The evolution of streams in a time-dependent potential

Abstract

We study the evolution of streams in a time-dependent spherical gravitational potential. Our goal is to establish what are the imprints of this time evolution on the properties of streams as well as their observability. To this end, we have performed a suite of test-particle experiments for a host system that doubles its mass during the integration time and for a variety of initial conditions. In these experiments we found that the most striking imprint is a misalignment of ~10° in the angular location of the apocentres of the streams compared to the static case (and to the orbit of the centre of mass), which only becomes apparent for sufficiently long streams. We have also developed an analytic model using action-angle variables which allows us to explain this behaviour and to identify the most important signature of time evolution, namely a difference in the slope defined by the distribution of particles along a stream in frequency and in angle space. Although a difference in slope can arise when the present-day potential is not correctly modelled, this shortcoming can be by-passed because in this case, streams are no longer straight lines in angle space, but depict a wiggly appearance and an implausible energy gradient. The difference in slope due to time evolution is small, typically ~10-2 and its amplitude depends on the growth rate of the potential, but nonetheless we find that it could be observable if accurate full-space information for nearby long streams is available. On the other hand, disregarding this effect may bias the determination of the present-day characteristics of the potential.