Black Hole Torus Covering Fractions

Class providing the covering fraction of the dusty torus around the central black hole of a galaxy.

Default implementation: blackHoleTorusCoveringFractionRecedingTorus

Methods

coveringFraction → double precision

Return the fraction of the sky, as seen from the accretion disk of the central black hole of node, which is covered by its dusty torus. The result lies between zero and one.

• type(treeNode) node [inout]

blackHoleTorusCoveringFractionFixed

A covering fraction of the dusty torus around an AGN which is the same, [coveringFraction], for every black hole, whatever its luminosity.

Parameters

• [coveringFraction] (real; 0..1; default 0.5d0) — The fraction of the sky, as seen from the accretion disk, covered by the dusty torus.

blackHoleTorusCoveringFractionRecedingTorus

The covering fraction of the dusty torus around an AGN in the modified receding torus model of Simpson (2005), a generalization of that of Lawrence (1991):

\[f_\mathrm{cov} = \left[ 1 + 3 \left( \frac{L}{L_0} \right)^{1-2\xi} \right]^{-1/2}.\]

In the receding torus the inner edge of the torus lies at the dust sublimation radius, which grows as \(L^{1/2}\), while its height grows as \(L^\xi\); so the torus becomes thinner, and covers less of the sky, as the AGN becomes more luminous. \(\xi=0\) is the original model of Lawrence (1991), and \(\xi=1/2\) gives a covering fraction of \(1/2\) independent of luminosity.

\(L\) is the bolometric luminosity of the accretion disk of the central black hole, \(\epsilon \dot{M} c^2\), where the accretion rate \(\dot{M}\) (summed over all of its sources) is given by the [blackHoleAccretionRate] object and the radiative efficiency \(\epsilon\) by the [accretionDisks] object—the same luminosity from which the spectrum of the accretion disk is computed. A galaxy with no accreting black hole is fully covered.

The defaults are the best fit of Simpson (2005), \(\xi=0.23\) and \(L_0=10^{35.37}\,\hbox{W}\) in [O III] luminosity, converted to a bolometric luminosity with the correction \(L/L_\mathrm{[O III]}=3500\) of Heckman et al. (2004), which gives \(L_0=2.13\times 10^{12}\,L_\odot\).

(Default implementation)

Parameters

• [luminosityCharacteristic] (real; 0..1; default 2.13d12) — The bolometric luminosity, \(L_0\) in \(L_\odot\), at which the covering fraction of the torus is \(1/2\). Default from: Simpson (2005) with the bolometric correction of Heckman et al. (2004).

• [exponentHeight] (real; 0..1; default 0.23d0) — The exponent, \(\xi\), of the dependence of the height of the torus on luminosity, \(h \propto L^\xi\). Default from: Simpson (2005).