Parabolic Jets from the Spinning Black Hole in M87
  The M87 jet is extensively examined by utilizing general relativistic
magnetohydrodynamic (GRMHD) simulations as well as the steady axisymmetric
force-free electrodynamic (FFE) solution. Quasi-steady funnel jets are obtained
in GRMHD simulations up to the scale of $\sim 100$ gravitational radius
($r_{\rm g}$) for various black hole (BH) spins. As is known, the funnel edge
is approximately determined by the following equipartitions; i) the magnetic
and rest-mass energy densities and ii) the gas and magnetic pressures. Our
numerical results give an additional factor that they follow the outermost
parabolic streamline of the FFE solution, which is anchored to the event
horizon on the equatorial plane. We also identify the matter dominated,
non-relativistic corona/wind play a dynamical role in shaping the funnel jet
into the parabolic geometry. We confirm a quantitative overlap between the
outermost parabolic streamline of the FFE jet and the edge of jet sheath in
VLBI observations at $\sim 10^{1}$-$10^{5} \, r_{\rm g}$, suggesting that the
M87 jet is likely powered by the spinning BH. Our GRMHD simulations also
indicate a lateral stratification of the bulk acceleration (i.e., the
spine-sheath structure) as well as an emergence of knotty superluminal
features. The spin characterizes the location of the jet stagnation surface
inside the funnel. We suggest that the limb-brightened feature could be
associated with the nature of the BH-driven jet, if the Doppler beaming is a
dominant factor. Our findings can be examined with (sub-)mm VLBI observations,
giving a clue for the origin of the M87 jet.
