TILARA: Template-Independent Line-by-line Algorithm for Radial velocity Analysis. I. Description of the code and application on a Sun-like star

Abstract

Precise radial velocities (RVs) are commonly derived through cross-correlation or template-matching methods, both of which rely on a reference spectrum that can introduce biases when the data are variable, contaminated, or sparsely sampled. Line-by-line methods offer an alternative way to compute RVs but generally still rely on template creation and therefore share its inherent limitations. We introduce TILARA, a template-independent, line-by-line RV extraction code designed to allow us to derive line-by-line RVs and to operate effectively even when spectral template construction is not recommended. While originally motivated by future PoET disk-resolved solar observations, TILARA has been built with the flexibility to work with different stellar spectral types and instruments. A curated list of individual absorption lines is used as a reference to automatically measure line centers with via Gaussian fitting with ARES. Then, using the reference lines list, and the lines measured with ARES on the spectra of the target star, TILARA computes the RVs and applies configurable outlier rejection through sigma-clipping or down-weighting methods. We tested different configurations of the code, RV uncertainty estimation methods, and line selection criteria. The code was applied to 520 ESPRESSO observations of the Sun-like star HD 102365 to evaluate its performance. TILARA was then tested against other RV extraction methods. Both in its sigma-clipping and its down-weighting mode, TILARA provided resulting RV time-series with similar standard deviation and error bars as the ones derived using existing methods that follow different approaches.

Figures (9)

• Figure 1: Flowchart of TILARA steps. Dark grey bubbles indicate computational steps, and light grey bubbles show intermediate inputs/outputs. The first two steps correspond to the work done with linesearcher and ARES before using TILARA, while the last two steps correspond to the work done by TILARA.
• Figure 2: Example of the telluric correction done with Molecfit applied to the solar ESPRESSO spectra. The dark violet spectrum shows the original observation, while the lilac spectrum displays the same observation after the removal of telluric H$_2$O, O$_3$ and O$_2$ features. Top panel: Full spectral range. Bottom panel: Zoomed-in wavelength range between 5871 and 5886 $\AA$.
• Figure 3: Distribution of the measured and derived properties of the final set of absorption lines used in the analysis. The panels show the depth, the $\sigma_{NMAD}/median$ values (computed as (1.4826 × MAD)/median) for depth, EW, FWHM, and the $\sigma_{NMAD}$ values (computed as 1.4826 × MAD) of the RV, as well as the standard deviation ($\sigma$) of the RV measurements across observations. Vertical dashed lines indicate the reference thresholds adopted during the line-selection process (0 and 1 for depth, 0.1 for the $\sigma_{NMAD}/median$ of the depth, and 0.3 for the other parameters).
• Figure 4: Top: Part of the spectrum of one observation, with the reference line centers (from the solar line list) marked as dashed lines and the adopted line windows shown in purple. The observed line centers are slightly shifted relative to the solar reference due to differences in convective blueshift and gravitational redshift between the Sun and HD 102365. Middle: First derivative of the flux ($dF/d\lambda$), used to locate the extrema that define the window limits. Bottom: Second derivative ($d^{2}F/d\lambda^{2}$), used to confirm the line minima ($d^{2}F/d\lambda^{2} < 0$). The master spectrum includes 2738 lines.
• Figure 5: Summary of the down-weighting procedures tested for TILARA (for a detailed description of them see Appendix \ref{['down-weight-tests']}). Top left panel: Distribution of the RV values (mean-subtracted and $\sigma$-normalized) per observation, together with the best-fit Gaussian (blue) and Lorentzian (red) models. Top right panel: Distribution of the RV standard deviation per line, showing the histogram (gray) and the corresponding truncated Gaussian and truncated Lorentzian fits. Bottom left panel: Residual RV time-series obtained by subtracting the RVs derived using a Lorentzian fit from those derived using a Gaussian fit (mean-subtracted and $\sigma$-normalized) per observation. The residuals are centered around zero with comparable scatter. Bottom right panel: Residual RV time-series obtained by subtracting the RVs derived using a truncated Lorentzian fit from those derived using a truncated Gaussian fit when modeling the distribution of the RV standard deviation per line. The residuals are centered around zero with comparable scatter. A vertical black line marks 27 June 2019, indicating the transition from ESPRESSO18 to ESPRESSO19 on both bottom panels.