  Planets with non-zero obliquity and/or orbital eccentricity experience
seasonal variations of stellar irradiation at local latitudes. The extent of
the atmospheric response can be crudely estimated by the ratio between the
orbital timescale and the atmospheric radiative timescale. Given a set of
atmospheric parameters, we show that this ratio depends mostly on the stellar
properties and is independent of orbital distance and planetary equilibrium
temperature. For Jupiter-like atmospheres, this ratio is $\ll1$ for planets
around very-low-mass M dwarfs and $\gtrsim1$ when the stellar mass is greater
than about 0.6 solar mass. Complications can arise from various factors,
including varying atmospheric metallicity, clouds, and atmospheric dynamics.
Given the eccentricity and obliquity, the seasonal response is expected to be
systematically weaker for gaseous exoplanets around low-mass stars and stronger
for those around more massive stars. The amplitude and phase lag of atmospheric
seasonal variations as a function of host stellar mass are quantified by
idealized analytic models. At the infrared emission level in the photosphere,
the relative amplitudes of thermal flux and temperature perturbations are
negligible, and their phase lags are closed to $-90^{\circ}$ for Jupiter-like
planets around very-low-mass stars. The relative amplitudes and phase lags
increase gradually with increasing stellar mass. With a particular stellar
mass, the relative amplitude and phase lag decrease from low to high infrared
optical depth. We also present numerical calculations for a better illustration
of the seasonal behaviors. Lastly, we discuss implications for the atmospheric
circulation and future atmospheric characterization of exoplanets in systems
with different stellar masses.
