diff --git a/joss.06587/10.21105.joss.06587.crossref.xml b/joss.06587/10.21105.joss.06587.crossref.xml new file mode 100644 index 0000000000..4f3aa3aefa --- /dev/null +++ b/joss.06587/10.21105.joss.06587.crossref.xml @@ -0,0 +1,271 @@ + + + + 20240601212255-eff6fb38ce561d4d86651ee8b239234ddd9857f0 + 20240601212255 + + JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 06 + 2024 + + + 9 + + 98 + + + + KerrGeoPy: A Python Package for Computing Timelike +Geodesics in Kerr Spacetime + + + + Seyong + Park + https://orcid.org/0009-0002-1152-9324 + + + Zachary + Nasipak + https://orcid.org/0000-0002-5109-9704 + + + + 06 + 01 + 2024 + + + 6587 + + + 10.21105/joss.06587 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.11386563 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/6587 + + + + 10.21105/joss.06587 + https://joss.theoj.org/papers/10.21105/joss.06587 + + + https://joss.theoj.org/papers/10.21105/joss.06587.pdf + + + + + + Array programming with NumPy + Harris + Nature + 7825 + 585 + 10.1038/s41586-020-2649-2 + 1476-4687 + 2020 + Harris, C. R., Millman, K. J., Walt, +S. J. van der, Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., +Taylor, J., Berg, S., Smith, N. J., Kern, R., Picus, M., Hoyer, S., +Kerkwijk, M. H. van, Brett, M., Haldane, A., Río, J. F. del, Wiebe, M., +Peterson, P., … Oliphant, T. E. (2020). Array programming with NumPy. +Nature, 585(7825), 357–362. +https://doi.org/10.1038/s41586-020-2649-2 + + + SciPy 1.0: Fundamental Algorithms for +Scientific Computing in Python + Virtanen + Nature Methods + 17 + 10.1038/s41592-019-0686-2 + 2020 + Virtanen, P., Gommers, R., Oliphant, +T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, +P., Weckesser, W., Bright, J., Walt, S. J. van der, Brett, M., Wilson, +J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., +Larson, E., … SciPy 1.0 Contributors. (2020). SciPy 1.0: Fundamental +Algorithms for Scientific Computing in Python. Nature Methods, 17, +261–272. +https://doi.org/10.1038/s41592-019-0686-2 + + + Matplotlib: A 2D graphics +environment + Hunter + Computing in Science & +Engineering + 3 + 9 + 10.1109/MCSE.2007.55 + 2007 + Hunter, J. D. (2007). Matplotlib: A +2D graphics environment. Computing in Science & Engineering, 9(3), +90–95. https://doi.org/10.1109/MCSE.2007.55 + + + tqdm: A fast, Extensible Progress Bar for +Python and CLI + Costa-Luis + 10.5281/zenodo.8233425 + 2023 + Costa-Luis, C. da, Larroque, S. K., +Altendorf, K., Mary, H., richardsheridan, Korobov, M., Yorav-Raphael, +N., Ivanov, I., Bargull, M., Rodrigues, N., Chen, G., Lee, A., Newey, +C., CrazyPython, JC, Zugnoni, M., Pagel, M. D., mjstevens777, Dektyarev, +M., … Boyle, M. (2023). tqdm: A fast, Extensible Progress Bar for Python +and CLI (Version v4.66.1). Zenodo. +https://doi.org/10.5281/zenodo.8233425 + + + Gravitational waves from bodies orbiting the +Galactic center black hole and their detectability by +LISA + Gourgoulhon + Astronomy and Astrophysics + 627 + 10.1051/0004-6361/201935406 + 0004-6361 + 2019 + Gourgoulhon, E., Le Tiec, A., +Vincent, F. H., & Warburton, N. (2019). Gravitational waves from +bodies orbiting the Galactic center black hole and their detectability +by LISA. Astronomy and Astrophysics, 627, A92. +https://doi.org/10.1051/0004-6361/201935406 + + + The unique potential of extreme mass-ratio +inspirals for gravitational-wave astronomy + Berry + Bulletin of the American Astronomical +Society + 51 + 10.48550/arXiv.1903.03686 + 2019 + Berry, C., Hughes, S., Sopuerta, C., +Chua, A., Heffernan, A., Holley-Bockelmann, K., Mihaylov, D., Miller, +C., & Sesana, A. (2019). The unique potential of extreme mass-ratio +inspirals for gravitational-wave astronomy. Bulletin of the American +Astronomical Society, 51, 42. +https://doi.org/10.48550/arXiv.1903.03686 + + + The Laser Interferometer Space Antenna: +Unveiling the Millihertz Gravitational Wave Sky + Thorpe + 51 + 10.48550/arXiv.1907.06482 + 2019 + Thorpe, J. I., Ziemer, J., Thorpe, +I., Livas, J., Conklin, J. W., Caldwell, R., Berti, E., McWilliams, S. +T., Stebbins, R., Shoemaker, D., Ferrara, E. C., Larson, S. L., +Shoemaker, D., Key, J. S., Vallisneri, M., Eracleous, M., Schnittman, +J., Kamai, B., Camp, J., … Wass, P. (2019). The Laser Interferometer +Space Antenna: Unveiling the Millihertz Gravitational Wave Sky. 51, 77. +https://doi.org/10.48550/arXiv.1907.06482 + + + KerrGeodesics + Warburton + 10.5281/zenodo.8108265 + 2023 + Warburton, N., Wardell, B., Long, O., +Upton, S., Lynch, P., Nasipak, Z., & Stein, L. C. (2023). +KerrGeodesics. Zenodo. +https://doi.org/10.5281/zenodo.8108265 + + + Location of the last stable orbit in Kerr +spacetime + Stein + Physical Review D + 101 + 10.1103/PhysRevD.101.064007 + 1550-7998 + 2020 + Stein, L. C., & Warburton, N. +(2020). Location of the last stable orbit in Kerr spacetime. Physical +Review D, 101, 064007. +https://doi.org/10.1103/PhysRevD.101.064007 + + + Analytical solutions of bound timelike +geodesic orbits in Kerr spacetime + Fujita + Classical and Quantum Gravity + 26 + 10.1088/0264-9381/26/13/135002 + 0264-9381 + 2009 + Fujita, R., & Hikida, W. (2009). +Analytical solutions of bound timelike geodesic orbits in Kerr +spacetime. Classical and Quantum Gravity, 26, 135002. +https://doi.org/10.1088/0264-9381/26/13/135002 + + + Kerr-fully diving into the abyss: Analytic +solutions to plunging geodesics in Kerr + Dyson + Classical and Quantum Gravity + 40 + 10.1088/1361-6382/acf552 + 0264-9381 + 2023 + Dyson, C., & Meent, M. van de. +(2023). Kerr-fully diving into the abyss: Analytic solutions to plunging +geodesics in Kerr. Classical and Quantum Gravity, 40, 195026. +https://doi.org/10.1088/1361-6382/acf552 + + + Celestial mechanics in Kerr +spacetime + Schmidt + Classical and Quantum Gravity + 10 + 19 + 10.1088/0264-9381/19/10/314 + 2002 + Schmidt, W. (2002). Celestial +mechanics in Kerr spacetime. Classical and Quantum Gravity, 19(10), +2743–2764. +https://doi.org/10.1088/0264-9381/19/10/314 + + + + + + diff --git a/joss.06587/10.21105.joss.06587.pdf b/joss.06587/10.21105.joss.06587.pdf new file mode 100644 index 0000000000..f9bccfcc5b Binary files /dev/null and b/joss.06587/10.21105.joss.06587.pdf differ diff --git a/joss.06587/paper.jats/10.21105.joss.06587.jats b/joss.06587/paper.jats/10.21105.joss.06587.jats new file mode 100644 index 0000000000..ad21cc2495 --- /dev/null +++ b/joss.06587/paper.jats/10.21105.joss.06587.jats @@ -0,0 +1,599 @@ + + +
+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6587 +10.21105/joss.06587 + +KerrGeoPy: A Python Package for +Computing Timelike Geodesics in Kerr Spacetime + + + +https://orcid.org/0009-0002-1152-9324 + +Park +Seyong + + + + + +https://orcid.org/0000-0002-5109-9704 + +Nasipak +Zachary + + + + + +NASA Goddard Space Flight Center, Greenbelt, MD, +USA + + + + +University of Maryland, College Park, MD, USA + + + + +15 +12 +2023 + +9 +98 +6587 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Python +black holes +perturbation theory +gravitational waves + + + + + + Summary +

