The Location of the Core in M81
  We report on VLBI observations of M81*, the northwest-southeast oriented nuclear core-jet source of the spiral galaxy M81, at five different frequencies between 1.7 and 14.8 GHz. By phase referencing to supernova 1993J we can accurately locate the emission region of M81* in the galaxy's reference frame. Although the emission region's size decreases with increasing frequency while the brightness peak moves to the southwest, the emission region seems sharply bounded to the southwest at all frequencies. We argue that the core must be located between the brightness peak at our highest frequency (14.8 GHz) and the sharp bound to the southwest. This narrowly constrains the location of the core, or the purported black hole in the center of the galaxy, to be within a region of +/-0.2 mas or +/-800 AU (at a distance of ~4 Mpc). This range includes the core position that we determined earlier by finding the most stationary point in the brightness distribution of M81* at only a single frequency. This independent constraint therefore strongly confirms our earlier core position. Our observations also confirm that M81* is a core-jet source, with a one-sided jet that extends to the northeast from the core, on average curved somewhat to the east, with a radio spectrum that is flat or inverted near the core and steep at the distant end. The brightness peak is unambiguously identified with the variable jet rather than the core, which indicates limitations in determining the proper motion of nearby galaxies and in refining the extragalactic reference frame. 
M. F. Bietenholz, N. Bartel and M. P. Rupen