3D Binary Neutron Star Merger Ejecta Evolution up to Seconds Timescale: Dynamics, Element Distribution, and Light Curves

Fabio Magistrelli; Luis Felipe Longo Micchi; Maximilian Jacobi; Sebastiano Bernuzzi

REVIEW 4 major objections 5 minor 131 references

3D Binary Neutron Star Merger Ejecta Evolution up to Seconds Timescale: Dynamics, Element Distribution, and Light Curves

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

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Pith's one-line read Full 3D simulations of binary neutron star merger ejecta show that 2D ray-by-ray kilonova light curves are robust upper limits, and that increased dimensionality alone cannot reconcile theoretical models with the AT2017gfo observations.

desk verdict A valuable but slightly over-claimed 3D ejecta evolution paper: the new data and the 2D-vs-3D light-curve comparison are worth engaging, but the central dimensionality conclusion is weakened by a confounded control. read the letter →

arxiv 2608.10100 v1 pith:DRCB7RYB submitted 2026-08-10 astro-ph.HE gr-qc

Luis Felipe Longo Micchi , Fabio Magistrelli , Maximilian Jacobi , Sebastiano Bernuzzi This is my paper · ORCID

classification astro-ph.HEgr-qc

keywords kilonovabinaryneutronstarmergersejectaevolutionnuclearheatingr-processnucleosynthesisray-by-raylightcurvesAT2017gfo3Dhydrodynamics

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 the standard shortcut of averaging a neutron-star merger's ejecta into an axisymmetric 2D profile before computing the kilonova light curve is reliable. It runs the same ejecta in full 3D out to about one second after merger, with nuclear heating included, and finds that the 2D light curves are broadly correct in shape but systematically too bright: they are upper limits. The negative side of the result is that going to 3D makes the gap between simulated and observed light curves (specifically the kilonova AT2017gfo) slightly wider, not narrower. The paper concludes that missing ejecta components, most likely neutron-rich outflows from the remnant disk, are the more plausible explanation for the discrepancy than the assumed geometry. This matters because it changes where the community should look for the missing physics.

What carries the argument

The argument is carried by a pipeline that uses the ejecta crossing a radius of 300 solar masses during the numerical-relativity window as a time-dependent inner boundary for a 3D general-relativistic hydrodynamics evolution on a Schwarzschild background, with a hybrid equation of state that switches from a nuclear-statistical-equilibrium table to a low-density Helmholtz-type EOS, and with nuclear heating injected through fitted heating-rate tables. The identical ejecta are then mapped onto a Lagrangian ray-by-ray radiation-hydrodynamics light-curve code, once as fully 3D multi-angle profiles and once after a mass-weighted azimuthal average, so that the only difference between the two light-curve sets is the dimensionality of the input. A Newtonian homology parameter quantifies how far the ejecta still are from free homologous expansion at one second, and tracer trajectories post-processed through a nuclear reaction network produce the element sky-maps and isotopic yields.

What would settle it

Re-run the same 3D pipeline after adding the missing viscous disk outflows (or otherwise extending the simulation until the remnant disk has finished ejecting): if the 3D bolometric light curve then matches AT2017gfo while the azimuthally averaged 2D curve still falls short, the paper's central claim that dimensionality is not the missing ingredient is falsified.

Watch

Extended reading notes

Core claim

Using four numerical-relativity merger simulations as boundary data, the authors evolve the ejected matter in full 3D for about one second with a transition equation of state and fitted nuclear heating rates. They find that nuclear heating delays the onset of homologous expansion, keeps non-radial motions alive in the most asymmetric binary, and reshuffles heavy elements on the sky: extending the evolution from ~150 ms to ~1 s widens the polar region containing 90% of the heavy-element mass from within 15 degrees of the equator to within 30 degrees. The central comparative discovery is that azimuthally averaged (2D) ray-by-ray light curves are broadly robust but should be treated as upper limits; the 3D light curves peak later, are dimmer, and depend more strongly on viewing angle for unequal-mass binaries, with the 3D emission matching its 2D counterpart only for observers who look straight into the densest part of a lanthanide curtain. From this the authors conclude that dimensionality alone is unlikely to close the gap between ab-initio models and the observed AT2017gfo kilonova, and that the gap points instead to missing ejecta, most plausibly viscous disk outflows.

