Can we detect long-period sub-Neptune progenitors using HRCCS with ELT/ANDES YJH band observations?

Ground-based high-resolution cross-correlation spectroscopy (HRCCS) has become a crucial tool to detect and/or characterize atmospheres of ultra-hot and hot-Jovian exoplanets, and more recently, warm sub-Neptunes as well. High-resolution spectrographs mounted on state-of-the-art future ground based telescopes, like the Extremely Large Telescope (ELT), will potentially extend the usage of this technique for detecting and characterizing the atmospheres of a wider variety of sub-Neptunes, super-Earths and potentially terrestrial exoplanets. In this context, we aim to study whether the HRCCS technique can be used to accurately retrieve the correct exoplanetary orbital parameters, corresponding to injected signals of the young, long-period sub-Neptunes V1298 Tau b and TOI-451 c, using the ANDES spectrograph that will be mounted at the ELT. For long-period exoplanets, the orbital velocity does not vary appreciably within the night of observation. Hence, this would presumably remove most of the exoplanetary signal during the detrending procedure before cross-correlation analysis. However, previous studies have shown that the presence of out-of-transit exposures during the detrending process is expected to have a positive effect on the detectability of the exoplanet signal, and we test this phenomenon in this study. We synthesise nights of observations of V1298 Tau b and TOI-451 c in transmission using the YJH band of ANDES. Then we use an HRCCS detrending and analysis pipeline to retrieve orbital parameters corresponding to an injected Doppler-shifted signal of the best fit spectrum obtained using HST+Spitzer and JWST observations (for the case of V1298 Tau b), and by assuming diverse C/O ratios for modelling the atmospheric composition (for TOI-451 c). We find that including a number of out-of-transit exposures in synthetic observations does indeed make it possible to confidently detect the atmospheres of both V1298 Tau b and TOI-451 c, with the observations ranging between 4-5 hours each. However, the usage of a reprocessing step is also essential before performing the cross-correlation analysis. Without transferring the proper effect of application of the detrending pipeline onto the template model, the obtained orbital parameters can be far off from the injected values or present less significant detections at the injected values. For the case of V1298 Tau b, we find that injection of a signal equivalent to that suggested by HST+Spitzer and JWST observations would make detections of H2O, H2S and CO amenable within a reasonable amount of observing time (< 10 hours) in the near-infrared. For the case of TOI-451 c, we should be able to both detect and differentiate between sub-solar and super-solar atmospheric C/O ratios within 18 hours of observing time in the near-infrared. Thus, the HRCCS technique will prove to be a vital tool to detect and catalogue the variety of young, long-period sub-Neptunes and their progenitors in the ELT era.