The CARMENES search for exoplanets around M dwarfs : Understanding the wavelength dependence of radial velocity measurements

TL;DR

This study leverages the full CARMENES GTO data set to quantify how radial-velocity measurements of M dwarfs depend on wavelength through the chromatic index CRX. By defining and analyzing CRX, its gradient and length, and by correlating it with a broad suite of activity indicators, the authors identify a ~17% subset of stars with significant CRX–RV correlations and demonstrate that subtracting the CRX-predicted RV can reduce RV rms by up to ~4x, enabling the detection of lower-mass planets. The work links CRX behavior to stellar parameters, rotation, magnetic fields, and BIS, and discusses implications for planet detection thresholds and surface mapping, while highlighting the importance of sampling and the limitations of NIR RVs in this context. Overall, CRX provides a powerful, wavelength-dependent activity diagnostic that enhances the search for low-mass rocky planets around active M dwarfs. The updated convective turnover time scaling for M dwarfs improves the Rossby-number framework used to contextualize activity. These findings underscore the practical value of wavelength-resolved RV analyses for mitigating stellar activity in exoplanet surveys.

Abstract

Context. Current exoplanet surveys are focused on detecting small exoplanets orbiting in the liquid-water habitable zones of their host stars. Despite the recent significant advancements in instrumental developments, the current limitation in detecting these exoplanets is the intrinsic variability of the host star itself. Aims. Our aim is to use the full CARMENES guaranteed time observations (GTO) data set spanning more than 8 years of observations of over 350 stars to investigate the wavelength dependence of high-precision radial velocities (RV), as stellar activity features should exhibit a wavelength dependence while the RV variation due to an orbiting planet will be wavelength independent. Methods. We use the chromatic index (CRX) to quantify the slope of the measured RVs as a function of logarithmic wavelength. We investigate the dependence of the CRX in the full CARMENES GTO sample on 24 stellar activity indices in the visible and near-infrared channels of the CARMENES spectrograph and each star's stellar parameters. We also present an updated convective turnover time scaling for the calculation of the stellar Rossby number for M dwarfs. Results. Our results show that approximately 17\% of GTO stars show a strong or a moderate correlation between CRX and RV. We can improve the measured RVs by a factor of up to nearly 4 in rms by subtracting the RV predicted by the CRX-RV correlation from the measured RVs. Mid M dwarfs with moderate rotational velocities, moderate CRX-gradients and quasi-stable activity features have the best rms improvement factors. Conclusions. We conclude that the CRX is a powerful diagnostic in mitigation of stellar activity and the search for low mass rocky planets.

Figures (22)

• Figure 1: Illustration of the RV variation with wavelength, where the central wavelength is given for each order. Shown are the same data as in Figure \ref{['fig:EVLac_CRX']}, with the steepest positive slope shown by red points. The green line indicates the slope of these points, which is the CRX-index for each individual spectrum. The weighted RV measurement is shown by the purple line. The wavelength spacing is logarithmic.
• Figure 2: Illustration of the behaviour of the CARMENES visible channel CRX for the mid-M dwarf EV Lac. Top Left: Variation of RV as a function of wavelength (spacing is logarithmic). The CRX-index is the slope of RV vs log($\lambda$) for each spectrum. A total of 10 CARMENES spectra are shown covering approximately one stellar rotation. The upper and lower boundaries are the fits to the most positive and negative RV values. Top right: The CRX-gradient, illustrating the CRX-index as a function of mean RV. Bottom Left and Bottom Right: CRX vs rotation phase and RV vs rotation phase illustrating the anti-correlation of CRX-index (i.e. the negative CRX-gradient shown in the top right panel). The plotted points in each panel are colour coded according to stellar rotation phase.
• Figure 3: Revised photospheric to spot temperature. Original photometric data points from berdyugina05starspots are shown as light blue open circles. Doppler imaging values are shown as filled red circles where the values are taken from Table \ref{['tab:temp_contrast_DI']} and the values for the Sun are shown as two large open light blue circles with a temperature of 5800 K.
• Figure 4: Spectral type distribution (left panel) and the distribution of $v \sin i$ of the CRX-all sample, coloured in blue. Also shown are all of the CARMENES GTO stars with more than 25 observations as indicated by shaded grey bars.
• Figure 5: Distribution of CRX-length for the CARMENES GTO sample (light grey) and the CRX-all sample (navy). For clarity, the CRX-length values of the CARMENES GTO sample are only shown up to a value of 3000 m s$^{-1}$