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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
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  1. 1
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  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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  3. 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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  4. 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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  5. 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. 6
    © John Spencer 1996
    Rathbun & Spencer 2010
    Time variability of Loki
    Occultation by Jupiter

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  7. 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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  8. 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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  9. The model
    9
    Spherical Harmonic basis
    Simulated
    occultation
    f = A y
    Flux All of starry
    Spherical harmonic
    Coefficients
    Predicted flux

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  10. 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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  11. Switching to a pixel basis
    11

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  12. 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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  13. 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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  14. Fitting a static map
    14
    l = 16

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  15. 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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  16. Nonnegative Matrix Factorization
    Y = B Q
    B
    Q
    Y
    Basis
    Maps Time variability
    Map for the -th
    light curve
    l

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  17. Results (simulated data)
    17
    Time variability

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  18. 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

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  19. Delicious food I’ve made during quarantine
    fbartolic
    19
    [email protected]

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