MINDS. The DR Tau disk I: Combining JWST-MIRI data with high-resolution CO spectra to characterise the hot gas

The MRS mode of the JWST-MIRI instrument has been shown to be a powerful tool to characterise the molecular gas emission of the inner region of planet-forming disks. Investigating their spectra allows us to infer the composition of the gas in these regions and, subsequently, the potential atmospheric composition of the forming planets. We present the JWST-MIRI observations of the compact T-Tauri disk, DR Tau, which are complemented by ground-based, high spectral resolution ($R CO ro-vibrational observations. The aim of this work is to investigate the power of extending the JWST-MIRI CO observations with complementary, high-resolution, ground-based observations acquired through the SpExoDisks database, as JWST-MIRI's spectral resolution ($R is not sufficient to resolve complex CO line profiles. In addition, we aim to infer the excitation conditions of other molecular features present in the JWST-MIRI spectrum of DR Tau and link those with CO The archival complementary, high-resolution CO ro-vibrational observations were analysed with rotational diagrams. We extended these diagrams to the JWST-MIRI observations by binning and convolution with JWST-MIRI's pseudo-Voigt line profile. In parallel, local thermal equilibrium (LTE) 0D slab models were used to infer the excitation conditions of the detected molecular species. Various molecular species, including CO CO_2 HCN and C_2H_2 are detected in the JWST-MIRI spectrum of DR Tau, with H_2O being discussed in a subsequent paper. The high-resolution observations show evidence for two CO components: a broad component (full width at half maximum of FWHMsim 33.5 km s$^ $) tracing the Keplerian disk and a narrow component (FWHMsim 11.6 km s$^ $) tracing a slow disk wind. The rotational diagrams yield CO excitation temperatures of $T K. Consistently lower excitation temperatures are found for the narrow component, suggesting that the slow disk wind is launched from a larger radial distance. In contrast to the ground-based observations, much higher excitation temperatures are found if only the high-$J$ transitions probed by JWST-MIRI are considered in the rotational diagrams. Additional analysis of the CO line wings suggests a larger emitting area than inferred from the slab models, hinting at a misalignment between the inner ($i and the outer disk ($i Compared to CO we retrieved lower excitation temperatures of $T K for CO_2 HCN and C_2H_2 We show that complementary, high-resolution CO ro-vibrational observations are necessary to properly investigate the excitation conditions of the gas in the inner disk and they are required to interpret the spectrally unresolved JWST-MIRI CO observations. These additional observations, covering the lower-$J$ transitions, are needed to put better constraints on the gas physical conditions and they allow for a proper treatment of the complex line profiles. A comparison with JWST-MIRI requires the use of pseudo-Voigt line profiles in the convolution rather than simple binning. The combined high-resolution CO and JWST-MIRI observations can then be used to characterise the emission, in addition to the physical and chemical conditions of the other molecules with respect to CO . The inferred excitation temperatures suggest that CO originates from the highest atmospheric layers close to the host star, followed by HCN and C_2H_2 which emit, together with CO from slightly deeper layers, whereas the CO_2 emission originates from even deeper inside or further out of the disk.