# Wobble: A Data-driven Analysis Technique for Time-series Stellar Spectra

## TL;DR

Wobble is a data-driven technique that extracts precise radial velocities and stellar/telluric spectra from high-resolution time-series spectra, improving analysis without relying on external templates or telluric models.

## Contribution

The paper introduces wobble, an open-source Python tool that uses a convex optimization approach to simultaneously derive stellar and telluric spectra along with radial velocities from spectral data.

## Key findings

- Successfully recovered known exoplanet signals like 51 Pegasi b.
- Detected secular radial velocity changes in Barnard's Star.
- Produced high-quality composite stellar and telluric spectra.

## Abstract

In recent years, dedicated extreme-precision radial velocity (EPRV) spectrographs have produced vast quantities of high-resolution, high-signal-to-noise time-series spectra for bright stars. These data contain valuable information for the dual purposes of planet detection via the measured RVs and stellar characterization via the co-added spectra. However, considerable data analysis challenges exist in extracting these data products from the observed spectra at the highest possible precision, including the issue of poorly-characterized telluric absorption features and the common use of an assumed stellar spectral template. In both of these examples, precision-limiting reliance on external information can be sidestepped using the data directly. Here we propose a data-driven method to simultaneously extract precise RVs and infer the underlying stellar and telluric spectra using a linear model (in the log of flux). The model employs a convex objective and convex regularization to keep the optimization of the spectral components fast. We implement this method in wobble, an open-source python package which uses TensorFlow in one of its first non-neural-network applications to astronomical data. In this work, we demonstrate the performance of wobble on archival HARPS spectra. We recover the canonical exoplanet 51 Pegasi b, detect the secular RV evolution of the M dwarf Barnard's Star, and retrieve the Rossiter-McLaughlin effect for the Hot Jupiter HD 189733b. The method additionally produces extremely high-S/N composite stellar spectra and detailed time-variable telluric spectra, which we also present here.