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Motivated by the development of high-dispersion spectrographs in themid-infrared (MIR) range, we study their application to the atmosphericcharacterization of nearby non-transiting temperate terrestrial planets aroundM-type stars. We examine the detectability of CO$_2$, H$_2$O, N$_2$O, and O$_3$in high-resolution planetary thermal emission spectra at 12-18 $\mu $m assumingan Earth-like profile and a simplified thermal structure. The molecular linewidth of such planets can be comparable to or broader than the Doppler shiftdue to the planetary orbital motion. Given the likely difficulty in knowing thehigh-resolution MIR spectrum of the host star with sufficient accuracy, wepropose to observe the target system at two quadrature phases and extract thedifferential spectra as the planetary signal. In this case, the signals can besubstantially suppressed compared with the case where the host star spectrum isperfectly known, as some parts of the spectral features do not remain in thedifferential spectra. Despite this self-subtraction, the CO$_2$ and H$_2$Ofeatures of nearby ($\lesssim $ 5~pc) systems with mid-/late-M host stars wouldbe practical with a 6.5-meter-class cryogenic telescope, and orbitalinclination could also be constrained for some of them. For CO$_2$ and N$_2$Oin a 1~bar Earth-like atmosphere, this method would be sensitive when themixing ratio is 1-10$^3$ ppm. The detectability of molecules except O$_3$ isnot significantly improved when the spectral resolution is higher than$\mathcal{R}\gtrsim 10,000$, although the constraint on the orbital inclinationis improved. This study provides some benchmark cases useful for assessing thevalue of MIR high-resolution spectroscopy in terms of characterization ofpotentially habitable planets.

Detecting Atmospheric Molecules of Temperate Terrestrial Exoplanets using High-Resolution Spectroscopy in the Mid Infrared Domain