Effects of a dark matter caustic passing through the Oort Cloud

We investigate the effect of a dark matter caustic passing through the Solar System. We find, confirming a previous result, that the Sun tracks the caustic surface for some time. We integrate numerically the equations of motion of the Sun and a comet for a large number of initial conditions and of caustic passage properties. We calculate the probability for the comet to escape the Solar System and the probability for it to fall within 50 A.U. of the Sun, given the initial semi-major axis and eccentricity of its orbit. We find that the average probability for a comet to fall within 50 A.U. of the Sun is of order $3 \times 10^{-4}$ and that comets which are initially at a distance larger than about $10^5$ A.U. have a probability of order one to be ejected from the Solar System.