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A survey of exoplanet phase curves with Ariel

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Abstract

The ESA-Ariel mission will include a tier dedicated to exoplanet phase curves corresponding to \(\sim 10\%\) of the science time. We present here the current observing strategy for studying exoplanet phase curves with Ariel. We define science questions, requirements and a list of potential targets. We also estimate the precision of phase curve reconstruction and atmospheric retrieval using simulated phase curves. Based on this work, we found that full-orbit phase variations for 35-40 exoplanets could be observed during the 3.5-yr mission. This statistical sample would provide key constraints on atmospheric dynamics, composition, thermal structure and clouds of warm exoplanets, complementary to the scientific yield from spectroscopic transits/eclipses measurements.

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Notes

  1. Backup ERS targets are WASP-103b and KELT-16b

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Acknowledgements

B.C. acknowledges financial support from CNES. J.M.M. work on Ariel is supported by PRODEX grant (PEA: 4000127377). T.J.B. acknowledges support from the McGill Space Institute Graduate Fellowship, the Natural Sciences and Engineering Research Council of Canada’s Postgraduate Scholarships-Doctoral Fellowship, and from the Fonds de recherche du Québec – Nature et technologies through the Centre de recherche en astrophysique du Québec. L.V.M. and E.P. were funded by the ASI grant n. 2018.22.HH.O. C.A. Haswell’s work on Ariel is supported by STFC under grant ST/T00178X/1

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Authors and Affiliations

  1. LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, 92195, Meudon, France

    Benjamin Charnay

  2. National Space Institute, Technical University of Denmark, Lyngby, Denmark

    João M. Mendonça

  3. Max Planck Institute for Astronomy, Heidelberg, Germany

    Laura Kreidberg

  4. Department of Earth, Planetary Sciences, Department of Physics, McGill University, Montréal, Canada

    Nicolas B. Cowan

  5. Department of Physics (Atmospheric, Oceanic and Planetary Physics), University of Oxford, Oxford, UK

    Jake Taylor

  6. Department of Physics, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada

    Taylor J. Bell

  7. Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, Porto, Portugal

    Olivier Demangeon

  8. Department of Physics and Astronomy, University College London, London, UK

    Billy Edwards

  9. School of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK17 8TT, UK

    Carole A. Haswell & Giovanna Tinetti

  10. AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, Gif-sur-Yvette, France

    Giuseppe Morello

  11. Dipartimento di Fisica, La Sapienza Università di Roma, P.le A. Moro 2, 00185, Roma, Italy

    Lorenzo V. Mugnai & Enzo Pascale

  12. Université Paris-Saclay, UVSQ, CNRS, CEA, Maison de la Simulation, 91191, Gif-sur-Yvette, France

    Pascal Tremblin

  13. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USA

    Robert T. Zellem

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Appendix A: Expression of the SNR for phase curves

Appendix A: Expression of the SNR for phase curves

1.1 A.1 A simple metric for phase curves

We assume that the relative thermal flux variation with time (for an orbital period P) is given by:

$$ F(t)= \frac{F_{\max}}{F_{\text{star}}}\times \frac{\left( \cos(2\pi t/P)+1 \right)}{2} $$
(3)

Phase curve data can be fitted with a cosine function \(f(t)=A\times \cos \limits (2 \pi t/P) + B\). For P ≫ 1h, the uncertainty on the amplitude A is:

$$ \delta A= \sqrt{\frac{2}{P}}\sigma_{\text{1h}} $$
(4)

where σ1h is the noise (in ppm) in the given spectral or photometric band for a 1-hour observation of the host star and obtained with Ariel-Rad, and P is expressed in hours. With \(A=\frac {F_{\max \limits }}{2F_{\text {star}}}\), the SNR of the full phase curve is:

$$ SNR_{\text{orbit}} = \frac{A}{\delta A} = 0.5\times SNR_{\text{1h}}\times \sqrt{P/2} $$
(5)

where \(SNR_{\text {1h}}=\frac {F_{\max \limits }}{F_{\text {star}}}\frac {1}{\sigma _{\text {1h}}}\) is the SNR for a 1-hour observation at full phase given in equation (1).

1.2 A.2 Comparison to Spitzer data of LHS 3844b

We compared our expressions (4) and (5) to the analysis of the Spitzer phase curves of LHS 3844b [51]. In this study, the planet-to-star flux variation is binned over 25 equally spaced intervals over the orbital period with 1-sigma uncertainties of \(\sim \)50 ppm. The peak-to-trough amplitude of the phase variation is 350 ± 40 ppm from MCMC fitting. This corresponds to a SNR of \(\sim \)9. Applying formula (4) and (5), we find an uncertainty of the peak-to-trough amplitude of \(\sim \)30 ppm and a SNR of 12. We note that our basic fitting tends to underestimate the uncertainty on the amplitude of the phase curve since it assumes a perfect sine wave and does not take into account the transit and the eclipse. In addition, our formula gives the statistical uncertainty, so there would naturally be some deviation compared to a given dataset. Finally, the uncertainty on the peak-to-trough sine amplitude for real LHS 3844b data is higher than predicted by the idealized model because it was simultaneously fit with an instrument systematic noise model. The instrument systematics for Ariel are expected to be much less severe than for Spitzer, so the Ariel uncertainties are expected to match those calculated with Equation (4). Using noise estimations from Ariel-Rad, we predict a SNR of \(\sim \)13 with Ariel for the same observing duration (\(\sim \)3.8 days) and the same spectral range (4-5 μ m) as Spitzer. The SNR is consistent with our previous estimation and it would rises up to 17 with AIRS-CH1. We conclude that our metric compares favourably with previous Spitzer observations and analysis of LHS 3844b.

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Charnay, B., Mendonça, J.M., Kreidberg, L. et al. A survey of exoplanet phase curves with Ariel. Exp Astron 53, 417–446 (2022). https://doi.org/10.1007/s10686-021-09715-x

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