Dynamical model of an obscuring clumpy torus in AGNs – I. Velocity and velocity dispersion maps for interpretation of ALMA observations

Abstract

We have developed the dynamical model of a clumpy torus in an active galactic nucleus (AGN) and compared to recent ALMA observations. We present N-body simulations of a torus in the field of a supermassive black hole (SMBH), made of up to N = 105 gravitationally interacting clouds. As initial conditions, we choose random distributions of the orbital elements of the clouds with a cut-off in the inclination to mimic the presence of wind cones produced at the early AGN stage. When the torus reaches an equilibrium, it has a doughnut shape. We discuss the presence of box orbits. We have then constructed the velocity and velocity dispersion maps using the resulting distributions of the clouds at equilibrium. The effects of torus inclination and cloud sizes are duly analyzed. We discuss the obscuration effects of the clouds using a ray tracing simulation matching the model maps to ALMA resolution. By comparing the model with the observational maps of NGC 1068 we find that the SMBH mass is Msmbh = 5 × 106 M⊙ for the range of the torus inclination angles 45○–60○. We also construct the velocity dispersion maps for NGC 1326 and NGC 1672. They show that the peaks in the ALMA dispersion maps are related to the emission of the torus throat. Finally, we obtain the temperature distribution maps with parameters that correspond to our model velocity maps for NGC 1068. They show stratification in temperature distribution with the shape of the high temperature region as in the VLTI/MIDI map.

Apparent counter-rotation in the torus of NGC 1068: influence of an asymmetric wind

“…In the following, we will consider two values of ε cl = 0.01 and 0.025. They satisfy the ALMA velocity and velocity dispersion maps (Bannikova et al 2021).…”

“…Such an initial condition is a simple representation of the wind influence -see Fig. 1 in (Bannikova et al 2021).…”

“…The values of the velocity were calculated here and in all the figures below for the following physical parameters of NGC 1068: M smbh = 5 × 10 6 M and a mean major radius of the torus Rtorus = 3.5 pc. We obtained these parameters in our previous estimation when we compared our model maps to the ALMA velocity map and VLTI temperature distribution (Bannikova et al 2020(Bannikova et al , 2021.…”

“…The hot central component was explained by the emission of the throat which penetrates throughout the torus body. An alternative explanation takes into account the orientation of the torus which allows the observer to see the part of the inner throat not obscured by the clouds (Bannikova et al 2021).…”

“…In this paper we use our dynamical model (Bannikova et al 2012(Bannikova et al , 2020Bannikova & Sergeyev 2017) adding the outflow forces in order to check whether the apparent counter-rotation in the torus in NGC 1068 can be explained by the influence of the wind. In Section 2 we present our N-body simulations of a self-gravitating clumpy torus in the field of a SMBH.…”