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JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 08 + 2024 + + + 9 + + 100 + + + + squishyplanet: modeling transits of non-spherical +exoplanets in JAX + + + + Ben + Cassese + https://orcid.org/0000-0002-9544-0118 + + + Justin + Vega + https://orcid.org/0000-0003-1481-8076 + + + Tiger + Lu + https://orcid.org/0000-0003-0834-8645 + + + Malena + Rice + https://orcid.org/0000-0002-7670-670X + + + Avishi + Poddar + https://orcid.org/0009-0000-5314-5770 + + + David + Kipping + https://orcid.org/0000-0002-4365-7366 + + + + 08 + 30 + 2024 + + + 6972 + + + 10.21105/joss.06972 + + + 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.13377036 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/6972 + + + + 10.21105/joss.06972 + https://joss.theoj.org/papers/10.21105/joss.06972 + + + https://joss.theoj.org/papers/10.21105/joss.06972.pdf + + + + + + Analytic Planetary Transit Light Curves and +Derivatives for Stars with Polynomial Limb Darkening + Agol + Astronomical Journal + 3 + 159 + 10.3847/1538-3881/ab4fee + 2020 + Agol, E., Luger, R., & +Foreman-Mackey, D. (2020). Analytic Planetary Transit Light Curves and +Derivatives for Stars with Polynomial Limb Darkening. Astronomical +Journal, 159(3), 123. +https://doi.org/10.3847/1538-3881/ab4fee + + + Analytic Light Curves for Planetary Transit +Searches + Mandel + Astrophysical Journal, +Letters + 2 + 580 + 10.1086/345520 + 2002 + Mandel, K., & Agol, E. (2002). +Analytic Light Curves for Planetary Transit Searches. Astrophysical +Journal, Letters, 580(2), L171–L175. +https://doi.org/10.1086/345520 + + + batman: BAsic Transit Model cAlculatioN in +Python + Kreidberg + Publications of the ASP + 957 + 127 + 10.1086/683602 + 2015 + Kreidberg, L. (2015). batman: BAsic +Transit Model cAlculatioN in Python. Publications of the ASP, 127(957), +1161. https://doi.org/10.1086/683602 + + + exoplanet: Gradient-based probabilistic +inference for exoplanet data & other astronomical time +series + Foreman-Mackey + The Journal of Open Source +Software + 62 + 6 + 10.21105/joss.03285 + 2021 + Foreman-Mackey, D., Luger, R., Agol, +E., Barclay, T., Bouma, L., Brandt, T., Czekala, I., David, T., Dong, +J., Gilbert, E., Gordon, T., Hedges, C., Hey, D., Morris, B., +Price-Whelan, A., & Savel, A. (2021). exoplanet: Gradient-based +probabilistic inference for exoplanet data & other astronomical time +series. The Journal of Open Source Software, 6(62), 3285. +https://doi.org/10.21105/joss.03285 + + + exoplanet-dev/jaxoplanet: Astronomical time +series analysis with JAX + Hattori + 10.5281/zenodo.10736936 + 2024 + Hattori, S., Garcia, L., Murray, C., +Dong, J., Dholakia, S., Degen, D., & Foreman-Mackey, D. (2024). +exoplanet-dev/jaxoplanet: Astronomical time series analysis with JAX +(Version v0.0.2). Zenodo. +https://doi.org/10.5281/zenodo.10736936 + + + ellc: A fast, flexible light curve model for +detached eclipsing binary stars and transiting +exoplanets + Maxted + Astronomy and Astrophysics + 591 + 10.1051/0004-6361/201628579 + 2016 + Maxted, P. F. L. (2016). ellc: A +fast, flexible light curve model for detached eclipsing binary stars and +transiting exoplanets. Astronomy and Astrophysics, 