Exploring the ultrahot Neptune LTT 9779 b with CRIRES+. Non-detection of helium transmission spectra and detection of H$_2$O on the dayside
Ultrahot Neptunes reside in the most extreme irradiation regime of the hot Neptune desert and remain challenging targets for atmospheric characterization because of their low planet-to-star flux ratios. We present high-resolution transit and dayside thermal emission spectroscopy of the ultrahot Neptune LTT 9779 b obtained with CRIRES$^+$, to probe atmospheric escape and dayside molecular emission. No significant absorption is detected in the metastable He I $λ1083$ nm triplet during transit, yielding a $3σ$ upper limit of 0.45% on the excess helium absorption depth and supporting previous non-detections that suggest weak ongoing atmospheric escape. For the dayside emission spectra in the $K$ band, our cross-correlation analysis reveals an $\mathrm{H_2O}$ absorption signal and a tentative $\mathrm{CO}$ feature, with the combined signal reaching a detection significance of $4.8σ$. Both the CRIRES$^+$ and previous JWST data favor a non-inverted temperature structure, providing no evidence of a thermal inversion on the planetary dayside. We further perform a joint atmospheric retrieval combining the CRIRES$^+$ high-resolution spectra with JWST/NIRISS SOSS secondary-eclipse observations. The joint retrieval yields a low $\mathrm{H_2O}$ abundance, while the $\mathrm{CO}$ abundance remains weakly constrained. The inferred planetary equatorial rotational velocity, $v_{\rm eq}=4.9^{+4.4}_{-3.0}~\mathrm{km\,s^{-1}}$, is consistent within $1σ$ with the synchronous rotation velocity expected for a tidally locked planet ($\sim2.8~\mathrm{km\,s^{-1}}$). However, the large uncertainties prevent us from placing strong constraints on the planet's rotation state. Future phase-resolved CRIRES$^+$ observations with broader orbital-phase coverage and higher signal-to-noise ratios would improve the abundance constraints and probe the atmospheric dynamics of this rare ultrahot Neptune.