In general relativity, the motion of a free-falling test particle + in a curved spacetime is described by a timelike geodesic - the + minimal path between two points in space. Intuitively, geodesics are + analogous to straight line paths in flat spacetime. The timelike + geodesics of Kerr spacetime are of particular interest in the field of + black hole perturbation theory because they describe the zeroth-order + motion of a small object moving through the background spacetime of a + much more massive spinning black hole. For this reason, computing + geodesics is an important step in modeling the gravitational radiation + emitted by an extreme-mass-ratio inspiral (EMRI) - an astrophysical + binary in which a stellar mass compact object, such as a neutron star + or black hole (with mass + + 101−102M⊙), + spirals into a massive black hole (with mass + + + 104−107M⊙).

+

Kerr spacetime has several nice properties which simplify the + problem of computing geodesics. Since it has both time-translation + symmetry and rotational symmetry, energy and (the + + + z-component + of) angular momentum are conserved quantities. It is also equipped + with a higher order symmetry which gives rise to a third constant of + motion called the Carter constant. These three constants of motion, + along with the spin of the black hole, uniquely define a geodesic up + to initial conditions + (Schmidt, + 2002). Alternatively, geodesics can be identified using a + suitably generalized version of the parameters used to define a + Keplerian orbit (eccentricity, semi-latus rectum, and inclination + angle). Bound geodesics also possess fundamental frequencies since + their radial, azimuthal, and polar motions are periodic.

+

KerrGeoPy is a Python package which computes + both stable and plunging timelike geodesics in Kerr spacetime using + the analytic solutions to the geodesic equation derived in Fujita + & Hikida + (2009) and + Dyson & Meent + (2023). It + mirrors and builds upon much of the functionality of the + KerrGeodesics + (Warburton + et al., 2023) Mathematica library. Geodesic solutions are + written in terms of Legendre elliptic integrals, which are evaluated + using SciPy. Users can construct a geodesic by + providing the initial position and four-velocity, or by providing + either the constants of motion or the Keplerian parameters described + above.

+

KerrGeoPy provides methods for computing the + four-velocity, fundamental frequencies, and constants of motion + associated with a given geodesic and also implements the algorithm + described in Stein & Warburton + (2020) for + finding the location of the last stable orbit, known as the + separatrix. The package also includes several methods for visualizing + and animating geodesics.

+

KerrGeoPy is a part of the + Black + Hole Perturbation Toolkit. The source code is hosted on + Github + and the package is distributed through both + PyPI + and + conda-forge. + Automated unit tests are run using + Github + Actions and comprehensive documentation is available on + Read + the Docs.

+ +

Example of an equatorial (left), spherical (center) and + generic (right) orbit computed by + KerrGeoPy

+ + + + + Statement of Need +

EMRIs are expected to be a major source observable by the Laser + Interferometer Space Antenna (LISA), a future space-based + gravitational wave observatory consisting of a triangular + constellation of three satellites in orbit around the sun. LISA is an + ESA-led mission with significant contributions from NASA which is set + to launch in the 2030s. It will complement existing ground-based + detectors by opening up the millihertz band of the gravitational wave + spectrum + (Thorpe + et al., 2019). Because sources in this band evolve more slowly + over time and remain observable for a period of days to years, LISA is + expected to detect many overlapping signals at all times. Thus, + accurate waveform models are needed in order to identify gravitational + wave sources and perform parameter estimation - the process of + approximating characteristics of a source.

+

For most LISA sources, well-developed waveform models based on + either numerical relativity or post-Newtonian theory already exist. + However, EMRIs are instead more naturally described by black hole + perturbation theory, and the EMRI waveform models that currently exist + are underdeveloped compared to other LISA sources. In a perturbation + theory model, the orbital trajectory is assumed to be a geodesic at + leading order. Higher-order corrections are then computed by + introducing the gravitational field of the inspiraling object as a + perturbation to the background spacetime of the massive black hole, + expanded in powers of the mass ratio.

