Comparison of the S(a₀) function obtained by employing the local (solid lines) vs orbit-averaged (dashed lines) treatment of two-body relaxation. The vertical dotted lines mark, for each case, the value of a₀/R_inf at which q = 1, thus marking the transition from the empty (at smaller a₀) to the full loss cone regime. The crosses indicate the points for which the orbit-averaged procedure explained in Sect. 3.3 failed many times.