References
==========

The mathematical model and numerical scheme of neoVULCAN are documented
in the following papers. Equation numbers cited throughout this
documentation refer to these publications.

.. [Tsai2017] Tsai, S.-M., Lyons, J. R., Grosheintz, L., Rimmer, P. B.,
   Kitzmann, D., & Heng, K., 2017,
   *VULCAN: An Open-source, Validated Chemical Kinetics Python Code
   for Exoplanetary Atmospheres*,
   The Astrophysical Journal Supplement Series, 228, 20.
   `doi:10.3847/1538-4365/228/2/20
   <https://doi.org/10.3847/1538-4365/228/2/20>`_

.. [Tsai2018] Tsai, S.-M., Kitzmann, D., Lyons, J. R., Mendonça, J.,
   Grimm, S. L., & Heng, K., 2018,
   *Toward Consistent Modeling of Atmospheric Chemistry and Dynamics
   in Exoplanets: Validation and Generalization of the Chemical
   Relaxation Method*,
   The Astrophysical Journal, 862, 31.
   `doi:10.3847/1538-4357/aac834
   <https://doi.org/10.3847/1538-4357/aac834>`_

.. [Tsai2021] Tsai, S.-M., Malik, M., Kitzmann, D., Lyons, J. R.,
   Fateev, A., Lee, E., & Heng, K., 2021,
   *A Comparative Study of Atmospheric Chemistry with VULCAN*,
   The Astrophysical Journal, 923, 264.
   `doi:10.3847/1538-4357/ac29bc
   <https://doi.org/10.3847/1538-4357/ac29bc>`_

.. [Malik2019] Malik, M., Kitzmann, D., Mendonça, J. M., et al., 2019,
   *Self-consistent Modeling of the Atmosphere and Climate of
   Tidally Locked Earth-like Exoplanets*,
   The Astronomical Journal, 157, 170.

.. [Heng2014] Heng, K., Mendonça, J. M., & Lee, J.-M., 2014,
   *Analytical Models of Exoplanetary Atmospheres. II. Radiative
   Transfer via the Two-stream Approximation*,
   The Astrophysical Journal Supplement Series, 215, 4.

.. [Verwer1999] Verwer, J. G., Spee, E. J., Blom, J. G., & Hundsdorfer, W.,
   1999, *A Second-Order Rosenbrock Method Applied to Photochemical
   Dispersion Problems*,
   SIAM Journal on Scientific Computing, 20, 1456.

.. [Sandu1997] Sandu, A., Verwer, J. G., Van Loon, M., Carmichael, G. R.,
   Potra, F. A., Dabdub, D., & Seinfeld, J. H., 1997,
   *Benchmarking Stiff ODE Solvers for Atmospheric Chemistry
   Problems I: Implicit vs. Explicit*,
   Atmospheric Environment, 31, 3151.

.. [Heays2017] Heays, A. N., Bosman, A. D., & van Dishoeck, E. F., 2017,
   *Photodissociation and photoionisation of atoms and molecules
   of astrophysical interest*,
   Astronomy & Astrophysics, 602, A105.

.. [Hu2012] Hu, R., Seager, S., & Bains, W., 2012,
   *Photochemistry in Terrestrial Exoplanet Atmospheres. I.
   Photochemistry Model and Benchmark Cases*,
   The Astrophysical Journal, 761, 166.


Citations in the rest of this documentation use the standard Sphinx
footnote-style syntax ``[Tsai2017]_`` etc., which Sphinx resolves to
the entries above.