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@ARTICLE{Danehkar:2013,
author = {{Danehkar}, A. and {Parker}, Q.~A. and {Ercolano}, B.},
title = "{Observations and three-dimensional ionization structure of the planetary nebula SuWt 2}",
journal = {Monthly Notices of the Royal Astronomical Society},
archivePrefix = "arXiv",
eprint = {1307.2974},
primaryClass = "astro-ph.SR",
year = 2013,
volume = 434,
pages = {1513-1530},
doi = {10.1093/mnras/stt1116},
adsurl = {http://adsabs.harvard.edu/abs/2013MNRAS.434.1513D},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Danehkar:2014,
author = {{Danehkar}, A. and {Todt}, H. and {Ercolano}, B. and {Kniazev}, A.~Y.
},
title = "{Observations and three-dimensional photoionization modelling of the Wolf-Rayet planetary nebula Abell 48}",
journal = {Monthly Notices of the Royal Astronomical Society},
archivePrefix = "arXiv",
eprint = {1403.0567},
primaryClass = "astro-ph.SR",
year = 2014,
volume = 439,
pages = {3605-3615},
doi = {10.1093/mnras/stu203},
adsurl = {http://adsabs.harvard.edu/abs/2014MNRAS.439.3605D},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@PHDTHESIS{Danehkar:2014b,
author = {{Danehkar}, A.},
title = "{Evolution of Planetary Nebulae with WR-type Central Stars}",
school = {Macquarie University, Australia},
year = 2014,
doi = {10.5281/zenodo.47794},
adsurl = {http://adsabs.harvard.edu/abs/2014PhDT........76D},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Danehkar:2016,
author = {{Danehkar}, A. and {Parker}, Q.~A. and {Steffen}, W.},
title = "{Fast, Low-ionization Emission Regions of the Planetary Nebula M2-42}",
journal = {The Astronomical Journal},
archivePrefix = "arXiv",
eprint = {1601.01702},
primaryClass = "astro-ph.SR",
year = 2016,
volume = 151,
eid = {38},
pages = {38},
doi = {10.3847/0004-6256/151/2/38},
adsurl = {http://adsabs.harvard.edu/abs/2016AJ....151...38D},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Danehkar:2018a,
author = {{Danehkar}, A.},
title = "{Bi-Abundance Ionisation Structure of the Wolf-Rayet Planetary Nebula PB 8}",
journal = {Publications of the Astronomical Society of Australia},
archivePrefix = "arXiv",
eprint = {1801.00892},
primaryClass = "astro-ph.SR",
year = 2018,
volume = 35,
eid = {e005},
pages = {e005},
doi = {10.1017/pasa.2018.1},
adsurl = {http://adsabs.harvard.edu/abs/2018PASA...35....5D},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Danehkar:2018b,
author = {{Danehkar}, A.},
title = "{proEQUIB: IDL Library for Plasma Diagnostics and Abundance Analysis}",
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@ARTICLE{Danehkar:2020,
author = {{Danehkar}, A.},
title = "{AtomNeb: Python Package for Atomic Data of Ionized Nebulae}",
title = "{AtomNeb Python Package, an addendum to AtomNeb: IDL Library for Atomic Data of Ionized Nebulae}",
journal = {The Journal of Open Source Software},
year = 2020,
volume = submitted,
}

