Kinematics and Structure of Clumps in Broad-line Regions in Active Galactic Nuclei

Abstract

We use the Jeans equations for an ensemble of collisionless particles to describe the distribution of broad-line region (BLR) cloud in three classes: (A) non disc (B) disc-wind (c) pure disc structure. We propose that clumpy structures in the brightest quasars belong to class A, fainter quasars and brighter Seyferts belong to class B, and dimmer Seyfert galaxies and all low-luminosity AGNs (LLAGNs) belong to class C. We derive the virial factor, $f$, for disc-like structures and find a negative correlation between the inclination angle, $\theta_{0}$, and $f$. We find similar behaviour for $f$ as a function of the FWHM and $\sigma_{z}$, the $z$ component of velocity dispersion. For different values of $\theta_{0}$ we find that $ 1.0 \lesssim f \lesssim 9.0 $ in type1 AGNs and $ 0.5 \lesssim f \lesssim 1.0 $ in type2 AGNs. Moreover we have $ 0.5 \lesssim f \lesssim 6.5 $ for different values of FWHM and $ 1.4 \lesssim f \lesssim 1.8 $ for different values of $ \sigma_{z} $. We also find that $ f $ is relatively insensitive to the variations of bolometric luminosity and column density of each cloud and the range of variation of $ f $ is in order of 0.01. Considering wide range of $ f $ we see the use of average virial factor $ \langle f \rangle $ is not very safe. Therefore we propose AGN community to divide a sample into a few subsamples based on the value of $ \theta_{0}$ and FWHM of members and calculate $ \langle f \rangle $ for each group separately to reduce uncertainty in black hole mass estimation.