Velocity Profile of the Ionized Disk and the Mass of the Black Hole in   M87
  We present a theoretical model for the ionized disk in M87 which includes spiral shock waves. The line emission profiles computed from this model at various positions on the disk are found to be in agreement with the recent Hubble Space Telescope results. Based on this model, we find that the ionized disk comprises two-armed giant spiral shock waves which extend from around $0.1$ arc sec from the center to at least $1$ arc second or more. Our model requires that the mass of the black hole be $(4 \pm 0.2) \times 10^9 M_\odot$ and the inclination angle to be $(42\pm 2)^{\deg}$. We predict the nature of the line profiles at many other locations of the disk which could be verified in future observations. 
Sandip K. Chakrabarti