2011A&A...531A..10T

Oepik derived the distance to M31 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. 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 Oepik's method we assess hypothetical Eddington radiators (M/L=M/L_Edd). We describe ways of calibrating Oepik-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∝L^αΔλ² does not depend on H₀, whereas the Eddington ratio L_bol/L_Edd does (as ∝ H₀^–2). This is illustrated using very luminous yet quiescent radio quasars at redshifts 0.5-1.6.