The time evolution of gaps in tidal streams

TL;DR

This paper models the growth of gaps in tidal streams caused by dark matter subhalos, deriving an analytic expression for their evolution, verified by simulations, with implications for understanding dark matter substructure.

Contribution

It provides a new analytic model for the time evolution of gaps in tidal streams due to subhalo impacts, validated by N-body simulations.

Findings

Gap size increases linearly with time in spherical potentials.

Subhalo mass and velocity influence gap growth rate.

Gaps can reach tens of kpc after several Gyr.

Abstract

We model the time evolution of gaps in tidal streams caused by the impact of a dark matter subhalo, while both orbit a spherical gravitational potential. To this end, we make use of the simple behaviour of orbits in action-angle space. A gap effectively results from the divergence of two nearby orbits whose initial phase-space separation is, for very cold thin streams, largely given by the impulse induced by the subhalo. We find that in a spherical potential the size of a gap increases linearly with time for sufficiently long timescales. We have derived an analytic expression that shows how the growth rate depends on the mass of the perturbing subhalo, its scale and its relative velocity with respect to the stream. We have verified these scalings using N-body simulations and find excellent agreement. For example, a subhalo of mass 10^8 Msun directly impacting a very cold thin stream on an inclined orbit can induce a gap that may reach a size of several tens of kpc after a few Gyr. The gap size fluctuates importantly with phase on the orbit, and it is largest close to pericentre. This indicates that it may not be fully straightforward to invert the spectrum of gaps present in a stream to recover the mass spectrum of the subhalos.