Load-bearing premise

The comparison assumes that the ejecta recorded in the first ~100 ms of the numerical-relativity simulations are the whole inventory powering the light curve, even though later viscous disk outflows are missing.

Editorial extensions

If this is right

Published kilonova light curves computed from azimuthally averaged profiles should be interpreted as upper limits on the bolometric luminosity, not as best estimates.
For unequal-mass mergers, the kilonova's brightness and color depend strongly on viewing angle, with a one-sided 'lanthanide bullet' producing a red, slow-declining direction and a bluer, faster direction opposite to it.
The 56Ni to 56Co to 56Fe decay chain dominates the heating around 100 days, and the associated gamma-ray lines at 846.77 and 1238.288 keV should be strongest when the binary is viewed close to face-on.
The residual mismatch with AT2017gfo is more likely explained by missing neutron-rich viscous disk outflows than by the difference between 2D and 3D geometry, redirecting modeling effort toward including late-time disk ejecta.
Since homologous expansion is not yet reached at one second in the asymmetric models, radiative-transfer light curves that assume homology at earlier times may carry a systematic offset; evolving the ejecta closer to the ~2.5 s homology time would produce more reliable inputs.

Reading between the lines

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

If the 2D upper-limit interpretation is right, many previously published kilonova light-curve calculations that azimuthally averaged 3D merger data may have systematically overestimated the emitting mass; re-reading those results as upper limits could revise inferred r-process yields from GW170817/AT2017gfo.
The predicted one-sided lanthanide bullet in asymmetric mergers implies a measurable late-time spectropolarimetric signature; archival or future polarimetric observations of kilonovae could test this geometry directly.
The paper's four models span only two equations of state and two mass-ratio ranges; whether the 2D-versus-3D upper-limit behavior is universal across the neutron-star population remains an open question that a broader parameter survey could settle.
A natural next step the authors do not take is to map the 1 s 3D profiles into a full 3D radiative-transfer solver rather than ray-by-ray sections; the ray-by-ray approximation itself could be tested by comparing its 3D output against a true multi-dimensional transport calculation.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The real news here is the data: four BNS merger ejecta profiles evolved to about one second in full 3D with nuclear heating coupled to the hydrodynamics, plus element-distribution sky maps and a systematic 2D-vs-3D ray-by-ray light-curve comparison. That combination is new and useful, even though previous work reached similar timescales with different methods. The paper also does a nice job with internal diagnostics: the homology parameter, the E_theta^Kinetic energy, the 150-ms versus 1-s element redistribution, and the Appendix A mass-flux comparisons all hang together and support the qualitative picture. The nucleosynthesis findings (56Ni/56Co dominance at about 100 days, the absence of 44Ti, the 88Sr overproduction) are concrete and testable, and the authors are honest about the missing viscous ejecta and the simplified Ye treatment. The soft spot is the central 3D-vs-2D comparison. The authors claim that increased dimensionality alone is unlikely to close the gap with AT2017gfo, but the 2D runs are not evolved in Athena++: they use azimuthally averaged THC data at r=300 M_sun, so they differ from the 3D runs in both dimensionality and in about one second of additional hydrodynamical evolution, including heating and the approach to homology. The authors explicitly say the 2D results are 'also representative of an earlier homology assumption,' which is precisely the confound. The BLh_150 run helps but does not fully isolate dimensionality, because it is still a 3D run truncated at 150 ms, not a 2D version of the 1-s profiles. So the abstract's strongest claim is not cleanly supported by its own comparison. The conclusion may still be true, and the paper's other arguments (mass overestimation, analytic scaling) point in the same direction, but the specific causality is muddier than the abstract suggests. Minor issues: no resolution convergence study, no error bars on light curves, and the opacity model is deliberately simplified. These are not fatal for a work of this scope, but they should be acknowledged more prominently. The data availability statement promises tracer release after peer review, which is fine. This paper deserves a serious referee. The simulation data are valuable, the analysis is mostly careful, and the conclusions are interesting even if the headline claim about dimensionality needs softening or a cleaner control. I would engage with it in a reading group and likely cite it. Recommend sending to peer review with requests for a clearer comparison and more explicit caveats.

