In a recent paper (news release here) Lisa Randall and Matthew Reece propose that a dark matter disk coinciding with the galactic plane together with the solar system's oscillations through the galactic plane could explain the 35 million year periodicity in mass extinctions. They propose that the solar system passes through this dark matter disk in the galactic plane every 35 million years, disrupting bodies in the Oort cloud and causing some of them to collide with Earth. An image of the proposed cycles from the news release is below.
My question is: What mechanism is responsible for this 35 million year oscillation about the galactic plane? Is there a companion body to the sun? Are we orbiting around one of the arms of our galaxy? Is this a well known phenomenon or are they proposing the 35 million year oscillation as well as the dark matter disk?