Mitigating stellar radial velocity jitter using orthogonal activity indices and a time-aware neural network
Despite recent advances in the precision of high-resolution spectrographs, the detection of Earth-like exoplanets is still limited by the effects of stellar activity, which introduce radial velocity variations at the metre-per-second level or larger. We present a framework to disentangle stellar effects from planetary signals by exploiting high-order distortions of the cross-correlation function (CCF; a measure of the average spectral line profile), thus moving beyond the commonly applied Gaussian fit approximation. We decomposed the CCF using a Gram-Schmidt orthogonal basis function, enabling the separation of pure line shifts from line-shape distortions. To model activity-induced contributions to the radial velocities, we have developed a time-aware convolutional attention network dubbed CANSTAR. This network was trained on synthetic line-shape distortion coefficients produced with the realistic stellar simulator StarSim to learn the temporal evolution of stellar activity features. We validated our framework using HARPS and CARMENES observations of two active stars, $ε$ Eridani and TZ Arietis. The network effectively mitigates stellar activity, reducing the radial velocity RMS to 52.5 % and 62.4 % of the uncorrected variability, respectively. This correction enables a more precise determination of the orbital parameters of TZ Arietis b compared to a Gaussian process regression. Our results demonstrate that neural networks that incorporate the temporal context can outperform state-of-the-art methods in complex activity regimes. Future improvements on StarSim that will allow us to train CANSTAR on 3D magnetohydrodynamic spectra and more complex instrumental modelling are expected to bridge the performance gap between synthetic and real data, offering a robust pathway towards detecting Earth-mass planets around Sun-like stars.