Thermal light-curve analysis is a powerful approach to probe the thermal structures of exoplanetary atmospheres, which are greatly influenced by the planetary obliquity and eccentricity. Here we investigate the thermal light curves of eccentric-tilted exoplanets across various radiative timescales, eccentricities, obliquities, and viewing geometries using results of shallow-water simulations presented in Ohno $&$ Zhang (2019). We also achieve an analytical theory of the thermal light curve that can explain general trends in the light curves of tilted exoplanets. For tilted planets in circular orbits, the orbital phase of the flux peak is largely controlled by either the flux from the hot spot projected onto the orbital plane or the pole heated at the summer solstice, depending on the radiative timescale $tau_{rm rad}$, planetary day $P_{rm orb}$, and obliquity $theta$. We find that tilted planets potentially produce the flux peak after the secondary eclipse when obliquity is $theta$ > 90 deg for the hot regime $tau_{rm rad}<P_{rm rot}$, or $theta>18$ deg for the cool regime ${tau}_{rm rad} > P_{rm rot}$. For tilted planets in eccentric orbits, the shape of the light curve is considerably influenced by the heating at the periapse. The flux peak occurring after the secondary eclipse can be used to distinguish tilted planets from nontilted planets when the periapse takes place before the secondary eclipse. Our results could help to constrain exoplanet obliquities in future observations.
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