Auto-Differentiable Spectrum Model for High-Dispersion Characterization of Exoplanets and Brown Dwarfs

Abstract

We present an auto-differentiable 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 , developed in this study, was written in Python using the GPU/TPU compatible package for automatic differentiation and accelerated linear algebra, JAX (Bradbury et al. 2018). We validated the model by comparing it with existing opacity calculators and a radiative transfer code and found reasonable agreements of 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 H 2 /He collision induced absorption was well fitted to the observed spectrum (R = 10 5 and 2.28-2.30 µm). As a result, we found that T 0 = 1295 ± 14 K at 1 bar and C/O = 0.62 ± 0.01, which is slightly higher than the solar value. This work demonstrates the potential of 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.

Mapping stellar surfaces III: An Efficient, Scalable, and Open-Source Doppler Imaging Model

“…Fortunately, our model is computationally efficient to evaluate and, given its analyticity, trivial to differentiate using an autodifferentiation scheme (see §11). It can therefore be used out-of-the-box within gradient-based sampling schemes such as pymc3 (Salvatier et al 2016), in particular the No-U-Turn Sampler (NUTS), a variant of Hamiltonian Monte Carlo that harnesses gradient information to greatly speed up the convergence of the MCMC chains (for a recent application of HMC in the context of spectroscopy, see Kawahara et al 2021). Our model may also be useful in the context of variational inference (VI), and in particular automatic differentiation variational inference (ADVI; Kucukelbir et al 2016), which casts posterior inference as an optimization problem; both VI and ADVI are also implemented in pymc3.…”

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

“…Modern deep learning libraries such as Tensorflow (Abadi et al 2015a), PyTorch (Paszke et al 2019) and JAX (Bradbury et al 2018) provide easy access to model training and evaluation. Our implementation will be solely based on the Tensorflow framework, other deep learning frameworks can also be used (Kawahara et al 2021).…”

“…There have been several recent attempts within the field of exoplanets to develop differentiable physical models within these frameworks. Initial results show that these differentiable models may hold the keys to overcome the curse of dimensionality brought by our increasingly complex models (Kawahara et al 2021) and may one day enable us to perform population study without placing significant demand on computational resources.…”

“…Differentiable models open up the possibility to construct "physics-aware" neural network, a type of network that respects physical laws (Raissi et al 2019). For instance, Kawahara et al (2021) 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 lightcurve-fitting (e.g.…”