Formation of dusty clumps in the torus of active galactic nuclei

Abstract

The putative dusty torus is a key ingredient of the unification scheme of active galactic nuclei (AGN), but its origin remains a mystery. Here we put forward a new physical model to explain how a large number of small dusty gas clumps form and they collectively appear as a geometrically thick dynamic dusty torus. The circumnuclear hot gas flows towards the central black hole (BH) and forms a rotating disk on sub-pc scales. A fraction of inflowing hot gas condenses to form small cold clumps due to thermal instabilities, when the accretion rate is sufficiently high. These cold dusty gas clumps are irradiated by the central accretion disk and re-radiate as dust emission mostly in the infrared. We propose that the dusty torus in AGN consists of such cold clumps vertically supported by the radiation force against gravity. For clumps with suitable column density, the vertical component of the BH gravity is in quasi-static equilibrium with the infrared radiation force together with the vertical component of the disk radiation force. Our model is robust in the sense that for any reasonable range of parameters concerning clump vertical dynamical equilibrium a torus exists. We further show that the hot gas in the rotating flow condenses to cold clumps only if its accretion rate is higher than about one percent of the Eddington rate. The radiation force is unable to lift the cold gas clumps up away from the mid-plane when the luminosity of the disk surrounding the BH is lower than 0.1 percent of the Eddington luminosity. These two features of our model may provide a physical explanation for the lack of evidence of dusty tori in low-luminosity AGNs.

Figures (10)

• Figure 1: Illustration of the model (not to scale in size and number of the clumps). Only the clumps with suitable column density can be vertically supported by the radiation force against the gravity, while the remainder are either driven away or sinking down. Part clumps may fall onto the BH through a cold disk.
• Figure 2: The critical accretion rate of the hot rotating disk varies with the Eddington ratio of the cold disk emission. The parameters, $\alpha=0.1$, and $\tilde{H}_{\rm h}=0.5$, are adopted in the calculations. The solid lines are the results calculated with $R=R_{\rm torus}$, while the dashed lines are for the cases of $R=2R_{\rm torus}$. The colored lines correspond to the results with different values of black hole mass, $m=10^7$ (red), $10^8$ (green), and $10^9$ (blue), respectively. The dotted line indicates $\dot{m}_{\rm h}=\lambda_{\rm d}$.
• Figure 3: The critical wavelengths of perturbations normal to the magnetic field vary with the Eddington ratio of the cold disk emission. The thermal instability is suppressed by the thermal conduction only if the wavelength of the perturbation $\lambda<\lambda_{\perp,\rm cr}$. The parameters, $\alpha=0.1$, and $\tilde{H}_{\rm h}=0.5$, are adopted in the calculations. The solid lines are the results calculated with $\beta_{\rm h}=10$, while the dashed and dotted lines are for the cases of $\beta_{\rm h}=100$ and 1000 respectively. The dots indicate the critical Eddington ratios of the disk luminosity. The colored lines correspond to the results with different values of black hole mass, $m=10^7$ (red), $10^8$ (green), and $10^9$ (blue), respectively.
• Figure 4: The ratios of the cooling rate to the heating rate of the gas with temperature $T=10^4$ K due to the incident radiation flux of the disk vary with $\lambda_{\rm d}$. The colored lines correspond to the results with different values of black hole mass, $m=10^7$ (red), $10^8$ (green), and $10^9$ (blue), respectively.
• Figure 5: The relation of the column density $N_{\rm cl}$ of the cold gas clumps with the Eddington ratio $\lambda_{\rm d}$ of the disk (see Equation \ref{['lambda_d']}). The red and green lines are the results for $\tilde{H}_{\rm torus}=0.2$ and $0.5$ respectively. The solid lines indicate the results calculated with $\Delta R_{\rm torus}=R_{\rm torus}$, while the dashed lines are for $\Delta R_{\rm torus}=2R_{\rm torus}$. The black dashed and dotted lines indicate $\tau_{\rm cl}=1$ for the UV and infrared photons respectively. The vertical lines indicate the critical Eddington ratios of the disk luminosity for thermal instability with different values of BH masses: $m=10^7$ (red), $10^8$ (green), and $10^9$ (blue).