Referee Report

4 major / 5 minor

Summary. The paper presents long-term (about 1 s) three-dimensional general-relativistic hydrodynamics simulations of ejecta from four binary neutron star merger simulations, using THC numerical-relativity data injected as boundary conditions into Athena++. The code includes a transition from a nuclear-statistical-equilibrium EOS to the Timmes/Helmholtz EOS, an effective nuclear-heating prescription based on reaction-network fits, and passive scalars for electron fraction, entropy, expansion timescale, and injection flag. The authors analyze ejecta dynamics and geometry, report a homology parameter and heating diagnostics, post-process tracers with the WinNet nuclear network to obtain element distributions and nucleosynthesis yields, and compute multi-angle kilonova light curves with KNEC using both 3D and azimuthally-averaged 2D profiles. The main claims are that nuclear heating significantly affects the ejecta dynamics and redistributes heavy elements on the sky, that the 56Ni-56Co-56Fe chain dominates heating around 100 days, that 2D ray-by-ray light curves are broadly robust but should be treated as upper limits, and that increased dimensionality alone cannot bridge the gap between ab-initio simulated light curves and AT2017gfo observations.

Significance. If the central claims hold, this is a valuable step forward: it provides one of the first consistent extensions of NR merger ejecta to second-long timescales in 3D with non-NSE thermodynamics and coupled nuclear heating, and it quantifies how early truncation of the hydrodynamical evolution affects nucleosynthesis and element sky maps. The paper includes useful internal diagnostics, such as the mass-flux comparison in Appendix A, the homology parameter in Fig. 4, and the E_theta^Kinetic diagnostic in Fig. 6, which support the dynamical conclusions. The authors also release tracer data on Zenodo upon acceptance, which is commendable. The heating-rate input is taken from external SkyNet-based fits rather than fitted to observations, and the 56Ni dominance at 100 days is a post-processing result from WinNet, so the light-curve comparison is not circular. However, the headline conclusion about 2D-versus-3D light curves and the AT2017gfo gap is weakened by a methodological confound in the comparison, as detailed below.

major comments (4)