@TECHREPORT{Howarth:1981,
author = {{Howarth}, I.~D. and {Adams}, S.},
title = "{Program EQUIB}",
howpublished = {University College London},
year = 1981,
adsurl = {http://adsabs.harvard.edu/abs/1981ucl..rept.....H},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@MISC{Howarth:2016,
author = {{Howarth}, I.~D. and {Adams}, S. and {Clegg}, R.~E.~S. and {Ruffle}, D.~P. and
{Liu}, X.-W. and {Pritchet}, C.~J. and {Ercolano}, B.},
title = "{EQUIB: Atomic level populations and line emissivities calculator}",
howpublished = {Astrophysics Source Code Library, ascl:1603.005},
year = 2016,
archivePrefix = "ascl",
eprint = {1603.005},
adsurl = {http://adsabs.harvard.edu/abs/2016ascl.soft03005H},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Ercolano:2003,
author = {{Ercolano}, B. and {Barlow}, M.~J. and {Storey}, P.~J. and {Liu}, X.-W.
},
title = "{MOCASSIN: a fully three-dimensional Monte Carlo photoionization code}",
journal = {Monthly Notices of the Royal Astronomical Society},
eprint = {astro-ph/0209378},
year = 2003,
volume = 340,
pages = {1136-1152},
doi = {10.1046/j.1365-8711.2003.06371.x},
adsurl = {http://adsabs.harvard.edu/abs/2003MNRAS.340.1136E},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Ercolano:2005,
author = {{Ercolano}, B. and {Barlow}, M.~J. and {Storey}, P.~J.},
title = "{The dusty MOCASSIN: fully self-consistent 3D photoionization and dust radiative transfer models}",
journal = {Monthly Notices of the Royal Astronomical Society},
eprint = {astro-ph/0507050},
year = 2005,
volume = 362,
pages = {1038-1046},
doi = {10.1111/j.1365-2966.2005.09381.x},
adsurl = {http://adsabs.harvard.edu/abs/2005MNRAS.362.1038E},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@INPROCEEDINGS{Bushouse:1994,
author = {{Bushouse}, H. and {Simon}, B.},
title = "{The IRAF/STSDAS Synthetic Photometry Package}",
booktitle = {Astronomical Data Analysis Software and Systems III},
year = 1994,
series = {Astronomical Society of the Pacific Conference Series},
volume = 61,
editor = {{Crabtree}, D.~R. and {Hanisch}, R.~J. and {Barnes}, J.},
pages = {339},
adsurl = {http://adsabs.harvard.edu/abs/1994ASPC...61..339B},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@INPROCEEDINGS{Shaw:1994,
author = {{Shaw}, R.~A. and {Dufour}, R.~J.},
title = "{The FIVEL Nebular Modelling Package in STSDAS}",
booktitle = {Astronomical Data Analysis Software and Systems III},
year = 1994,
series = {Astronomical Society of the Pacific Conference Series},
volume = 61,
editor = {{Crabtree}, D.~R. and {Hanisch}, R.~J. and {Barnes}, J.},
pages = {327},
adsurl = {http://adsabs.harvard.edu/abs/1994ASPC...61..327S},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@INPROCEEDINGS{Landsman:1993,
author = {{Landsman}, W.~B.},
title = "{The IDL Astronomy User's Library}",
booktitle = {Astronomical Data Analysis Software and Systems II},
year = 1993,
series = {Astronomical Society of the Pacific Conference Series},
volume = 52,
editor = {{Hanisch}, R.~J. and {Brissenden}, R.~J.~V. and {Barnes}, J.},
pages = {246},
adsurl = {http://adsabs.harvard.edu/abs/1993ASPC...52..246L},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@INPROCEEDINGS{Landsman:1995,
author = {{Landsman}, W.~B.},
title = "{The IDL Astronomy User's Library}",
booktitle = {Astronomical Data Analysis Software and Systems IV},
year = 1995,
series = {Astronomical Society of the Pacific Conference Series},
volume = 77,
editor = {{Shaw}, R.~A. and {Payne}, H.~E. and {Hayes}, J.~J.~E.},
pages = {437},
adsurl = {http://adsabs.harvard.edu/abs/1995ASPC...77..437L},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@INPROCEEDINGS{Arabas:2010,
author = {{Arabas}, S. and {Schellens}, M. and {Coulais}, A. and {Gales}, J. and
{Messmer}, P.},
title = "{GNU Data Language (GDL) - a free and open-source implementation of IDL}",
booktitle = {EGU General Assembly Conference},
year = 2010,
series = {Geophysical Research Abstracts},
volume = 12,
pages = {924},
adsurl = {http://adsabs.harvard.edu/abs/2010EGUGA..12..924A},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@INPROCEEDINGS{Coulais:2010,
author = {{Coulais}, A. and {Schellens}, M. and {Gales}, J. and {Arabas}, S. and
{Boquien}, M. and {Chanial}, P. and {Messmer}, P. and {Fillmore}, D. and
{Poplawski}, O. and {Maret}, S. and {Marchal}, G. and {Galmiche}, N. and
{Mermet}, T.},
title = "{Status of GDL - GNU Data Language}",
booktitle = {Astronomical Data Analysis Software and Systems XIX},
year = 2010,
series = {Astronomical Society of the Pacific Conference Series},
volume = 434,
archivePrefix = "arXiv",
eprint = {1101.0679},
primaryClass = "astro-ph.IM",
editor = {{Mizumoto}, Y. and {Morita}, K.-I. and {Ohishi}, M.},
pages = {187},
adsurl = {http://adsabs.harvard.edu/abs/2010ASPC..434..187C},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Wesson:2012,
author = {{Wesson}, R. and {Stock}, D.~J. and {Scicluna}, P.},
title = "{Understanding and reducing statistical uncertainties in nebular abundance determinations}",
journal = {Monthly Notices of the Royal Astronomical Society},
year = 2012,
volume = {422},
number = {4},
pages = {3516-3526},
doi = {10.1111/j.1365-2966.2012.20863.x},
archivePrefix = {arXiv},
eprint = {1203.0567},
primaryClass = {astro-ph.GA},
adsurl = {https://ui.adsabs.harvard.edu/abs/2012MNRAS.422.3516W},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Walt:2011,
author = {{van der Walt}, S. and {Colbert}, S. C. and
{Varoquaux}, G.},
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23 changes: 4 additions & 19 deletions paper/paper.md
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---
title: "pyEQUIB: Python Package for Plasma Diagnostics and Abundance Analysis"
title: "pyEQUIB Python Package, an addendum to proEQUIB: IDL Library for Plasma Diagnostics and Abundance Analysis"
tags:
- python
- astrophysics
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bibliography: paper.bib
---

