Panel a: radial profiles of the normalized disk flux (thin relativistic disk) and the Keplerian and epicyclic frequencies of geodesic orbital motion calculated for a Schwarzschild BH. The gray region between rISCO and r90% emphasizes the radial part of the disk that radiates more than 90% of the whole disk luminosity. Several particular resonant orbits are denoted. Indexes i and j in ri : j are chosen such that i/j = νθ/νr. Panel b: mass-spin relations inferred for XMMUJ134736.6+173403 from the observed QPO frequencies and their models in Kerr spacetimes. The solid and dashed black lines are drawn for the set of resonance models considered by Carpano & Jin (2018). The red line denotes the prediction of the ER model, while the blue line corresponds to the RP model. The dashed red-blue line denotes the consideration of the ER3 : 2 model. The gray region corresponds to the association of the QPO frequency with the Keplerian frequency at orbits inside a part of the disk that radiates more than 90% of the whole disk luminosity. The lower boundary of the gray region corresponds to r90% , while the upper boundary corresponds to rISCO. The yellow region emphasizes the range covered by the assumed QPO models. The nine spots denote boundaries of relation (5) for a ∈ [ − 1, 1].
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