On Öpik’s distance evaluation method in a cosmological context

Abstract

Aims. Opik derived the distance to M 31 using its rotation, flux and angular size. We describe his method and its reliance on the mass-to-luminosity ratio M/L in an instructive way and consider it formally within a family of dynamical cosmic distance indicators. Methods. We consider ways of overcoming the M/d degeneracy in methods where together with the dynamical equation one uses an auxiliary relation M ∼ dn to infer the distance d (with examples for n = 0, 1, 2, 3). As a possible deep space analog to Opik’s method we assess hypothetical Eddington radiators (M/L = M/LEdd). Results. We describe ways of calibrating Opik-related methods that do not use directly the angular size and consider their sensitivity to the used local H0. We find, for instance, that when the size-luminosity relation is calibrated using distance-independent reverberation mapping to infer the BLR size, the derived mass M ∝ LαΔλ2 does not depend on H0, whereas the Eddington ratio Lbol/LEdd does (as ∝H−2 0 ). This is illustrated using very luminous yet quiescent radio quasars at redshifts 0.5–1.6.