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<?xml version="1.0" encoding="utf-8" ?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.2 20190208//EN"
"JATS-publishing1.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="1.2" article-type="other">
<front>
<journal-meta>
<journal-id></journal-id>
<journal-title-group>
<journal-title>Journal of Open Source Software</journal-title>
<abbrev-journal-title>JOSS</abbrev-journal-title>
</journal-title-group>
<issn publication-format="electronic">2475-9066</issn>
<publisher>
<publisher-name>Open Journals</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">7273</article-id>
<article-id pub-id-type="doi">10.21105/joss.07273</article-id>
<title-group>
<article-title>Krang: Kerr Raytracer for Analytic Null
Geodesics</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9939-5257</contrib-id>
<name>
<surname>Chang</surname>
<given-names>Dominic</given-names>
</name>
<xref ref-type="aff" rid="aff-1"/>
<xref ref-type="aff" rid="aff-2"/>
</contrib>
<aff id="aff-1">
<institution-wrap>
<institution>Department of Physics, Harvard University,
USA</institution>
</institution-wrap>
</aff>
<aff id="aff-2">
<institution-wrap>
<institution>Black Hole Initiative at Harvard University,
USA</institution>
</institution-wrap>
</aff>
</contrib-group>
<pub-date date-type="pub" publication-format="electronic" iso-8601-date="2024-09-05">
<day>5</day>
<month>9</month>
<year>2024</year>
</pub-date>
<volume>9</volume>
<issue>102</issue>
<fpage>7273</fpage>
<permissions>
<copyright-statement>Authors of papers retain copyright and release the
work under a Creative Commons Attribution 4.0 International License (CC
BY 4.0)</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>The article authors</copyright-holder>
<license license-type="open-access" xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>Authors of papers retain copyright and release the work under
a Creative Commons Attribution 4.0 International License (CC BY
4.0)</license-p>
</license>
</permissions>
<kwd-group kwd-group-type="author">
<kwd>Julia</kwd>
<kwd>black hole</kwd>
<kwd>general relativity</kwd>
<kwd>astronomy</kwd>
<kwd>ray-tracing</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="summary">
<title>Summary</title>
<p><monospace>Krang</monospace> is a
<ext-link ext-link-type="uri" xlink:href="https://julialang.org">Julia</ext-link>
(<xref alt="Bezanson et al., 2017" rid="ref-Bezanson2017" ref-type="bibr">Bezanson
et al., 2017</xref>) package that implements efficient algorithms for
raytracing emission geometries in the Kerr black hole space time. It
is GPU compatible and is specialized for studies of sub-image
contributions from gravitationally lensed sources
(<xref alt="Johnson et al., 2020" rid="ref-JohnsonRing" ref-type="bibr">Johnson
et al., 2020</xref>). Such algorithms are of interest for modeling the
sources seen by Very Long Baseline Interferometry (VLBI) observations
of Low Luminosity Active Galactic Nuclei (LLAGN) such as those imaged
by the Event Horizon Telescope Collaboration (EHTC).</p>
</sec>
<sec id="statement-of-need">
<title>Statement of need</title>
<p>Studies of electromagnetic signatures around black holes have
increased in interest due to results from the horizon-scale
observations of supermassive black holes by the Gravity Collaboration,
the Atacama Large Millimeter Array (ALMA), and the EHTC. The Event
Horizon Telescope, in particular (EHT,
<xref alt="Event Horizon Telescope Collaboration, 2019b" rid="ref-M87PaperII" ref-type="bibr">Event
Horizon Telescope Collaboration, 2019b</xref>), produced the first
images of the shadows of the supermassive black holes in the centers
of M87
(<xref alt="Event Horizon Telescope Collaboration, 2019a" rid="ref-M87PaperI" ref-type="bibr">Event
Horizon Telescope Collaboration, 2019a</xref>) and the Milky Way
(<xref alt="Event Horizon Telescope Collaboration, 2022" rid="ref-SgrAPaperI" ref-type="bibr">Event
Horizon Telescope Collaboration, 2022</xref>) at event-horizon scales,
with emission being sourced from the interactions of accreting
