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