[Sec. IIE and Sec. IIIC, Fig. 16] The central 2D-versus-3D light-curve comparison conflates dimensionality with the additional ~1 s of hydrodynamical evolution. As stated in Sec. IIE, the 2D KNEC runs are built from azimuthally averaged THC data at r = 300 M_sun, without the Athena++ 3D extension, and the authors explicitly note that the 2D results are 'also representative of an earlier homology assumption.' The BLh_150 run in Fig. 16 is not a control for this comparison: it is a 3D Athena++ run truncated at 150 ms, differing from the 2D calculation in both dimensionality and data origin. Therefore the observed luminosity enhancement of 2D over 3D cannot be uniquely attributed to the axisymmetry assumption. The conclusion in Sec. IV that 'the 2D ray-by-ray approach remains a robust but upper-limit estimate' and that 'increased dimensionality alone is not sufficient' is not yet cleanly supported. A conclusive test would be to azimuthally average the 1 s Athena++ profiles and feed those into KNEC, or otherwise perform a same-time, same-ejecta 2D control.
[Sec. IIIA and Sec. IIIC] The ejecta inventory used in the comparison is incomplete in a way that limits the AT2017gfo conclusion. The authors state in Sec. IIIA that 'mass ejection from long-lived remnants would still continue past the NR simulated time,' and in Sec. IIIC they attribute a large part of the AT2017gfo gap to missing viscous ejecta. The 3D-vs-2D light-curve comparison, however, is based only on the ejecta that crossed r = 300 M_sun during the ~100 ms covered by the THC simulations. If the later disk outflows are massive and lanthanide-rich, the relative importance of dimensionality versus missing ejecta components could be different for the total ejecta. The paper should either restrict the dimensionality claim to the modeled ejecta component or provide a quantitative estimate of how the missing component would affect the upper-limit interpretation.
[Sec. IIA and Sec. IIIC] The absence of a resolution study weakens the quantitative claims about light curves and element distributions. The Athena++ grid uses N_theta = 16 and N_phi = 32, which is coarse for capturing the small-scale features of tidal arms and the lanthanide curtain, and the KNEC mapping uses 512 angular sections derived from this grid. No convergence test is presented for the 3D profiles, the opening angles quoted in the abstract (e.g., 15 to 30 degrees), or the light-curve differences in Figs. 16-18. Since several conclusions are phrased in terms of angular structure and luminosity differences of order tens of percent, a resolution study (at least for one model) is needed to establish that the reported 3D features are converged.
[Sec. IIC and Sec. IIIA] The treatment of Ye as a fixed passive scalar after injection is a potentially load-bearing simplification for the light-curve comparison. The authors note in Sec. IIIA that beta-decay and e± capture can drive Ye to ~0.4 on the second timescale, and the KNEC opacity model in Sec. IIE uses a constant opacity set by the initial Ye. Since the lanthanide fraction and hence the opacity depend on Ye, the 2D-versus-3D luminosity comparison could be affected by the frozen-Ye assumption. The a posteriori pressure-error check in Sec. IIC (12% maximum for 90% of the mass) bounds the thermodynamic impact but does not directly bound the opacity or light-curve impact. A test with a simple Ye-evolution prescription, or at least an estimate of the opacity uncertainty, would strengthen the light-curve conclusions.

minor comments (5)

[Fig. 6 caption] The last label in the legend reads 'Kinetic Energy' twice; one of the entries should presumably be 'E_theta^Kinetic' as defined in Eq. (19).
[Sec. IIIA surrounding Eq. (16)] There is a typo: 'accelatation in the Lagrangian grame' should read 'acceleration in the Lagrangian frame.'
[Sec. IIIC, paragraph near Fig. 18] The sentence 'the AB magnitudes are increased when the dimensionality was increased' is ambiguous; since larger AB magnitudes correspond to dimmer objects, the wording should be clarified (e.g., 'the AB magnitudes become larger, i.e., the model becomes dimmer').
[Fig. 15 caption] The phrase 'The right captions are insets of the left plots' appears to mean 'the right panels are insets of the left plots' and should be reworded.
[Sec. IIE, Eq. (14)] The projection weights p_k are defined with a vector solid-angle integral; the notation is somewhat terse. A brief explanation of how the bins are constructed and how the weights are normalized would improve reproducibility.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: central claims rest on independent hydrodynamics, network nucleosynthesis, and unfitted light-curve comparisons; self-citations are not load-bearing.

full rationale

The paper's central claims do not reduce by construction to their inputs. The long-term Athena++ evolutions are driven by NR boundary data and a transition EOS plus an effective heating prescription; the heating rates of [46,70] are fits to external SkyNet network trajectories, not to the light curves or element yields being predicted. The WinNet post-processing is an independent single-zone network calculation, and the 56Ni->56Co->56Fe dominance at ~100 days is a computed confirmation, not an input constant imposed to match a target. The KNEC light curves use those rates, Ye-dependent opacities, and a thermalization model, and are compared directly with AT2017gfo without fitting; the conclusion that 3D does not close the gap is a null result, not a circular prediction. Self-citations to [35] and [46] serve as comparison benchmarks and methodological sources. [35] is explicitly described as using the same THC data but with a 2D azimuthally averaged, online-network pipeline, and the present paper quantifies why its 56Ni masses differ. The nearest thing to a circularity concern is the 2D-versus-3D light-curve comparison: Sec. II E states that the 2D profiles are constructed directly from azimuthally averaged THC data at r=300 M_sun without the Athena++ extension, so the 2D results combine lower dimensionality, an earlier homology assumption, and a non-mass-conserving averaging. However, the paper explicitly addresses this in Sec. IV, attributing the 2D/3D luminosity differences to positive-flux selection and to the mass-weighted average not preserving total mass, and it includes the BLh_150 control to assess the shorter-evolution-time effect. Whether or not that attribution is fully clean, it is an interpretation of a controlled numerical comparison, not a definitional equivalence; no equation or fitted parameter is recycled as a prediction. The acknowledged missing viscous ejecta and the continued mass ejection from long-lived remnants (Secs. III A and III C) are completeness limitations, not circularity. Overall, the derivation chain is self-contained against external benchmarks and the central claims have independent content.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The results depend on the completeness of the injected NR ejecta, the accuracy of the fitted heating rates, the validity of the Schwarzschild background, and the free-expansion nucleosynthesis assumption. No new particles, forces, or physical entities are introduced.

