Accretion-induced overstability of density waves in a self-gravitating disk

Abstract

A two-component differentially rotating disk of self-gravitating particles is considered in the hydrodynamical framework. This system is shown to sustain two pairs of density waves, corresponding to the familiar Jeans modes and an acoustic type of modes (similar to ion-acoustic modes in plasmas). As a result of mass and momentum transfer from the gaseous to the stellar component (an accretion process), the acoustic modes suffer a strong damping, whereas the Jeans modes which were oscillatory, now become overstable provided the thermal velocity of stars is larger than that of gaseous component. The waves with frequencies near the corotation have a rather large growth rate. This amplification can explain the maintenance of spiral structure and a selective amplification could even determine the wave-frequency (or pattern velocity).