Inferring a time-dependent map of Io from occultations and phase curves

Inferring a time-dependent map of Io from occultations and phase curves

Talk I've given at the Center for Computational Astrophysics at Flatiron Institute in New York.


Fran Bartolić

June 25, 2020


  1. 2.

    Volcanism on Io • Io is the most volcanically active

    body in the Solar System, the volcanism is driven by tides from Jupiter and sustained by the Laplace resonance • Its surface in NIR is covered with bright volcanic spots, they are time- variable and non persistent • Science goals: geology, Io as analogue of exoplanet volcanism 2 (de Kleer et. al. 2016)
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    Volcanism on exoplanets • Three main sources: • Radioactive decay

    - volcanism similar to Earth, stronger for newly formed planets with abundant radioactive elements • Extreme insolation - lava worlds • Tidal heating - Io like volcanism • Promising candidates: 55 Cancri e, CoRoT-7b, Kepler-10b…. • Volcanism on Super-Earths potentially observable with JWST 3 © NASA
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    Occultations of Io • Io has been observed from both

    space (Galileo, Juno) and ground (IRTF, Keck, LBTI…) • Although the surface can be resolved, occultation light curves have the longest time baseline (decades) • Occultation light curves encode information about the surface features LBTI observations (de Kleer et. al. 2017) Resolved occultation of Io by Europa 4
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    Not all occultations are equal • Occultations by Jupiter every

    ~day • Mutual occultations between Galilean moons every ~6 years • Mutual occultations by far the most informative 5
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    6 © John Spencer 1996 Rathbun & Spencer 2010 Time

    variability of Loki Occultation by Jupiter
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    1. Obtain archival data of occultations and phase curves 2.

    Compute the geometry of events for all times (JPL Horizons) 3. Build a probabilistic model using starry which generates one map per light curve 4. Extract time variability of individual spatial features 7 Our goals
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    The data ~4 min volcano! Occultations by Jupiter, data from

    NASA IRTF, kindly provided by Julie Rathbun Large variations in the baseline 8
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    The model 9 Spherical Harmonic basis Simulated occultation f =

    A y Flux All of starry Spherical harmonic Coefficients Predicted flux
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    Switching to a pixel basis 10 • To ensure that

    the inferred maps are physical we need to enforce positivity everywhere • We fit the models in the pixel basis but compute the flux and report all results in the spherical harmonic basis • So our priors are approximate y ← P y p ← P† p SH to pixels Pixels to SH Approximate Mapping
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    Inference 12 • We use PyMC3 to build our models

    • The models have thousands of parameters • starry has automatic differentiation so we can deal with high dimensional spaces • We use optimization (MAP estimate) and Variational Inference to fit the models • We also use Normalizing Flow VI to capture some off-diagonal structure in the posterior covariance matrix
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    Fitting a static map 13 • 1.3k parameters, <100 data

    points • MAP estimate, exponential priors • We’re probably overfitting • At least for this light curve, the spot is exactly where it should be (location of Loki) l = 16
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    Fitting a time dependent map 15 • In principle there’s

    one map per data point • Many ways of reducing the dimensionality of this problem: • Fitting one map per light curve • Expand SH coefficients into a Taylor or Fourier series • Parametrize features on the surface and fit for those parameters • Matrix factorization
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    Nonnegative Matrix Factorization Y = B Q B Q Y

    Basis Maps Time variability Map for the -th light curve l
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    Open questions 18 • Priors for NMF, need sparse orthogonal

    maps • Avoiding artifacts from the spherical harmonic basis (ringing) • Calibrating uncertainties from Variational Inference • Sampling an NMF model with Hamiltonian Monte Carlo