Quasar bolometric corrections: theoretical considerations

Bolometric corrections based on the optical-to-ultraviolet continuum spectrum of quasars are widely used to quantify their radiative output, although such estimates are affected by a myriad of uncertainties, such as the generally unknown line-of-sight angle to the central engine. In order to shed light on these issues, we investigate the state-of-the-art models of Hubeny et al. that describe the continuum spectrum of thin accretion discs and include relativistic effects. We explore the bolometric corrections as a function of mass accretion rates, black hole masses and viewing angles, restricted to the parameter space expected for type-1 quasars. We find that a nonlinear relationship log L_bol=A + B log(lambda L_lambda) with B<=0.9 is favoured by the models and becomes tighter as the wavelength decreases. We calculate from the model the bolometric corrections corresponding to the wavelengths lambda = 1450A, 3000A and 5100A. In particular, for lambda=3000A we find A=9.24 +- 0.77 and B=0.81 +- 0.02. We demonstrate that the often-made assumption that quasars emit isotropically may lead to severe systematic errors in the determination of L_bol, when using the method of integrating the "big blue bump" spectrum. For a typical viewing angle of ~30 degrees to the quasar central engine, we obtain that the value of L_bol resulting from the isotropy assumption has a systematic error of ~30% high compared to the value of L_bol which incorporates the anisotropic emission of the accretion disc. These results are of direct relevance to observational determinations of the bolometric luminosities of quasars, and may be used to improve such estimates.