  Motivated by the development of high-dispersion spectrographs in the
mid-infrared (MIR) range, we study their application to the atmospheric
characterization of nearby non-transiting temperate terrestrial planets around
M-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 $m assuming
an Earth-like profile and a simplified thermal structure. The molecular line
width of such planets can be comparable to or broader than the Doppler shift
due to the planetary orbital motion. Given the likely difficulty in knowing the
high-resolution MIR spectrum of the host star with sufficient accuracy, we
propose to observe the target system at two quadrature phases and extract the
differential spectra as the planetary signal. In this case, the signals can be
substantially suppressed compared with the case where the host star spectrum is
perfectly known, as some parts of the spectral features do not remain in the
differential spectra. Despite this self-subtraction, the CO$_2$ and H$_2$O
features of nearby ($\lesssim $ 5~pc) systems with mid-/late-M host stars would
be practical with a 6.5-meter-class cryogenic telescope, and orbital
inclination could also be constrained for some of them. For CO$_2$ and N$_2$O
in a 1~bar Earth-like atmosphere, this method would be sensitive when the
mixing ratio is 1-10$^3$ ppm. The detectability of molecules except O$_3$ is
not significantly improved when the spectral resolution is higher than
$\mathcal{R}\gtrsim 10,000$, although the constraint on the orbital inclination
is improved. This study provides some benchmark cases useful for assessing the
value of MIR high-resolution spectroscopy in terms of characterization of
potentially habitable planets.

Earth and Planetary Astrophysics