Exact model for phase curves, eclipses, and transits of stars and their planets for TESS
Abstract
Any spherical body may have its surface brightness expressed in terms of a sum of spherical harmonics, Ylm. We have derived exact, analytic expressions for the eclipses, transits, occultations, and phase curves of spherical bodies comprised of any linear combination of spherical harmonics, of arbitrary l and m, with which we can rapidly compute light curves for fitting to various astrophysical objects, including transits of stars with arbitrary polynomial limb-darkening and transits/eclipses of stars with star spots observed with TESS. We have paid special care to numerical accuracy and computational speed, and have developed open-source software for this computation, dubbed starry, in Python and C++ (https://github.com/rodluger/starry/), and (partly) Julia (https://github.com/rodluger/limbdark/). In addition, we have computed the first derivatives of these light curves with respect to the model parameters using automatic differentiation, as well as analytic derivatives for the m = 0 cases. The derivatives may be used to accelerate the optimization of model fits to TESS data and to utilize Hamiltonian Markov Chain Monte Carlo, which may enable fast computation of the posterior of light curve parameters, to efficiently "map" astronomical bodies. The code has been documented extensively with examples, and, in addition to TESS, may be used in fitting primary and secondary transit light curves from ground-based telescopes, as well as HST, Spitzer, Kepler, K2, Corot, PLATO and JWST light curves, and future direct-imaging missions including LUVOIR and HabEX, which may make maps of exo-Earths with phase-curves and planet-moon mutual events. Support for this work was provided by NASA, NSF and the Guggenheim Foundation.
- Publication:
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American Astronomical Society Meeting Abstracts #233
- Pub Date:
- January 2019
- Bibcode:
- 2019AAS...23320205A