Gesicki K., Grosdidier Y., Durand S., 2002, @doi [ ] 10.1051/0004-6361:20020009 , https://ui.adsabs.harvard.edu/abs/2002A&A...384..620A 384, 620

    work page doi:10.1051/0004-6361:20020009 2002

  4. [4]

    Astropy Collaboration et al., 2013, @doi [ ] 10.1051/0004-6361/201322068 , http://adsabs.harvard.edu/abs/2013A

    work page doi:10.1051/0004-6361/201322068 2013

  5. [5]

    Astropy Collaboration et al., 2018, @doi [ ] 10.3847/1538-3881/aabc4f , https://ui.adsabs.harvard.edu/abs/2018AJ....156..123A 156, 123

    work page doi:10.3847/1538-3881/aabc4f 2018

  6. [6]

    Astropy Collaboration et al., 2022, @doi [ ] 10.3847/1538-4357/ac7c74 , https://ui.adsabs.harvard.edu/abs/2022ApJ...935..167A 935, 167

    work page internal anchor Pith review doi:10.3847/1538-4357/ac7c74 2022

  7. [7]

    M., Ali A., Dopita M

    Basurah H. M., Ali A., Dopita M. A., Alsulami R., Amer M. A., Alruhaili A., 2016, @doi [ ] 10.1093/mnras/stw468 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.458.2694B 458, 2694

    work page doi:10.1093/mnras/stw468 2016

  8. [8]

    Boffin H. M. J., Jones D., 2019, The Importance of Binaries in the Formation and Evolution of Planetary Nebulae . Springer Cham, @doi 10.1007/978-3-030-25059-1

    work page doi:10.1007/978-3-030-25059-1 2019

  9. [9]

    R., 1992, @doi [ ] 10.1093/mnras/259.4.629 , https://ui.adsabs.harvard.edu/abs/1992MNRAS.259..629B 259, 629

    Bryce M., Meaburn J., Walsh J. R., 1992, @doi [ ] 10.1093/mnras/259.4.629 , https://ui.adsabs.harvard.edu/abs/1992MNRAS.259..629B 259, 629

    work page doi:10.1093/mnras/259.4.629 1992

  10. [10]

    De Marco O., et al., 2022, @doi [Nature Astronomy] 10.1038/s41550-022-01845-2 , https://ui.adsabs.harvard.edu/abs/2022NatAs...6.1421D 6, 1421

    work page doi:10.1038/s41550-022-01845-2 2022

  11. [11]

    C., Walker D

    Diego F., Charalambous A., Fish A. C., Walker D. D., 1990, in Crawford D. L., ed., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 1235, Instrumentation in Astronomy VII. pp 562--576, @doi 10.1117/12.19119

    work page doi:10.1117/12.19119 1990

  12. [12]

    doi:10.26624/CETF5821

    Fitzpatrick M., Placco V., Bolton A., Merino B., Ridgway S., Stanghellini L., 2025, in Jacques A., Seaman R., Gandilo N., Linder T., eds, Astronomical Society of the Pacific Conference Series Vol. 541, Astronomical Data Analysis Software and Systems XXXIII. p. 461 ( @eprint arXiv 2401.01982 ), @doi 10.26624/CETF5821

    work page doi:10.26624/cetf5821 2025

  13. [13]

    Garc \' a-Rojas J., Morisset C., Jones D., Wesson R., Boffin H. M. J., Monteiro H., Corradi R. L. M., Rodr \' guez-Gil P., 2022, @doi [ ] 10.1093/mnras/stab3523 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.510.5444G 510, 5444

    work page doi:10.1093/mnras/stab3523 2022

  14. [14]

    E., Ricker P

    Garc \' a-Segura G., Taam R. E., Ricker P. M., 2022, @doi [ ] 10.1093/mnras/stac2824 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.517.3822G 517, 3822

    work page doi:10.1093/mnras/stac2824 2022

  15. [15]

    J., Casta \ n eda H

    Garc \' a-V \'a zquez J., Henney W. J., Casta \ n eda H. O., 2023, @doi [ ] 10.1093/mnras/stad1631 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.523.4202G 523, 4202

    work page doi:10.1093/mnras/stad1631 2023

  16. [16]

