IMAGES OF THE RADIATIVELY INEFFICIENT ACCRETION FLOW SURROUNDING A KERR BLACK HOLE: APPLICATION IN Sgr A*

In fully general relativity, we calculate the images of the radiatively inefficient accretion flow (RIAF) surrounding a Kerr black hole (BH) with arbitrary spins, inclination angles, and observational wavelengths. For the same initial conditions, such as the fixed accretion rate, it is found that the intrinsic size and radiation intensity of the images become larger, but the images become more compact in the inner region, while the size of the BH shadow decreases with the increase of the BH spin. With the increase of the inclination angles, the shapes of the BH shadows change and become smaller, even disappear completely due to the obscuration by the thick disks. For median inclination angles, the radial velocity observed at infinity is larger because of both the rotation and radial motion of the fluid in the disk, which results in the luminous part of the images being much brighter. For larger inclination angles, such as the disk is edge-on, the emission becomes dimmer at longer observational wavelengths (such as at 7.0 mm and 3.5 mm wavelengths), or brighter at shorter observational wavelengths (such as at 1.3 mm wavelength) than that of the face on case, except for the high-spin and high-inclination images. These complex behaviors are due to the combination of the Lorentz boosting effect and the radiative absorption in the disk. We hope our results are helpful to determine the spin parameter of the BH in low-luminosity sources, such as the Galactic center. A primary analysis by comparison with the observed sizes of Sgr A* at millimeter wavelengths strongly suggests that the disk around the central BH at Sgr A* is highly inclined or the central BH is rotating fast.