free parameters (2)

EOS transition boundaries = T_start=0.7 MeV, T_end=0.05 MeV, n_start=1e-10 fm^-3, n_end=1e-12 fm^-3
Chosen by hand to produce a smooth transition between the NSE table and Helmholtz EOS (Table I, Eqs. 2-5); the thermodynamics and heating in the transition layer depend on these values, and no sensitivity study is reported.
Ejecta definition and heating activation flag cuts = F in (0.9, 1.1) for heating; |F-1| < 0.01 for ejecta analysis
Used to separate physical ejecta from atmosphere and late-time spurious injection (Sec. II C); the reported ejecta masses, the widening from 15 to 30 degrees, and the light curves depend on these thresholds.

assumptions (5)

domain assumption The NR ejecta recorded at r=300 M_sun over the ~100 ms THC simulations constitute the complete ejecta inventory for the first second (no missing disk or viscous outflows).
Used to construct the Athena++ boundary condition (Sec. II B). The paper itself states that long-lived remnants would continue ejecting mass past the NR simulated time (Sec. III A), and later attributes the AT2017gfo discrepancy to missing viscous ejecta (Sec. IIIC).
domain assumption The fitted heating rates of [46, 70], evaluated with fixed Ye0, s0, tau0, reproduce the true nuclear heating accurately enough for dynamics and light curves.
Used in Eq. 7 as the only energy source from nuclear burning; the paper verifies pressure errors around 8 to 12 percent for BLh_q1.43 tracers but does not propagate this check to all models.
domain assumption Hydrodynamics on a Schwarzschild background with mass parameters of each binary is a valid approximation for radii above 300 M_sun.
Used throughout the Athena++ setup (Sec. II A); this ignores remnant spin and dynamical spacetime effects beyond 300 M_sun.
domain assumption The WinNet post-processing with free expansion and no neutrino absorption correctly predicts element production from the Athena++ 1s state.
Used for all nucleosynthesis and element distribution claims (Sec. II D); mixing between neighboring cells is neglected, and the adiabatic free-expansion trajectory is assumed from [34].
domain assumption The opacity model (constant opacity set by initial Ye) and thermalization factor f_th=0.5 are adequate for the light curve comparison.
Used in KNEC light curve calculations (Sec. II E); these are known simplifications and could affect the absolute brightness and color evolution.

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Pith. "Pith review of 3D Binary Neutron Star Merger Ejecta Evolution up to Seconds Timescale: Dynamics, Element Distribution, and Light Curves." pith.science (2026). https://pith.science/paper/DRCB7RYB

