Method (Paper E Appendix A, browser-reduced sample counts). For each log-spaced radius bin a ∈ [10⁻³, stripping radius] AU: draw encounters with impact parameter from the gravitationally focused distribution truncated at b
max = 30a, velocity from a Maxwellian at dispersion σ, and mass from the perturber mass function; compute the impulsive eccentricity-kick variance ⟨δ²⟩; convert to a survival time via the random-walk first-passage estimate n
★ = e
cross²/⟨δ²⟩ divided by the encounter rate, with CLT scatter giving the 16–84% band; cap at 12 Gyr. Deliberately conservative: no adiabatic suppression applied.
Perturber mass function & the fBH control (referee-M1 revision, Paper E v0.4). The background is two-component stellar (0.35 M☉ weight 0.70, 0.60 M☉ white-dwarf tail weight 0.30). A mass-segregated heavy-remnant extension adds neutron stars (1.4 M☉, fixed number fraction f
NS = 2%) and stellar-mass black holes (10 M☉, segregated fraction
f_BH, fiducial 1%, grid 0.1/1/3%). The 10 M☉ BH tail is the controlling perturber: heavy masses dominate the kick variance, so raising f
BH shortens the floor sharply. This
supersedes the stars-only result (a ~3×10⁹ yr floor comparable to the cluster age) that this page previously reported. At the fiducial f
BH = 1% the envelope floor drops to ~3×10⁸ yr (the paper quotes ~1.5×10⁸–5×10⁸ yr across the grid). That stays well above the 10⁶ yr passive-safety criterion, though it is no longer comparable to the cluster lifetime. Set f
BH = 0 to recover the superseded stars-only baseline.
Paper reference mode. Ticking
paper reference plots the exact fiducial arrays from
fig1_results.json verbatim (2×10⁵ encounter draws × 2×10⁴ histories × 40 bins, fixed seed 20260717, σ = 21 km/s,
fig1_envelope.py, full bundle at
/papers/source/): no live sampling, so it reproduces the published numbers rather than approximating them. The live MC trades sample count for interactivity; expect its median to sit inside the reference band, not land on it. The
paper MC floor summary card always shows the published floor for the grid f
BH nearest your setting, for side-by-side comparison. σ default from
measurements.js clusterParams (18.2 km/s, cluster-averaged); Paper E adopts σ = 21 km/s, the midpoint of the 20–23 km/s central-region range of Baumgardt & Vasiliev (2021) and Nitschai et al. (2023). The difference lengthens survival times by tens of per cent and is inside the paper’s stated parameter variations.