Stability of a finite disc under the influence of a spherical halo

We have studied the stability of finite gaseous discs, against large-scale perturbations, under the influence of spherical, massive haloes. A surface-density distribution consistent with the observed spiral-tracer profiles in disc galaxies is considered for the disc. We find that growing eigenmodes with both ‘trailing’ and ‘leading’ spirals exist in ‘cold’ discs for a wide range of values of the halo mass and its radius. The amplification rates of the unstable modes reduce as the ratio of the mass of the halo to the mass of the disc is increased. A uniform halo is not very effective towards stabilizing the disc against these modes. The results from the present study are consideredvis-a-vis previous studies on the global modes of self-gravitating discs.