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 ($\dot{M_{\rm w}}$), momentum flux ($\dot{p_{\rm w}}$), and kinetic luminosity ($\dot{E_{\rm w}}$) are in the region containing 90% of the posterior probability distribution in the $\dot M_{\rm w}$-$L_{\rm bol}$ plane, $\dot p_{\rm w}$-$L_{\rm bol}$ plane, and $\dot E_{\rm w}$-$L_{\rm bol}$ plane shown in Gofford et al., where $M_{\rm BH}$ is the black hole mass, $\varepsilon$ is the Eddington ratio, and $L_{\rm bol}$ 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, $d\log\dot{M_{\rm w}}/d\log{L_{\rm bol}}\sim 9/8$, $d\log\dot{p_{\rm w}}/d\log{L_{\rm bol}}\sim 10/8$, 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 $\varepsilon \lesssim 0.01$, since the winds do not appear. Also, only AGNs with $M_{\rm BH} \lesssim 10^8 M_\odot$ exhibit the UFOs when $\varepsilon \sim 0.025$. 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.