Granulation on a quiet K dwarf: HD 166620 I. Spectral signatures as a function of line-formation temperature

TL;DR

This study targets granulation as a limiting RV noise source in extreme-precision RV measurements by observing the magnetically quiet K-dwarf HD 166620 with HARPS-N (and contemporaneously EXPRES). After identifying and removing a new instrumental signature linked to CCD illumination and fibre injection, the authors detect granulation using structure-function analysis and a one-component Gaussian Process with an aperiodic SHO kernel, obtaining a characteristic timescale of $43.5 \,\pm\, 16.9$ minutes and a granulation amplitude of $0.23 \,\pm\, 0.07$ m s$^{-1}$. By constructing temperature-sensitive RVs with two formation-depth bins using both ${ m CCF}_{T}$ and ${ m LBL}_{T}$ methods, they show granulation signals are present in both depth regimes, but the cooler bin (shallower layers) aligns more closely with predictions. The results highlight depth-dependent granulation signatures in a K-dwarf, offer a practical path to depth-resolved granulation diagnostics for EPRV, and emphasize the importance of correcting instrumental systematics in precision RV work.

Abstract

As Radial velocity (RV) spectrographs reach unprecedented precision and stability below 1 m/s, the challenge of granulation in the context of exoplanet detection has intensified. Despite promising advancements in post-processing tools, granulation remains a significant concern for the EPRV community. We present a pilot study to detect and characterise granulation using the High-Accuracy Radial-velocity Planet Searcher for the Northern hemisphere (HARPS-N) spectrograph. We observed HD166620, a K2 star in the Maunder Minimum phase, intensely for two successive nights, expecting granulation to be the dominant nightly noise source in the absence of strong magnetic activity. Following the correction for a newly identified instrumental signature arising from illumination variations across the CCD, we detected the granulation signal using structure functions and a one-component Gaussian Process (GP) model. The granulation signal exhibits a characteristic timescale of 43.65$\pm$15.8 minutes, within one $σ$, and a standard deviation of 22.9$\pm$0.77 cm/s, with in three $σ$ of the predicted value. By examining spectra and RVs as a function of line formation temperature , we investigated the sensitivity of granulation-induced RV variations across different photospheric layers. We extracted RVs from various photospheric depths using both the line-by-line (LBL) and cross-correlation function (CCF) methods to mitigate any extraction method biases. Our findings indicate that granulation variability is detectable in both temperature bins, with the cooler bins, corresponding to the shallower layers of the photosphere, aligning more closely with predicted values.

Figures (28)

• Figure 1: 141 intra-night pairs of 900-s HARPS-N RPS observations of HD 166620 secured between 100 minutes and 5 hours apart since 2012. These show statistically significant RMS velocity scatter, expected to be due to granulation, that increases with the lag between observations. The bifurcation in the RMS distribution is concerning, as we cannot establish any time dependency if it is instrumental, demanding immediate investigation. The grey squares in the background shows comparable pairs from the synthetic granulation time series mentioned in Section \ref{['sec:SF_GP_simulations']}. The teal squares represent corresponding pairs from solar HARPS-N data obtained on a spot-free clear day during activity minimum.
• Figure 2: Top: The contemporaneously acquired HARPS-N (black) and EXPRES (red) radial-velocity observations of HD 166620. Middle: Diagnostic ratios CCD counts/exposure-meter counts (dark blue) and SN60/SN30 (dark pink), plotted against Julian date of the HARPS-N observations. Both metrics display a striking resemblance, with measured correlation coefficients of 0.99 and 0.98 for nights 1 and 2, respectively. The airmass is shown in grey. Bottom: The residuals after subtracting the airmass from the ratios, revealing distinct structures. This suggests that the observed patterns are not solely attributable to the colour effect.
• Figure 3: Density plot showing relative flux variations in the 4x4 array of sub-regions used to characterise the CCD illumination. The 16 columns show the centred, whitened flux variations in the blocks.
• Figure 4: Optimal re-ordering of the columns of the left-singular matrix $\bm{U}$ shows the $\chi^2$ and BIC of the fit to the radial velocity as a function of the rank $k$ of the SVD reconstruction from the CCD illumination variations. This illustrates that the 4th and 7th principal components of the CCD illumination variations project most strongly onto the radial velocity.
• Figure 5: HARPS-N RVs are plotted as a function of Julian date of observation. The upper (blue) markers trace the velocities produced by the DRS. The middle (orange) sequence shows the projection of the RVs into a rank-4 SVD representation of the CCD illumination variations arising from fibre-injection instability. The bottom (green) markers trace the residual variation containing the astrophysical signal plus photon noise. The RVs are plotted with an offset for better illustration.