relativistic plasmas and magnetic fields within the vicinity of the
black holes. Scientific analysis of the data from these sources often
requires complicated source modelling that includes various
relativistic effects that can leave characteristic signatures in the
observed images. The large scale of the black holes allows for many of
these effects to be described within the geometric optics limit of
electro-magnetism. Raytracing techniques thus present viable options
for modeling images of supermassive black holes.</p>
<p>A relativistic image feature that has been theorized to exist, but
is yet to be resolved, are the individual sub-image contributions to
the overall image structure known as photon-rings,
(<xref alt="Johnson et al., 2020" rid="ref-JohnsonRing" ref-type="bibr">Johnson
et al., 2020</xref>). Photon rings are of particular interest because
of their strong dependence on gravitational effects and their
insensitivity to variations in the emission physics around the black
hole. The observation of a photon ring would therefore serve as
effective probe for measurements of black hole characteristics like
spin or help facilitate tests of gravity. This feature could
potentially be seen in the near future with a recently proposed space
extension to the EHT aimed at detection and measurement
(<xref alt="Lupsasca et al., 2024" rid="ref-lupsasca2024blackholeexplorerphoton" ref-type="bibr">Lupsasca
et al., 2024</xref>).</p>
<p>Scientific studies of black hole images within the current software
landscape often require great compromise due to the computational
complexity of the problem. Other difficulties can arise from
interfacing existing raytracing software with the wider ecosystem of
tools; it is difficult, for example, to apply machine learning
optimization algorithms to existing Python raytracing codes since they
typically rely on special functions that are not implemented within
current machine learning frameworks. Existing Python implementations
are also bounded to CPU evaluations, limiting their capability of
accessing acceleration from specialized hardware. A Julia
implementation of raytracing algorithms is thus beneficial because of
the language’s modular design, differentiable programming and
efficient execution. Krang therefore benefits from the ‘plug and play’
nature of the Julia programming language, allowing for easy
development and synergy with existing analysis pipelines, and fast
CPU/GPU executions.</p>
</sec>
<sec id="similar-packages">
<title>Similar Packages</title>
<list list-type="bullet">
<list-item>
<p><monospace>AART</monospace>
(<xref alt="Cárdenas-Avendaño et al., 2023" rid="ref-cardenas-avendano" ref-type="bibr">Cárdenas-Avendaño
et al., 2023</xref>): An adaptive analytical raytracing code for
geodesics in the Kerr space time in Python.</p>
</list-item>
<list-item>
<p><monospace>KerrBam</monospace>
(<xref alt="Palumbo et al., 2022" rid="ref-Palumbo_2022" ref-type="bibr">Palumbo
et al., 2022</xref>): An analytical raytracing code for equatorial
synchrotron models in Python.</p>
</list-item>
<list-item>
<p><monospace>Gradus</monospace>
(<xref alt="Baker &amp; Young, 2022" rid="ref-Gradus" ref-type="bibr">Baker
&amp; Young, 2022</xref>): A Julia implementation of a numeric,
general relativistic raytracer with radiative transfer.</p>
</list-item>
</list>
</sec>
<sec id="acknowledgements">
<title>Acknowledgements</title>
<p>The authors thank Michael Johnson, Iniyan Natarajan, Alexander
Plavin, and Paul Tiede for helpful discussions. Support for this work
was provided by the NSF (AST-1935980, AST-2034306) and by the Gordon
and Betty Moore Foundation through grant GBMF-10423. This work was
supported by the Black Hole Initiative, which is funded by grants from
the John Templeton Foundation (Grant #62286) and the Gordon and Betty
Moore Foundation (Grant GBMF-8273), although the opinions expressed in
this work are those of the author(s) and do not necessarily reflect
the views of these Foundations.</p>
</sec>
</body>
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