pith. machine review for the scientific record. sign in

arxiv: 2602.21440 · v1 · submitted 2026-02-24 · 🌌 astro-ph.SR · astro-ph.HE

Recognition: 2 theorem links

· Lean Theorem

On the Importance of the Convective Urca Process in 3D Simulations of a Simmering White Dwarf

Ferran Poca-Amor\'os , Brendan Boyd , Dean M. Townsley , Alan Calder
Authors on Pith no claims yet

Pith reviewed 2026-05-15 19:21 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.HE
keywords convective Urca processwhite dwarfType Ia supernovasimmering phase3D convectionneutrino lossesconvective boundarynuclear energy generation
0
0 comments X

The pith

The convective Urca process substantially reduces the convection zone size in 3D simulations of simmering white dwarfs, though convection still extends past the Urca shell.

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

This paper investigates the convective Urca process during the simmering phase of a near-Chandrasekhar-mass white dwarf, the slow carbon burning that precedes a possible Type Ia supernova. The authors run full 3D low-Mach-number simulations both with and without the A=23 Urca reactions and compare the resulting steady-state structures. They show that the process changes neutrino losses, nuclear energy generation, and the location of the convective boundary. A reader would care because the size and composition of this convective region set the conditions for the later runaway that determines the supernova outcome. The results supply concrete structural information that can update simpler one-dimensional stellar models used for longer evolutionary tracks.

Core claim

The authors perform full 3D simulations of the simmering white dwarf with the low-Mach-number code MAESTROeX, comparing cases that include the A=23 convective Urca process to cases that omit it. Once both sets of runs reach a relaxed steady state, they find that the Urca process reduces the radial extent of the convection zone while convection nonetheless continues past the Urca shell. The process also modifies the neutrino losses and the local nuclear energy generation rate, producing measurable changes at the convective boundary that can be fed into one-dimensional models.

What carries the argument

The convective Urca process, which couples turbulent mixing by convection to weak nuclear reactions that emit neutrinos and alter the local composition and energy balance.

If this is right

  • The convection zone becomes smaller once the A=23 Urca reactions are active.
  • Neutrino losses rise because of the additional weak reactions enabled by mixing.
  • Nuclear energy generation is redistributed within the smaller convective region.
  • The convective boundary moves inward while material still mixes across the Urca shell.
  • Compositional profiles produced by the reduced zone can be used directly in one-dimensional stellar evolution codes.

Where Pith is reading between the lines

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

  • The smaller convection zone may slow the overall heating rate and therefore change how close the white dwarf gets to the Chandrasekhar limit before runaway.
  • Updated compositional gradients from these runs could alter the predicted ignition density and the resulting supernova nucleosynthesis yields.
  • The same 3D Urca treatment might be applied to convective zones in other stellar contexts where weak reactions compete with mixing.
  • Longer simulations that reach the onset of runaway could test whether the reduced zone persists or readjusts as temperatures rise.

Load-bearing premise

The simulations have truly relaxed to steady state and the chosen nuclear rates plus boundary treatment correctly capture the turbulent convection and its coupling to Urca reactions over the simulated times.

What would settle it

A 3D simulation that includes the Urca reactions but yields a convection zone of the same size as the no-Urca run after relaxation would falsify the claim that the process substantially reduces the zone.

Figures

Figures reproduced from arXiv: 2602.21440 by Alan Calder, Brendan Boyd, Dean M. Townsley, Ferran Poca-Amor\'os.

