A Hydrodynamical Thermal Irradiated Wind from the Outer Thin Accretion Disk in Low-luminosity Active Galactic Nuclei

TL;DR

This paper develops a hydrodynamical model for a thermally driven wind from the outer geometrically thin disk in LLAGNs, energized by irradiation from the inner hot flow (parameterized by $x$) and heated mainly by photoionization. Solving the steady, axisymmetric HD equations in cylindrical coordinates along the $z$-axis at fixed radius, the authors show that wind launching occurs from a sonic height $z^{max}$ with an isobaric regime above it, and the launching height grows with irradiation strength. The wind is predominantly equatorial ($i>85^ ^"+, with $v_{wind}\sim v_\phi$) and can be constrained by observed bolometric luminosities and Bondi accretion rates; the model also accounts for disk self-gravity, showing it reduces scale height but leaves wind properties largely unchanged. When applied to NGC 1097, the predicted wind densities and kinetic luminosities are compatible with ALMA molecular gas measurements and with LLAGN wind signatures, implying outer-disk winds are a common, observable feature of LLAGNs. The work provides a framework linking inner-disk irradiation, vertical hydrostatic balance, and wind launching, with implications for line profiles and the mass inflow/outflow balance in LLAGNs.

Abstract

Evidently, low-luminosity active galactic nuclei (LLAGNs) are comprised of an inner advective disk and an outer geometrically thin disk. Wind is inevitable in LLAGNs, mainly interpreted in an indirect way, also the evidence is growing for the presence of wind in the outer thin disk. We present a hydrodynamics (HD) model for wind from the outer thin disk, where the main driver is the inner disk irradiation (which is parameterized by a number $x$ in hydrostatic equilibrium equation) and the heating mechanism is photoionization. The model works for low-intensity irradiation or from a height $z_s$ in the optically thin medium. We solve the model equations in cylindrical coordinates along the $z$-axis for a given radius $r$ with assuming a tiny vertical speed $v_z$ ($\ll c_s$ sound speed). The sonic point conditions assure an isobaric regime above the sonic height ($z^{max}$); in addition to the height $z_f (\ll z^{max}$), the radial pressure gradient also supports the fluid rotation, and both jointly assure a wind ejection from the $z^{max}$ with fluid speed. The $z^{max}$ increases with $x$, and beyond a large $z^{max}$ (say $z^{max}_t$ corresponding to maximum $x$), there is no physical solution. We start the computation from the outer radius $r_o^{thin}$ to the inner $r_{in}^{thin}$ with a Bondi mass accretion rate $\dot{M}_{Bondi}$, to explore the $r$ dependency of the mass inflow rate $\dot{M}$ and wind properties. We constrain the model by fixing $\dot{M}$ at $r_{in}^{thin}$ from the observations of NGC 1097 and check the feasibility of the model by comparing the energetics with the observed bolometric luminosity. The wind is an equatorial with a viewing angle $i>85$ degrees and capable to generate red/blueshifted lines, which would be a general characteristics for LLAGNs.

Figures (16)

