Separating planetary reflex Doppler shifts from stellar variability in the wavelength domain

Abstract

Stellar magnetic activity produces time-varying distortions in the photospheric line profiles of solar-type stars. These lead to systematic errors in high-precision radial-velocity measurements, which limit efforts to discover and measure the masses of low-mass exoplanets with orbital periods of more than a few tens of days. We present a new data-driven method for separating Doppler shifts of dynamical origin from apparent velocity variations arising from variability-induced changes in the stellar spectrum. We show that the autocorrelation function (ACF) of the cross-correlation function used to measure radial velocities is effectively invariant to translation. By projecting the radial velocities on to a subspace labelled by the observation identifiers and spanned by the amplitude coefficients of the ACF’s principal components, we can isolate and subtract velocity perturbations caused by stellar magnetic activity. We test the method on a 5-year time sequence of 853 daily 15-minute observations of the solar spectrum from the HARPS-N instrument and solar-telescope feed on the 3.58-m Telescopio Nazionale Galileo. After removal of the activity signals, the heliocentric solar velocity residuals are found to be Gaussian and nearly uncorrelated. We inject synthetic low-mass planet signals with amplitude K = 40 cm s−1 into the solar observations at a wide range of orbital periods. Projection into the orthogonal complement of the ACF subspace isolates these signals effectively from solar activity signals. Their semi-amplitudes are recovered with a precision of ∼ 6.6 cm s−1, opening the door to Doppler detection and characterization of terrestrial-mass planets around well-observed, bright main-sequence stars across a wide range of orbital periods.

The EXPRES Stellar Signals Project II. State of the Field in Disentangling Photospheric Velocities

“…SCALPELS uses PCA on the auto-correlation function of the CCFs while the FDPCA method implements PCA on the Fourier series of the RV and indicator time series. Note that while there is a description of a leave-one-out-framework with SCALPELS in Collier Cameron et al (2021), no crossvalidation framework is implemented for the results submitted here.…”

“…This introduction of a GP model introduces relevant data requirements to the method, such as dense-sampling in time. More information about both implementations of SCALPELS can be found in Collier Cameron et al (2021) as well as Appendix B.1.…”

TOI-1634 b: An Ultra-short-period Keystone Planet Sitting inside the M-dwarf Radius Valley

“…We note that we did make additional attempts at more complete RV models that included a treatment of evolving stellar activity. Our first attempt to assess the impact of stellar activity was to use the SCALPELS methodology of Collier Cameron et al (2021). In summary, SCALPELS attempts to distinguish dynamically produced RV variations from activityinduced distortions on each spectrum's CCF by projecting the RV time series onto the 10 highest variance principal components of the autocorrelation function of each CCF.…”

FIESTA – disentangling stellar variability from exoplanets in the Fourier domain

“…Collier Cameron et al (2021) introduced SCALPELS to study the CCF variability using the autocorrelation function (ACF) of the cross-correlation function of each spectrum with a mask. SCALPELS was able to reduce the RMS of daily averaged HARPS-N solar spectra from 1.76 m/s to 1.25 m/s, a 29% reduction in the RV scatter.…”

“…SCALPELS was able to reduce the RMS of daily averaged HARPS-N solar spectra from 1.76 m/s to 1.25 m/s, a 29% reduction in the RV scatter. In order to make a more direct comparison to this result, We conducted a preliminary analysis of the same HARPS-N solar observations as Collier Cameron et al (2021). When applied to the 5 year time-series, ΦESTA reduced the weighted daily RV RMS to 1.09 m/s using the same approach as in Section 5.6.…”