## 1. Introduction

Thin stellar streams such as GD-1 carry gaps where a dark matter subhalo passed close to the stream. Counting gaps is one of the few ways to count subhalos too small to hold stars of their own. A gap does not last forever. Stars inside the gap keep phase mixing along the orbit, and the density contrast fades until the gap can no longer be told apart from noise. This paper estimates how long a gap stays visible.

## 2. Method

We treat a gap as a small density perturbation on a stream of stars that share one orbit. Differential orbital phase mixing spreads the perturbation along the stream at a rate set by the spread in orbital frequency across the stream. For a stream at galactocentric radius R with velocity dispersion σ_v the perturbation is erased after t_gap ≈ πR/σ_v. The earlier version counted the phase-mixing time twice, once for each side of the gap, which doubled the lifetime. The estimate depends only on the velocity dispersion and the radius of the stream, and not on the mass of the subhalo that opened the gap.

## 3. Results

For a GD-1-like stream at 14 kpc with a velocity dispersion of 2 km/s we find gap lifetimes of 0.6 Gyr. This is consistent with the N-body gap growth found by Erkal & Belokurov (2015). Table 1 lists lifetimes for four streams at radii from 10 to 20 kpc, and Table 2 gives the fraction of impacts in the last 3 Gyr that still leave a visible gap.

## 4. Discussion

Gaps are erased after about 0.6 Gyr, so subhalo counts from older streams are incomplete. The incompleteness factor in Table 2 corrects a count for the gaps that have already faded.

## References

Erkal, D. and Belokurov, V. (2015). Properties of dark subhaloes from gaps in tidal streams. MNRAS 454, 3542.