Dust inflated accretion disc as the origin of the Broad Line Region in Active Galactic Nuclei

TL;DR

This work proposes that the Broad Line Region in AGN arises from a dust-inflated disc atmosphere where radiation pressure on large graphite grains lifts and sustains a thick, torus-like structure. Dust properties, notably graphite survival at BLR densities and the associated high IR opacity, inflate the disc and place the BLR on the illuminated disc surface, with the inner edge set by dust sublimation and the outer edge by the sublimation of the largest grains. Radiative transfer and dynamics predict a peak height near R_max that scales with luminosity and metallicity, yielding a BLR radius matching the Kaspi relation while forecasting a covering factor that approaches observed values only when dynamic winds and ablation are included. The model offers concrete, testable predictions for reverberation mapping, high-ionization line emission, and near-IR hot dust signatures, linking BLR properties to metallicity, accretion efficiency, and variability.

Abstract

The Broad Line Region (BLR) in AGN is composed of dense gas ($\sim 10^{11}$ cm$^{-3}$) on sub-pc scale, which absorbs about 30 per cent of the ionising continuum. The outer size of the BLR is likely set by dust sublimation, and its density by the incident radiation pressure compression (RPC). But, what is the origin of this gas, and what sets its covering factor (CF)? Czerny & Hryniewicz (2011) suggested that the BLR is a failed dusty wind from the outer accretion disc. We explore the expected dust properties, and the implied BLR structure. We find that graphite grains sublimate only at $T\simeq 2000$ K at the predicted density of $\sim 10^{11}$ cm$^{-3}$, and therefore large graphite grains ($\ge 0.3$ $μ$m) survive down to the observed size of the BLR, $R_{\rm BLR}$. The dust opacity in the accretion disc atmosphere is $\sim 50$ times larger than previously assumed, and leads to an inflated torus-like structure, with a predicted peak height at $R_{\rm BLR}$. The illuminated surface of this torus-like structure is a natural place for the BLR. The BLR CF is mostly set by the gas metallicity, the radiative accretion efficiency, a dynamic configuration, and ablation by the incident optical-UV continuum. This model predicts that the BLR should extend inwards of $R_{\rm BLR}$ to the disc radius where the surface temperature is $\simeq 2000$ K, which occurs at $R_{\rm in}\simeq 0.18 R_{\rm BLR}$. The value of $R_{\rm in}$ can be tested by reverberation mapping of the higher ionisation lines, predicted by RPC to peak well inside $R_{\rm BLR}$. The dust inflated disc scenario can also be tested based on the predicted response of $R_{\rm BLR}$ and the CF to changes in the AGN luminosity and accretion rate.

Figures (15)

• Figure 1: The grain sublimation temperature as a function of gas density for graphite and silicate grains (for $T=10^4$ K). The sublimation temperature of graphite is larger by $\sim 300-500$ K compared to that of silicate, as the graphite C atoms are more tightly bound than the Si atoms in silicates. Thus, graphite grains sublimate at a smaller distance from the AGN continuum source. At the BLR, $\hbox{$n$}\sim10^{11}$ cm$^{-3}$, which implies $\hbox{$T_{\rm sub}$}\simeq 2000$ K, rather than 1500 K, as commonly assumed in earlier studies.
• Figure 2: The sublimation time-scale as a function of $T_{\rm sub}$ for a graphite grain of various radii $a$, embedded in gas with $T=10^4$ K. For $\hbox{$T_{\rm sub}$}=2000$ K, relevant for grains at the BLR density, the time-scale is typically a few hours. It reaches $\sim 3$ days for the largest grain assumed here, of $a=1$$\mu$m. This time-scale is shorter than the light crossing time of the BLR. Thus, sublimation is effectively instantanous for most grain sizes.
• Figure 3: The grain temperature as a function of grain radius for graphite and silicate grains. The illuminating continuum has $L_{\rm bol}=10^{45}$ erg s$^{-1}$. The grains are located at $R_{\rm BLR}=0.1L_{\rm bol, 46}^{1/2}$ pc and an inclination angle of $\mu=0.1$. The small silicate grains are hotter than graphite grains, at a given $a$, by $\sim 1000$ K, because of their lower emission efficiency in the near IR. Note that for graphites, $\hbox{$T_{\rm grain}$}<\hbox{$T_{\rm sub}$}\simeq2000$ K is achieved in the BLR only for grains with $a\ga 0.1$$\mu$m. For silicates, $\hbox{$T_{\rm grain}$}>\hbox{$T_{\rm sub}$}\simeq1600$ K for all grains, and thus none of the silicate grains survive at $R_{\rm BLR}$.
• Figure 4: The graphite grain temperature as a function of the AGN flux, as measured by $T_{\rm eff}$, for various grain sizes. The $a=1$$\mu$m grain $T_{\rm grain}$ deviates from $T_{\rm BB}$ ($=4^{-1/4}\,T_{\rm eff}$; denoted by a dashed line) only at the lowest $T_{\rm eff}$, where the grain emission efficiency falls below unity. As the grains get smaller, $T_{\rm grain}$ becomes larger, due to the decreasing emission efficiency. The value of $T_{\rm sub}$ for various gas densities is marked by the horizontal dotted lines. Sublimation can occur in the range $T_{\rm eff}=580-2670$ K, which corresponds to $R\sim 1-20R_{\rm BLR}$.
• Figure 5: The sublimation radius, measured in units of $R_{\rm BLR}$, versus $a$, for graphite grains at different gas densities (i.e. different $T_{\rm sub}$), for $\mu=0.1$. Grains with $a>0.2$$\mu$m can survive in dense gas ($n\ge 10^{10}$ cm$^{-3}$) at the BLR. All grains survive, essentially irrespective of $n$, once $R>20R_{\rm BLR}$. Since $R/R_{\rm BLR}$ sets the value of $T_{\rm eff}$, the above solution applies in all AGN, independent of $L_{\rm bol}$.