  Using the linearized Boltzmann equation, we investigate how grooves carved in
the phase space of a half-mass Mestel disc can trigger the vigorous growth of
two-armed spiral eigenmodes. Such grooves result from the collisional dynamics
of a disc subject to finite-N shot noise, as swing-amplified noise patterns
push stars towards lower-angular momentum orbits at their inner Lindblad
radius. Supplementing the linear theory with analytical arguments, we show that
the dominant spiral mode is a cavity mode with reflections off the forbidden
region around corotation and off the deepest groove. Other subdominant modes
are identified as groove modes. We provide evidence that the depletion of
near-circular orbits, and not the addition of radial orbits, is the crucial
physical ingredient that causes these new eigenmodes.
  Thus, it is possible for an isolated, linearly stable stellar disc to
spontaneously become linearly unstable via the self-induced formation of
phase-space grooves through finite-N dynamics. These results may help explain
the growth and maintenance of spiral patterns in real disc galaxies.
