= Toomre marginal algebraic growth
{c}
{title2=$Q=1,\quad |k|=\kappa/c_s$}
At the marginal radial <wavenumber>, the <forced axisymmetric density mode with vortensity> has zero squared frequency. Its <mass density> amplitude is $C_0+C_1t-\Omega\Sigma_0^2q't^2$. Thus there is no exponential instability but nonzero conserved <vortensity> can force quadratic growth, and a homogeneous generalized mode can grow linearly. The spectral boundary $Q=1$ of the <Toomre stability criterion> must not be mistaken for boundedness of every initial-value solution.
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