Model Simulations of a Shock-Cloud Interaction in the Cygnus Loop

We present optical observations and two-dimensional hydrodynamic modeling of an isolated shocked ISM cloud. H(alpha) images taken in 1992.6 and 2003.7 of a small optical emission cloud along the southwestern limb of the Cygnus Loop were used to measure positional displacements of ~0"1 yr-1 for surrounding Balmerdominated emission filaments and 0"025-0"055 yr-1 for internal cloud emission features. These measurements imply transverse velocities of ~250 and ~80-140 km s-1 for ambient ISM and internal cloud shocks, respectively. A lack of observed turbulent gas stripping at the cloud-ISM boundary in the H(alpha) images suggests that there is not an abrupt density change at the cloud-ISM boundary. Also, the complex shock structure visible within the cloud indicates that the cloudʹs internal density distribution is two-phased-a smoothly varying background density that is populated by higher density clumps. Guided by the H(alpha) images, we present model results for a shock interacting with a nonuniform ISM cloud. We find that this cloud can be well modeled by a smoothly varying power-law core with a density contrast of ~4 times the ambient density, surrounded by a low-density envelope with a Lorentzian profile. The lack of sharp density gradients in such a model inhibits the growth of Kelvin-Helmholtz instabilities, consistent with the cloudʹs appearance. Our model results also suggest that cloud clumps have densities ~10 times the ambient ISM density and account for ~30% of the total cloud volume. Moreover, the observed spacing of internal cloud shocks and model simulations indicate that the distance between clumps is ~4 clump radii. We conclude that this diffuse ISM cloud is best modeled by a smoothly varying, lowdensity distribution coupled to higher density, moderately spaced internal clumps.