Orbital nodal phase as a pipeline invariant in black hole timing

Official URL: https://dx.doi.org/10.1142/S0218271826500240

Timing analyses of accreting black holes often package nodal information in ways that depend on benign choices of time and azimuthal convention. We identify the corresponding pipeline-invariant content for slightly tilted circular rings and express it as an orbital nodal phase, Δψorb. In Kerr, this quantity gives the clean geodesic baseline for nodal timing: it equals the nodal precession per orbit, is invariant under the benign remappings considered here, and, for prograde Kerr spin, decreases monotonically with radius outside the innermost stable circular orbit. A fixed-Ωϕ transport framework then isolates genuine metric sensitivity from trivial radius drift and provides the natural framework for far-field quadrupolar and higher-multipolar timing-response calculations. Two small analysis-level effects are also identified, namely a second-order bias from coherent radial breathing and the absence of an intrinsic geometric offset from exact slow fixed-Ωϕ loops. A limited published-data illustration for GRO J1655−40 shows that the observational proxy for Δψorb can be reconstructed directly from standard reported quasi-periodic oscillation frequencies once an orbital-frequency anchor and an identification convention are specified. Within the thin-ring limit, Δψorb therefore provides a pipeline-robust reporting quantity and a Kerr-baseline diagnostic for source-level, simulation-level and strong-gravity comparison applications.