    Gesicki K., Acker A., 1996, @doi [ ] 10.1007/BF00645502 , https://ui.adsabs.harvard.edu/abs/1996Ap&SS.238..101G 238, 101

    work page doi:10.1007/bf00645502 1996

  17. [17]

    Gesicki K., Acker A., Szczerba R., 1996, , https://ui.adsabs.harvard.edu/abs/1996A&A...309..907G 309, 907

    1996

  18. [18]

    A., 2003, @doi [ ] 10.1051/0004-6361:20030079 , https://ui.adsabs.harvard.edu/abs/2003A&A...400..957G 400, 957

    Gesicki K., Acker A., Zijlstra A. A., 2003, @doi [ ] 10.1051/0004-6361:20030079 , https://ui.adsabs.harvard.edu/abs/2003A&A...400..957G 400, 957

    work page doi:10.1051/0004-6361:20030079 2003

  19. [19]

    A., Villaver E., Manchado A., 1998, @doi [ ] 10.1086/306368 , https://ui.adsabs.harvard.edu/abs/1998ApJ...507..889G 507, 889

    Guerrero M. A., Villaver E., Manchado A., 1998, @doi [ ] 10.1086/306368 , https://ui.adsabs.harvard.edu/abs/1998ApJ...507..889G 507, 889

    work page doi:10.1086/306368 1998

  20. [20]

    R., Millman, K

    Harris C. R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

    work page doi:10.1038/s41586-020-2649-2 2020

  21. [21]

    L., Latter W

    Hora J. L., Latter W. B., Smith H. A., Marengo M., 2006, @doi [ ] 10.1086/507944 , https://ui.adsabs.harvard.edu/abs/2006ApJ...652..426H 652, 426

    work page doi:10.1086/507944 2006

  22. [22]

    J., Frank A., 2006, in Barlow M

    Huggins P. J., Frank A., 2006, in Barlow M. J., M \'e ndez R. H., eds, IAU Symposium Vol. 234, Planetary Nebulae in our Galaxy and Beyond. pp 271--276 ( @eprint arXiv astro-ph/0605307 ), @doi 10.1017/S1743921306003085

    work page doi:10.1017/s1743921306003085 2006

  23. [23]

    Computing in Science and Engineering , keywords =

    Hunter J. D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    work page doi:10.1109/mcse.2007.55 2007

  24. [24]

    Jones D., Boffin H. M. J., 2017, @doi [Nature Astronomy] 10.1038/s41550-017-0117 , https://ui.adsabs.harvard.edu/abs/2017NatAs...1E.117J 1, 0117

    work page doi:10.1038/s41550-017-0117 2017

  25. [25]

    D., West K

    Kahn F. D., West K. A., 1985, @doi [ ] 10.1093/mnras/212.4.837 , https://ui.adsabs.harvard.edu/abs/1985MNRAS.212..837K 212, 837

    work page doi:10.1093/mnras/212.4.837 1985

  26. [26]

    Ralchenko Reader J., and NIST ASD Team 2024, NIST Atomic Spectra Database (ver

    Kramida A., Yu. Ralchenko Reader J., and NIST ASD Team 2024, NIST Atomic Spectra Database (ver. 5.12), [Online]. Available: https://physics.nist.gov/asd [Mar 07 2025]. National Institute of Standards and Technology, Gaithersburg, MD

    2024

  27. [27]

    R., Fitzgerald P

    Kwok S., Purton C. R., Fitzgerald P. M., 1978, @doi [ ] 10.1086/182621 , https://ui.adsabs.harvard.edu/abs/1978ApJ...219L.125K 219, L125

    work page doi:10.1086/182621 1978

  28. [28]

    , keywords =

    Liu X.-W., Storey P. J., Barlow M. J., Danziger I. J., Cohen M., Bryce M., 2000, @doi [ ] 10.1046/j.1365-8711.2000.03167.x , https://ui.adsabs.harvard.edu/abs/2000MNRAS.312..585L 312, 585

    work page doi:10.1046/j.1365-8711.2000.03167.x 2000

  29. [29]

