The mystery of water in the atmosphere of $\tau$ Bo\"otis b continues: insights from revisiting archival CRIRES observations

The chemical abundances of gas-giant exoplanet atmospheres hold clues to the formation and evolution pathways that sculpt the exoplanet population. Recent ground-based high-resolution spectroscopic observations of the non-transiting hot Jupiter $\tau$ Bo\"otis b from different instruments have resulted in a tension on the presence of water vapour in the planet's atmosphere, which impact the planet's inferred C/O and metallicity. To investigate this, we revisit the archival CRIRES observations of the planet's dayside in the wavelength range 2.28 to 2.33 $\mu$m. We reanalyse them using the latest methods for correcting stellar and telluric systematics, and free-chemistry Bayesian atmospheric retrieval. We find that a spurious detection of CH$_{4}$ can arise from inadequate telluric correction. We confirm the detection of CO and constrain its abundance to be near solar $\log_{10}(\mathrm{CO})$ = -3.44$^{+1.63}_{-0.85}$ VMR. We find a marginal evidence for H$_{2}$O with $\log_{10}(\mathrm{H_{2}O})$ = -5.13$^{+1.22}_{-6.37}$ VMR. This translates to super solar C/O (0.95$^{+0.06}_{-0.31}$), marginally sub-solar metallicity (-0.21 $^{+1.66}_{-0.87}$). Due to the relatively large uncertainty on H$_{2}$O abundance, we cannot confidently resolve the tension on the presence of H$_{2}$O and the super-solar atmospheric metallicity of $\tau$ Bo\"otis b. We recommend further observations of $\tau$ Bo\"otis b in the wavelength ranges simultaneously covering CO and $\mathrm{H_{2}O}$ to confirm the peculiar case of the planet's super-solar C/O and metallicity.