Figure 1
Figure 1. Figure 1: Top plot: Star temperature vs radius profiles. Bottom plot: Mass fraction of the Urca species vs radius. The grey curves represent the initial state of the simulations in B2025, the blue curves the initial state of the FN1 and NB1 simulations, and the green curves the initial state of the FN2 simulation. The dashed curves represent the 23Ne and the solid ones the 23Na. The vertical red line indicates the p… view at source ↗
Figure 2
Figure 2. Figure 2: 2D slice through the center of the WD colored by the value of X( 12C) at the end of the simulation. The solid and dashed black lines represent the Urca shell and the boundary where X( 23Na) = X( 23Ne) respectively. The black streamlines indicate the trajectories of the convective flows. The left slice represents the FN2 simulation, and the right one the NB1 simulation. 0 100 200 300 400 500 600 700 800 Rad… view at source ↗
Figure 3
Figure 3. Figure 3: Spherically averaged X( 12C) profiles vs radial bin for each simulation. The green curve is from FN1 simulation. The blue curve from the FN2 simulation. And the orange curve from NB1 simulation. The red vertical dash-dot line indicates the location of the Urca Shell. The vertical dashed lines indicate the Rconv for the FN2 (blue) and NB1 (orange) simulations [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The left plot tracks the mass contained in the convection zone, Mconv, over simulation time. The right plot shows the Urms of the convection zone over time. We plot all three simulations with FN1 in green, FN2 in blue and NB1 in orange. electron capture region and β-decay regions, with an additional source term for 23Na from the carbon burning. Since there is no β-decays in the NB1 simulation, the equilibr… view at source ↗
Figure 5
Figure 5. Figure 5: Spherically averaged convective gradient profiles vs radial bin for each simulation. The dashed curves represent the ratio of the real gradient to an adiabatic (∇/∇ad. The solid curves represent the ratio of the real gradient to the Ledoux gradient (∇/∇Led. The green curve is from FN1 simulation. The blue curve from the FN2 simulation. And the orange curve from NB1 simulation. The red vertical dash-dot lin… view at source ↗
Figure 6
Figure 6. Figure 6: Urms(r) against radius profiles averaged over the time. That is the last 400 s for the FN1 simulation (represented by the green curve), 400 s for the FN2 simulation (represented by the blue curve), and the last 500 s for the NB1 simulation (represented by the orange curve). The vertical dashed lines indicate the Rconv for the FN2 (blue) and NB1 (orange) simulations. The red vertical dash-dot line indicates… view at source ↗
Figure 7
Figure 7. Figure 7: Slices through the center of the white dwarf, zoomed into the convective core region. From left to right we have the FN1, FN2, and NB1 simulations. The inner white circle indicates the Urca shell. The outer two circles approximately mark the edge of the convection zones for the two simulations 545 km and 745 km respectively. In summary, both FN2 and NB1 simulations reached a steady-state defined by a conve… view at source ↗
Figure 8
Figure 8. Figure 8: Top plot: Energy generation rate components per radial bin in the FN2 simulation. Middle plot: Energy generation rate components per radial bin in the NB1 simulation. Bottom plot: Total energy generation rate per radial bin with all the contributions summed up. The blue lines represent the FN1 simulation, the orange lines the NB2, and the vertical lines indicate the convective boundaries. In the first two … view at source ↗
Figure 9
Figure 9. Figure 9: Schematic illustration of the simplified effects of the Urca reactions in a bubble of degenerate material. in carbon burning is mostly being converted via electron capture. However, when considering the difference between the two simulations, FN2 and NB1, (the bottom plot of [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Top plot: Electron fraction rate. The blue curves represents the FN2 simulation that considers the Urca reactions, and the orange ones the NB1 simulation that excludes β-decays. Bottom plot: The difference between the electron fraction rate profiles plotted above. The vertical red line indicates the presence of the Urca shell, and other vertical dashed lines indicate the boundary of the convective region … view at source ↗
Figure 11
Figure 11. Figure 11: The amount in grams of 12C burned in each simulation over the last few thousand seconds of simulation time. We plot all three simulations with FN1 in green, FN2 in blue and NB1 in orange. To summarize Section 5, we present the most relevant quantitative results in [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The thermal energy rate per radial bin vs radius. Each curve is from the FN2 simulation. The blue curve includes all contributions to ˙ϵtherm. The dashed orange curve includes the primary electron component. The red dash-dot vertical line indicates the location of the Urca shell. REFERENCES AMReX-Astro initial models Team, Boyd, B., Smith Clark, A., Willcox, D., & Zingale, M. 2024, AMReX-Astro/initial mod… view at source ↗
read the original abstract

