**References:**- Chappell & Pereira 2021:
Title: SunnyNet: A neural network approach to 3D non-LTE radiative transfer.
They use convolutional neural networks.

- Chen, Jeffery, et al. 2022: Title: Using Physics Informed Neural Newtorks for Supernova Radiative Transfer Simulation. \bibitem[Chen etal.(2022)]{chen2022} Chen, X. et al. 2022, arXiv 2211.05219
- Collins, G. W., II 2003, The Fundamentals of Stellar Astrophysics: Chapters 9--16 cover radiative transfer in stars at about the level of Mihalas (1978). Seems good. \citet{fleck1984}
- Fleck, Jr., J.A., & Canfield, E.H. 1984, Journal of Computational Physics, 54, 508: Title: A random walk procedure for improving the computational efficiency of the implicit Monte Carlo method. The pdf link is on the second-from-top toolbar. They had the idea before Jeffery, D. J., Mazzali, P. A. 2007, in The Multicoloured Landscape of Compact Objects and their Explosive Origins, AIP Conf. Pro. 924, Vol. 1 Cefalu, Sicily, 2006 June 11---24, ed. L.A. Antonelli et al. (Melville, New York: American Institute of Physics), 401.
- Jeffery, D. J. 1993, ApJ, 415, 734: Title: The Relativistic Sobolev Method Applied to Homologously Expanding Atmospheres. See section 3 for my proof that photons always redshift in the comoving frame no matter what the degree of special relativistic effects.
- Jeffery, D. J. 1995a, ApJ, 440, 810: Title: The Sobolev Optical Depth for Time-dependent Relativistic Systems.
- Jeffery, D. J. 1998, arXiv:astro-ph/9811356: Title: A Grey Radiative Transfer Procedure For Gamma-ray Transfer in Supernovae.
- Jeffery, D. J. 1999, astro-ph/9907015: Title: Radioactive Decay Energy Deposition in Supernovae and the Exponential/Quasi-Exponential Behavior of Late-Time Supernova Light Curves. The quasi-exponential lightcurve paper. It gives the exponential density profile expressions for mass, energy, etc. The paper on radioactive decay energy deposition in supernovae and the exponential/quasi-exponential behavior of late-time supernova light curves. The exponential supernova model is developed in formulae in Appendix A.
- Jeffery, D.J., 2008, Giant Steps: A Technique for Accelerating Monte Carlo Radiative Transfer in Optically Thick Atmospheres, unpublished, incomplete.
- Jeffery, D. J. 2021, unpublished: Title: An Educational Note on the Saha Equation and its Solution for the Ionization State of a Gas. Nearly complete.
- Jeffery, D. J. 2022, in preparation: Title: Vague ideas for an advanced Monte Carlo radiative code.
- Jeffery, D. J., & Branch, D. 1990, in Jerusalem Winter School for Theoretical Physics, Vol. 6, Supernovae, ed. J.C. Wheeler, T. Piran, & S. Weinberg (Singapore: World Scientific), 149: Title: Analysis of Supernova Spectra. Keywords: Sobolev method, model supernova, demonstration calculations, and SN 1987A analysis. The demonstration calculations are really the useful part of this article. A higher quality version without figures is jerus.pdf.
- Jeffery, D. J., Leibundgut, B.,
Kirshner, R. P., Benetti, S., Branch, D., \&~Sonneborn, G. 1992, \apj, 397, 304:
Title: Analysis of the photospheric epoch spectra of type 1a supernovae SN 1990N and SN 1991T.
The 90N/91T paper.
Some useful analytic results are given for the exponential supernova model such as the
electron photospheric time as a function electron photospheric
velocity and the exponential spherical gray atmosphere temperature profile.
I do tentatively identify C II lines.

