## 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 ≈ 2πR/σ_v. 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 1.2 Gyr. This agrees with the simulations of Carlberg & Grillmair (2013b), who report gaps that stay visible for about a gigayear. Table 1 lists lifetimes for four streams at radii from 10 to 20 kpc.

## 4. Discussion

Gaps older than 1 Gyr cannot be used to count subhalos, because they have faded below the noise of current surveys. Subhalo counts from streams therefore describe only the most recent gigayear of impacts.

## References

Carlberg, R. G. and Grillmair, C. J. (2013b). Gaps in the GD-1 star stream. ApJ 768, 171.

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