Cyclic changes in dust-to-gas ratio

We discuss the time variation of the dust-to-gas mass ratio in spiral galaxies, using the multiphase model of interstellar medium. The typical timescale of the phase change of an interstellar gas is similar to 10(7-8) yr in spiral galaxies. Since the phase transition changes the filling factor of the cold gas where the dust growth occurs, the dust growth rate varies on that timescale. In order to examine the response of the dust-to-gas ratio to the phase transition, we construct a model of the time evolution of the dust-to-gas ratio. We adopt the three-phase model for the interstellar gas and the Ikeuchi-Tomita model for the mass exchange between the phases. According to the model, three types of solutions are possible: (1) all the gas is transformed to a hot gas; (2) a stable stationary state of three phases is realized; and (3) the filling factor of each phase cyclically changes. For the three types of solutions, the dust-to-gas ratio behaves as follows: for solution 1, almost all the dust is destroyed (the dust-to-gas ratio becomes similar to 0); for solution 2, the dust-to-gas ratio converges to a stationary state; and for solution 3, the dust-to-gas ratio varies cyclically In response to the phase transition. In the case of solution 3, the amplitude of the variation of the dust-to-gas ratio is large (nearly an order of magnitude) if the dust growth timescale is shorter than the phase transition timescale. This condition is easily satisfied in spiral galaxies. However, it is difficult for dwarf galaxies to realize the condition, because their small metallicity makes the dust growth timescale long.