Spiral-arm instability: giant clump formation via fragmentation of a
  galactic spiral arm
  Fragmentation of a spiral arm is thought to drive the formation of giant
clumps in galaxies. Using linear perturbation analysis for self-gravitating
spiral arms, we derive an instability parameter and define the conditions for
clump formation. We extend our analysis to multi-component systems that consist
of gas and stars in an external potential. We then perform numerical
simulations of isolated disc galaxies with isothermal gas, and compare the
results with the prediction of our analytic model. Our model describes
accurately the evolution of the spiral arms in our simulations, even when
spiral arms dynamically interact with one another. We show that most of the
giant clumps formed in the simulated disc galaxies satisfy the instability
condition. The clump masses predicted by our model are in agreement with the
simulation results, but the growth time-scale of unstable perturbations is
overestimated by a factor of a few. We also apply our instability analysis to
derive scaling relations of clump properties. The expected scaling relation
between the clump size, velocity dispersion, and circular velocity is slightly
different from that given by the Toomre instability analysis, but neither is
inconsistent with currently available observations. We argue that the
spiral-arm instability is a viable formation mechanism of giant clumps in
gas-rich disc galaxies.