591, A111. +https://doi.org/10.1051/0004-6361/201628579 + + + Early Release Science of the exoplanet +WASP-39b with JWST NIRSpec PRISM + Rustamkulov + Nature + 7949 + 614 + 10.1038/s41586-022-05677-y + 2023 + Rustamkulov, Z., Sing, D. K., +Mukherjee, S., May, E. M., Kirk, J., Schlawin, E., Line, M. R., Piaulet, +C., Carter, A. L., Batalha, N. E., Goyal, J. M., López-Morales, M., +Lothringer, J. D., MacDonald, R. J., Moran, S. E., Stevenson, K. B., +Wakeford, H. R., Espinoza, N., Bean, J. L., … Zieba, S. (2023). Early +Release Science of the exoplanet WASP-39b with JWST NIRSpec PRISM. +Nature, 614(7949), 659–663. +https://doi.org/10.1038/s41586-022-05677-y + + + Quadax + Conlin + 10.5281/zenodo.11062823 + 2024 + Conlin, R. (2024). Quadax. Zenodo. +https://doi.org/10.5281/zenodo.11062823 + + + JAX: Composable transformations of +Python+NumPy programs + Bradbury + 2018 + Bradbury, J., Frostig, R., Hawkins, +P., Johnson, M. J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., +VanderPlas, J., Wanderman-Milne, S., & Zhang, Q. (2018). JAX: +Composable transformations of Python+NumPy programs (Version 0.3.13). +http://github.com/google/jax + + + Constraining the Oblateness of Kepler +Planets + Zhu + Astrophysical Journal + 1 + 796 + 10.1088/0004-637X/796/1/67 + 2014 + Zhu, W., Huang, C. X., Zhou, G., +& Lin, D. N. C. (2014). Constraining the Oblateness of Kepler +Planets. Astrophysical Journal, 796(1), 67. +https://doi.org/10.1088/0004-637X/796/1/67 + + + starry: Analytic Occultation Light +Curves + Luger + Astronomical Journal + 2 + 157 + 10.3847/1538-3881/aae8e5 + 2019 + Luger, R., Agol, E., Foreman-Mackey, +D., Fleming, D. P., Lustig-Yaeger, J., & Deitrick, R. (2019). +starry: Analytic Occultation Light Curves. Astronomical Journal, 157(2), +64. https://doi.org/10.3847/1538-3881/aae8e5 + + + Measuring the Oblateness and Rotation of +Transiting Extrasolar Giant Planets + Barnes + Astrophysical Journal + 1 + 588 + 10.1086/373893 + 2003 + Barnes, J. W., & Fortney, J. J. +(2003). Measuring the Oblateness and Rotation of Transiting Extrasolar +Giant Planets. Astrophysical Journal, 588(1), 545–556. +https://doi.org/10.1086/373893 + + + Empirical Constraints on the Oblateness of an +Exoplanet + Carter + Astrophysical Journal + 2 + 709 + 10.1088/0004-637X/709/2/1219 + 2010 + Carter, J. A., & Winn, J. N. +(2010). 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+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6972 +10.21105/joss.06972 + +squishyplanet: modeling transits +of non-spherical exoplanets in JAX + + + +https://orcid.org/0000-0002-9544-0118 + +Cassese +Ben + + + +* + + +https://orcid.org/0000-0003-1481-8076 + +Vega +Justin + + + + +https://orcid.org/0000-0003-0834-8645 + +Lu +Tiger + + + + +https://orcid.org/0000-0002-7670-670X + +Rice +Malena + + + + +https://orcid.org/0009-0000-5314-5770 + +Poddar +Avishi + + + + +https://orcid.org/0000-0002-4365-7366 + +Kipping +David + + + + + +Dept. of Astronomy, Columbia University, 550 W 120th +Street, New York NY 10027, USA + + + + +Dept. of Astronomy, Yale University, New Haven, CT 06511, +USA + + + + +* E-mail: + + +1 +5 +2024 + +9 +100 +6972 + +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 +astronomy +exoplanets +exoplanet transits + + + + + + Summary +

