Introduction

There is growing evidence for circumstellar discs associated with young stellar objects (YSOs). Motivated by observational evidence suggesting that these discs produce significant luminosity, LD ∼ L⋆, and have moderate masses, MD ∼ M⋆, (Adams, Lada & Shu 1988), we explore the possibility that the accretion mechanism ultimately owes its origin to the growth of spiral gravitational instabilities. As a start, we study the growth and structure of linear, global, gravitational disturbances in star/disc systems.

The physics of m = 1 modes

For simplicity, we take the unperturbed discs to be infinitesimally thin and in centrifugal equilibrium; we characterize the surface density and temperature profiles in the disc as power-laws in radial distance from the star. Since the potential well of the star dominates that of the disc everywhere except near the disc's outer edge, the rotation curve is nearly Keplerian throughout most of the disc's radial extent.

Our study concentrates on modes with azimuthal wave number m = 1, since these modes can be global in extent and may also be the most difficult modes to suppress in unstable protostellar discs. Modes with m = 1 correspond to elliptic streamlines (i.e. eccentric particle orbits), which play a unique role in Keplerian potentials, a fundamental point explicitly recognized by Kato (1983). In an exactly Keplerian potential, circular streamlines of zero pressure are neutrally stable to kinematic perturbations that make them ellipses.