Effect of the inclination of the BLR on the virial factor
Abstract
In the last decade, observational relationships have been identified between the mass of supermassive black holes and the properties of their host galaxies, such as the star dispersion velocity, luminosity, or bulge mass. The structure and kinematics of the broad-line region (BLR) is a key problem in modern astrophysics, as properties of the broad emission lines are used to find the mass of the central black hole. In type-1 AGNs, the virial theorem is the tool to determine the black hole mass. In this approach, the cloud velocity is usually inferred from the width of the broad lines, and the size of the BLR is derived from reverberation measures. However, the virial method shows uncertainties that suggest to include a virial factor $f$. In this work, we take into account the effect of the BLR inclination $i$, assumed to have a planar distribution of radius $R$ and height $H$, given by $f=(4(\sin^{2} i + (H/R)^{2}))^{-1}$. We also assume that radiation pressure, determined by the luminosity, can diverge slightly from gravitational equilibrium and push the clouds of the BLR slightly outward. This effect offers a new way to obtain the BLR size, $R_\mathrm{BLR}=R^{0}_\mathrm{BLR}(a_{1}L^{\alpha\mathrm{Line}}+a_{2}L_{\lambda}/M_\mathrm{BH})$, where $R^{0}_\mathrm{BLR}$ is a typical size of the BLR, $L$ the luminosity, ${\alpha\mathrm{Line}}$ a dimensionless parameter, $L_\lambda$ the luminosity at wavelength $\lambda$, $M_\mathrm{BH}$ the mass of the black hole, and $a_1$ and $a_2$ are constants. Also we identify relations between inclination and the virial factor derived for radiation pressure $f_{\text{rad}}$. In this case, we obtain the relation $f_{\text{rad}} \propto (2\sin i)^{-1}$, that takes into account the effects of the inclination in a planar distribution of BLRs, and of the radiation pressure.
- Publication:
-
Boletin de la Asociacion Argentina de Astronomia La Plata Argentina
- Pub Date:
- August 2020
- Bibcode:
- 2020BAAA...61C..91H
- Keywords:
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- quasars: supermassive black holes;
- quasars: emission lines