While astronomers often assume that exoplanets are perfect spheres + when analyzing observations, the subset of these distant worlds that + are subject to strong tidal forces and/or rapid rotations are expected + to be distinctly ellipsoidal or even triaxial. Since a planet’s + response to these forces is determined in part by its interior + structure, measurements of an exoplanet’s deviations from spherical + symmetry can lead to powerful insights into its composition and + surrounding environment. These shape deformations will imprint + themselves on a planet’s phase curve and transit lightcurve and cause + small (1s-100s of parts per million) deviations from their + spherical-planet counterparts. Until recently, these deviations were + undetectable in typical real-world datasets due to limitations in + photometric precision. Now, however, current and soon-to-come-online + facilities such as JWST will routinely deliver observations that + warrant the consideration of more complex models. To this end we + present squishyplanet, a + JAX-based Python package that implements an + extension of the polynomial limb-darkened transit model presented in + Agol et al. + (2020) to + non-spherical (triaxial) planets, as well as routines for modeling + reflection and emission phase curves.

+
+ + Statement of need +

The study of exoplanets, or planets that orbit stars beyond the + sun, is a major focus of the astronomy community. Many of these + studies center on the analysis of time series photometric (or + spectroscopic) observations collected when a planet happens to pass + through the line of sight between an observer and its host star. By + modeling the fraction of starlight intercepted by the coincident + planet, astronomers can deduce basic properties of the system such as + the planet’s relative size, its orbital period, and its orbital + inclination.

+

The past 20 years have seen extensive work both on theoretical + model development and computationally efficient implementations of + these models. Notable examples include Mandel & Agol + (2002), + Kreidberg + (2015), and + Foreman-Mackey et al. + (2021), + though many other examples can be found. Though each of these packages + make different choices, the majority of them (with notable exceptions, + including Maxted + (2016)1) + do share one common assumption: the planet under examination is a + perfect sphere.

+

This is both a reasonable and immensely practical assumption. It is + reasonable because firstly, a substantial fraction of planets, + especially rocky planets, are likely quite close to perfect spheres + (Earth’s equatorial radius is only 43 km greater than its polar + radius, a difference of 0.3%). Secondly, at the precision of most + survey datasets (e.g. Kepler and + TESS), even substantially flattened planets would be + nearly indistinguishable from a spherical planet with the same on-sky + projected area + (Zhu et + al., 2014). It is practical since, somewhat miraculously, this + assumption enables an analytic solution for the amount of flux blocked + by the planet at each timestep. This is true even if the intensity of + the stellar surface varies radially according to a nearly arbitrarily + complex polynomial + (Agol et + al., 2020).

+

However, for a small but growing number of datasets and targets, + the reasonableness of this assumption will break down and lead to + biased results. Many gas giant planets, in particular, are expected to + be distinctly oblate or triaxial, either due to the effects of tidal + deformation or rapid rotation + (Barnes + & Fortney, 2003). Looking within our own solar system, + Jupiter and Saturn have oblateness values of roughly 0.06 and 0.1, + respectively, due to their fast spins.

+

To illustrate the effects of shape deformation on a lightcurve, + consider + [fig:example], + which shows a selection of differences between time series generated + under the assumption of a spherical planet and those generated + assuming a planet with Saturn-like flattening. Depending on the + obliquity, precession, impact parameter, and whether the planet is + tidally locked, we can generate a wide variety of residual + lightcurves. In some cases the deviations from a spherical planet + occur almost exclusively in the ingress and egress phases of the + transit, while others evolve throughout the transit. Some residual + curves are mirrored about the transit midpoint, though in general, + they will not always be symmetric + (Carter + & Winn, 2010).

+ +

A sampling of differences between transits of spherical + and non-spherical planets. A more complete description of how each + of these curves were generated can be found in the + online + documentation.

+ +
+

The amplitudes of these effects are quite small compared to the + full depth of the transit, but could be detectable with a facility + such as JWST, which is capable of a white-light precision of a few 10s + of ppm + (Rustamkulov + et al., 2023).

+

We leave a detailed description of the mathematics and a + corresponding series of visualizations for the online documentation. + There we also include confirmation that our implementation, when + modeling the limiting case of a spherical planet, agrees with previous + well-tested models even for high-order polynomial limb darkening laws. + More specifically, we show that that lightcurves of spherical planets + generated with squishyplanet deviate by no more + than 100 ppb from those generated with + jaxoplanet + (Hattori + et al., 2024), the JAX-based rewrite of + the popular transit modeling package exoplanet + (Foreman-Mackey + et al., 2021) that also implements the arbitrary-order + polynomial limb darkening algorithm presented in Agol et al. + (2020). + Finally, we demonstrate squishyplanet’s limited + support for phase curve modeling.

