Feathering Instability of Spiral Arms. I: Formulation of the Problem
  In this paper we study the feathering substructures along spiral arms by
considering the perturbational gas response to a spiral shock. Feathers are
density fluctuations that jut out from the spiral arm to the inter-arm region
at pitch angles given by the quantum numbers of the doubly-periodic structure.
In a localized asymptotic approximation, related to the shearing sheet except
that the inhomogeneities occur in space rather than in time, we derive the
linearized perturbation equations for a razor-thin disk with turbulent
interstellar gas, frozen-in magnetic field, and gaseous self-gravity. Apart
from the modal quantum numbers, the individual normal modes of the system
depend on seven dimensionless quantities that characterize the underlying
time-independent axisymmetric state plus its steady, nonlinear, two-armed
spiral-shock (TASS) response to a hypothesized background density-wave
supported by the disk stars of the galaxy. We show that some of these normal
modes have positive growth rates. Their over-density contours in the post-shock
region are very reminiscent of observed feathering substructures in full
magnetohydrodynamic (MHD) simulations. The feathering substructures are
parasitic instabilities intrinsic to the system; thus, their study not only
provides potential diagnostics for important parameters that characterize the
interstellar medium of external galaxies, but also yields a deeper
understanding of the basic mechanism that drives the formation of the giant
molecular clouds (GMCs) and the OB stars that outline observed grand-design
spirals.
