Research Note

On Öpik’s distance evaluation method in a cosmological context

Tuorla ObservatoryDepartment of Physics and Astronomy, University of Turku, 21500 Piikkiö, Finland
e-mail: pekkatee@utu.fi

Received: 9 February 2011
Accepted: 19 April 2011

Abstract

Aims. Öpik 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 Öpik’s method we assess hypothetical Eddington radiators (M/L = M/L_Edd).

Results. We describe ways of calibrating Öpik-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.