% \citep[e.g.,][p.~307]{jeffery1992} for exponential density profile

% \citep[][p.~308]{jeffery1992} for exponential spherical grey temperature

% \bibitem[Jeffery et al.(1992)]{jeffery1992}

- Jeffery, D. J., Mazzali, P. A. 2007, in The Multicoloured Landscape of Compact Objects and their Explosive Origins, AIP Conf. Pro. 924, Vol. 1 Cefalu, Sicily, 2006 June 11---24, ed. L.A. Antonelli et al. (Melville, New York: American Institute of Physics), 401: A short paper on a rediscovery of speed-up technique for Monte Carlo radiative transfer. An incomplete development of Giant Steps is Jeffery, D.J., 2008, Giant Steps: A Technique for Accelerating Monte Carlo Radiative Transfer in Optically Thick Atmospheres, unpublished, incomplete.
- Kasen, D., Thomas, R.C., & Nugent, P. 2006, ApJ, 651, 366, 16 pages: Title: Time-dependent Monte Carlo Radiative Transfer Calculations for Three-dimensional Supernova Spectra, Light Curves, and Polarization. Dan's method paper. The code is called SEDONA. Among many other things stationarity is found to be a somewhat reasonable approximation.
- Kerzendorf, W., & Sim, S. A., 2014, MNRAS, ???, ???, 18 pages: A spectral synthesis code for rapid modelling of supernovae. Original Tardis description paper.
- Krishnan, Praveen Krishnan, et al. 2012: Title: An artificial neural network based fast radiative transfermodel for simulating infrared sounder radiances. Maybe dated by now.
- Le, Tianhao Le, et al. 2020, 3 pages?: Title: Application of machine learning to hyperspectral radiative transfer simulations.
- Lucy, L. B. 1999a, A&A, 344, 282: Title: Computing radiative equilibria with Monte Carlo techniques. Lucy's self-consistent LTE with Monte Carlo and his tau-prescription for MCAA. This paper shows the Lambda-iteration works with MC for LTE atmospheres.
- Lucy, L. B. 1999b, A&A, 345, 211: Title: Improved Monte Carlo techniques for the spectral synthesis of supernovae. Transition probabilities governing the interaction of energy packets and matter are derived that allow Monte Carlo NLTE transfer codes to be constructed without simplifying the treatment of line formation. These probabilities are such that the Monte Carlo calculation asymptotically recovers the local emissivity of a gas in statistical equilibrium. Macro-atom paper I.
- Lucy, L. B. 2002, A&A, 384, 725: Title: Monte Carlo transition probabilities.
- Lucy, L. B. 2003, A&A, 403, 261: Title: Monte Carlo transition probabilities. II.
- Lucy, L. B. 2005a, A&A, 429, 19: Title: Monte Carlo techniques for time-dependent radiative transfer in 3-D supernovae.
- Lucy, L. B. 2005b, A&A, 429, 31: Title: Similarity solutions for radiation in time-dependent relativistic flows. No obvious relation to the relativistic Sobolev method of HS and Jeffery (1993,1995).
- Mazzali, P. A., & Lucy, L. B. 1993, A&A, 279, 447: Title: The application of Monte Carlo methods to the synthesis of early-time supernovae spectra.
- Mishra, Siddhartha Mishra, Roberto Molinaro,
2021, 25 pages:
Title: Physics Informed Neural Networks for Simulating Radiative Transfer.
See also the
ScienceDirect version,
but it seems to have the same typos.

\bibitem[Mishra \& Molinaro(2021)]{mishra2021} Mishra, S., \& Molinaro, R. 2021, JQSRT, 270, arXiv:2009.13291 % https://arxiv.org/abs/2009.13291 - Modest, M. F., 2013, Radiative Heat Transfer: A very superficial glance such it is a good reference for the physics of heat transfer, but it's not specialized to astrophysical atmospheres. Only the first 199 pages are available for preview.
- A. Peraiah 1975, A&A, 40, 75, Numerical solution of radiative transfer equation in extended spherical atmospheres with Rayleigh phase function: Sequel to A. PERAIAH, I. P. GRANT 1973, Journal of Applied Mathematics, 12, 75, Numerical Solution of the Radiative Transfer Equation in Spherical Shells. See also I.P. Grant, G.E. Hunt, 1968, JQSRT, 18, 1817, Radiative transfer in a Rayleigh scattering atmosphere: you have to scoll down to the second article in the list. Equation (2.3) of Grant & Hunt (1968) is correct and same result equation (6) of Peraiah (1975) is wrong. Chandrasekhar (1960, p. 43) gives the correct result too.
- Rybicki, G. B., & Hummer, D. G. 1978, ApJ, 219, 654: Title: A generalization of the Sobolev method for flows with nonlocal radiative coupling: a standard Sobolev method paper reference. The treatment of radiative line coupling follows straightforwardly from this paper. Either George or David told me, the formalism had been worked out in 1969 or so and they had just not got around to publishing it until later.
- Swartz, D.A., Sutherland, P.G., & Harkness, R.P., ApJ, 446, 766: Title: Gamma-Ray Transfer and Energy Deposition in Supernovae.