+

To meet the accuracy requirements for LISA parameter estimation, + EMRI waveform models must include both first- and second-order + corrections to the orbital trajectory. However, to date, second-order + corrections are only available for the most simple systems, + quasi-circular inspirals in Schwarzschild + (Berry + et al., 2019). Open-source tools can aid in rapidly expanding + EMRI models to more complicated orbits in Kerr spacetime, but at the + moment many tools for modeling EMRIs are only available in + Mathematica, which is an expensive and proprietary piece of software. + KerrGeoPy is intended to support future + development of higher-order waveform models in preparation for LISA by + providing a free alternative to the existing + KerrGeodesics Mathematica library for other + researchers to build on in their own projects.

+

Although other Python packages + (Gourgoulhon + et al., 2019) with similar functionality do exist, they mostly + rely on numerical integration to compute geodesics. The analytic + solutions used by KerrGeoPy have two main + advantages over this approach. First, they can be much more + numerically stable over long time periods and can be quickly evaluated + at any point in time. This is essential for EMRI models, which + typically require taking long time-averages over the geodesic motion. + Second, they produce several useful intermediate terms which are not + calculated by other packages. Therefore, + KerrGeoPy, with its analytic solutions and + various orbital parametrizations, is specifically tuned to support + perturbative models of binary black holes and their gravitational + waves.

+ + + Software Citations +

KerrGeoPy has the following + dependencies:

+ + +

NumPy + (Harris + et al., 2020)

+ + +

SciPy + (Virtanen + et al., 2020)

+ + +

Matplotlib + (Hunter, + 2007)

+ + +

tqdm + (Costa-Luis + et al., 2023)

+ + + + + Acknowledgements +

We would like to thank Niels Warburton and Barry Wardell for their + assistance in releasing KerrGeoPy as part of + the Black Hole Perturbation Toolkit. SP acknowledges support through + NASA’s Office of STEM Engagement, while ZN acknowledges support by an + appointment to the NASA Postdoctoral Program at the NASA Goddard Space + Flight Center, administered by Oak Ridge Associated Universities under + contract with NASA.

