In the near future, direct imaging missions will search for Earth-like planets around nearby stars. One of the problems is how to characterize the planet surface. To address this question, we are developing a surface map and components reconstruction method using a one-dimensional light curve of a direct-imaged planet. The orbital motion and spin rotation of a planet conveys information about the spherical surface to the time-series of the light curve. In the future, this theoretical work will be tested in the era of space direct imaging of exoplanets. See wiki for further description.

Spin-Orbit Tomography (SOT) is a retrieval technique of a 2 dimensinal map of an Exo Earth from time-series data of integrated reflection light.

python setup.py install

Jupyter notebook based tutorial. See sot/tutorial

• sotl2.ipynb -- L2-SOT from scratch
• sotl2_sklearn_ridge.ipynb -- using Scikit-Learn ridge
• sotl2_pytorch.ipynb -- using an ADAM optimizer in pytorch
• sotl2_jax.ipynb -- using an ADAM optimizer in JAX

• sot_Bayesian.ipynb -- Bayesian static SOT

• dynamic SOT for a rotating Earth.ipynb -- dynamic SOT (point estimate)

See sot/bin

• dysot_pest -- Point estimate of time-varying map using dynamic SOT
• dysot_sampling -- Sampling geometric parameters for Bayesian dynamic SOT
• dysot_bayesmap -- Bayesian dynamic mapping using the sampling of geometric parameters
• stsou_pest_qf -- Static spin-orbit unmixing using a NMF (L2-VR) for a cloudless toy model.

SOT for time-varying geometry with a full Bayesian modeling (dynamic SOT) based on Kawahara and Masuda (2020). It also includes codes for the Bayesian version of the static SOT.

• sot/dymap

Figure (Click): Dynamic map using the real light curve (PC1) of Earth by Deep Space Climate Observatory.

SOT-Sparse uses L1 and Total Squared Variation (TSV).

• Spare (external)

The algorithm is based on Aizawa, Kawahara, Fan, ApJ, 896, 22 (2020).

Spin-Orbit Unmixing (SOU) is a unified retrieval model for spectral unmixing and spin-orbit tomography.

Spin-Orbit Unmixing using the non-negative matrix factorization (NMF) and L2 and volume regularization (SOU-NMF) based on Kawahara, ApJ, 894, 58 (2020).

• sot/nmfmap

Figure: The recovered composite map of the real light curve of Earth by Deep Space Climate Observatory using SOU-NMF.

• exomap, Kuwata, H.K., Aizawa et al. to be submitted.

The orientation of the spin axis can be inferred from frequency modulation (FM) of the light curve.

• fm/rottheory.py the modulation factor. It can reproduce Figure 2 in Kawahara (2016).

• juwvid Code for the Wigner-Ville analysis written in Julia-0.6.

The algorithm is based on Kawahara (2016). See also Nakagawa et al. (2020).

• ReflectDirect Python suite for analysis of planet reflected light by Joel Schwartz et al.
• exocartographer Bayesian framework of a 2D mapping and obliquity measurement by Ben Farr et al.
• EARL Spherical harmonics decomposition of reflected light by Hal Haggard et al.
• samurai Rotational Unmixing by Lustig-Yaeger et al.
• starry/starrynight Tools for mapping planets and stars by Rodrigo Luger et al and Rodrigo Luger et al.
• neural_exocartography mapping with learned denoiser (dnn) by Asensio-Ramos and Palle
• bluedot A pale blue dot simulater by Hajime Kawahara (beta version).