- Chappell & Pereira 2021:
Title: SunnyNet: A neural network approach to 3D non-LTE radiative transfer.
They use convolutional neural networks.
**Resources for Atomic Data, Etc.:**- Chianti: An Atomic Database for Spectroscopic Diagnostics of Astrophysical Plasmas: So probably just line opacities.
- CMFGEN: This may be one-stop shopping.
- Kurucz/linelists: The description of them is a bit curt.
- Los Alamos Opactiy Tables: Colgan et al. 2016.
But their lowest temperature is 5000 K.
Not OPAL.
- LANL: TOPS Opacities: Lower limit on T=5000 K. Not low enough for SNe. We need to 3000 K, I'd say.

- NIST: Atomic Spectra Database: It is not obvious how to obtain this data in a machine readable form suitable for computer use. Also only line opacities and no data for H-.
- Opacity/Iron Project database: Lots of data, but at first glance the interface is opaque. But no ff opacity it seems.
- OPAL interface: But these seem to be Rosseland mean opacities only.
- Optab: Public code for generating gas opacity tables for radiation hydrodynamics simulations (2021dec10): Maybe this is best resource for LTE opacities.

**References in reverse time order:**- 2023mar13: Frequency-dependent Discrete Implicit Monte-Carlo Scheme for the Radiative Transfer Equation: Elad Steinberg, Shay I. Heizler. Sounds different from the Lucy method.
- 2022sep25: StaNdaRT: A repository of standardized test models and outputs for supernova radiative transfer: Blondin et al. and lots of other including John Hillier, Dan Kasen, Stan Woosley.
- 2022sep20: Probabilistic Dalek -- Emulator framework with probabilistic prediction for supernova tomography: Wolfgang Kerzendorf, et al.
- 2022aug29: PINION: Physics informed neural network for accelerating radiative transfer simulations for cosmic reionization, Damien Korber, et al., 2022: 11 pages.
- 2022apr01: Messenger Monte-Carlo MAPPINGS V (M^3) -- A self-consistent three-dimensional photoionization code, Yifei Jin, et al., 2022: 28 pages.
- 2022apr01: Modelling the ionisation state of Type Ia supernovae in the nebular-phase, Shingles et al.: 14 pages.
- 2022mar23: On thermalization of radiation in hydrostatic atmospheres: Analytic, just 5 pages.
- 2022mar04: A Practical Guide to the Partition Function of Atoms and Ions, P. Alimohamadi, G. J. Ferland: Badly needed.
- 2022feb21: New mass estimates for massive binary systems: a probabilistic approach using polarimetric radiative transfer, Andrew G. Fullard, et al.: "To avoid the biases present in analytic models of polarization while retaining computational expediency, we used a Monte Carlo radiative transfer model accurately emulated by a neural network."
- 2022feb17: Photon frequency diffusion process, Guilherme Eduardo Freire Oliveira, et al.: "In the case of Compton scattering with thermal electrons, the limiting process describes the dynamical fluctuations around the Kompaneets equation."
- Novel framework for the three-dimensional NLTE inverse problem Jiri Stepan, Tanausu del Pino Aleman, Javier Trujillo Bueno: "The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics."
- 2021dec27: SunnyNet: A neural network approach to 3D non-LTE radiative transfer Bruce A. Chappell, et al.: "we trained a convolutional neural network, SunnyNet, to learn the translation from LTE to non-LTE atomic populations."
- 2021oct: Variance-reduction methods for Monte Carlo simulation of radiation transport GarcĂa-Pareja, Salvado, et al.: pdf, 13 pages: Probably a good general reference for Monte Carlo radiative transfer.
- 2021oct29: 3D radiative-transfer for exoplanet atmospheres. gCMCRT: a GPU accelerated MCRT code, Elspeth K.H. Lee, et al.: Probably state of the art Monte Carlo radiative transfer calculations.
- 2016: Center-to-limb variation of intensity and polarization in continuum spectra of FGK stars for spherical atmospheres, N. M. Kostogryz , I. Milic, S. V. Berdyugina, and P. H. Hauschildt: Pages 6--7 correspond to Chandrasekhar, S. 1960, p. 247--248 and Peraiah 1975.
- 1999: Radioactive Decay Energy Deposition in Supernovae and the Exponential/Quasi-Exponential Behavior of Late-Time Supernova Light Curves, Jeffery, David J.: Lots of basic stuff in this old effort.
- 1991nov: Catalog of SN 1987A Polarimetry Corrected for Interstellar Polarization, Jeffery 1991.
- 1991jul: Analysis of SN 1987A Polarimetry.