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.