# Introduction
# Addendum

The interpretation of emission-line spectra from ionized gases are crucial in studying planetary nebulae and H II regions in our Galaxy and other galaxies. Physical properties of the interstellar medium such as the electron temperature and concentration can be determined from nebular emission lines. Moreover, chemical elements can be probed using the collisionally excited lines (CEL) and recombination lines (RL) emitted from ionized gases in the interstellar medium [see e.g. @Danehkar:2013; @Danehkar:2016; @Danehkar:2018a]. The interstellar extinction can also be derived from the observed Balmer decrements.
`pyEQUIB` is a pure Python open-source package containing several application programming interface (API) functions that can be employed for plasma diagnostics and abundance analysis of nebular emission lines. This package is a Python implementation of the IDL library `proEQUIB` [@Danehkar:2018b] that is coupled to the IDL library `AtomNeb` [@Danehkar:2019]. The collisional excitation and recombination units of this package need to have the energy levels, collision strengths, transition probabilities, and recombination coefficients, which can be retrieved from the Python package `AtomNeb` for _Atomic Data of Ionized Nebulae_ [@Danehkar:2020]. The API functions of this package can be used to deduce the electron temperature, electron concentration, chemical elements from CELs and Rls, and the interstellar extinction from the Balmer decrements emitted from ionized gaseous nebulae. This package can simply be used by astronomers, who are familiar with the high-level, general-purpose programming language Python.

# Statement of Need

The spectral analysis of nebular emission lines with the Python programming language requires a package that can calculate emissivities for collisional excitation and recombination processes with the given electron temperature and density, and estimate the reddening factor for the given interstellar extinction law and physical condition. The previous package `proEQUIB` [@Danehkar:2018b] requires the Interactive Data Language (IDL) compiler. It was necessary to make a similar package purely developed in Python that can be widely used by astronomers and researchers, who prefer to conduct the data analysis of nebular spectra with the high-level programming language Python that is freely available for all operating systems.