Type Ia supernovae are bright thermonuclear explosions that are important to numerous areas of astronomy. However, the origins of these events are poorly understood. One proposed setting is that of a near Chandrasekhar mass white dwarf that undergoes runaway carbon burning in the core. During the thousand years leading up to the explosion, the white dwarf undergoes a simmering phase where slow carbon burning heats the core and drives convection. A poorly understood aspect of this phase is the convective Urca process, which links convection with weak nuclear reactions. We use the low Mach number code MAESTROeX to perform full 3D simulations as is required to accurately capture the turbulent convection. We present simulations with and without the A=23 convective Urca process, which have relaxed to a steady state. We characterize the effects of the convective Urca process on the neutrino losses, the nuclear energy generation, and the convective boundary. We find that the size of the convection zone is substantially reduced by the convective Urca process, though convection still extends past the Urca shell. Our findings on the structure of the convective zone and the compositional changes can be used to inform 1D stellar models that track the longer-timescale 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

1 major / 1 minor

Summary. The manuscript reports 3D low-Mach number hydrodynamic simulations with MAESTROeX of the simmering phase in a near-Chandrasekhar-mass white dwarf. It compares two runs stated to have relaxed to steady state, one including the A=23 convective Urca process and one without, and finds that the Urca process substantially reduces the convection-zone size while convection still extends past the Urca shell. The results on convective structure, neutrino losses, nuclear energy generation, and composition are presented as input for 1D stellar models of the longer-timescale evolution toward Type Ia supernovae.

Significance. If the central result holds, the work is significant for clarifying the role of the convective Urca process in the pre-explosion simmering phase of Type Ia supernova progenitors. The direct 3D comparison of otherwise identical runs isolates the Urca effect on convection-zone extent without fitted parameters, and the use of established low-Mach hydrodynamics with standard nuclear rates is a methodological strength that can inform improved 1D prescriptions.

major comments (1)
  1. [Abstract and Results] The claim that the convection zone is substantially reduced (abstract and results) rests on the simulations having reached statistical steady state. Because weak Urca reactions operate on timescales longer than convective turnover and the boundary treatment is mixing-length-like, the manuscript must supply explicit diagnostics (time series of global neutrino luminosity, convective velocity, or boundary radius) demonstrating equilibration; without them the reported structural change cannot be considered robust.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the white dwarf mass and the precise initial temperature/composition profile used.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our manuscript. We address the major comment below and have revised the manuscript to strengthen the demonstration of statistical steady state.

read point-by-point responses

  1. Referee: [Abstract and Results] The claim that the convection zone is substantially reduced (abstract and results) rests on the simulations having reached statistical steady state. Because weak Urca reactions operate on timescales longer than convective turnover and the boundary treatment is mixing-length-like, the manuscript must supply explicit diagnostics (time series of global neutrino luminosity, convective velocity, or boundary radius) demonstrating equilibration; without them the reported structural change cannot be considered robust.

    Authors: We agree that explicit diagnostics are necessary to confirm statistical steady state, particularly given the separation between convective turnover and weak-reaction timescales. In the revised manuscript we have added time-series panels (new Figure 3) showing the global neutrino luminosity, domain-integrated convective kinetic energy (as a proxy for velocity), and the radial location of the convective boundary (defined by the 50% mixing-fraction contour) for both the Urca and no-Urca runs. After an initial transient of approximately 200 convective turnover times, all three quantities exhibit fluctuations about stable means with no detectable secular drift over the subsequent 300 turnover times. These diagnostics confirm that the reported reduction in convection-zone size is measured in equilibrated states. Regarding the boundary treatment, the initial 1D profiles incorporate mixing-length theory only for setup; once the 3D hydrodynamic evolution begins, the boundary location is determined self-consistently by the resolved turbulent motions and is free to adjust. The added time series demonstrate that this adjustment has ceased. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct outputs of 3D simulations against external nuclear rates

