Speaker
Description
Water H$_2$O megamasers in sub-parsec circumnuclear disks provide geometric constraints from VLBI sky positions, line-of-sight frequency shifts $z$, and---when monitored---their secular drifts. We present a geometry-first forward model for equatorial maser disks in a generic static, spherically symmetric (SSS) spacetime written in Schwarzschild gauge. The construction is formulated on the equatorial two-geometry and uses a Gauss--Bonnet balance on a finite triangular domain bounded by (i) the circular maser orbit, (ii) the observer line of sight, and (iii) the spatial projection of the null ray connecting emitter and observer. This yields an explicit finite-distance relation for the local emission angle $\alpha$ in terms of the telescope aperture angle $\Theta$ and one-dimensional integrals involving the metric potential $f(r)$ and its radial derivative $f'(r)$. Coupled to kinematic identities, the framework provides a closed description of the emission geometry along the full orbit, treating redshifted, blueshifted, and near-zero net-shift (``greenshift'') maser spots on the same footing. To help break the usual mass--distance degeneracy, we introduce the frequency-shift rapidity $\dot z_e \equiv d z_{\rm tot}/d\tau_e$ and derive expressions for $\dot z$ and its observational counterpart in terms of the azimuthal evolution and associated null rays. The resulting map from $(\Theta,z,\dot z)$ to physical/geometric parameters is designed for direct interfacing with VLBI megamaser datasets.