Context : The nearby spiral galaxy M 81 harbors in its core a Low-Luminosity AGN ( LLAGN ) , and appears closely related to the more distant and powerful AGNs seen in quasars and radio galaxies .
The intrinsic size of this object is unknown due to scattering , and it has shown a core-jet morphology with weak extended emission rotating with wavelength .

Aims : The proximity of M 81 ( D = 3.63 Mpc ) allows a detailed investigation of its nucleus to be made .
The nucleus is four orders of magnitude more luminous than the Galactic centre , and is therefore considered a link between Sgr A ^ { \star } and the more powerful nuclei of radio galaxies and quasars .
Our main goal was to determine the size of M 81 $ ^* $ at a shorter wavelength thus directly testing whether the frequency-size dependent law \Theta \propto \nu ^ { -0.8 } was still valid for wavelengths shorter than 1 cm .
In addition , we also aimed to confirm the rotation of the source as a function of frequency .

Methods : We observed the continuum 7 mm radio emission of M 81 $ ^* $ using the Very Long Baseline Array on Sep 13 , 2002 , using nearby calibrators to apply their interferometric observables to the target source , to increase the chances of detection .
The source was detected on all baselines and hybrid mapping was possible .

Results : We present the first 7 mm VLBI image of the core of M 81 $ ^* $ , which represents the highest resolution image ever of this source .
Modeling the interferometric visibilities with two Gaussian functions sets constraints on the angular size of its core down to 38 microarcseconds , corresponding to a maximum ( projected ) linear size of 138 AU , and shows extended emission towards the NE with a position angle of \sim 50 ^ { \circ } .
A fit of one Gaussian elliptical function yields a position angle of 28 \pm 8 degrees for its elongated , compact structure .
Combining the 7 mm size with earlier measurements at other frequencies we determine a frequency-size dependence of \Theta \propto \nu ^ { ( -0.88 \pm 0.04 ) } .

Conclusions : Our VLBI imaging of M 81 $ ^* $ has clearly detected its core-jet structure , and has allowed us to estimate a size for its core , with a minimum size of 138 AU ( \approx 100 Schwarzschild radii ) .
Our work opens the avenue for further observations of M 81 $ ^* $ at high-angular resolution , including the monitoring of its structure , given that much higher bandwidths are currently available on the interferometric networks .
In particular , this would allow testing for possible proper motions of the core or of its components in the inner jet of M 81 $ ^* $ , as well as for the speed of the detected jet components .