Orbital Nodal Phase as a Pipeline Invariant in Black Hole Timing

Abstract

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, $\Delta\psi_{\rm orb}$. 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-$\Omega_\phi$ 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-$\Omega_\phi$ loops. A limited published-data illustration for GRO J1655$-$40 shows that the observational proxy for $\Delta\psi_{\rm orb}$ 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, $\Delta\psi_{\rm orb}$ therefore provides a pipeline-robust reporting quantity and a Kerr-baseline diagnostic for source-level, simulation-level, and strong-gravity comparison applications.