Modeling Line-Driven Disk Wind for Broad Absorption Lines of Quasars

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Abstract The disk wind, which is powered by the radiation force due to spectral lines (line force), has been studied concerning broad absorption line (BAL) quasars. We investigated the structure of the disk wind based on a non-hydrodynamic method, and compared it with wind properties inferred from X-ray observations of BAL quasars. In the present work, we applied the stellar wind theory to the initial condition (the mass outflow rate at the base of the wind). We found funnel-shaped winds with a half opening angle of $ \sim$ 50$ ^{\circ}$ for the case of $ \epsilon$$ =$ 0.3–0.9 and $ M_{\rm BH}$$ =$ 10$ ^{7-8.5}$$ M_\odot$ , where $ \epsilon$ is the Eddington ratio and $ M_{\rm BH}$ is the black-hole mass. Thus, the absorption features are observed for an observer of which the viewing angle is around 50$ ^{\circ}$ . A probability of BAL quasars is $ \sim$ 7%–11%, which is roughly consistent the abundance ratio of BAL quasars, $ \sim$ 10%–15%. Here, the probability is estimated by the solid angle, that the absorbing features would be detected, divided by 4$ \pi$ . In contrast, if the Eddington ratio is smaller than 0.01, or if the black hole is very massive, $ M_{\rm BH}$$ \gtrsim$ 10$ ^{9}$$ M_{\odot}$ , the disk wind is not launched due to the less effective line force. Then, the quasars are identified as non-BAL quasars independently of the observer's viewing angle.