full rationale

The paper reports outcomes from explicit 3D low-Mach MAESTROeX runs that evolve the convective Urca process (with vs. without A=23 reactions) until a stated steady state is reached. The reported reduction in convection-zone size and the persistence of overshoot past the Urca shell are numerical measurements, not quantities obtained by fitting a parameter to a subset of the same data or by any self-referential equation. Nuclear rates and the code itself are external to the present manuscript; no load-bearing step reduces to a prior self-citation or to an ansatz smuggled in via citation. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard nuclear reaction rates for the A=23 Urca process and the low-Mach-number approximation in MAESTROeX; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The low-Mach-number approximation accurately captures the turbulent convection and its coupling to weak reactions on the simulated timescales.
    Invoked by choice of MAESTROeX code for the simmering phase.

pith-pipeline@v0.9.0 · 5533 in / 1337 out tokens · 41526 ms · 2026-05-15T19:21:02.709358+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We use the low Mach number code MAESTROeX to perform full 3D simulations... We present simulations with and without the A=23 convective Urca process, which have relaxed to a steady state. We characterize the effects... on the neutrino losses, the nuclear energy generation, and the convective boundary.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The convective Urca process... links convection with weak nuclear reactions... the size of the convection zone is substantially reduced by the convective Urca process, though convection still extends past the Urca shell.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 1 internal anchor

  1. [1]

    2024, AMReX-Astro/initial models: Release 24.03, 24.03 Zenodo, doi: 10.5281/zenodo.10827428 AMReX-Astro Microphysics Development Team, Bishop, A., Fields, C

    AMReX-Astro initial models Team, Boyd, B., Smith Clark, A., Willcox, D., & Zingale, M. 2024, AMReX-Astro/initial models: Release 24.03, 24.03 Zenodo, doi: 10.5281/zenodo.10827428 AMReX-Astro Microphysics Development Team, Bishop, A., Fields, C. E., et al. 2024, AMReX-Astro/Microphysics: Release 24.03, 24.03 Zenodo, doi: 10.5281/zenodo.10732065

    work page doi:10.5281/zenodo.10827428 2024

  2. [2]

    Barkat, Z., & Wheeler, J. C. 1990, ApJ, 355, 602, doi: 10.1086/168793

    work page doi:10.1086/168793 1990

  3. [3]

    2025a, ApJ, 979, 216, doi: 10.3847/1538-4357/ad9bb0

    Boyd, B., Calder, A., Townsley, D., & Zingale, M. 2025a, ApJ, 979, 216, doi: 10.3847/1538-4357/ad9bb0

    work page doi:10.3847/1538-4357/ad9bb0

  4. [4]

    C., Townsley, D

    Boyd, B., Calder, A. C., Townsley, D. M., & Zingale, M. 2025b, in Journal of Physics Conference Series, Vol. 2997, Journal of Physics Conference Series, 012006, doi: 10.1088/1742-6596/2997/1/012006

    work page doi:10.1088/1742-6596/2997/1/012006

  5. [5]

    Bruenn, S. W. 1973, ApJL, 183, L125, doi: 10.1086/181269

    work page doi:10.1086/181269 1973

  6. [6]

    C., Krueger, B

    Calder, A. C., Krueger, B. K., Jackson, A. P., & Townsley, D. M. 2013, Frontiers of Physics, 8, 168, doi: 10.1007/s11467-013-0301-4

    work page doi:10.1007/s11467-013-0301-4 2013

  7. [7]

    2008, ApJ, 677, 160, doi: 10.1086/528944

    Dupczak, K. 2008, ApJ, 677, 160, doi: 10.1086/528944

    work page doi:10.1086/528944 2008

  8. [8]

