FIESTA II. Disentangling stellar and instrumental variability from exoplanetary Doppler shifts in Fourier domain

The radial velocity (RV) detection of exoplanets is challenged by stellar spectroscopic variability that can mimic the presence of planets and by instrumental instability that can further obscure the detection. Both stellar and instrumental changes can distort the spectral line profiles and be misinterpreted as apparent RV shifts. We present an improved FourIEr \textit{phase} SpecTrum Analysis (FIESTA a.k.a. $\mathit{\phi}$ESTA) to disentangle apparent velocity shifts due to a line deformation from a true Doppler shift. $\mathit{\phi}$ESTA projects stellar spectrum's cross correlation function (CCF) onto a truncated set of Fourier basis functions. Using the amplitude and phase information from each Fourier mode, we can trace the line variability at different CCF width scales to robustly identify and mitigate multiple sources of RV contamination. For example, in our study of the 3 years of HARPS-N solar data, $\mathit{\phi}$ESTA reveals the solar rotational effect, the long-term trend due to solar magnetic cycle, instrumental instability and apparent solar rotation rate changes. Applying a multiple linear regression model on $\mathit{\phi}$ESTA metrics, we reduce the weighted rms noise from 1.89 m/s to 0.98 m/s. In addition, we observe a $\sim$3 days lag in the $\mathit{\phi}$ESTA metrics, similar to the findings from previous studies on BIS and FWHM.