THE DYNAMICS OF STAR STREAM GAPS

A massive object crossing a narrow stream of stars orbiting in the halo of the galaxy induces velocity changes both along and transverse to the stream that can lead to the development of a visible gap. For a stream narrow relative to its orbital radius, the stream crossing time is sufficiently short that the impact approximation can be used to derive the changes in angular momenta and radial actions along the star stream. The epicyclic approximation is used to calculate the evolution of the density of the stream as it orbits around in a galactic potential. Analytic expressions are available for a point mass, however, the general expressions are easily numerically evaluated for perturbing objects with arbitrary density profiles. With a simple allowance for the velocity dispersion of the stream, moderately warm streams can be modeled. The predicted evolution agrees well with the outcomes of simulations of stellar streams for streams with widths up to 1% of the orbital radius of the stream. The angular momentum distribution within the stream shears out gaps with time, further reducing the visibility of streams, although the size of the shear effect requires more detailed simulations that account for the creation of the stream. An illustrative model indicates that shear will set a lower limit of a few times the stream width for the length of gaps that persist. In general, the equations are useful for dynamical insights into the development of stream gaps and their measurement.