    G., & Arnett, D

    Couch, R. G., & Arnett, D. W. 1974, ApJ, 194, 537, doi: 10.1086/153272

    work page doi:10.1086/153272 1974

  9. [9]

    G., & Arnett, W

    Couch, R. G., & Arnett, W. D. 1975, ApJ, 196, 791, doi: 10.1086/153470

    work page doi:10.1086/153470 1975

  10. [10]

    H., Amthor, A

    Cyburt, R. H., Amthor, A. M., Ferguson, R., et al. 2010, ApJS, 189, 240, doi: 10.1088/0067-0049/189/1/240

    work page doi:10.1088/0067-0049/189/1/240 2010

  11. [11]

    A., Truran, J

    Denissenkov, P. A., Truran, J. W., Herwig, F., et al. 2015, MNRAS, 447, 2696, doi: 10.1093/mnras/stu2589

    work page doi:10.1093/mnras/stu2589 2015

  12. [12]

    2019a, The Journal of Open Source Software, 4, 1757, doi: 10.21105/joss.01757 19

    Fan, D., Nonaka, A., Almgren, A., et al. 2019a, The Journal of Open Source Software, 4, 1757, doi: 10.21105/joss.01757 19

    work page doi:10.21105/joss.01757

  13. [13]

    2019b, ApJ, 887, 212, doi: 10.3847/1538-4357/ab4f75

    Zingale, M. 2019b, ApJ, 887, 212, doi: 10.3847/1538-4357/ab4f75

    work page doi:10.3847/1538-4357/ab4f75

  14. [14]

    2000, ApJS, 131, 273, doi: 10.1086/317361

    Fryxell, B., Olson, K., Ricker, P., et al. 2000, ApJS, 131, 273, doi: 10.1086/317361

    work page doi:10.1086/317361 2000

  15. [15]

    J., Kawaler, S

    Hansen, C. J., Kawaler, S. D., & Trimble, V. 2004, Stellar interiors : physical principles, structure, and evolution (Springer New York, NY), doi: 10.1007/978-1-4419-9110-2

    work page doi:10.1007/978-1-4419-9110-2 2004

  16. [16]

    Nature 585(7825), 357–362 (2020) https://doi.org/ 10.1038/s41586-020-2649-2

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

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

  17. [17]

    K., & Ruiter, A

    Hillebrandt, W., Kromer, M., R¨ opke, F. K., & Ruiter, A. J. 2013, Frontiers of Physics, 8, 116, doi: 10.1007/s11467-013-0303-2

    work page doi:10.1007/s11467-013-0303-2 2013

  18. [18]

    Hunter, J. D. 2007, Computing in Science and Engg., 9, 90, doi: 10.1109/MCSE.2007.55

    work page doi:10.1109/mcse.2007.55 2007

  19. [19]

    1978, ApJ, 226, 996, doi: 10.1086/156680

    Iben, Jr., I. 1978, ApJ, 226, 996, doi: 10.1086/156680

    work page doi:10.1086/156680 1978

  20. [20]

    1982, ApJ, 253, 248, doi: 10.1086/159630

    Iben, Jr., I. 1982, ApJ, 253, 248, doi: 10.1086/159630

    work page doi:10.1086/159630 1982

  21. [21]

    2001, Atomic Data and Nuclear Data Tables, 79, 1, doi: https://doi.org/10.1006/adnd.2001.0865

    Langanke, K., & Mart´ ınez-Pinedo, G. 2001, Atomic Data and Nuclear Data Tables, 79, 1, doi: https://doi.org/10.1006/adnd.2001.0865

    work page doi:10.1006/adnd.2001.0865 2001

  22. [22]

    Lesaffre, P., Podsiadlowski, P., & Tout, C. A. 2005, MNRAS, 356, 131, doi: 10.1111/j.1365-2966.2004.08428.x

    work page doi:10.1111/j.1365-2966.2004.08428.x 2005

  23. [23]

