Renewal of Transient Spiral Modes in Disk Galaxies
  Spiral structure in disk galaxies could arise from transient modes that
create conditions conducive for their regeneration; this is the proposal of
Sellwood and Carlberg, based on simulations of stellar disks. The linear
response of an axisymmetric stellar disk, to an adiabatic non-axisymmetric
transient mode, gives a final distribution function (DF) that is equal to the
initial DF everywhere in phase space, except at the Lindblad and corotation
resonances where the final DF is singular. We use the nonlinear theory of
adiabatic capture into resonance to resolve the singularities and calculate the
finite changes in the DF. These take the form of axisymmetric "scars"
concentrated around resonances, whose DFs have simple general forms. Global
changes in the physical properties are explored for a cool Mestel disk: we
calculate the DFs of scars, and estimate the changes in the disk angular
momentum, surface density and orbital frequencies leading to shifts of
resonances. Resonant torques between disk stars and any new linear
non-axisymmetric mode are suppressed within a scar, as is epicyclic heating.
Since all the resonances of a linear mode with the same angular wavenumber and
pattern speed as its precursor lie inside the scars of the precursor, it
suffers less damping. Hence, scars filter the spectrum of noise-generated
modes, promoting the renewal of a few select modes. Relic scars sustained by a
galaxy disk, due to past tidal interaction with a passing companion, may still
be active enablers of non-axisymmetric modes, such as the two-armed "grand
design" spiral patterns.