@misc{pith2026260810100,
  author       = {Pith},
  title        = {Pith review of: 3D Binary Neutron Star Merger Ejecta Evolution up to Seconds Timescale: Dynamics, Element Distribution, and Light Curves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DRCB7RYB}},
  note         = {Machine review of arXiv:2608.10100}
}

abstract

We present long-term, three-dimensional simulations of ejecta from four binary neutron star mergers to second-long time-scales. Numerical-relativity data serve as boundary conditions for a general-relativistic hydrodynamics evolution incorporating an equation of state valid outside nuclear statistical equilibrium and an effective nuclear-heating prescription based on reaction-network calculations. We investigate the ejecta's dynamical and geometrical properties, the impact of nuclear heating, the formation and spatial distribution of elements, and compute multi-angle kilonova light curves. % Nuclear heating significantly affects ejecta dynamics, delaying homologous expansion beyond second time-scales and reshapes the spatial distribution of heavy nuclei. This effect is largest for asymmetric binaries with long-lived remnants; extending the evolution from ${\sim}150$~ms to ${\sim}1$~s widens the angular polar region containing 90\% of the heavy-element mass (\eg, $Z=56$, $Z=79$) from $|\theta|\lesssim15^{o}$ to $|\theta|\lesssim30^{o}$. Our nucleosynthesis results confirm that the $^{56}$Ni$\rightarrow^{56}$Co$\rightarrow^{56}$Fe decay chain dominates the heating at $\sim$100 days, with cobalt decay producing gamma-ray lines at 846.77 and 1238.288~keV. % Comparing kilonova ray-by-ray light curves obtained from multi-angle 3D profiles and averaged 2D profiles, we find the latter approach broadly robust, although 2D light curves should be treated as upper limits. Increasing dimensionality generally lowers the bolometric luminosity, with binary asymmetry strengthening the viewing-angle dependence. For observers aligned with a lanthanide curtain's densest region, 3D emission can match its 2D counterpart in brightness. We conclude that increased dimensionality alone is unlikely to reconcile current theoretical models with AT2017gfo observations.

Figures

Figures reproduced from arXiv: 2608.10100 by the authors.

**Figure 1.** FIG. 1. Scatter plot of temperature of fluid elements as a [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** FIG. 2. Total and unbound masses in our simulations as a [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

Figures from the paper (17 more)

**Figure 3.** Figure 3: We investigate the ejecta expansion by means of a Newtonian homology parameter [52] χ = |a|t |v| , (15) where the overbar denotes the mass average, and a and v are the acceleration and the velocity in the Lagrangian reference frame. As usual for our analysis, we o…

**Figure 3.** Figure 3: FIG. 3. Components of the three-velocity of the ejecta for the DD2_q1.67 and SFHo_q1.0 model. While the left columns of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png]

**Figure 4.** Figure 4: While individual contributions are shown in dis [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. Nuclear heating rates obtained through the fit formulas of [46, 70] for DD2_q1.67 at [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: FIG. 8. In this corner plot we show the distribution and correlation of several quantities of interest for our models by [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: FIG. 9. Sky location of elements as a function of atomic number for our models. We note the large asymmetry in the DD2_q1.67 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

**Figure 10.** Figure 10: FIG. 10. Element masses as a function of sections of varying [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

**Figure 11.** Figure 11: FIG. 11. Element masses as a function of sections of varying [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

**Figure 13.** Figure 13: FIG. 13. Here we display the sky regions containing 90% of [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]

**Figure 12.** Figure 12: FIG. 12. In this figure we show the impact of an early as [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]

**Figure 14.** Figure 14: FIG. 14. Evolution of [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]

**Figure 15.** Figure 15: FIG. 15. Total nuclear heating and its different sources. The right captions are insets of the left plots for better comparison. At [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]

**Figure 16.** Figure 16: FIG. 16. Bolometric luminosity evolution of the mod [PITH_FULL_IMAGE:figures/full_fig_p019_16.png]

**Figure 17.** Figure 17: FIG. 17. Observed luminosities as a function of time and angles of view with colored lines representing different azimuthal [PITH_FULL_IMAGE:figures/full_fig_p020_17.png]

**Figure 18.** Figure 18: FIG. 18. Here we present the AB magnitudes at 40 Mpc obtained when feeding our 3D ray-by-ray version of the [PITH_FULL_IMAGE:figures/full_fig_p021_18.png]

**Figure 19.** Figure 19: FIG. 19. Here we show the comparison of the mass flux at [PITH_FULL_IMAGE:figures/full_fig_p022_19.png]

Discussion (0). Continue with ORCID to comment.

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