The Astropy Project supports and fosters the development of opensource and openly developed Python packages that provide commonly needed functionality to the astronomical community. A key element of the Astropy Project is the core package astropy which serves as the foundation for more specialized projects and packages. In this article we provide an overview of the organization of the Astropy project and summarize key features in the core package as of the recent major release version 2.0. We then describe the project infrastructure designed to facilitate and support development for a broader ecosystem of interoperable packages. We conclude with a future outlook of planned new features and directions for the broader Astropy Project. P .
['methods: data analysis', 'methods: miscellaneous', 'methods: statistical', 'reference systems', 'Astrophysics - Instrumentation and Methods for Astrophysics']
The Astropy Project Building an Openscience Project and Status of the v2.0 Core Package
{'No Header': 'Draft version January 17, 2018  \nTypeset using L A T X modern style in AASTeX61  \nE', 'THE ASTROPY PROJECT: BUILDING AN INCLUSIVE, OPEN-SCIENCE PROJECT AND STATUS OF THE V2.0 CORE PACKAGE': "The Astropy Collaboration, A. M. Price-Whelan, 1 B. M. Sipőcz, H. M. Günther, 2 P. L. Lim, 3 S. M. Crawford, 4 S. Conseil, 5 D. L. Shupe, 6 M. W. Craig, 7 N. Dencheva, 3 A. Ginsburg, 8 J. T. VanderPlas, 9 L. D. Bradley, 3 D. Pérez-Suárez, 10 and M. de Val-Borro 11  \n(primary paper contributors) T. L. Aldcroft, 12 K. L. Cruz, 13, 14, 15 T. P. Robitaille, 16 and E. J. Tollerud 3 (Astropy coordination committee) C. Ardelean, 17 T. Babej, 18 M. Bachetti, 19 A. V. Bakanov, S. P. Bamford, 20 G. Barentsen, 21 P. Barmby, 17 A. Baumbach, 22 K. L. Berry, F. Biscani, 23 M. Boquien, 24 K. A. Bostroem, 25 L. G. Bouma, 1 G. B. Brammer, 3 E. M. Bray, H. Breytenbach, 4, 26 H. Buddelmeijer, 27 D. J. Burke, 12 G. Calderone, 28 J. L. Cano Rodríguez, M. Cara, 3 J. V. M. Cardoso, 29, 21, 30 S. Cheedella, 31 Y. Copin, 32 D. Crichton, 33 D. D'Avella, 3 C. Deil, 34 É. Depagne, 4 J. P. Dietrich, 35, 36 A. Donath, 34 M. Droettboom, 3 N. Earl, 3 T. Erben, 37 S. Fabbro, 38 L. A. Ferreira, 39 T. Finethy, R. T. Fox, L. H. Garrison, 12 S. L. J. Gibbons, 40 D. A. Goldstein, 41, 42 R. Gommers, 43 J. P. Greco, 1 P. Greenfield, 3 A. M. Groener, 44 F. Grollier, A. Hagen, 45, 46 P. Hirst, 47 D. Homeier, 48 A. J. Horton, 49 G. Hosseinzadeh, 50, 51 L. Hu, 52 J. S. Hunkeler, 3 Ž. Ivezić, 53 A. Jain, 54 T. Jenness, 55 G. Kanarek, 3 S. Kendrew, 56 N. S. Kern, 41 W. E. Kerzendorf, 57 A. Khvalko, J. King, 34 D. Kirkby, 58 A. M. Kulkarni, 59 A. Kumar, 60 A. Lee, 61 D. Lenz, 62 S. P. Littlefair, 63 Z. Ma, 64 D. M. Macleod, 65 M. Mastropietro, 66 C. McCully, 50, 51 S. Montagnac, 67 B. M. Morris, 53 M. Mueller, 68 S. J. Mumford, 69 D. Muna, 70 N. A. Murphy, 12 S. Nelson, 7 G. H. Nguyen, 71 J. P. Ninan, 46 M. Nöthe, 72 S. Ogaz, 3 S. Oh, 1 J. K. Parejko, 53 N. Parley, 73 S. Pascual, 74 R. Patil, A. A. Patil, 75 A. L. Plunkett, 76 J. X. Prochaska, 77 T. Rastogi, V. Reddy Janga, 78 J. Sabater, 79 P. Sakurikar, 80 M. Seifert, L. E. Sherbert, 3 H. Sherwood-Taylor, A. Y. Shih, 81 J. Sick, 82 M. T. Silbiger, S. Singanamalla, 83 L. P. Singer, 84, 85 P. H. Sladen, 86 K. A. Sooley, S. Sornarajah, O. Streicher, 87 P. Teuben, 88 S. W. Thomas, 40 G. R. Tremblay, 89 J. E. H. Turner, 47 V. Terrón, 90 M. H. van Kerkwijk, 91 A. de la Vega, 33 L. L. Watkins, 3 B. A. Weaver, 92 J. B. Whitmore, 93 J. Woillez, 57 and V. Zabalza  \nCorresponding author: Astropy Coordination Committee  \ncoordinators@astropy.org  \nThe author list has three parts: the authors that made significant contributions to the writing of the paper in order of contribution, the four members of the Astropy Project coordination committee, and contributors to the Astropy Project in alphabetical order. The position in the author list does not correspond to contributions to the Astropy Project as a whole. A more complete list of contributors to the core package can be found in the package repository, and at the Astropy team webpage.", 'The Astropy Collaboration': '(Astropy contributors)  \n- 1 Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA  \n- 13 Department of Physics and Astronomy, Hunter College, City University of New York, 695 Park Avenue, New York, NY 10065  \n- 15 Department of Astrophysics, American Museum of Natural History, New York, NY, USA  \n- 19 INAF-Osservatorio Astronomico di Cagliari, via della Scienza 5, I-09047, Selargius, Italy', 'Astropy Project II': "- 28 Istituto Nazionale di Astrofisica, via Tiepolo 11 Trieste, Italy\n- 29 Universidade Federal de Campina Grande, Campina Grande, PB 58429-900, Brazil\n- 30 Bay Area Environmental Research Institute, Petaluma, CA 94952, USA\n- 31 Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA\n- 32 Université de Lyon, F-69622, Lyon, France; Université de Lyon 1, Villeurbanne; CNRS/IN2P3, Institut de Physique Nucléaire de Lyon\n- 33 Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA\n- 34 Max-Planck-Institut für Kernphysik, PO Box 103980, 69029 Heidelberg, Germany\n- 35 Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 Munich, Germany\n- 36 Excellence Cluster Universe, Boltzmannstr. 2, 85748 Garching b. München, Germany\n- 37 Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany\n- 38 National Research Council Herzberg Astronomy & Astrophysics, 4071 West Saanich Road, Victoria, BC\n- 39 Instituto de Matemática Estatística e Física - IMEF, Universidade Federal do Rio Grande FURG, Rio Grande, RS 96203-900, Brazil\n- 40 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK\n- 41 Department of Astronomy, UC Berkeley, 501 Campbell Hall #3411, Berkeley, CA 94720, USA\n- 42 Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA\n- 43 Scion, Private Bag 3020, Rotorua, New Zealand\n- 44 Drexel University, Physics Department, Philadelphia, PA 19104, USA\n- 45 Vizual.ai, 3600 O'Donnell St, Suite 250, Baltimore, MD 21224\n- 46 Dept of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802\n- 47 Gemini Observatory, 670 N. Aohoku Pl, Hilo, HI 96720, USA\n- 48 Zentrum für Astronomie der Universität Heidelberg, Landessternwarte, Königstuhl 12, 69117 Heidelberg, Germany\n- 49 Australian Astronomical Observatory, 105 Delhi Road, North Ryde NSW 2113, Australia\n- 50 Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA\n- 51 Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA\n- 52 Imperial College London, Kensington, London SW7 2AZ, United Kingdom\n- 53 Department of Astronomy, University of Washington, Seattle, WA 98155\n- 54 BITS PILANI/Computer Science, Pilani Campus, Rajasthan, India\n- 55 Large Synoptic Survey Telescope, 950 N. Cherry Ave., Tucson, AZ, 85719, USA\n- 56 European Space Agency, Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218, USA\n- 57 European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching bei München, Germany\n- 58 Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA\n- 59 College of Engineering Pune/Department of Computer Engineering and IT, Shivajinagar, Pune 411005, India  \n- 61 Department of Physics, University of Berkeley, Califonia, CA94709, USA  \n- 62 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA\n- 63 Department of Physics & Astronomy, University of Sheffield, Sheffield, S3 7RH, UK\n- 64 Department of Physics and Astronomy, University of Missouri, Columbia, Missouri, 65211, USA 65 Cardiff University, Cardiff CF24 3AA, UK\n- 66 Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, B-9000 Gent, Belgium", 'ABSTRACT': 'The Astropy project supports and fosters the development of open-source and openly-developed Python packages that provide commonly-needed functionality to the astronomical community. A key element of the Astropy project is the core package astropy , which serves as the foundation for more specialized projects and packages. In this article, we provide an overview of the organization of the Astropy project and summarize key features in the core package as of the recent major release, version 2.0. We then describe the project infrastructure designed to facilitate and support development for a broader ecosystem of inter-operable packages. We conclude with a future outlook of planned new features and directions for the broader Astropy project.  \nKeywords: Astrophysics - Instrumentation and Methods for Astrophysics - methods: data analysis - methods: miscellaneous', '1. INTRODUCTION': 'All modern astronomical research makes use of software in some way. Astronomy as a field has thus long supported the development of software tools for astronomical tasks, such as scripts that enable individual scientific research, software packages for small collaborations, and data reduction pipelines for survey operations. Some software packages are, or were, supported by large institutions and are intended for a wide range of users. These packages therefore typically provide some level of documentation and user support or training. Other packages are developed by individual researchers or research groups and are then typically used by smaller groups for more domain-specific purposes. For both packages meant for wider distribution and for scripts specific to particular research projects, a library that addresses common astronomical tasks simplifies the software development process. The users of such a library then also benefit from a community and ecosystem built around a shared foundation. The Astropy project has grown to become this community for Python astronomy software, and the astropy core package is a feature-rich Python library.  \nThe development of the astropy core package began as a largely community-driven effort to standardize core functionality for astronomical software in Python . In this way, its genesis differs from, but builds upon, many substantial and former astronomical software development efforts that were commissioned or initiated through large institutional support, such as IRAF (developed at NOAO; Tody 1993), MIDAS (developed at ESO; Banse et al. 1988), or Starlink (originally developed by a consortium of UK institutions and now maintained by the East Asian Observatory; Disney & Wallace 1982; Currie et al. 2014). More recently, community-driven efforts have seen significant success in the astronomical sciences (e.g., Turk et al. 2011).  \nPython 1 is an increasingly popular, general-purpose programming language that is available under a permissive open source software license and is free of charge for all major operating systems. The programming language has become especially popular in the quantitative sciences, where researchers must simultaneously produce research, perform data analysis, and develop software. A large part of this success owes itself to the vibrant community of developers and a continuously-growing ecosystem of tools, web services, and stable well-developed packages that enable easier collaboration on software development, easier writing and sharing of software documentation, and continuous testing and validation of software. While dedicated libraries provide support for array representation and arithmetic ( numpy ; Van der Walt et al. 2011), a wide variety of functions for scientific computing ( scipy ; Jones et al. 2001-), and publication-quality plotting ( matplotlib ; Hunter 2007), tens of thousands of other high-quality and easy-to-use packages are available, which can help with tasks that are not specific to astronomy but might be performed in the course of astronomical research, e.g., interfacing with databases, or statistical inferences. More recently,  \nthe development and mainstream adoption of package managers such as Anaconda 2 has significantly streamlined the installation process for many libraries, lowering the barriers to entry.  \nThe Astropy project aims to provide an open-source and open-development core package ( astropy ) and an ecosystem of affiliated packages that support astronomical functionality in the Python programming language. The astropy core package is now a feature-rich library of sufficiently general tools and classes that supports the development of more specialized code. An example of such functionality is reading and writing FITS files: It would be time consuming and impractical for multiple groups to implement the FITS standard (Pence et al. 2010) and maintain software for such a general-purpose need. Another example of such a common task is in dealing with representations of and transformations between astronomical coordinate systems.  \nThe Astropy project aims to develop and provide high-quality code and documentation according to the best practices in software development. The project makes use of different tools and web services to reach those goals without central institutional oversight. The first public release of the astropy package is described in Astropy Collaboration et al. (2013). Since then, the astropy package has been used in hundreds of projects and the scope of the package has grown considerably. At the same time, the scientific community contributing to the project has grown tremendously and an ecosystem of packages supporting or affiliated with the astropy core has developed. In this paper, we describe the current status of the Astropy community and the astropy core package and discuss goals for future development.  \nWe start by describing the way the Astropy project functions and is organized in Section 2. We then describe the main software efforts developed by the Astropy project itself: a core package called astropy (Section 3) and several separate packages that help maintain the infrastructure for testing and documentation (Section 4). We end with a short vision for the future of Astropy and astronomical software in general in Section 5. The full paper, including the code to produce the figures, is available in a GitHub repository 3  \nThis article is not intended as an introduction to astropy , nor does it replace the astropy documentation. Instead, it describes the way the Astropy community is organized and the current state of the astropy package.', '2.1. Coordination of Astropy': "From its inception, Astropy has required coordination to ensure the project as a whole and its coding efforts are consistent and reasonably efficient. While many Python projects adopt a 'Benevolent Dictator For Life' (BDFL) model, Astropy has instead opted for a coordination committee . This is in part due to the nature of the  \nFigure 1. Left panel : Distribution of number of commits per committer. Right panel : Cumulative number of commits to the astropy core package over time.  \n<!-- image -->  \nproject as a large-scale collaboration between many contributors with many interests, and in part due to simply the amount of work that needs to get done. For the latter reason, the project has expanded the committee from three to four members starting in 2016.  \nFor resolving disagreements about the astropy core package or other Astropymanaged code, the coordination committee primarily acts to work toward consensus, or when consensus is difficult to achieve, generally acts as a 'tie-breaker.' The committee also oversees affiliated package applications to ensure that they are in keeping with Astropy's vision and philosophy, 4 as well as the associated procedures. Additionally, the committee oversees the assignment of roles (primarily driven by already-existing contributions), and increasingly has acted as the 'face' of the Project, providing contact with organizations like NumFOCUS (the body that holds any potential funding in trust for Astropy) and the American Astronomical Society (AAS).", '2.2. Astropy development model': "Code is contributed to the astropy core package or modified through 'pull requests' (via GitHub 5 ) that often contain several git commits. Pull requests may fix bugs, implement new features, or improve or modify the infrastructure that supports the development and maintenance of the package. Individual pull requests are generally limited to a single conceptual addition or modification to make code review tractable. Pull requests that modify or add code to a specific subpackage must be reviewed and approved by one of the subpackage maintainers before they are merged into the core codebase. Bugs and feature requests are reported via the GitHub issue tracker and  \nlabeled with a set of possible labels that help classify and organize the issues. The development workflow is detailed in the astropy documentation. 6  \nAs of version 2.0, astropy contains 212244 lines of code 7 contributed by 232 unique contributors over 19270 git commits. Figure 1, left, shows the distribution of total number of commits per contributor as of November 2017. The relative flatness of this distribution (as demonstrated by its log-log slope of -0 . 5 ) shows that the astropy core package has been developed by a broad contributor base. A leading group of 6 developers have each added over 1000 commits to the repository, and ∼ 20 more core contributors have contributed at least 100 commits. However, the distribution of contribution level (number of commits) continues from 100 down to a single commit. In this sense, the development of the core package has been a true community effort and is not dominated by a single individual. It is also important to note that the number of commits is only a rough metric of contribution, as a single commit could be a critical fix in the package or a fix for a typographical error. Figure 1, right, shows the number of commits as a function of time since the genesis of the astropy core package. The package is still healthy: new commits are and have been contributed at a steady rate throughout its existence.", '2.3. APEs - Astropy Proposals for Enhancement': "Central to the success of Astropy is an open environment where anybody can contribute to the project. This model leads to an 'organic' growth, where features are implemented by different people with different programming styles and interfaces. Thus, Astropy has a mechanism to more formally propose significant changes to the core package (e.g., re-writing the coordinates subpackage; Tollerud et al. 2014), to plan out major new features (e.g., a new file format; Aldcroft 2015), or institute new organization-wide policies (e.g., adopting a code of conduct; Cruz et al. 2015). This mechanism is called 'Astropy Proposal for Enhancement' (APE) and is modeled after the 'Python Enhancement Proposals' (PEP) that guide the development of the Python programming language. In an APE, one or more authors describe in detail the proposed changes or additions, including a rationale for the changes, how these changes will be implemented, and in the case of code, what the interface will be (Greenfield 2013). The APEs are discussed and refined by the community before much work is invested into a detailed implementation; anyone is welcome to contribute to these discussions during the open consideration period. APEs are proposed via pull requests on a dedicated GitHub repository 8 ; anyone can therefore read the proposed APEs and leave in-line comments. When a community consensus emerges, the APEs are accepted and become the basis for future work. In cases where consensus cannot be reached, the Astropy coordination committee may decide to close the dis-  \ncussion and make an executive decision based on the community input on the APE in question.", '2.4. Concept of affiliated packages': "A major part of the Astropy project is the concept of 'Affiliated Packages.' An affiliated package is an astronomy-related Python package that is not part of the astropy core package, but has requested to be included as part of the Astropy project's community. These packages support the goals and vision of Astropy of improving code re-use, interoperability, and embracing good coding practices such as testing and thorough documentation.  \nAffiliated packages contain functionality that is more specialized, have license incompatibilities, or have external dependencies (e.g., GUI libraries) that make these packages more suitable to be separate from the astropy core package. Affiliated packages may also be used to develop substantial new functionality that will eventually be incorporated into the astropy core package (e.g., wcsaxes ). New functionality benefits from having a rapid development and release cycle that is not tied to that of the astropy core (Section 2.5).  \nAffiliated packages are listed on the main Astropy website and advertised to the community through Astropy mailing lists; a list of current affiliated packages is included in Table A. Becoming an affiliated package is a good way for new and existing packages to gain exposure while promoting Astropy's high standard for code and documentation quality. This process of listing and promoting affiliated packages is one way in which the Astropy project tries to increase code re-use in the astronomical community.  \nPackages can become affiliated to Astropy by applying for this status on a public mailing list. The coordination committee (Section 2.1) reviews such requests and issues recommendations for the improvement of a package, where applicable.", '2.5. Release cycle and Long Term Support': "The astropy package has a regular release schedule consisting of new significant releases every 6 months, with bugfix releases as needed (Tollerud 2013). The major releases contain new features or any significant changes, whereas the bugfix releases only contain fixes to code or documentation but no new features. Some versions are additionally designated as 'Long-term support' (LTS) releases, which continue to receive bug fixes for 2 years following the release with no changes to the API. The LTS versions are ideal for pipelines and other applications in which API stability is essential. The latest LTS release (version 2.0) is also the last one that supports Python 2; it will receive bug fixes until the end of 2019 (Robitaille 2017).  \nThe version numbering of the astropy core package reflects this release scheme: the core package version number uses the form x.y.z , where 'x' is advanced for LTS releases, 'y' for non-LTS feature releases, and 'z' for bugfix releases.  \nThe released versions of the astropy core package are available from several of the Python distributions for scientific computing (e.g., Anaconda) and from the Python Package Index (PyPI). 9 Effort has been made to make astropy available and easily installable across all platforms; the package is constantly tested on different platforms as part of a suite of continuous integration tests.", '2.6. Support of Astropy': 'The Astropy project, as of the version 2.0 release, does not receive any direct financial support for the development of astropy . Development of the software, all supporting materials, and community support are provided by individuals who work on the Astropy project in their own personal time, by individuals or groups contributing to Astropy as part of a research project, or contributions from institutions that allocate people to work on Astropy. A list of organizations that have contributed to Astropy in this manner can be found in the Acknowledgments.  \nDifferent funding models have been proposed for support of Astropy (e.g., Muna et al. 2016), but a long-term plan for sustainability has not yet been established. The Astropy project has the ability to accept financial contributions from institutions or individuals through the NumFOCUS 10 organization. NumFOCUS has, to date, covered the direct costs incurred by the Astropy project.', '3. ASTROPY CORE PACKAGE VERSION 2.0': 'The Astropy project aims to provide Python -based packages for all tasks that are commonly needed in a large subset of the astronomical community. At the foundation is the astropy core package, which provides general functionality (e.g., coordinate transformations, reading and writing astronomical files, and units) or base classes for other packages to utilize for a common interface (e.g., NDData ). In this section, we highlight new features introduced or substantially improved since version 0.2 (previously described in Astropy Collaboration et al. 2013). The astropy package provides a full log of changes 11 over the course of the entire project and more details about individual subpackages are available in the documentation. 12 Beyond what is mentioned below, most subpackages have seen improved performance since the release of the version 0.2 package.', '3.1. Units': "The astropy.units subpackage adds support for representing units and numbers with associated units - 'quantities' - in code. Historically, quantities in code have often been represented simply as numbers, with units implied or noted via comments in the code because of considerations about speed: having units associated  \nwith numbers inherently adds overhead to numerical operations. In astropy.units , Quantity objects extend numpy array objects and have been designed with speed in mind.  \nAs of astropy version 2.0, units and quantities, prevalent in most of its subpackages, have become a key concept for using the package as a whole. Units are intimately entwined in the definition of astronomical coordinates; thus, nearly all functionality in the astropy.coordinates subpackage (see Section 3.3) depends on them. For most other subpackages, quantities are at least accepted and often expected by default.  \nThe motivation and key concepts behind this subpackage were described in detail in the previous paper (Astropy Collaboration et al. 2013). Therefore, we primarily highlight new features and improvements here.", '3.1.1. Interaction with numpy arrays': 'Quantity objects extend numpy.ndarray objects and therefore work well with many of the functions in numpy that support array operations. For example, Quantity objects with angular units can be directly passed in to the trigonometric functions implemented in numpy . The units are internally converted to radians, which is what the numpy trigonometric functions expect, before being passed to numpy .', '3.1.2. Logarithmic units and magnitudes': 'By default, taking the logarithm of a Quantity object with non-dimensionless units intentionally fails. However, some well-known units are actually logarithmic quantities, where the logarithm of the value is taken with respect to some reference value. Examples include astronomical magnitudes, which are logarithmic fluxes, and decibels, which are more generic logarithmic ratios of quantities. Logarithmic, relative units are now supported in astropy.units .', '3.1.3. Defining functions that require quantities': 'When writing code or functions that expect Quantity objects, we often want to enforce that the input units have the correct physical type. For example, we may want to require only length-type Quantity objects. astropy.units provides a tool called quantity\\_input() that can perform this verification automatically to avoid repetitive code.', '3.2. Constants': "The astropy.constants subpackage provides a selection of physical and astronomical constants as Quantity objects (see Section 3.1). A brief description of this package was given in Astropy Collaboration et al. (2013). In version 2.0, the built-in constants have been organized into modules for specific versions of the constant values. For example, physical constants have codata2014 (Mohr et al. 2016) and codata2010 versions. Astronomical constants are organized into iau2015 and iau2012 modules to indicate their sources (resolutions from the International Astronomical Union, IAU). The codata2014 and iau2015 versions are combined into the  \ndefault constant value version: astropyconst20 . For compatibility with astropy version 1.3, astropyconst13 is available and provides access to the adopted versions of the constants from earlier versions of astropy . To use previous versions of the constants as units (e.g., solar masses), the values have to be imported directly; with version 2.0, astropy.units uses the astropyconst20 versions.  \nAstronomers using astropy.constants should take particular note of the constants provided for Earth, Jupiter, and the Sun. Following IAU 2015 Resolution B3 (Mamajek et al. 2015), nominal values are now given for mass parameters and radii. The nominal values will not change even as 'current best estimates' are updated.", '3.3. Coordinates': 'The astropy.coordinates subpackage is designed to support representing and transforming celestial coordinates and, new in version 2.0, velocities. The framework heavily relies on the astropy.units subpackage, and most inputs to objects in this subpackage are expected to be Quantity objects. Some of the machinery also relies on the Essential Routines of Fundamental Astronomy (ERFA) C library for some of the critical underlying transformation machinery (Tollerud et al. 2017), which is based on the Standards Of Fundamental Astronomy (SOFA) effort (Hohenkerk 2011).  \nA key concept behind the design of this subpackage is that coordinate representations and reference systems / frames are independent of one another. For example, a set of coordinates in the International Celestial Reference System (ICRS) reference frame could be represented as spherical (right ascension, declination, and distance from solar system barycenter) or Cartesian coordinates ( x , y , z with the origin at barycenter). They can therefore change representations independent of being transformed to other reference frames (e.g., the Galactic coordinate frame).  \nThe classes that handle coordinate representations (the Representation classes) act like three-dimensional vectors and thus support vector arithmetic. The classes that represent reference systems and frames (the Frame classes) internally use Representation objects to store the coordinate data-that is, the Frame classes accept coordinate data, either as a specified Representation object, or using shorthand keyword arguments to specify the components of the coordinates. These preferred representation and short-hand component names differ between various astronomical reference systems. For example, in the ICRS frame, the spherical angles are right ascension ( ra ) and declination ( dec ), whereas in the Galactic frame, the spherical angles are Galactic longitude ( l ) and latitude ( b ). Each Frame class defines its own component names and preferred Representation class. The frame-specific component names map to corresponding components on the underlying Representation object that internally stores the coordinate data. For most frames, the preferred representation is spherical, although this is determined primarily by the common use in the astronomical community.  \nFigure 2. The full graph of possible reference frame transformations implemented in astropy.coordinates . Arrows indicate transformations from one frame to another. Arrows that point back to the same frame indicate self-transformations that involve a change of reference frame parameters (e.g., equinox).  \n<!-- image -->  \nMany of the Frame classes also have attributes specific to the corresponding reference system that allow the user to specify the frame. For example, the Fifth Fundamental Catalogue (FK5) reference system requires specifying an equinox to determine the reference frame. If required, these additional frame attributes must be specified along with the coordinate data when a Frame object is created. Figure 2 shows the network of possible reference frame transformations as currently implemented in astropy.coordinates . Custom user-implemented Frame classes that define transformations to any reference frame in this graph can then be transformed to any of the other connected frames.  \nThe typical user does not usually have to interact with the Frame or Representation classes directly. Instead, astropy.coordinates provides a highlevel interface to representing astronomical coordinates through the SkyCoord class, which was designed to provide a single class that accepts a wide range of possible  \ninputs. It supports coordinate data in any coordinate frame in any representation by internally using the Frame and Representation classes.  \nIn what follows, we briefly highlight key new features in astropy.coordinates .', '3.3.1. Local Earth coordinate frames': 'In addition to representing celestial coordinates, astropy now supports specifying positions on the Earth in a number of different geocentric systems with the EarthLocation class. With this, astropy now supports Earth-location-specific coordinate systems such as the altitude-azimuth ( AltAz ) or horizontal system. Transformations between AltAz and any Barycentric coordinate frame also requires specifying a time using the Time class from astropy.time . With this new functionality, many of the common tasks associated with observation planning can now be completed with astropy or the Astropy-affiliated package astroplan (Morris et al. 2017).', '3.3.2. Proper motion and velocity transformations': 'In addition to positional coordinate data, the Frame classes now also support velocity data. As the default representation for most frames is spherical, most of the Frame classes expect proper motion and radial velocity components to specify the velocity information. The names of the proper motion components all start with pm and adopt the same longitude and latitude names as the positional components. Transforming coordinates with velocity data is also supported, but in some cases the transformed velocity components have limited accuracy because the transformations are done numerically instead of analytically. The low-level interface for specifying and transforming velocity data is currently experimental. As such, in version 2.0, only the Frame classes (and not the SkyCoord class) support handling velocities.', '3.3.3. Solar System Ephemerides': 'Also new is support for computing ephemerides of major solar system bodies and outputting the resulting positions as coordinate objects. These ephemerides can be computed either using analytic approximations from ERFA or from downloaded JPL ephemerides (the latter requires the jplephem 13 optional dependency and an internet connection).', '3.3.4. Accuracy of coordinate transformations': "In order to check the accuracy of the coordinate transformations in astropy.coordinates , we have created a set of benchmarks that we use to compare transformations between a set of coordinate frames for a number of packages 14 . Since no package can be guaranteed to implement all transformations to arbitrary precision and some transformations are sometimes subject to interpretation of standards (in particular in the case of Galactic coordinates), we do not designate any  \nof the existing packages as the 'ground truth' but instead compare each tool to all other tools. The benchmarks are thus useful beyond the Astropy project since they allow all of the tools to be compared to all other tools. The tools included in the benchmark at the moment include the astropy core package, Kapteyn (Terlouw & Vogelaar 2015), NOVAS (Barron et al. 2011), PALpy (Jenness & Berry 2013), PyAST (a wrapper for AST, described in Berry et al. 2016), PyTPM 15 , PyEphem (Rhodes 2011), and pySLALIB (a Python wrapper for SLALIB, described in Wallace 1994).  \nThe benchmarks are meant to evolve over time and include an increasing variety of cases. At the moment, the benchmarks are set up as follows - we have generated a standard set of 1000 pairs of random longitudes/latitudes that we use in all benchmarks. Each benchmark is then defined using an input and output coordinate frame, using all combinations of FK4, FK5, Galactic, ICRS, and Ecliptic frames. For now, we set the epoch of observation to J2000. We also set the frame to J2000 (for FK5 and Ecliptic) and B1950 (for FK4). In the future, we plan to include a larger variety of epochs and equinoxes, as well as tests of conversion to/from Altitude/Azimuth. For each benchmark, we convert the 1000 longitudes/latitudes from the input/output frame with all tools and quantify the comparison by looking at the median, mean, maximum, and standard deviation of the absolute separation of the output coordinates from each pair of tools.  \nFigure 3 visualizes the relative accuracy of the conversion from FK4 to Galactic coordinates for all pairs of tools that implement this transformation. In this figure, the color of the cell indicates the maximum difference (in arcseconds) between the two tools over the 1000 longitude-latitude pairs tested. This figure shows, for example, that astropy , Kapteyn, and PyTPM agree with sub-milliarcsecond differences (light colors, small differences), while PALpy, pySLALIB, and PyAST also agree amongst themselves. However, there is an offset of around 0.2 '' between the two groups. Finally, PyEphem disagrees with all other packages by 0.4-0.8 '' (darker colors, large differences). These values are only meant to be illustrative and will change over time as the benchmarks are refined and the packages updated.", '3.4. Time': 'The astropy.time subpackage focuses on supporting time scales (e.g., UTC, TAI, UT1) and time formats (e.g., Julian date, modified Julian date) that are commonly used in astronomy. This functionality is needed, for example, to calculate barycentric corrections or sidereal times. astropy.time is currently built on the ERFA (Tollerud et al. 2017) C library, which replicates the Standards of Fundamental Astronomy (SOFA; Hohenkerk 2011) but is licensed under a three-clause BSD license. The package was described in detail in Astropy Collaboration et al. (2013) and has stayed stable for the last several versions of astropy . Thus, in what follows, we only highlight significant changes or new features since the previous Astropy paper.  \nFigure 3. Comparison matrix of the maximum difference between longitude-latitude values in a set of 1000 random points transformed from FK4 to Galactic with the different packages. Darker colors (larger differences) are more significant disagreements.  \n<!-- image -->', '3.4.1. Barycentric and Heliocentric corrections': "Detailed eclipse or transit timing requires accounting for light travel time differences from the source to the observatory because of the Earth's motion. It is therefore common to instead convert times to the Solar System barycenter or heliocenter where the relative timing of photons is standardized. With the location of a source on the sky (i.e., a SkyCoord object), the location of an observatory on Earth (i.e., an EarthLocation object), and time values as Time objects, the time corrections to shift to the solar system barycenter or heliocenter can now be computed with astropy.time using the light\\_travel\\_time method of a Time object.", '3.5.1. nddata': 'The astropy.nddata subpackage provides three types of functionality: an abstract interface for representing generic arbitrary-dimensional datasets intended primarily for subclassing by developers of other packages, concrete classes building on this interface, and utilities for manipulating these kind of datasets.  \nThe NDDataBase class provides the abstract interface for gridded data with attributes for accessing metadata, the world coordinate system (WCS), uncertainty arrays matched to the shape of the data, and other traits. Building on this interface, the NDData class provides a minimal working implementation for storing numpy arrays. These classes serve as useful base classes for package authors wishing to develop their own classes for specific use cases and as containers for exchanging gridded data.  \nThe classes NDDataRef , NDDataArray , and CCDData extend the base storage functionality with options to do basic arithmetic (addition, subtraction, multiplication, and division), including error propagation in limited cases, and slicing of the dataset based on grid coordinates that appropriately handles masking, errors, and units (if present). Additionally, the CCDData class also provides reading and writing from and to FITS files and uses data structures from astropy , like WCS , to represent the file contents abstractly.  \nThe astropy.nddata.utils module provides utilities that can operate on either plain numpy arrays or any of the classes in the astropy.nddata subpackage. It features a class for representing two-dimensional image cutouts, allowing one to easily link pixels in the cutout to those in the original image or vice versa, to convert between world and pixel coordinates in the cutout, and to overlay the cutout on images. Functions to enlarge or reduce an image by doing block replication or reduction are also provided.', '3.5.2. Tables': "The astropy.table subpackage provides functionality for representing and manipulating heterogeneous data. In some respects, this is similar to numpy record arrays (Van der Walt et al. 2011) or pandas dataframes (McKinney 2010) but with modifications for astronomical data. Most notably, tables from astropy.table allow for table or column metadata and can handle vectors or arrays as table entries. The subpackage was described in detail in Astropy Collaboration et al. (2013). Thus, in what follows, we only summarize key new features or updates to astropy.table since the previous Astropy paper. These are support for grouped table operations, table concatenation, and using array-valued astropy objects as table columns.  \nA table can contain data that naturally form groups; for example, it may contain multiple observations of a few sources at different points in time and in different bands. Then, we may want to split the table into groups based on the combination of source observed and the band, after which we combine the results for each combination of source and band in some way (e.g., finding the mean or standard deviation of  \nthe fluxes or magnitudes over time) or filter the groups based on user-defined criteria. These kinds of grouping and aggregation operations are now fully supported by Table objects.  \nTable objects can now be combined in several different ways. If two tables have the same columns, we may want to stack them 'vertically' to create a new table with the same columns but all rows. If two tables are row-matched but have distinct columns, we may want to stack them 'horizontally' to create a new table with the same rows but all columns. For other situations, more generic table concatenation or join are also possible when two tables share some columns.  \nThe Table object now allows array-valued Quantity , celestial coordinate ( SkyCoord ), and date/time ( Time ) objects to be used as columns. It also provides a general way for other user-defined array-like objects to be used as columns. This makes it possible, for instance, to easily represent catalogs of sources or time series in Astropy, while having both the benefits of the Table object (e.g., accessing specific rows/columns or groups of them and combining tables) and of, for example, the SkyCoord or the Time classes (e.g., converting the coordinates to a different frame or accessing the date/time in the desired time scale).", '3.6. io': 'The astropy.io subpackage provides support for reading and writing data to a variety of ASCII and binary file formats, such as a wide range of ASCII data table formats, FITS, HDF5, and VOTable. It also provides a unified interface for reading and writing data with these different formats using the astropy.table subpackage. For many common cases, this simplifies the process of file input and output (I/O) and reduces the need to master the separate details of all the I/O packages within astropy . The file interface allows transparent compression of the gzip , bzip2 and lzma ( .xz ) formats; for the latter two if the Python installation was compiled with support the respective libraries.', '3.6.1. ASCII': 'One of the problems when storing a table in an ASCII format is preserving table meta-data such as comments, keywords and column data types, units, and descriptions. The newly defined Enhanced Character Separated Values (ECSV, Aldcroft 2015) format makes it possible to write a table to an ASCII-format file and read it back with no loss of information. The ECSV format has been designed to be both human-readable and compatible with most simple CSV readers.  \nThe astropy.io.ascii subpackage now includes a significantly faster Cython/C engine for reading and writing ASCII files. This is available for most of the common formats. It also offers some additional features like parsing of different exponential notation styles, such as commonly produced by Fortran programs. On average, the new engine is about 4 to 5 times faster than the corresponding purePython implementation and is often comparable to the speed of the pandas (McKinney 2010) ASCII  \nfile interface. The fast reader has a parallel processing option that allows harnessing multiple cores for input parsing to achieve even greater speed gains. By default, read() and write() will attempt to use the fast Cython/C engine when dealing with compatible formats. Certain features of the full read / write interface are unavailable in the fast version, in which case the reader will by default fall back automatically to the purePython version.  \nThe astropy.io.ascii subpackage now provides the capability to read a table within an HTML file or web URL into an astropy Table object. A Table object can now also be written out as an HTML table.', '3.6.2. FITS': 'The astropy.io.fits subpackage started as a direct port of the PyFITS project (Barrett & Bridgman 1999). Therefore, it is pretty stable, with mostly bug fixes but also a few new features and performance improvements. The API remains mostly compatible with PyFITS, which is now deprecated in favor of astropy .  \nCommand-line scripts are now available for printing a summary of the HDUs in FITS file(s) ( fitsinfo ) and for printing the header information to the screen in a human-readable format ( fitsheader ).  \nFITS files are now loaded lazily by default, i.e., an object representing the list of HDUs is created but the data are not loaded into memory until requested. This approach should provide substantial speed-ups when using the convenience functions (e.g., getheader() or getdata() ) to get an HDU that is near the beginning in a file with many HDUs.', '3.7. Modeling': 'The astropy.modeling subpackage provides a framework for representing analytical models and performing model evaluation and parameter fitting. The main motivation for this functionality was to create a framework that allows arbitrary combination of models to support the Generalized World Coordinate System (GWCS) package. 16 The current FITS WCS specification lacks the flexibility to represent arbitrary distortions and does not meet the needs of many types of current instrumentation. The fact that the astropy modeling framework now supports propagating units also makes it a useful tool for representing and fitting astrophysical models within data analysis tools.  \nModels and fitters are independent of each other: a model can be fit with different fitters and new fitters can be added without changing existing models. The framework is designed to be flexible and easily extensible. The goal is to have a rich set of models, but to also facilitate creating new ones, if necessary.  \n3.7.1. Single Model Definition and Evaluation  \nModels are defined by their parameters and initialized by providing values for them. The names of the parameters are stored in a list, Model.param\\_names . Parameters are complex objects. They store additional information - default value, default unit, and parameter constraints. Parameter values and constraints can be updated by assignment. Supported constraints include fixed , and tied parameters, and bounds on parameter values. The framework also supports models for which the number of parameters and their names are defined by another argument. A typical example is a polynomial model defined by its degree. A model is evaluated by calling it as a function.  \nIf an analytical inverse of a model exists it can be accessed by calling Model.inverse . In addition, Model.inverse can be assigned another model which represents a computed inverse.  \nAnother useful settable property of models is Model.bounding\\_box . This attribute sets the domain over which the model is defined. This greatly improves the efficiency of evaluation when the input range is much larger than the characteristic width of the model itself.', '3.7.2. Model Sets': 'astropy.modeling provides an efficient way to set up the same type of model with many different sets of parameter values. This creates a model set that can be efficiently evaluated. For example, in PSF (point spread function) photometry, all objects in an image will have a PSF of the same functional form, but with different positions and amplitudes.', '3.7.3. Compound Models': 'Models can be combined using arithmetic expressions. The result is also a model, which can further be combined with other models. Modeling supports arithmetic (+, -, *, /, and **), join ( & ), and composition ( | ) operators. The rules for combining models involve matching their inputs and outputs. For example, the composition operator, | , requires the number of outputs of the left model to be equal to the number of inputs of the right one. For the join operator, the total number of inputs must equal the sum of number of inputs of both the left and the right models. For all arithmetic operators, the left and the right models must have the same number of inputs and outputs. An example of a compound model could be a spectrum with interstellar absorption. The stellar spectrum and the interstellar extinction are represented by separate models, but the observed spectrum is fitted with a compound model that combines both.', '3.7.4. Fitting Models to Data': 'astropy.modeling provides several fitters which are wrappers around some of the numpy and scipy.optimize functions and provide support for specifying parameter constraints. The fitters take a model and data as input and return a copy of  \nthe model with the optimized parameter values set. The goal is to make it easy to extend the fitting framework to create new fitters. The optimizers available in astropy version 2.0 are Levenberg-Marquardt ( scipy.optimize.leastsq ), Simplex ( scipy.optimize.fmin ), SLSQP ( scipy.optimize.slsqp ), and LinearLSQFitter ( numpy.linalg.lstsq which provides exact solutions for linear models).  \nModeling also supports a plugin system for fitters, which allows using the astropy models with external fitters. An example of this is SABA 17 , which is a bridge between Sherpa (Doe et al. 2007), and astropy.modeling , to bring the Sherpa fitters into astropy .', '3.7.5. Creating New Models': 'If arithmetic combinations of existing models is not sufficient, new model classes can be defined in different ways. The astropy.modeling package provides tools to turn a simple function into a full-featured model, but it also allows extending the built-in model class with arbitrary code.', '3.7.6. Unit Support': 'The astropy.modeling subpackage now supports the representation, evaluation, and fitting of models using Quantity objects, which attach units to scalar values or arrays of values. In practice, this means that one can, for example, fit a model to data with units and get parameters that also have units out, or initialize a model with parameters with units and evaluate it using input values with different but equivalent units. For example, the blackbody model ( BlackBody1D ) can be used to fit observed flux densities in a variety of units and as a function of different units of spectral coordinates (e.g., wavelength or frequency).', '3.8. Convolution': 'The astropy.convolution subpackage implements normalized convolution (e.g., Knutsson & Westin 1993), an image reconstruction technique in which missing data are ignored during the convolution and replaced with values interpolated using the kernel. An example is given in Figure 4. In astropy versions ≤ 1 . 3 , the direct convolution and Fast Fourier Transform (FFT) convolution approaches were inconsistent, with only the latter implementing normalized convolution. As of version 2.0, the two methods now agree and include a suite of consistency checks.', '3.9. Visualization': "The astropy.visualization subpackage provides functionality that can be helpful when visualizing data. This includes a framework (previously the standalone wcsaxes package) for plotting astronomical images with coordinates with matplotlib , functionality related to image normalization (including both scaling and stretching), smart  \n(a) Original  \n(b) Scipy  \n(c) Scipy nan->zero  \n<!-- image -->  \n(d) Default astropy  \n<!-- image -->  \nFigure 4. An example showing different modes of convolution available in the Python ecosystem. Each red x signifies a pixel that is set to NaN in the original data (a). If the data are convolved with a Gaussian kernel on a 9 × 9 grid using scipy 's direct convolution (b), any pixel within range of the original NaN pixels is also set to NaN . Panel (c) shows what happens if the NaN s are set to zero first: the originally NaN regions are depressed relative to their surroundings. Finally, panel (d) shows astropy 's convolution behavior, where the missing pixels are replaced with values interpolated from their surroundings using the convolution kernel.  \n<!-- image -->  \nhistogram plotting, red-green-blue (RGB) color image creation from separate images, and custom plotting styles for matplotlib .  \n<!-- image -->  \nastropy.visualization provides a framework for transforming values in images (and more generally any arrays), typically for the purpose of visualization. Two main types of transformations are normalization and stretching of image values.  \nNormalization transforms the image values to the range [0 , 1] using lower and upper limits ( v min , v max ) ,  \ny = x -v min v max -v min , (1)  \nwhere x represents the values in the original image.  \nStretching transforms the image values in the range [0 , 1] again to the range [0 , 1] using a linear or non-linear function,  \nz = f ( y ) . (2)  \nSeveral classes are provided for automatically determining intervals (e.g., using image percentiles) and for normalizing values in this interval to the [0 , 1] range.  \nmatplotlib allows a custom normalization and stretch to be used when displaying data by passing in a normalization object. The astropy.visualization package also provides a normalization class that wraps the interval and stretches objects into a normalization object that matplotlib understands.", '3.9.2. Plotting image data with world coordinates': 'Astronomers dealing with observational imaging commonly need to make figures with images that include the correct coordinates and optionally display a coordinate grid. The challenge, however, is that the conceptual coordinate axes (such as longitude/latitude) need not be lined up with the pixel axes of the image. The astropy.visualization.wcsaxes subpackage implements a generalized way of making figures from an image array and a WCS object that provides the transformation between pixel and world coordinates.  \nWorld coordinates can be, for example, right ascension and declination, but can also include, for example, velocity, wavelength, frequency, or time. The main features from this subpackage include the ability to control which axes to show which coordinate on (e.g., showing longitude ticks on the top and bottom axes and latitude on the left and right axes), controlling the spacing of the ticks either by specifying the positions to use or providing a tick spacing or an average number of ticks that should be present on each axis, setting the format for the tick labels to ones commonly used by astronomers, controlling the visibility of the grid/graticule, and overlaying ticks, labels, and/or grid lines from different coordinate systems. In addition, it is possible to pass data with more than two dimensions and slice on-the-fly. Last but not least, it is also able to define non-rectangular frames, such as, for example, Aitoff projections.  \nThis subpackage differs from APLpy (Robitaille & Bressert 2012), in that the latter focuses on providing a very high-level interface to plotting that requires very few lines of code to get a good result, whereas wcsaxes defines an interface that is much  \nFigure 5. An example of figure made using the astropy.visualization.wcsaxes subpackage, using Spitzer /IRAC 8.0 µ mdata from the Cygnus-X Spitzer Legacy survey (Beerer et al. 2010).  \n<!-- image -->  \ncloser to that of matplotlib (Hunter 2007). This enables significantly more advanced visualizations.  \nAn example of a visualization made with wcsaxes is shown in Figure 5. This example illustrates the ability to overlay multiple coordinate systems and customize which ticks/labels are shown on which axes around the image. This also uses the image stretching functionality from Section 3.9.1 to show the image in a square-root stretch (automatically updating the tick positions in the colorbar).', '3.9.3. Choosing Histogram Bins': "astropy.visualization also provides a histogram function, which is a generalization of matplotlib 's histogram function, to allow for a more flexible specification of histogram bins. The function provides several methods of automatically tuning the histogram bin size. It has a syntax identical to matplotlib 's histogram function, with the exception of the bins parameter, which allows specification of one of four different methods for automatic bin selection: 'blocks', 'knuth', 'scott', or 'freedman'.  \nFigure 6. An RGB color image of the region near the Hickson 88 group constructed from SDSS images and the astropy.visualization tools. This example uses astropy.visualization.wcsaxes to display the sky coordinate grid, and the astropy.visualization.make\\_lupton\\_rgb() function to produce the RGB image from three SDSS filter images ( g , r , i ). The left and right panel images show two different parameter choices for the stretch and softening parameters (shown in the titles).  \n<!-- image -->", '3.9.4. Creating color RGB images': "Lupton et al. (2004) describe an 'optimal' algorithm for producing RGB composite images from three separate high-dynamic range arrays. The astropy.visualization subpackage provides a convenience function to create such a color image. It also includes an associated set of classes to provide alternate scalings. This functionality was contributed by developers from the Large Synoptic Survey Telescope (LSST) and serves as an example of contribution to Astropy from a more traditional engineering organization (Jenness et al. 2016).  \nThe Sloan Digital Sky Survey (SDSS) SkyServer color images were made using a variation on this technique. As an example, in Figure 6, we show an RGB color image of the Hickson 88 group, centered near NGC 6977. 18 This image was generated from SDSS images using the astropy.visualization tools.", '3.10. Cosmology': 'The cosmology subpackage contains classes for representing different cosmologies and functions for calculating commonly used quantities such as look-back time and distance. The subpackage was described in detail in Astropy Collaboration et al. (2013). The default cosmology in astropy version 2.0 is given by the values in Planck Collaboration et al. (2016).', '3.11. Statistics': 'The astropy.stats package provides statistical tools that are useful for astronomy and are either not found in or extend the available functionality of other Python  \nstatistics packages, such as scipy (Jones et al. 2001-) or statsmodels (Seabold & Perktold 2010). astropy.stats contains a range of functionality used by many different disciplines in astronomy. It is not a complete set of statistical tools, but rather a still growing collection of useful features.', '3.11.1. Robust Statistical Estimators': 'Robust statistics provide reliable estimates of basic statistics for complex distributions that largely mitigate the effects of outliers. astropy.stats includes several robust statistical functions that are commonly used in astronomy, such as sigma clipping methods for rejecting outliers, median absolute deviation functions, and biweight estimators, which have been used to calculate the velocity dispersion of galaxy clusters (Beers et al. 1990).', '3.11.2. Circular Statistics': 'Astronomers often need to compute statistics of quantities evaluated on a circle, such as sky direction or polarization angle. A set of circular statistical estimators based on Jammalamadaka & Sengupta (2001) are implemented in astropy.stats . These functions provide measurements of the circular mean, variance, and moment. All of these functions work with both numpy.ndarrays (assumed to be in radians) and Quantity objects. In addition, the subpackage includes tests for Rayleigh Test, vtest , and a function to compute the maximum likelihood estimator for the parameters of the von Mises distribution.', '3.11.3. Lomb-Scargle Periodograms': 'Periodic analysis of unevenly-spaced time series is common across many sub-fields of astronomy. The astropy.stats package now includes several efficient implementations of the Lomb-Scargle periodogram (Lomb 1976; Scargle 1982) and several generalizations, including floating mean models (Zechmeister & Kürster 2009), truncated Fourier models (Bretthorst 2003), and appropriate handling of heteroscedastic uncertainties. Importantly, the implementations make use of several fast and scalable computational approaches (e.g., Press & Rybicki 1989; Palmer 2009), and thus can be applied to much larger datasets than Lomb-Scargle algorithms available in, e.g., scipy.stats (Jones et al. 2001-). Much of the Lomb-Scargle code in astropy has been adapted from previously-published open-source code (VanderPlas et al. 2012; VanderPlas & Ivezic 2015).', '3.11.4. Bayesian Blocks and Histogram Binning': "astropy.stats also includes an implementation of Bayesian Blocks (Scargle et al. 2013), an algorithm for analysis of break-points in non-periodic astronomical timeseries. One interesting application of Bayesian Blocks is its use in determining optimal histogram binnings, particularly binnings with unequal bin sizes. This code was adapted, with several improvements, from the astroML package (VanderPlas et al.  \nFigure 7. Three approaches to a 1D histogram: left: a standard histogram using matplotlib 's default of 10 bins. center: a histogram with the number of equal-width bins determined automatically using numpy 's bins='auto' . right: a histogram created with astropy , with irregularly-spaced bins computed via the Bayesian Blocks algorithm. Compared to regularly-spaced bins, the irregular bin widths give a more accurate visual representation of features in the dataset at various scales.  \n<!-- image -->  \n2012). An example of a histogram fit using the Bayesian Blocks algorithm is shown in the right panel of Figure 7.", '4. INFRASTRUCTURE FOR ASTROPY AFFILIATED PACKAGES': 'In addition to astronomy-specific packages and libraries, the Astropy Project also maintains and distributes several general-purpose infrastructure packages that assist the maintenance and upkeep of the astropy core package and other affiliated packages. The following sections describe the most widely-used infrastructure packages developed by the Astropy Project.', '4.1. Package template': 'Astropy provides a package template - as a separate GitHub repository, astropy/package-template 19 -that aims to simplify setting up packaging, testing, and documentation builds for developers of affiliated packages or astropy -dependent packages. Any Python package can make use of this ready-to-go package layout, setup, installation, and Sphinx documentation build infrastructure that was originally developed for the astropy core package and affiliated packages maintained by the Astropy project. The package template also provides a testing framework, template configurations for continuous integration services, and Cython build support.', '4.2. Continuous integration helpers': 'Astropy also provides a set of scripts for setting up and configuring continuous integration (CI) services as a GitHub repository, astropy/ci-helpers . 20 These tools aim to enable package maintainers to control their testing setup and installation process for various CI services through a set of environment variables. While the current development is mostly driven by the needs of the Astropy ecosystem, the  \nactual usage of this package is extremely widespread. The current tools support configuration for Travis CI 21 and Appveyor CI 22 .', '4.3. Sphinx extensions': 'The documentation for many Python packages, including all the packages in the Astropy ecosystem, is written using the Sphinx documentation build system. Sphinx supports writing documentation using plain text files that follow a markup language called reStructuredText (RST). These files are then transformed into HTML, PDF, or L A T E Xdocuments during the documentation build process. For the Astropy project, we have developed several Sphinx extensions that facilitate automatically generating API documentation for large projects, like the astropy core package. The main extension we have developed is sphinx-automodapi 23 , which provides a convenient single RST command to generate a set of documentation pages, listing all of the available classes, functions, and attributes in a given Python module.', '5. THE FUTURE OF THE ASTROPY PROJECT': 'Following the release of version 2.0, development on the next major version of the astropy core package (version 3.0) has already begun. On top of planned changes and additions to the core package, we also plan to overhaul the Astropy educational/learning materials and further generalize the infrastructure utilities originally developed for the core package for the benefit of the community.', '5.1. Future versions of the Astropy core and affiliated packages': 'One of the most significant changes coming in this next major release will be removing the support for Python 2 (Robitaille 2017): future versions of astropy will only support Python 3.5 or higher. Removing Python 2 support will allow the use of new Python 3-only features, simplify the code base, and reduce the testing overhead for the package. astropy version 3.0 is currently scheduled for January 2018.  \nIn the next major release after version 3.0, scheduled for mid-2018, the focus will be on algorithm optimization and documentation improvement. To prepare for this release, we are subjecting the core package to testing, evaluation, and performance monitoring. As a result, less new functionality may be introduced as a trade-off for better performance.  \nBeyond the core code, the Astropy project is also further developing the Astropymanaged affiliated packages. While these may not be integrated into the astropy core package, these projects provide code that is useful to the astronomical community and meet the testing and documentation standards of Astropy. Some of these new efforts include an initiative to develop tools for spectroscopy (Crawford et al. 2017, specutils , specreduc , specviz ), integration of LSST software, and support for HEALPIX projection.', '5.2. Learn Astropy': "The documentation of the astropy core package contains narrative descriptions of the package's functionality, along with detailed usage notes for functions, classes, and modules. While useful as a reference for more experienced Python users, it is not the proper entry-point for other users or learning environments. In the near future, we will launch a new resource for learning to use both the astropy core package and the many packages in the broader Astropy ecosystem, under the name Learn Astropy .  \nThe new Learn Astropy site will present several different ways to engage with the Astropy ecosystem:  \nDocumentation: The astropy and affiliated package documentation contains the complete description of a package with all requisite details, including usage, dependencies, and examples. The pages will largely remain as-is, but will be focused towards more intermediate users and as a reference resource.  \nExamples: These are stand-alone code snippets that live in the astropy documentation that demonstrate a specific functionality within a subpackage. The astropy core package documentation will then gain a new 'index of examples' that links to all of the code or demonstrative examples within any documentation page.  \nTutorials: The Astropy tutorials are step-by-step demonstrations of common tasks that incorporate several packages or subpackages. Tutorials are more extended and comprehensive than examples, may contain exercises for the users, and are generally geared towards workshops or teaching. Several tutorials already exist 24 and are being actively expanded.  \nGuides: These are long-form narrative, comprehensive, and conceptually-focused documents (roughly one book chapter in length), providing stand-alone introductions to core packages in addition to the underlying astronomical concepts. These are less specific and more conceptual than tutorials. For example, 'using astropy and ccdproc to reduce imaging data.'  \nWe encourage any users who wish to see specific material to either contribute or comment on these efforts via the Astropy mailing list or astropy/astropy-tutorials GitHub repository. 25", '6. CONCLUSION': "The development of the astropy package and cultivation of the Astropy ecosystem are still maintaining significant growth while improving in stability, breadth, and reliability. As the astropy core package becomes more mature, several subpackages have reached stability with a rich set of features that help astronomers worldwide to  \nperform many daily tasks, such as planning observations, analyzing data or simulation results, and writing publications. The strong emphasis that the Astropy project puts on reliability and high coding standards helps users to trust the calculations performed with astropy and to publish reproducible results. At the same time, the Astropy ecosystem and core package are both growing: new functionality is still being contributed and new affiliated packages are being developed to support more specialized needs.  \nThe Astropy project is also spreading awareness of best practices in communitydriven software development. This is important as most practicing astronomers were not explicitly taught computer science and software development, despite the fact that a substantial fraction of many astronomers' workload today is related to software use and development. The astropy package leads by example, showing all interested astronomers how modern tools like git version control or CI testing can increase the quality, accessibility, and discoverability of astronomical software without overly complicating the development cycle. Within Astropy, all submitted code is reviewed by at least one, but typically more, member of the Astropy community, who provide feedback to contributors, which helps to improve their software development skills. As a community, Astropy follows an explicit code of conduct (Cruz et al. 2015) and treats all contributors and users with respect, provides a harassment-free environment, and encourages and welcomes new contributions from all. Thus, while the Astropy project provides and develops software and tools essential to modern astronomical research, it also helps to prepare the current and next generation of researchers with the knowledge to adequately use, develop, and contribute to those tools within a conscientious and welcoming community.  \nWe would like to thank the members of the community that have contributed to Astropy, that have opened issues and provided feedback, and have supported the project in a number of different ways. We would like to acknowledge Alex Conley and Neil Crighton for maintaining the cosmology subpackage.  \nThe Astropy community is supported by and makes use of a number of organizations and services outside the traditional academic community. We thank Google for financing and organizing the Google Summer of Code (GSoC) program, that has funded severals students per year to work on Astropy related projects over the summer. These students often turn into long-term contributors. We also thank NumFOCUS and the Python Software Foundation for financial support. Within the academic community, we thank institutions that make it possible that astronomers and other developers on their staff can contribute their time to the development of Astropy projects. We would like acknowledge the support of the Space Telescope Science Institute, Harvard-Smithsonian Center for Astrophysics, and the South African Astronomical Observatory.  \nThe following individuals would like to recognize support for their personal contributions. HMG was supported by the National Aeronautics and Space Administration through the Smithsonian Astrophysical Observatory contract SV3-73016 to MIT for Support of the Chandra X-Ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. JTV was supported by the UW eScience Institute, via grants from the Moore Foundation, the Sloan Foundation, and the Washington Research Foundation. SMC acknowledges the National Research Foundation of South Africa. TLA was supported by NASA contract NAS8-03060. Support for E.J.T. was provided by NASA through Hubble Fellowship grant No. 51316.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555, as well as a Giacconi Fellowship. MB was supported by the FONDECYT regular project 1170618 and the MINEDUC-UA projects codes ANT 1655 and ANT 1656. DH was supported through the SFB 881 'The Milky Way System' by the German Research Foundation (DFG). WEK was supported by an ESO Fellowship. C.M. is supported by NSF grant AST-1313484. SP was supported by grant AYA2016-75808-R (FEDER) issued by the Spanish government. JEHT was supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Brazil, Canada, Chile, and the United States of America.  \nFurthermore, the Astropy packages would not exist in their current form without a number of web services for code hosting, continuous integration, and documentation; in particular, Astropy heavily relies on GitHub, Travis CI, Appveyor, CircleCI, and Read the Docs.  \nastropy interfaces with the SIMBAD database, operated at CDS, Strasbourg, France. It also makes use of the ERFA library (Tollerud et al. 2017), which in turn derives from the IAU SOFA Collection 26 developed by the International Astronomical Union Standards of Fundamental Astronomy (Hohenkerk 2011).  \nSoftware: astropy (Astropy Collaboration et al. 2013), numpy (Van der Walt et al. 2011), scipy (Jones et al. 2001-), matplotlib (Hunter 2007), Cython (Behnel et al. 2011), SOFA (Hohenkerk 2011), ERFA (Tollerud et al. 2017)", 'REFERENCES': 'Aldcroft, T. 2015, Astropy Proposal for Enhancement 6: Enhanced Character Separated Values table format (APE 6), doi:10.5281/zenodo.1043901. https: //doi.org/10.5281/zenodo.1043901  \nAstropy Collaboration, Robitaille, T. P.,  \nTollerud, E. J., et al. 2013, A&A, 558,  \nStreicher, O., & Weilbacher, P. M. 2012, in Astronomical Society of the Pacific Conference Series, Vol. 461, Astronomical Data Analysis Software and Systems XXI, ed. P. Ballester, D. Egret, & N. P. F. Lorente, 853 Terlouw, J. P., & Vogelaar, M. G. R. 2015, Kapteyn Package, version 2.3, Kapteyn Astronomical Institute, Groningen, available from http://www. astro.rug.nl/software/kapteyn/ Tody, D. 1993, in Astronomical Society of the Pacific Conference Series, Vol. 52, Astronomical Data Analysis Software and Systems II, ed. R. J. Hanisch, R. J. V. Brissenden, & J. Barnes, 173 Tollerud, E. 2013, Astropy Proposal for Enhancement 2: Astropy Release Cycle and Version Numbering (APE 2), doi:10.5281/zenodo.1043888. https: //doi.org/10.5281/zenodo.1043888 Tollerud, E., Pascual, S., Nair, P., et al. 2017, doi:10.5281/zenodo.1021149 Tollerud, E., Price-Whelan, A., Aldcroft, T., & Robitaille, T. 2014, Astropy Proposal for Enhancement 5: Coordinates Subpackage Plan (APE 5), , , doi:10.5281/zenodo.1043897. https: //doi.org/10.5281/zenodo.1043897 Turk, M. J., Smith, B. D., Oishi, J. S., et al. 2011, ApJS, 192, 9', 'APPENDIX A. LIST OF AFFILIATED PACKAGES': 'T able 1 . Registry of affiliate d pac k ages.  \ntion  \nCita  \nMain tainer  \nName  \nPyPI  \nStable  \nName  \nge  \na  \nk  \nac  \nP  \nBressert  \nEli  \nand  \nRobitaille  \ns  \nThoma  \ny  \nAPLp  \nes  \nY  \ny  \nAPLp', 'v an Dokkum 2001': 'McCully  \nis  \nCurt  \ny  \nastroscrapp  \nes  \nY  \nAstro-SCRAPPY  \nanderplas  \nV  \ne  \nJak  \nastroML  \nes  \nY  \nastroML  \n2017  \nal.  \net  \nMorris  \nMorris  \nBrett  \nastroplan  \nNo  \nastroplan  \n2017a  \nal.  \net  \nGinsburg  \ncz  \no  \nip  \nS  \nBrigitta  \nand  \nGinsburg  \ndam  \nA  \nquery  \nastro  \nes  \nY  \nquery  \nastro  \nCraig et al. 2015  \nhael  \nMic  \nand  \nCraig,  \nMatt  \nwford,  \nCra  \nen  \nStev  \nc  \nccdpro  \nes  \nY  \nc  \nccdpro  \n2017  \nPrice-Whelan  \nPrice-Whelan  \ndrian  \nA  \nastro-gala  \nes  \nY  \ngala  \n17  \n20  \nal.  \net  \nDeil  \nDeil  \nChristoph  \ny  \ngammap  \nNo  \ny  \ngammap  \n2017  \nal.  \net  \ne  \nhk  \nejesc  \nLim  \ney-Lian  \nP  \nand  \ne  \nhk  \nJesc  \nEric  \nginga  \nes  \nY  \nginga  \nSeifert  \n2016  \nord  \nF  \nord  \nF  \nJes  \ner-lensing  \nclust  \nNo  \ncluster-lensing  \n2015  \nvy  \nBo  \nvy  \nBo  \nJo  \ny  \ngalp  \nes  \nY  \ny  \ngalp  \n2014  \nal.  \net  \nt  \nBeaumon  \nRobitaille  \nThomas  \nand  \nt  \nBeaumon  \nChris  \nglueviz  \nes  \nY  \nGlue  \n017  \n2  \nal.  \net  \na  \nhev  \nDenc  \na  \nhev  \nDenc  \na  \nNadi  \ncs  \ngw  \nNo  \ncs  \ngw  \n2017  \nal.  \net  \nn  \nHeari  \narin  \nHe  \nAndrew  \nols  \nhaloto  \nes  \nY  \nols  \nHaloto  \nhetti  \nBac  \nMatteo  \nhendrics  \nes  \nY  \nHENDRICS  \nh  \nc  \nBo  \nomas  \nTh  \nand  \nDeil  \nChristoph  \nps  \nhi  \nNo  \nhips  \nSosey 2017  \nSosey  \nMegan  \nimexam  \nNo  \nimexam  \nil  \nNe  \nand  \nejos,  \nT  \nNicolas  \na,  \nhask  \nc  \nPro  \nvier  \nXa  \nJ.  \nols  \nlineto  \nes  \nY  \nols  \nlineto  \nton  \nCrigh  \nT able 1 c ontinue d on next p age', 'T able 1 (c ontinue d)': 'Table 2.  \nAstropy Project II Registry of provisionally accepted affiliated packages.'}