A Hermite-Gaussian Based Radial Velocity Estimation Method
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As the first successful technique used to detect exoplanets orbiting distant stars, the Radial Velocity Method aims to detect a periodic Doppler shift in a star's spectrum. We introduce a new, mathematically rigorous, approach to detect such a signal that accounts for functional relationships of neighboring wavelengths, minimizes the role of wavelength interpolation, accounts for heteroskedastic noise, and easily allows for statistical inference. Using Hermite-Gaussian functions, we show that the problem of detecting a Doppler shift in the spectrum can be reduced to linear regression in many settings. A simulation study demonstrates that the proposed method is able to accurately estimate an individual spectrum's radial velocity with precision below 0.3 m/s. Furthermore, the new method outperforms the traditional Cross-Correlation Function approach by reducing the root mean squared error up to 15 cm/s. The proposed method is also demonstrated on a new set of observations from the EXtreme PREcision Spectrometer (EXPRES) for the star 51 Pegasi, and successfully recovers estimates that agree well with previous studies of this planetary system. Data and Python3 code associated with this work can be found at https://github.com/parkerholzer/hgrv_method. The method is also implemented in the open source R package rvmethod.
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