+

We hope that a publicly-available, well-documented, and highly + accurate model for non-spherical transiting exoplanets will enable + thorough studies of planets’ shapes and lead to more data-informed + constraints on their interior structures.

+
+ + Acknowledgements +

squishyplanet relies on + quadax + (Conlin, + 2024), an open-source library for numerical quadrature and + integration in JAX. + squishyplanet also uses the Kepler’s equation + solver from jaxoplanet + (Hattori + et al., 2024) and the finite exposure time correction from + starry + (Luger + et al., 2019). squishyplanet is built + with the JAX library + (Bradbury + et al., 2018). We thank the developers of these packages for + their work and for making their code available to the community.

+
+ + + + + + + + AgolEric + LugerRodrigo + Foreman-MackeyDaniel + + Analytic Planetary Transit Light Curves and Derivatives for Stars with Polynomial Limb Darkening + Astronomical Journal + 202003 + 159 + 3 + https://arxiv.org/abs/1908.03222 + 10.3847/1538-3881/ab4fee + 123 + + + + + + + MandelKaisey + AgolEric + + Analytic Light Curves for Planetary Transit Searches + Astrophysical Journal, Letters + 200212 + 580 + 2 + https://arxiv.org/abs/astro-ph/0210099 + 10.1086/345520 + L171 + L175 + + + + + + KreidbergLaura + + batman: BAsic Transit Model cAlculatioN in Python + Publications of the ASP + 201511 + 127 + 957 + https://arxiv.org/abs/1507.08285 + 10.1086/683602 + 1161 + + + + + + + Foreman-MackeyDaniel + LugerRodrigo + AgolEric + BarclayThomas + BoumaLuke + BrandtTimothy + CzekalaIan + DavidTrevor + DongJiayin + GilbertEmily + GordonTyler + HedgesChristina + HeyDaniel + MorrisBrett + Price-WhelanAdrian + SavelArjun + + exoplanet: Gradient-based probabilistic inference for exoplanet data & other astronomical time series + The Journal of Open Source Software + 202106 + 6 + 62 + https://arxiv.org/abs/2105.01994 + 10.21105/joss.03285 + 3285 + + + + + + + HattoriSoichiro + GarciaLionel + MurrayCatriona + DongJiayin + DholakiaShashank + DegenDavid + Foreman-MackeyDaniel + + exoplanet-dev/jaxoplanet: Astronomical time series analysis with JAX + Zenodo + 202403 + https://doi.org/10.5281/zenodo.10736936 + 10.5281/zenodo.10736936 + + + + + + MaxtedP. F. L. + + ellc: A fast, flexible light curve model for detached eclipsing binary stars and transiting exoplanets + Astronomy and Astrophysics + 201606 + 591 + https://arxiv.org/abs/1603.08484 + 10.1051/0004-6361/201628579 + A111 + + + + + + + RustamkulovZ. + SingD. K. + MukherjeeS. + MayE. M. + KirkJ. + SchlawinE. + LineM. R. + PiauletC. + CarterA. L. + BatalhaN. E. + GoyalJ. M. + López-MoralesM. + LothringerJ. D. + MacDonaldR. J. + MoranS. E. + StevensonK. B. + WakefordH. R. + EspinozaN. + BeanJ. L. + BatalhaN. M. + BennekeB. + Berta-ThompsonZ. K. + CrossfieldI. J. M. + GaoP. + KreidbergL. + PowellD. K. + CubillosP. E. + GibsonN. P. + LeconteJ. + MolaverdikhaniK. + NikolovN. K. + ParmentierV. + RoyP. + TaylorJ. + TurnerJ. D. + WheatleyP. J. + AggarwalK. + AhrerE. + AlamM. K. + AldersonL. + AllenN. H. + BanerjeeA. + BaratS. + BarradoD. + BarstowJ. K. + BellT. J. + BlecicJ. + BrandeJ. + CasewellS. + ChangeatQ. + ChubbK. L. + CrouzetN. + DaylanT. + DecinL. + DésertJ. + Mikal-EvansT. + FeinsteinA. D. + FlaggL. + FortneyJ. J. + HarringtonJ. + HengK. + HongY. + HuR. + IroN. + KatariaT. + KemptonE. M. -R. + KrickJ. + LendlM. + Lillo-BoxJ. + LoucaA. + Lustig-YaegerJ. + ManciniL. + MansfieldM. + MayneN. J. + MiguelY. + MorelloG. + OhnoK. + PalleE. + Petit