Shapes and Positions of Black Hole Shadows in Accretion Disks and Spin Parameters of Black Holes

摘要

Can we determine a spin parameter of a black hole by observation of a blackhole shadow in an accretion disk? In order to answer this question, we make aqualitative analysis and a quantitative analysis of a shape and a position of ablack hole shadow casted by a rotating black hole on an optically thickaccretion disk and its dependence on an angular momentum of a black hole. Wehave found black hole shadows with a quite similar size and a shape for largelydifferent black hole spin parameters and a same black hole mass. Thus, it ispractically difficult to determine a spin parameter of a black hole from a sizeand a shape of a black hole shadow in an accretion disk. We newly introduce abisector axis of a black hole shadow named a shadow axis. For a rotating blackhole a shape and a position of a black hole shadow are not symmetric withrespect to a rotation axis of a black hole shadow. So, in this case the minimuminterval between a mass center of a black hole and a shadow axis is finite. Anextent of this minimum interval is roughly proportional to a spin parameter ofa black hole for a fixed inclination angle between a rotation axis of a blackhole and a direction of an observer. In order to measure a spin parameter of ablack hole, if a shadow axis is determined observationally, it is cruciallyimportant to determine a position of a mass center of a black hole in a regionof a black hole shadow.