Interpreting High-resolution Spectroscopy of Exoplanets using Cross-correlations and Supervised Machine Learning

Abstract

We present a new method for performing atmospheric retrieval on ground-based, high-resolution data of exoplanets. Our method combines cross-correlation functions with a random forest, a supervised machine learning technique, to overcome challenges associated with high-resolution data. A series of cross-correlation functions are concatenated to give a "CCF-sequence" for each model atmosphere, which reduces the dimensionality by a factor of ∼ 100. The random forest, trained on our grid of ∼ 65, 000 models, provides a likelihood-free method of retrieval. The pre-computed grid spans 31 values of both temperature and metallicity, and incorporates a realistic noise model. We apply our method to HARPS-N observations of the ultra-hot Jupiter KELT-9b, and obtain a metallicity consistent with solar (log M = −0.2 ± 0.2). Our retrieved transit chord temperature (T = 6000 +0 −200 K) is unreliable as the ion cross-correlations lie outside of the training set, which we interpret as being indicative of missing physics in our atmospheric model. We compare our method to traditional nestedsampling, as well as other machine learning techniques, such as Bayesian neural networks. We demonstrate that the likelihood-free aspect of the random forest makes it more robust than nested-sampling to different error distributions, and that the Bayesian neural network we tested is unable to reproduce complex posteriors. We also address the claim in Cobb et al. (2019) that our random forest retrieval technique can be over-confident but incorrect. We show that this is an artefact of the training set, rather than the machine learning method, and that the posteriors agree with those obtained using nested-sampling.

An inventory of atomic species in the atmosphere of WASP-121b using UVES high-resolution spectroscopy

“…Our removal of the continuum prevents the measurement of any pressure-sensitive features which would allow the degeneracies between abundances, temperature, scattering properties and reference radius/pressure to be broken, and the cross-correlation method is not sensitive to changes in amplitude caused by differing scale heights. New and more complex approaches to high-resolution spectroscopic analysis have emerged in recent years, including the combination of low-and high-resolution spectroscopy (Brogi et al 2017;Pino et al 2018), principled statistical frameworks and likelihood mapping (Brogi & Line 2019;Gibson et al 2020;Nugroho et al 2020b;Hood et al 2020), machine learning (Fisher et al 2020) and Doppler tomography (Watson et al 2019, Matthews et al in prep). These sophisticated methods enable more stringent constraints to be placed on atmospheric parameters, and broad species searches such as ours present a starting-point for future work using these sophisticated and more computationally-intensive methods to further categorise the atmosphere of WASP-121b.…”

“…In reality, the statistics of these cross-correlation maps are poorly understood, and the detection significance can be changed by as much as 0.5 by simply changing the area used to calculate the standard deviation, or by increasing/decreasing the number of phase-shuffling iterations. New techniques are being pursued and have produced encouraging results (Brogi & Line 2019;Fisher et al 2020;Gibson et al 2020;Nugroho et al 2020b), but due to their computationally-intensive nature, these methods were not attempted here for our large range of species.…”

A temperature inversion with atomic iron in the ultra-hot dayside atmosphere of WASP-189b

“…Retrieval methods for high-resolution spectroscopy have been developed in recent years (e.g. Brogi et al 2017;Brogi & Line 2019;Shulyak et al 2019;Fisher et al 2020;Gibson et al 2020). Following these works, we established a framework to retrieve the T -P profile of WASP-189b.…”

The PHOENIX Exoplanet Retrieval Algorithm and Using H− Opacity as a Probe in Ultrahot Jupiters

“…Retrievals have been used to analyze transit (e.g., Benneke & Seager 2012;Line et al 2012;Waldmann et al 2015; Barstow et al 2017;Howe et al 2017;MacDonald & Madhusudhan 2017;Mollière et al 2019) and secondaryeclipse observations (e.g., Line et al 2014b;Waldmann et al 2015;Evans et al 2017;Gandhi & Madhusudhan 2018;Mollière et al 2019;Himes et al 2020;Kitzmann et al 2020), as well as observations of self-luminous objects like directlyimaged exoplanets (Lee et al 2013;Lavie et al 2017;Gravity Collaboration et al 2020) and brown dwarfs (Line et al 2015;Burningham et al 2017;Line et al 2017). Recently, the application of retrieval algorithms to combine low-and highresolution data has been explored (Brogi et al 2017(Brogi et al , 2019Fisher et al 2020;Gandhi et al 2019;Gibson et al 2020). See Madhusudhan (2018) for an overview of many existing retrieval algorithms and Barstow & Heng (2020) for a discussion of open problems in retrieval analysis.…”