Constraining the size of the dark region around the M87 black hole by space-VLBI observations

In order to examine if the next generation space VLBI,such as VSOP-2 (VLBI Space Observatory Programme-2), will make it possible to obtain direct images of the accretion flow around the M87 black hole, we calculate the expected observed images by the relativistic ray-tracing simulations under the considerations of possible observational errors. We consider various cases of electron temperature profiles, as well as a variety of the distance, mass, and spin of the M87 black hole. We find it feasible to detect an asymmetric intensity profile around the black hole caused by rapid disk rotation, as long as the electron temperature does not steeply rises towards the black hole, as was predicted by the accretion disk theory and the three dimensional magnetohydrodynamic simulations. Further, we can detect a deficit in the observed intensity around the black hole when the apparent size of the gravitational radius is larger than $\gtrsim 1.5 \mu$ arcseconds. In the cases that the inner edge of the disk is located at the radius of the innermost stable circular orbit (ISCO), moreover, even the black hole spin will be measured. We also estimate the required signal-to-noise ratio $\mathcal{R}_{\rm SN}$ for achieving the scientific goals mentioned above, finding that it should be at least 10 at 22 GHz. To conclude, direct mapping observations by the next generation space VLBI will provide us a unique opportunity to provide the best evidence for the presence of a black hole and to test the accretion disk theory.