The giant elliptical galaxy M87 in the constellation Virgo is about 15Mpc away from the Milky Way. Although it looks like nothing special, it is a strong radio source ("Virgo A"), and a short exposure photograph shows a "jet" emerging from the center. This suggests there is some small, powerful engine in the center of M87.
In this exercise you will use data from the Hubble Space Telescope to show that the central engine of M87 is most likely a super massive black hole. A closer look at the center shows the jet emerging from a small disk-shaped region. Data taken with the Faint Object Spectrograph (FOS) aboard the HST clearly shows a Doppler Shift profile which indicates that this disk is rotating.
The data displays the optical image of the disk (including the scale for one second of arc) along with circular regions that were measured with the FOS. These circles are color coded to match the spectra shown on the bottom. The black spectrum (taken at the center of the disk) shows broad emission lines. The red and blue spectra, however, clearly show that, in each case, the broad lines are red and blue shifted versions of a narrow line. That is, the disk is rotating.
Follow these questions and calculations to demonstrate the existence of the supermassive black hole in the center of M87.
Assume the disk is circular, but it looks like an ellipse because you see it tilted at an angle. Roughly measure the axes of the apparent ellipse to estimate the inclination angle. Note that if you saw the disk perfectly edge on, then i would be 90 degrees.
The angular scale is plotted in the figure. Use this to scale the distance between the red and blue circles. Combine it with the distance to M87 (about 15Mpc) to get the disk radius in meters.
Pick any pair of red and blue lines to determine the Doppler shift. Realize that the red line measure (1+vsini/c) times the unshifted wavelength, and (1-vsini/c) for the blue line. (This Doppler shift actually measures vsini instead of v because you are not looking perfectly edge on.) Use your estimate of i to determine v.
Use our standard formula for circular orbits to determine M. It is probably easiest to stick with SI or CGS units at this point. In the end, convert M to solar masses.
Use your results for the size of the disk, and the mass of the object at the center, to argue that it must be a supermassive black hole. It is likely best to argue in terms of the mass density near the center of the disk. Recall that the distance to the nearest star to our solar system is 1.3pc.