    A., 2022, @doi [Frontiers in Astronomy and Space Sciences] 10.3389/fspas.2022.925731 , https://ui.adsabs.harvard.edu/abs/2022FrASS...9.5731L 9, 925731

    L \'o pez J. A., 2022, @doi [Frontiers in Astronomy and Space Sciences] 10.3389/fspas.2022.925731 , https://ui.adsabs.harvard.edu/abs/2022FrASS...9.5731L 9, 925731

    work page doi:10.3389/fspas.2022.925731 2022

  30. [30]

    A., Richer M

    L \'o pez J. A., Richer M. G., Garc \' a-D \' az M. T., Clark D. M., Meaburn J., Riesgo H., Steffen W., Lloyd M., 2012, @doi [ ] 10.48550/arXiv.1110.4698 , https://ui.adsabs.harvard.edu/abs/2012RMxAA..48....3L 48, 3

    work page doi:10.48550/arxiv.1110.4698 2012

  31. [31]

    Matsuura M., et al., 2025, @doi [ ] 10.1093/mnras/staf1194 , https://ui.adsabs.harvard.edu/abs/2025MNRAS.542.1287M 542, 1287

    work page doi:10.1093/mnras/staf1194 2025

  32. [32]

    A., Guti \'e rrez L., Quir \'o z F., Murillo J

    Meaburn J., L \'o pez J. A., Guti \'e rrez L., Quir \'o z F., Murillo J. M., Vald \'e z J., Pedrayez M., 2003, , https://ui.adsabs.harvard.edu/abs/2003RMxAA..39..185M 39, 185

    2003

  33. [33]

    Medina S., Pe \ n a M., Morisset C., Stasi \'n ska G., 2006, @doi [ ] 10.48550/arXiv.astro-ph/0603651 , https://ui.adsabs.harvard.edu/abs/2006RMxAA..42...53M 42, 53

    work page doi:10.48550/arxiv.astro-ph/0603651 2006

  34. [34]

    E., Esteban C., Garc \' a-Rojas J., Kreckel K., Peimbert M., 2023, @doi [ ] 10.1038/s41586-023-05956-2 , https://ui.adsabs.harvard.edu/abs/2023Natur.618..249M 618, 249

    M \'e ndez-Delgado J. E., Esteban C., Garc \' a-Rojas J., Kreckel K., Peimbert M., 2023, @doi [ ] 10.1038/s41586-023-05956-2 , https://ui.adsabs.harvard.edu/abs/2023Natur.618..249M 618, 249

    work page doi:10.1038/s41586-023-05956-2 2023

  35. [35]

    Neiner C., Acker A., Gesicki K., Szczerba R., 2000, , https://ui.adsabs.harvard.edu/abs/2000A&A...358..321N 358, 321

    2000

  36. [36]

    Peimbert M., 1967, @doi [ ] 10.1086/149385 , https://ui.adsabs.harvard.edu/abs/1967ApJ...150..825P 150, 825

    work page doi:10.1086/149385 1967

  37. [37]

    Perinotto M., Sch \"o nberner D., Steffen M., Calonaci C., 2004, @doi [ ] 10.1051/0004-6361:20031653 , https://ui.adsabs.harvard.edu/abs/2004A&A...414..993P 414, 993

    work page doi:10.1051/0004-6361:20031653 2004

  38. [38]

    G., Su \'a rez G., L \'o pez J

    Richer M. G., Su \'a rez G., L \'o pez J. A., Garc \' a D \' az M. T., 2017, @doi [ ] 10.3847/1538-3881/aa5f53 , https://ui.adsabs.harvard.edu/abs/2017AJ....153..140R 153, 140

    work page doi:10.3847/1538-3881/aa5f53 2017

  39. [39]

    G., Arrieta A., Arias L., Casta \ n eda-Carlos L., Torres-Peimbert S., L \'o pez J

    Richer M. G., Arrieta A., Arias L., Casta \ n eda-Carlos L., Torres-Peimbert S., L \'o pez J. A., Galindo A., 2022, @doi [ ] 10.3847/1538-3881/ac9732 , https://ui.adsabs.harvard.edu/abs/2022AJ....164..243R 164, 243

    work page doi:10.3847/1538-3881/ac9732 2022

  40. [40]