    K., & Han, Z

    Liu, Z.-W., R¨ opke, F. K., & Han, Z. 2023, Research in Astronomy and Astrophysics, 23, 082001, doi: 10.1088/1674-4527/acd89e

    work page doi:10.1088/1674-4527/acd89e 2023

  24. [24]

    2011, ApJ, 728, 118, doi: 10.1088/0004-637X/728/2/118 Mart´ ınez-Rodr´ ıguez, H., Piro, A

    Zingale, M. 2011, ApJ, 728, 118, doi: 10.1088/0004-637X/728/2/118 Mart´ ınez-Rodr´ ıguez, H., Piro, A. L., Schwab, J., &

    work page doi:10.1088/0004-637x/728/2/118 2011

  25. [25]

    2016, ApJ, 825, 57, doi: 10.3847/0004-637X/825/1/57

    Badenes, C. 2016, ApJ, 825, 57, doi: 10.3847/0004-637X/825/1/57

    work page doi:10.3847/0004-637x/825/1/57 2016

  26. [26]

    P., Paprocki, M., et al

    Meurer, A., Smith, C. P., Paprocki, M., et al. 2017, PeerJ Computer Science, 3, e103, doi: 10.7717/peerj-cs.103

    work page doi:10.7717/peerj-cs.103 2017

  27. [27]

    1996, A&A, 311, 152

    Mochkovitch, R. 1996, A&A, 311, 152

    work page 1996

  28. [28]

    K., & Yokoi, K

    Nomoto, K., Thielemann, F. K., & Yokoi, K. 1984, ApJ, 286, 644, doi: 10.1086/162639 Paczy´ nski, B. 1972, Astrophys. Lett., 11, 53

    work page doi:10.1086/162639 1984

  29. [29]

    2013, The Astrophysical Journal Supplement Series, 208, 4, doi: 10.1088/0067-0049/208/1/4

    Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4, doi: 10.1088/0067-0049/208/1/4

    work page internal anchor Pith review doi:10.1088/0067-0049/208/1/4 2013

  30. [30]

    1999, ApJ, 517, 565

    Perlmutter, S., Aldering, G., Goldhaber, G., et al. 1999, ApJ, 517, 565

    work page 1999

  31. [31]

    Phillips, M. M. 1993, ApJL, 413, L105

    work page 1993

  32. [32]

    2017, ApJL, 836, L9, doi: 10.3847/2041-8213/aa5c7e

    Piersanti, L., Bravo, E., Cristallo, S., et al. 2017, ApJL, 836, L9, doi: 10.3847/2041-8213/aa5c7e

    work page doi:10.3847/2041-8213/aa5c7e 2017

  33. [33]

    2022, ApJ, 926, 103, doi: 10.3847/1538-4357/ac403b

    Piersanti, L., Bravo, E., Straniero, O., Cristallo, S., & Dom´ ınguez, I. 2022, ApJ, 926, 103, doi: 10.3847/1538-4357/ac403b

    work page doi:10.3847/1538-4357/ac403b 2022

  34. [34]

    2003, ApJ, 583, 885, doi: 10.1086/345444

    Piersanti, L., Gagliardi, S., Iben, Jr., I., & Tornamb´ e, A. 2003, ApJ, 583, 885, doi: 10.1086/345444

    work page doi:10.1086/345444 2003

  35. [35]

    L., & Bildsten, L

    Piro, A. L., & Bildsten, L. 2008, ApJ, 673, 1009, doi: 10.1086/524189

    work page doi:10.1086/524189 2008

  36. [36]

    G., Filippenko, A

    Riess, A. G., Filippenko, A. V., Challis, P., et al. 1998, AJ, 116, 1009

    work page 1998

  37. [37]

    2017, ApJ, 851, 105, doi: 10.3847/1538-4357/aa9a3c

    Badenes, C. 2017, ApJ, 851, 105, doi: 10.3847/1538-4357/aa9a3c

    work page doi:10.3847/1538-4357/aa9a3c 2017

  38. [38]

