2016A&A...587A..38W

Polish doughnuts (PDs) are geometrically thick disks that rotate with super-Keplerian velocities in their innermost parts, and whose long and narrow funnels along rotation axes collimate the emerging radiation into beams. In this paper we construct an extremal family of PDs that maximize both geometrical thickness and radiative efficiency. We then derive upper limits for these quantities and subsequently for the related ability to collimate radiation. PDs with such extreme properties may explain the observed properties of ultraluminous X-ray sources without the need for the black hole masses to exceed ∼10 M_☉. However, we show that strong advective cooling, which is expected to be one of the dominant cooling mechanisms in accretion flows with super-Eddington accretion rates, tends to reduce the geometrical thickness and luminosity of PDs substantially. We also show that the beamed radiation emerging from the PD funnels corresponds to isotropic luminosities that obey L_col≃0.1(dM/dt)c² for dM/dt≫dM/dt_Edd, and not the familiar and well-known logarithmic relation, L∼ln(dM/dt).