Fig. 3

Determination of black hole spin for several cases of doubled resonances. The functions , v ∈ { θ,K } are drawn for the frequency ratios n:m = 5:4 (black solid line), 4:3 (black dashed line), 3:2 (black dotted line), 5:3 (red solid line), 2:1 (red dashed line), 5:2 (red dotted line), 3:1 (blue solid line), 4:1 (blue dashed line), 5:1 (blue dotted line). Black thick line in T33, T44, and B33 represents νv = νv(a,xms), which denotes the frequency on the marginally stable orbit. Here we show how to determine the “magic” spin am = 0.983 in the case of a) “mixed identity” M13 with νθ:νr = 2:1 and νK:νθ = 3:2 giving the triple frequency set
and b) “top identity” T34 with νK:νθ = 3:2 and
giving the triple frequency set
.
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