Line-driven disk wind model for ultra-fast outflows in active galactic nuclei -- Scaling with luminosity

In order to reveal the origin of the ultra-fast outflows (UFOs) that are frequently observed in active galactic nuclei (AGNs), we perform two-dimensional radiation hydrodynamics simulations of the line-driven disk winds, which are accelerated by the radiation force due to the spectral lines. The line-driven winds are successfully launched for the range of $M_{\rm BH}=10^{6-9}M_\odot$and$\varepsilon$=0.1-0.5, and the resulting mass outflow rate ($\dot{M_{\mathrm{w}}}$), momentum flux ($\dot{p_{\mathrm{w}}}$), and kinetic luminosity ($\dot{E_{\mathrm{w}}}$) are in the region containing 90% of the posterior probability distribution in the ${\dot{M}}_{\mathrm{w}}$-$L_{\mathrm{b}\mathrm{o}\mathrm{l}}$ plane, ${\dot{p}}_{\mathrm{w}}$-$L_{\mathrm{b}\mathrm{o}\mathrm{l}}$ plane, and ${\dot{E}}_{\mathrm{w}}$-$L_{\mathrm{b}\mathrm{o}\mathrm{l}}$ plane shown in Gofford et al., where $M_{\mathrm{B}\mathrm{H}}$ is the black hole mass, $\epsilon$ is the Eddington ratio, and $L_{\mathrm{b}\mathrm{o}\mathrm{l}}$ is the bolometric luminosity. The best-fitting relations in Gofford et al., $d\log\dot{M_{\rm w}}/d\log{L_{\rm bol}}\sim 0.9$,$d\log\dot{p_{\rm w}}/d\log{L_{\rm bol}}\sim 1.2$,and$d\log\dot{E_{\rm w}}/d\log{L_{\rm bol}}\sim 1.5$, are roughly consistent with our results, $d\log \dot{M_{\mathrm{w}}}\mathrm{/}d\log L_{\mathrm{b}\mathrm{o}\mathrm{l}}\sim 9\mathrm{/}8$, $d\log \dot{p_{\mathrm{w}}}\mathrm{/}d\log L_{\mathrm{b}\mathrm{o}\mathrm{l}}\sim 10\mathrm{/}8$, and $d\log\dot{E_{\rm w}}/d\log{L_{\rm bol}}\sim 11/8$. In addition, our model predicts that no UFO features are detected for the AGNs with $\epsilon \lesssim 0.01$, since the winds do not appear. Also, only AGNs with $M_{\mathrm{B}\mathrm{H}}\lesssim {10}^8{M}_{\odot }$ exhibit the UFOs when $\epsilon \sim 0.025$. These predictions nicely agree with the X-ray observations (Gofford et al.). These results support that the line-driven disk wind is the origin of the UFOs.