• Figure 1: The solutions of model equations for $x$ = 0, $r$ = 2000$R_g$, and $f_v$ =1. The left panel is for three different velocities ($v_z$, $|v_r|$, $c_s$) as functions of $z$ (measured in units of the Keplerian scale height $h$, here $r/h$$\sim$118). The middle panel is for pressure $p/p_c$ and density $\rho/ \rho_c$, which are shown by solid curves 2 and 1, respectively. The dashed curves 2 and 1 are for model curves $\exp{\left(\frac{-z^2}{2(0.92h)^2}\right)}$ and $\exp{\left(\frac{-z^2}{2(1.2h)^2}\right)}$, respectively. The right panel shows the comparison between $v_r \frac{\partial v_r}{\partial r}$, $v_z \frac{\partial v_z}{\partial z}$ and force terms $\frac{1}{\rho} \frac{\partial p}{\partial r}$, $F_z$, and $F_r$, which are shown by the curves 5, 4, 3, 2, and 1, respectively. In the left panel, we have marked the $z^{max}$ or sonic height by a vertical line.
• Figure 2: The model solutions with $z_s =h$, for $x$ = 7.8 $\times$ 10$^{-9}$ (or $z^{max} \sim$ 60$h$), and $r$ = 2000 $R_g$. Panels [a], [b], and [d] are same as the left, middle, and right panels of Figure \ref{['fig:x0']}. Panel [c] shows the variations of $v_\phi$ and $v_{esc}$= $\sqrt{\frac{2GM}{\sqrt{r^2+z^2}}}$ with height. Here, for $z<z_s$ the solution is the same as the $x=0$ case as shown in Figure \ref{['fig:x0']}, and at $z \sim h$ the sharp change is due to the irradiation effect. In the inset figure of panel [b] the dashed curve is for $z_s$ = 0, $x$ = 7.0 $\times$ 10$^{-9}$ (or $z^{max} \sim$55$h$), shifted by $+h$ and lowered by a factor of 0.7, which shows that the sharp changes are consistent with the Paper I results.
• Figure 3: The density, pressure, and $\frac{\partial p}{\partial z}$ profile in the vertical direction are shown for different $x$ with $z_s=h$ in the left, middle, and right panels, respectively. Here the curves 1, 2, 3, 4, 5, 8, and 7 are for $x$ ($z^{max}$) $\sim$ 0 (2.2$h$), 0.5 (4$h$), 1.4 (10$h$), 3.6 (25$h$), 7.8 (60$h$), 8.36 (70$h$), and 8.69 $\times$ 10$^{-9}$ (100$h$), respectively. The inset Figure shows the variation of the power-law index around $z=2h$. Here, the results for $z<h$ are not shown, as they are identical to the Figure \ref{['fig:x0']}, and curve 5 of the left and middle panels is the same as curves 1 and 2 of panel [b] of Figure \ref{['fig:z60']}, respectively.
• Figure 4: The possible range of $x$ and the corresponding $z^{max}$ for the acceleration solutions of equation (\ref{['eq:master']}) with $z_s =h$. The left panel is for four different $f_v$ = 1, 2.5, 5, and 10 which are shown by curves 1, 2, 3, and 4, respectively, at fixed $r$ = 2000 $R_g$ and $\dot{M}$ = 0.001 $\dot{M}_{Edd}$. The middle panel is for $\dot{M}$ = 0.1, 0.01, and 0.001 $\dot{M}_{Edd}$ which are shown by curves 1b, 1a, and 1, respectively, at $r$ = 2000 $R_g$ and $f_v$ = 1. The right panel is for $r$ = 500, 2000, 10$^4$, and 10$^5$$R_g$ which are shown by curves 5, 1, 6, and 7, respectively at $\dot{M}$ = 0.001 $\dot{M}_{Edd}$ and $f_v$ = 1
• Figure 5: The top, middle, and bottom panels are for the $p/p_c$, $\rho/\rho_c$ and $\frac{\partial p}{\partial z}$ profiles in the vertical direction for $x \rightarrow x^{max}$, respectively. The left panel is for different $f_v$ and the curves 1, 2, and 3 are for $f_v$ = 1, 2, and 10, respectively. The centre panel is for different $r$, and the curves 1, 2, and 3 are for $r$ = 500, 2000, and 10$^4$$R_g$, respectively. The right panel is for different $z_s$, and the curves 1, 2, and 3 are for $z_s$ = 1.0, 1.5, and 1.95, respectively. The rest of the parameters are same as in Figure \ref{['fig:z60']}. Here curve 1 of the left, curve 2 of the middle, and curve 3 of the right panel are same as curve 5 of Figure \ref{['fig:p_x-r2e3']}, and for $2h<z<6h$ the power-law indexes of all curves are almost similar.