+ + + + + + + + HarrisCharles R. + MillmanK. Jarrod + WaltStéfan J. van der + GommersRalf + VirtanenPauli + CournapeauDavid + WieserEric + TaylorJulian + BergSebastian + SmithNathaniel J. + KernRobert + PicusMatti + HoyerStephan + KerkwijkMarten H. van + BrettMatthew + HaldaneAllan + RíoJaime Fernández del + WiebeMark + PetersonPearu + Gérard-MarchantPierre + SheppardKevin + ReddyTyler + WeckesserWarren + AbbasiHameer + GohlkeChristoph + OliphantTravis E. + + Array programming with NumPy + Nature + 202009 + 20231213 + 585 + 7825 + 1476-4687 + https://www.nature.com/articles/s41586-020-2649-2 + 10.1038/s41586-020-2649-2 + 357 + 362 + + + + + + VirtanenPauli + GommersRalf + OliphantTravis E. + HaberlandMatt + ReddyTyler + CournapeauDavid + BurovskiEvgeni + PetersonPearu + WeckesserWarren + BrightJonathan + WaltStéfan J. van der + BrettMatthew + WilsonJoshua + MillmanK. Jarrod + MayorovNikolay + NelsonAndrew R. J. + JonesEric + KernRobert + LarsonEric + CareyC J + Polatİlhan + FengYu + MooreEric W. + VanderPlasJake + LaxaldeDenis + PerktoldJosef + CimrmanRobert + HenriksenIan + QuinteroE. A. + HarrisCharles R. + ArchibaldAnne M. + RibeiroAntônio H. + PedregosaFabian + MulbregtPaul van + SciPy 1.0 Contributors + + SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python + Nature Methods + 2020 + 17 + 10.1038/s41592-019-0686-2 + 261 + 272 + + + + + + HunterJ. D. + + Matplotlib: A 2D graphics environment + Computing in Science & Engineering + 2007 + 9 + 3 + 10.1109/MCSE.2007.55 + 90 + 95 + + + + + + Costa-LuisCasper da + LarroqueStephen Karl + AltendorfKyle + MaryHadrien + richardsheridan + KorobovMikhail + Yorav-RaphaelNoam + IvanovIvan + BargullMarcel + RodriguesNishant + ChenGuangshuo + LeeAntony + NeweyCharles + CrazyPython + JC + ZugnoniMartin + PagelMatthew D. + mjstevens777 + DektyarevMikhail + RothbergAlex + PlavinAlexander + DillFabian + FichteFoll + SturmGregor + HeoHeo + KemenadeHugo van + McCrackenJack + MapleCCC + NordlundMax + BoyleMike + + tqdm: A fast, Extensible Progress Bar for Python and CLI + Zenodo + 202308 + https://doi.org/10.5281/zenodo.8233425 + 10.5281/zenodo.8233425 + + + + + + GourgoulhonE. + Le TiecA. + VincentF. H. + WarburtonN. + + Gravitational waves from bodies orbiting the Galactic center black hole and their detectability by LISA + Astronomy and Astrophysics + 201907 + 20231213 + 627 + 0004-6361 + https://ui.adsabs.harvard.edu/abs/2019A&A...627A..92G + 10.1051/0004-6361/201935406 + A92 + + + + + + + BerryChristopher + HughesScott + SopuertaCarlos + ChuaAlvin + HeffernanAnna + Holley-BockelmannKelly + MihaylovDeyan + MillerColeman + SesanaAlberto + + The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy + Bulletin of the American Astronomical Society + 201905 + 20231205 + 51 + https://ui.adsabs.harvard.edu/abs/2019BAAS...51c..42B + 10.48550/arXiv.1903.03686 + 42 + + + + + + + ThorpeJames Ira + ZiemerJohn + ThorpeIra + LivasJeff + ConklinJohn W. + CaldwellRobert + BertiEmanuele + McWilliamsSean T. + StebbinsRobin + ShoemakerDavid + FerraraElizabeth C. + LarsonShane L. + ShoemakerDeirdre + KeyJoey Shapiro + VallisneriMichele + EracleousMichael + SchnittmanJeremy + KamaiBrittany + CampJordan + MuellerGuido + BellovaryJillian + RiouxNorman + BakerJohn + BenderPeter L. + CutlerCurt + CornishNeil + HoganCraig + ManthripragadaSridhar + WareBrent + NatarajanPriyamvada + NumataKenji + SankarShannon R. + KellyBernard J. + McKenzieKirk + SlutskyJacob + SperoRobert + HewitsonMartin + FrancisSamuel + DeRosaRyan + YuAnthony + HornschemeierAnn + WassPeter + + The Laser Interferometer Space Antenna: Unveiling the Millihertz Gravitational Wave Sky + 201909 + 20231205 + 51 + https://ui.adsabs.harvard.edu/abs/2019BAAS...51g..77T + 10.48550/arXiv.1907.06482 + 77 + + + + + + + WarburtonNiels + WardellBarry + LongOliver + UptonSam + LynchPhilip + NasipakZachary + SteinLeo C. + + KerrGeodesics + Zenodo + 202307 + https://doi.org/10.5281/zenodo.8108265 + 10.5281/zenodo.8108265 + + + + + + SteinLeo C. + WarburtonNiels + + Location of the last stable orbit in Kerr spacetime + Physical Review D + 202003 + 20231127 + 101 + 1550-7998 + https://ui.adsabs.harvard.edu/abs/2020PhRvD.101f4007S + 10.1103/PhysRevD.101.064007 + 064007 + + + + + + + FujitaRyuichi + HikidaWataru + + Analytical solutions of bound timelike geodesic orbits in Kerr spacetime + Classical and Quantum Gravity + 200907 + 20231127 + 26 + 0264-9381 + https://ui.adsabs.harvard.edu/abs/2009CQGra..26m5002F + 10.1088/0264-9381/26/13/135002 + 135002 + + + + + + + DysonConor + MeentMaarten van de + + Kerr-fully diving into the abyss: Analytic solutions to plunging geodesics in Kerr + Classical and Quantum Gravity + 202310 + 20231127 + 40 + 0264-9381 + https://ui.adsabs.harvard.edu/abs/2023CQGra..40s5026D + 10.1088/1361-6382/acf552 + 195026 + + + + + + + SchmidtW. + + Celestial mechanics in Kerr spacetime + Classical and Quantum Gravity + 200205 + 19 + 10 + https://arxiv.org/abs/gr-qc/0202090 + 10.1088/0264-9381/19/10/314 + 2743 + 2764 + + + + +
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