Mid-IR Water-Vapor Seeing: Implications for ELT/METIS High-Contrast Imaging from VLTI Data
Direct imaging and characterization of rocky exoplanets remains one of the central challenges in exoplanetary science. The mid-infrared (mid-IR) offers a favorable high-contrast imaging (HCI) regime, as the planet-star contrast is more moderate than at shorter wavelengths. However, mid-IR observations with extremely large ground-based telescopes (ELTs) are strongly affected by spatio-temporal fluctuations in atmospheric water vapor (WV), which introduce chromatic wavefront errors that are largely invisible to adaptive optics systems operating at shorter wavelengths. This poses a significant challenge for mid-IR HCI instruments such as METIS, which aims to detect thermal emission from rocky exoplanets in the $N$-band (8--13 $μ$ m). To quantify WV-induced wavefront errors, we analyze $K$-band fringe-tracker data from the GRAVITY instrument at the VLTI and derive the optical path difference between group-delay and phase-delay measurements. This difference provides a direct measure of the differential WV column density ($Σ$) above the telescopes. We examine the dependence of the RMS differential WV column density ($σ_Σ$) on precipitable water vapor (PWV), airmass, seeing, and wind speed across multiple VLTI configurations. Among these parameters, PWV shows the strongest correlation with $σ_Σ$. We further explore the influence of the vertical PWV distribution on this relationship. Next, we use power-spectral-density analysis to quantify how increasing PWV modulates $Σ$ variability. The wavefront error associated with this phenomenon on ELT scale is approximately 15~nm RMS in the $L$-band and 175~nm RMS in the $N$-band, relative to the $K$-band. These results provide a quantitative framework for assessing and mitigating atmospheric WV effects in next-generation mid-IR HCI instruments.