dit de la RocheD. J. M. + RackhamB. V. + RadicaM. + Ramos-RosadoL. + RedfieldS. + RogersL. K. + ShkolnikE. L. + SouthworthJ. + TeskeJ. + TremblinP. + TuckerG. S. + VenotO. + WaalkesW. C. + WelbanksL. + ZhangX. + ZiebaS. + + Early Release Science of the exoplanet WASP-39b with JWST NIRSpec PRISM + Nature + 202302 + 614 + 7949 + https://arxiv.org/abs/2211.10487 + 10.1038/s41586-022-05677-y + 659 + 663 + + + + + + ConlinRory + + Quadax + Zenodo + 202404 + https://doi.org/10.5281/zenodo.11062823 + 10.5281/zenodo.11062823 + + + + + + BradburyJames + FrostigRoy + HawkinsPeter + JohnsonMatthew James + LearyChris + MaclaurinDougal + NeculaGeorge + PaszkeAdam + VanderPlasJake + Wanderman-MilneSkye + ZhangQiao + + JAX: Composable transformations of Python+NumPy programs + 2018 + http://github.com/google/jax + + + + + + ZhuWei + HuangChelsea X. + ZhouGeorge + LinD. N. C. + + Constraining the Oblateness of Kepler Planets + Astrophysical Journal + 201411 + 796 + 1 + https://arxiv.org/abs/1410.0361 + 10.1088/0004-637X/796/1/67 + 67 + + + + + + + LugerRodrigo + AgolEric + Foreman-MackeyDaniel + FlemingDavid P. + Lustig-YaegerJacob + DeitrickRussell + + starry: Analytic Occultation Light Curves + Astronomical Journal + 201902 + 157 + 2 + https://arxiv.org/abs/1810.06559 + 10.3847/1538-3881/aae8e5 + 64 + + + + + + + BarnesJason W. + FortneyJonathan J. + + Measuring the Oblateness and Rotation of Transiting Extrasolar Giant Planets + Astrophysical Journal + 200305 + 588 + 1 + https://arxiv.org/abs/astro-ph/0301156 + 10.1086/373893 + 545 + 556 + + + + + + CarterJoshua A. + WinnJoshua N. + + Empirical Constraints on the Oblateness of an Exoplanet + Astrophysical Journal + 201002 + 709 + 2 + https://arxiv.org/abs/0912.1594 + 10.1088/0004-637X/709/2/1219 + 1219 + 1229 + + + + + +

Though ellc, and + squishyplanet share the same goal of modeling + transits of non-spherical planets, they differ in a few key ways. + First, ellc requires users to select from a + set of predefined limb darkening laws, while + squishyplanet allows for any law that can be + cast as a polynomial (e.g. high-order approximations to grid-based + models). Second, ellc allows for + gravity-deformed stars, while squishyplanet + always models the central star as a sphere and restricts triaxial + deformations to the planet only. Third, ellc + allows users to model radial velocity curves, including the + Rossiter-McLaughlin effect, while + squishyplanet is focused on lightcurve + modeling only. In terms of implementation, + ellc is written in Fortran and wrapped in + Python, while squishyplanet is written in + Python/JAX. Also, ellc + integrates the flux blocked by the planet via 2D numerical + integration, while squishyplanet uses a 1D + numerical integration scheme. We believe that these tools will be + complementary and that users will benefit from having both + available.

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