The Impact of Elliptical Broad-line Regions on Reverberation-based Black Hole Mass Estimates

The virial factor f is critical for accurate supermassive black hole (SMBH) mass measurements using reverberation mapping (RM) and the radius–luminosity ( R – L ) relation, yet its value remains highly uncertain. While traditional models assume axisymmetric broad-line region (BLR) geometries, growing evidence suggests that BLRs may possess more complex, asymmetric structures. We systematically investigate the impact of elliptical-disk BLR geometries on SMBH mass determinations through comprehensive numerical simulations. By computing emission-line profiles, emissivity-weighted time lags, and the corresponding virial factor f over a wide range of eccentricities, orientations, and inclinations, we find that even in purely virialized systems, geometric effects alone can cause f to vary by more than 1 order of magnitude and can mimic observational signatures typically attributed to radiation pressure. Additionally, local broadening introduces further systematic uncertainties in velocity width measurements, biasing f by up to a factor of ∼3. Asymmetric BLR configurations also induce a scatter of ∼0.18 dex in the R – L relation due to projection effects, comparable to the intrinsic scatter observed in RM studies. These results challenge the conventional attribution of RM uncertainties to nonvirial motions or radiation pressure, and instead highlight the fundamental role of BLR geometry in SMBH mass measurements.