Four HD 209458 b transits through CRIRES+: Detection of H$_2$O and non-detections of C$_2$H$_2$, CH$_4$, and HCN

HD 209458 b is one of the most studied exoplanets to date. Despite this, atmospheric characterisation studies yielded inconsistent species detections and abundances. Values reported for the C/O ratio range from 0.1 to 1.0. Of particular interest is the simultaneous detection of H2O and HCN reported by some studies using high-resolution ground-based observations, which would require the atmospheric C/O ratio to be fine-tuned to a narrow interval around 1. HCN has however not been detected from recent space-based observations. We aim to provide an independent study of HD 209458 b's atmosphere with high-resolution observations, in order to infer the presence of several species, including H2O and HCN. We observed four primary transits of HD 209458 b at a high resolution (R=92000) with CRIRES+ in the near infrared (band H, 1.4--1.8 um). After reducing the data with pycrires, we prepared the data using the SysRem algorithm and performed a cross-correlation (CCF) analysis of the transmission spectra. We also compared the results with those obtained from simulated datasets constructed by combining the Exo-REM self-consistent model with the petitRADTRANS package. Combining the four transits, we detect H2O with a signal-to-noise CCF metric of 8.7. This corresponds to a signal emitted at $K_p=151.3^{+31.1}_{-23.4}$ km/s and blueshifted by $-6^{+1}_{-2}$ km/s, consistent with what is expected for HD 209458 b. We do not detect any other species among C2H2, CH4, CO, CO2, H2S, HCN, and NH3. Comparing this with our simulated datasets, this result is consistent with a C/O ratio of 0.1 and an opaque cloud top pressure of 50 Pa, at a 3 times solar metallicity. This would also be consistent with recent JWST observations. However, none of the simulated results obtained with a bulk C/O ratio of 0.8, a value suggested by previous studies using GIANO-B and CRIRES, are consistent with our observations.