# Description

`pyEQUIB` is a pure Python open-source package containing several application programming interface (API) functions that can be employed for plasma diagnostics and abundance analysis of nebular emission lines. This package is a Python implementation of the IDL library `proEQUIB` [@Danehkar:2018b] that is coupled to the IDL library `AtomNeb` [@Danehkar:2019]. The collisional excitation and recombination units of this package need to have the energy levels, collision strengths, transition probabilities, and recombination coefficients, which can be retrieved from the Python package `AtomNeb` for _Atomic Data of Ionized Nebulae_ [@Danehkar:2020]. The API functions of this package can be used to deduce the electron temperature, electron concentration, chemical elements from CELs and Rls, and the interstellar extinction from the Balmer decrements emitted from ionized gaseous nebulae. This package has three units, namely:

- the _collisional excitation unit_ that contains API functions for the interpretation of CELs. This unit was initially developed based on the algorithm of the FORTRAN program `EQUIB` [@Howarth:1981; @Howarth:2016], which was also incorporated into the nebular empirical analysis tool `NEAT` [@Wesson:2012].
The program `EQUIB` computes atomic level populations and emissivities for multi-level atoms in the equilibrium condition using collision strengths and transition probabilities for the specified temperature and density. These API functions are useful for deriving the electron temperature, electron density, and chemical abundances from CELs emitted from ionized gases in planetary nebulae and H II regions.

- the _recombination unit_ that contains API functions for the interpretation of RLs. This unit was originally developed based on the algorithm of the recombination scripts written by X. W. Liu and Y. Zhang used by the FORTRAN photoionization program `MOCASSIN` [@Ercolano:2003; @Ercolano:2005] and the FORTRAN spectral analysis program `NEAT` [@Wesson:2012], which calculates emissivities using recombination coefficients for the given physical condition. These API functions are valuable to deduce the chemical abundances from RLs emitted from gaseous nebulae.

- the _reddening unit_ that contains API functions for the extinction calculation and reddening correction. This unit was developed based on the reddening IRAF scripts included in the Space Telescope Science Data Analysis System, former `STSDAS` IRAF package [@Bushouse:1994; @Shaw:1994]. These API functions can be used to calculate the interstellar extinction from the observed Balmer decrements for different reddening laws, and perform the reddening correction on the observed fluxes of nebular emission lines.

`pyEQUIB` can simply be used by astronomers, who are familiar with the high-level, general-purpose programming language Python. The previous IDL version `proEQUIB` [@Danehkar:2018b] has been used for studies of gaseous nebulae [@Danehkar:2016; @Danehkar:2018a]. This package requires the Python packages `NumPy` [@Walt:2011; @Harris:2020], `SciPy` [@Virtanen:2020], and `AtomNeb` [@Danehkar:2020]. The API functions of this package can be used to analyze emission-line spectra from planetary nebulae and H II regions, as well as extragalactic sources [see e.g. @Danehkar:2014; @Danehkar:2014b; @Danehkar:2016]. This package is released under the GNU General Public License. The source code is publicly available on the GitHub platform. The latest version of this package can be installed directly from its repository on the GitHub, and its stable version from the Python Package Index (PyPi) via ``pip install pyequib`` or alternatively from the Anaconda Python package distributor via ``conda install -c conda-forge pyequib``. The online documentation, tutorials and examples are available on its GitHub page (https://equib.github.io/pyEQUIB/) and its Read the Docs documentation page (https://pyequib.readthedocs.io/).
This package requires the Python packages `NumPy` [@Walt:2011; @Harris:2020], `SciPy` [@Virtanen:2020], and `AtomNeb` [@Danehkar:2020]. This package is released under the GNU General Public License. The source code is publicly available on the GitHub platform. The latest version of this package can be installed directly from its repository on the GitHub, and its stable version from the Python Package Index (PyPi) via ``pip install pyequib`` or alternatively from the Anaconda Python package distributor via ``conda install -c conda-forge pyequib``. The online documentation, tutorials and examples are available on its GitHub page (https://equib.github.io/pyEQUIB/) and its Read the Docs documentation page (https://pyequib.readthedocs.io/).

# Acknowledgements

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