Fast open-source exomoon transit detection algorithm

Named after the imaginary 5th moon of the gas giant Polyphemus, orbiting Alpha Centauri A, in the film Avatar.

Pandora employs an analytical photodynamical model, including:

• Stellar limb darkening
• Full and partial planet-moon eclipses
• Barycentric motion of planet and moon

To search for moons, Pandora can be used with nested samplers, e.g. UltraNest or dynesty. We provide an example workflow for a planet+moon injection into Kepler-like data with Gaussian noise, UltraNest+Pandora recovery, cornerplots, and posterior exploration. Pandora is fast, calculating 10,000 models and log-likelihood evaluation per second (give or take an order of magnitude, depending on parameters and data). This means that a retrieval with 250 Mio. evaluations until convergence takes about 5 hours on a single core. Scaling with cores is worse than linear. For searches in large amounts of data, it is most efficient to assign one core per light curve.

Create transit light curve

The following Python code snippet illustrates how to work with Pandora. To keep it short, it omits the long list of required parameters. A complete and working example can be found here.

import pandoramoon as pandora
params = pandora.model_params()
params.per_bary = 365.25  # [days]
# (...) See tutorials for list of parameters
time = pandora.time(params).grid()
model = pandora.moon_model(params)
flux_total, flux_planet, flux_moon = model.light_curve(time)

plt.plot(time, flux_planet, color="blue")
plt.plot(time, flux_moon, color="red")
plt.plot(time, flux_total, color="black")
plt.show()

Create video

With Pandora, you can create transit videos to understand, teach, and explore exomoon transits. Try it out:

video = model.video(
    time=time,
    limb_darkening=True, 
    teff=3200,
    planet_color="black",
    moon_color="black",
    ld_circles=100
)
video.save(filename="video.mp4", fps=25, dpi=200)

Videos approximate the true light curve as calculated by Pandora very well. They are, however, not pixel-perfect due to the underlying Matplotlib render engine. Klick the image to view the video:

Installation

Install with pip install pandoramoon. If you end up in dependency hell, set up a fresh environment:

conda create -n pandora_env python=3.9
conda activate pandora_env
conda install numpy matplotlib numba 
pip install pandoramoon

For sampling, the following packages will be useful:

conda install cython scipy
pip install ultranest dynesty h5py

Attribution

Please cite Hippke & Heller (2022, A&A in press) if you find this code useful in your research. The BibTeX entry for the paper is:

@ARTICLE{2022arXiv220509410H
       author = {{Hippke}, Michael and {Heller}, Ren{\'e}},
        title = "{Pandora: A fast open-source exomoon transit detection algorithm}",
      journal = {arXiv e-prints},
     keywords = {Astrophysics - Earth and Planetary Astrophysics, Astrophysics - Instrumentation and Methods for Astrophysics},
         year = 2022,
        month = may,
          eid = {arXiv:2205.09410},
        pages = {arXiv:2205.09410},
archivePrefix = {arXiv},
       eprint = {2205.09410},
 primaryClass = {astro-ph.EP},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2022arXiv220509410H},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}