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Excitation and propagation of waves in a thermally stratified disk with anarbitrary vertical temperature profile are studied. Previous analytical studiesof three-dimensional waves had been focused on either isothermal or polytropicvertical disk structures. However, at the location in a protoplanetary diskwhere the dominant heating source is stellar irradiation, the temperaturegradient may become positive in the vertical direction. We extend the analysisto study the effects of the vertical temperature structure on the waves thatare excited at the Lindblad resonances. For a hotter disk atmosphere, the$f$-mode contributes less to the torque and remains confined near the midplaneas it propagates away from the resonances. On the other hand, the excitation ofthe $g$-modes is stronger. As they propagate, they channel to the top of diskatmosphere and their group velocities decrease. The differences compared toprevious studies may have implications in understanding the wave dynamics in arealistic disk structure.

The Effect of Vertical Temperature Gradient on the Propagation of Three-dimensional Waves in a Protoplanetary Disk