Autodifferentiable Spectrum Model for High-dispersion Characterization of Exoplanets and Brown Dwarfs

Abstract

We present an autodifferentiable spectral modeling of exoplanets and brown dwarfs. This model enables a fully Bayesian inference of the high-dispersion data to fit the ab initio line-by-line spectral computation to the observed spectrum by combining it with the Hamiltonian Monte Carlo in recent probabilistic programming languages. An open-source code, ExoJAX (https://github.com/HajimeKawahara/exojax), developed in this study, was written in Python using the GPU/TPU compatible package for automatic differentiation and accelerated linear algebra, JAX. We validated the model by comparing it with existing opacity calculators and a radiative transfer code and found reasonable agreements for the output. As a demonstration, we analyzed the high-dispersion spectrum of a nearby brown dwarf, Luhman 16 A, and found that a model including water, carbon monoxide, and H2/He collision-induced absorption was well fitted to the observed spectrum (R = 105 and 2.28–2.30 μm). As a result, we found that T 0 = 1295 − 32 + 35 K at 1 bar and C/O = 0.62 ± 0.03, which is slightly higher than the solar value. This work demonstrates the potential of a full Bayesian analysis of brown dwarfs and exoplanets as observed by high-dispersion spectrographs and also directly imaged exoplanets as observed by high-dispersion coronagraphy.

To Sample or Not to Sample: Retrieving Exoplanetary Spectra with Variational Inference and Normalizing Flows

“…Modern deep learning libraries such as Tensorflow (Abadi et al 2015), PyTorch (Paszke et al 2019), and JAX (Bradbury et al 2018) provide easy access to model training and evaluation. In this study, our implementation will be solely based on the Tensorflow framework, but other deep learning frameworks can similarly be used (Kawahara et al 2022).…”

“…Differentiable models open up the possibility to construct "physics-aware" neural networks, a type of network that is explicitly constrained by physical laws (e.g., Raissi et al 2019;Chen et al 2020;Morvan et al 2021;Amini Niaki et al 2021;Cai et al 2021;Haghighat et al 2021;Viana & Subramaniyan 2021;Cuomo et al 2022). For instance, Kawahara et al (2022) used Hamiltonian Monte Carlo (HMC), a gradient-informed Monte Carlo sampling algorithm (Duane et al 1987;Hoffman & Gelman 2011), to perform atmospheric retrieval of exoplanets on high-resolution spectroscopic data. Others have also applied HMC to speed up light curve fitting (e.g., Agol et al 2021;Foreman-Mackey et al 2021).…”

An Interpretable Machine-learning Framework for Modeling High-resolution Spectroscopic Data*

“…Existing open-source frameworks have overcome some of these challenges, or have been purpose-built for specialized applications. These frameworks include ROBOSPECT (Waters & Hollek 2013), specmatch (Petigura 2015), specmatchemp (Yee et al 2017), wobble (Bedell et al 2019), starfish (Czekala et al 2015), sick (Casey 2016), psoap (Czekala et al 2017), FAL (P. Cargile et al 2022, in preparation), CHIMERA (Line et al 2015), the Cannon (Ho et al 2017), MOOG (Sneden et al 2012), MOOGStokes (Deen 2013), MINESweeper (Cargile et al 2020), and recently ExoJAX (Kawahara et al 2022). The designs of these frameworks necessarily have to make a choice in the bias-variance trade-off: is the tool more data driven or more model driven?…”

“…where ζ is the convolution kernel for rigid-body rotation (e.g., Kawahara et al 2022), v is the spectral axis represented as relative velocity coordinates, and * denotes the convolution operator.…”

“…We currently employ the pseudo-Voigt profile for its low computational cost. We have a prototype exact Voigt-Hjerting implementation following Kawahara et al (2022). We coarsely estimate that moving to this exact Voigt implementation could decrease some residual regions by ∼30%, while increasing the computational cost by more than 10× over the existing pseudo-Voigt approximation.…”