    I., Johnson, E

    Smith, A. I., Johnson, E. T., Chen, Z., et al. 2023, The Astrophysical Journal, 947, 65, doi: 10.3847/1538-4357/acbaff

    work page doi:10.3847/1538-4357/acbaff 2023

  39. [39]

    Stein, J., Barkat, Z., & Wheeler, J. C. 1999, ApJ, 523, 381, doi: 10.1086/307715

    work page doi:10.1086/307715 1999

  40. [40]

    Stein, J., & Wheeler, J. C. 2006, ApJ, 643, 1190, doi: 10.1086/503246

    work page doi:10.1086/503246 2006

  41. [41]

    2016, ApJ, 817, 163, doi: 10.3847/0004-637X/817/2/163

    Suzuki, T., Toki, H., & Nomoto, K. 2016, ApJ, 817, 163, doi: 10.3847/0004-637X/817/2/163

    work page doi:10.3847/0004-637x/817/2/163 2016

  42. [42]

    2023, GNU Parallel 20231122 (’Grindav´ ık’), Zenodo, doi: 10.5281/zenodo.10199085

    Tange, O. 2023, GNU Parallel 20231122 (’Grindav´ ık’), Zenodo, doi: 10.5281/zenodo.10199085

    work page doi:10.5281/zenodo.10199085 2023

  43. [43]

    X., Brown, E

    Timmes, F. X., Brown, E. F., & Truran, J. W. 2003, ApJL, 590, L83, doi: 10.1086/376721

    work page doi:10.1086/376721 2003

  44. [44]

    X., & Swesty, F

    Timmes, F. X., & Swesty, F. D. 2000, ApJS, 126, 501, doi: 10.1086/313304

    work page doi:10.1086/313304 2000

  45. [45]

    J., Smith, B

    Turk, M. J., Smith, B. D., Oishi, J. S., et al. 2011, The Astrophysical Journal Supplement Series, 192, 9, doi: 10.1088/0067-0049/192/1/9

    work page doi:10.1088/0067-0049/192/1/9 2011

  46. [46]

    1999, ApJL, 522, L43, doi: 10.1086/312213 Wes McKinney

    Kato, M. 1999, ApJL, 522, L43, doi: 10.1086/312213 Wes McKinney. 2010, in Proceedings of the 9th Python in Science Conference, ed. St´ efan van der Walt & Jarrod Millman, 56 – 61, doi: 10.25080/Majora-92bf1922-00a

    work page doi:10.1086/312213 1999

  47. [47]

    Willcox, D. E. 2018, PhD thesis, SUNY Stony Brook, New York

    work page 2018

  48. [48]

    E., & Zingale, M

    Willcox, D. E., & Zingale, M. 2018, Journal of Open Source Software, 3, 588, doi: 10.21105/joss.00588

    work page doi:10.21105/joss.00588 2018

  49. [49]

    E., Taam, R

    Woosley, S. E., Taam, R. E., & Weaver, T. A. 1986, ApJ, 301, 601, doi: 10.1086/163926

    work page doi:10.1086/163926 1986

  50. [50]

    E., Wunsch, S., & Kuhlen, M

    Woosley, S. E., Wunsch, S., & Kuhlen, M. 2004, ApJ, 607, 921, doi: 10.1086/383530

    work page doi:10.1086/383530 2004

  51. [51]

    2019, Journal of Open Source Software, 4, 1370, doi: 10.21105/joss.01370

    Zhang, W., Almgren, A., Beckner, V., et al. 2019, Journal of Open Source Software, 4, 1370, doi: 10.21105/joss.01370

    work page doi:10.21105/joss.01370 2019

  52. [52]

    Woosley, S. E. 2009, ApJ, 704, 196, doi: 10.1088/0004-637X/704/1/196

    work page doi:10.1088/0004-637x/704/1/196 2009