Abstract:  The radial velocity detection of exoplanets is complicated by stellar spectroscopic variability that can mimic the presence of planets.  Of the numerous processes that contribute to stellar variability, stellar activity is particularly concerning, since the stellar rotation period and the active region evolution timescale are comparable to the orbit periods of common exoplanets. Stellar activity introduces additional inhomogeneities in the surface brightness of the stellar surface. These deform the spectral line profiles and can be misinterpreted as apparent radial velocity shifts.   

 

Zhao & Tinney (2019) proposed the method of FourIEr phase SpecTrum Analysis (FIESTA or ΦESTA) to disentangle apparent radial velocity shifts due to a line deformation from a true Doppler shift by using the phase information from the Fourier transform of stellar spectrum’s cross correlation function (CCF). We revisit the ΦESTA method and formulate the theoretical underpinning in terms of the discrete Fourier transform, now incorporating both the amplitude and the phase information in an effort to preserve more of the spectral information encoded in the CCF line profile.  

 

ΦESTA metrics show strong correlations with the apparent RVs induced by sunspots in the SOAP 2.0 simulations. We apply ΦESTA to HARP-N solar observations and demonstrate that ΦESTA metrics are capable of identifying apparent RV variations due to both stellar and instrumental sources.  Applying a simple multi-linear regression model to ΦESTA metrics reduces the rms of apparent RV variations in HARP-N solar observations from 1.73 m/s to 1.05 m/s. 

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