garleak
Gap lifetimes in thin stellar streams: an analytic estimate
We derive an analytic estimate for the lifetime of gaps opened in thin stellar streams by dark matter subhalo impacts. Treating a gap as a density perturbation that is erased by differential orbital phase mixing, we obtain t_gap ≈ 2πR/σ_v, which depends only on the stream's velocity dispersion and galactocentric radius. For a GD-1-like stream at 14 kpc this gives gap lifetimes of 1.2 Gyr, consistent with the N-body gap growth found by Erkal & Belokurov (2015). We conclude that gaps older than 1 Gyr cannot be used to count subhalos.
Not peer reviewed. Admitted after screening for scope and form only. Admission is not endorsement.
Verification history
[v3.0] 11 Sep, T3 Passed, S. Haddad, computational 1.0.0. Reran the gap-lifetime integrations for 3 of 5 potentials. Lifetimes agree with Table 2 to within 8 per cent.
[v3.0] 7 Sep, T2 Passed, M. Okafor, computational 1.0.0. All 8 required items pass. Code runs from the stated environment and outputs match within the stated 10 per cent tolerance.
[v3.0] 5 Sep, T1 Passed, citecheck 0.1, then M. Okafor, citations 1.0.0. All 44 references exist and match their metadata. Claim support read for the 9 references behind the central result.
[v2.0] 28 Aug, T2 Passed, J. Lindqvist, computational 1.0.0. All 8 required items pass. The corrected lifetimes trace to the code within the stated 10 per cent.
[v2.0] 23 Aug, T1 Passed, M. Okafor, citations 1.0.0. 42 references exist and match. Claim support re-read for the references behind the changed result.
[v1.1] 12 Aug, T2 Failed, J. Lindqvist, computational 1.0.0. The gap lifetime at 14 kpc is half the stated value when the stated code is run. Led to fix 12. Failed comp.T2.numbers-traceable, Running the integration at the pinned commit gives 0.6 Gyr at 14 kpc, not 1.2 Gyr. The factor of two comes from counting the phase-mixing time twice..
[v1.1] 9 Aug, T1 Passed, M. Okafor, citations 1.0.0. 42 references exist and match their metadata. Claim support read for the 9 references behind the central result.
[v1.0] 5 Aug, T1 Failed, citecheck 0.1, then M. Okafor, citations 1.0.0. Carlberg & Grillmair (2013b) could not be found. One DOI on a real reference had the wrong suffix. Failed cit.T1.exists, Carlberg & Grillmair (2013b) as cited could not be found in ADS, Crossref or OpenAlex. The 2013 paper by these authors has no 'b' and says nothing about gap lifetimes.. Failed cit.T1.metadata-agree, The DOI given for Erkal & Belokurov (2015) resolves to a different paper..
Submission history
From: R. Nakamura
[v1.0] 3 August 2026, first submission, T0 , 100% original
[v1.1] 7 August 2026, minor, citations fixed, T1 , 93% original, diff from v1.0
[v2.0] 21 August 2026, major, fix 12 halves the lifetime, T2 , 68% original, diff from v1.0
[v3.0] 4 September 2026, major, adds the barred potential, T3 , 49% original, diff from v1.0
Fixes
Fix 11, merged into v1.1, by R. Nakamura. Replace the citation that could not be found and correct one DOI.
Fix 12, merged into v2.0, by A. Ferreira. Factor of two in the phase-mixing time.
Fix 14, merged into v3.0, by R. Nakamura. Add the barred potential.
Fix 15, open, by S. Haddad. Pericentre table units.