From 992c776ee850f016c504b5389164f646f76be1a9 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Fri, 30 Aug 2024 14:22:32 +0100 Subject: [PATCH] Creating 10.21105.joss.06972.jats --- .../paper.jats/10.21105.joss.06972.jats | 630 ++++++++++++++++++ 1 file changed, 630 insertions(+) create mode 100644 joss.06972/paper.jats/10.21105.joss.06972.jats diff --git a/joss.06972/paper.jats/10.21105.joss.06972.jats b/joss.06972/paper.jats/10.21105.joss.06972.jats new file mode 100644 index 0000000000..b02678cfa2 --- /dev/null +++ b/joss.06972/paper.jats/10.21105.joss.06972.jats @@ -0,0 +1,630 @@ + + +
+ + + + +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.

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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.

+ + + +