    G., L \'o pez J

    Richer M. G., L \'o pez J. A., Arrieta A., Arias L., Torres-Peimbert S., 2025, in De Marco O., Zijlstra R., Szczerba R., eds, IAU Symposium Vol. S384, Planetary Nebulae: a Universal Toolbox in the Era of Precision Astrophysics. p. 136–142, @doi 10.1017/S1743921324000462

    work page doi:10.1017/s1743921324000462 2025

  41. [41]

    Sabbadin F., Turatto M., Benetti S., Ragazzoni R., Cappellaro E., 2008, @doi [ ] 10.1051/0004-6361:200809429 , https://ui.adsabs.harvard.edu/abs/2008A&A...488..225S 488, 225

    work page doi:10.1051/0004-6361:200809429 2008

  42. [42]

    Trier, S

    Stull R. B., 1988, An introduction to boundary layer meteorology . Kluwer Academic Publishers, Dordrecht, The Netherlands, @doi 10.1007/978-94-009-3027-8

    work page doi:10.1007/978-94-009-3027-8 1988

  43. [43]

    The Pandas Development Team 2023, pandas-dev/pandas: Pandas , @doi 10.5281/zenodo.7549438

    work page doi:10.5281/zenodo.7549438 2023

  44. [44]

    A., Arthur S

    Toal \'a J. A., Arthur S. J., 2014, @doi [ ] 10.1093/mnras/stu1360 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.443.3486T 443, 3486

    work page doi:10.1093/mnras/stu1360 2014

  45. [45]

    Instrumentation in astronomy VI , year = 1986, editor =

    Tody D., 1986, in Crawford D. L., ed., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 627, Instrumentation in astronomy VI. p. 733, @doi 10.1117/12.968154

    work page doi:10.1117/12.968154 1986

  46. [46]

    J., Brissenden R

    Tody D., 1993, in Hanisch R. J., Brissenden R. J. V., Barnes J., eds, Astronomical Society of the Pacific Conference Series Vol. 52, Astronomical Data Analysis Software and Systems II. p. 173

    1993

  47. [47]

    Virtanen P., et al., 2020, @doi [Nature Methods] 10.1038/s41592-019-0686-2 , https://rdcu.be/b08Wh 17, 261

    work page doi:10.1038/s41592-019-0686-2 2020

  48. [48]

    V., Jenkins C

    Wall J. V., Jenkins C. R., 2003, Practical Statistics for Astronomers . Vol. 3, Cambridge University Press, Cambridge, UK

    2003

  49. [49]

    A., et al., 2020, @doi [ ] 10.1051/0004-6361/202037998 , https://ui.adsabs.harvard.edu/abs/2020A&A...640A..10W 640, A10

    Weidmann W. A., et al., 2020, @doi [ ] 10.1051/0004-6361/202037998 , https://ui.adsabs.harvard.edu/abs/2020A&A...640A..10W 640, A10

    work page doi:10.1051/0004-6361/202037998 2020

  50. [50]

    Wesson R., Jones D., Garc \' a-Rojas J., Boffin H. M. J., Corradi R. L. M., 2018, @doi [ ] 10.1093/mnras/sty1871 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.480.4589W 480, 4589

    work page doi:10.1093/mnras/sty1871 2018

  51. [51]

    Wesson R., et al., 2024, @doi [ ] 10.1093/mnras/stad3670 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528.3392W 528, 3392

    work page doi:10.1093/mnras/stad3670 2024

  52. [52]

    C., 1950, @doi [ ] 10.1086/145264 , https://ui.adsabs.harvard.edu/abs/1950ApJ...111..279W 111, 279

    Wilson O. C., 1950, @doi [ ] 10.1086/145264 , https://ui.adsabs.harvard.edu/abs/1950ApJ...111..279W 111, 279

    work page doi:10.1086/145264 1950

  53. [53]

    van Hoof P. A. M., 2018, @doi [Galaxies] 10.3390/galaxies6020063 , https://ui.adsabs.harvard.edu/abs/2018Galax...6...63V 6, 63

    work page doi:10.3390/galaxies6020063 2018