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 ∼ 100 gravitational radius (r 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 ∼ 10 1 -10 5 r 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.

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We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind the application to the post-bounce phase of core-collapse supernovae (CCSNe). Such nonspherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch & Ott (2013) demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without the fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solved as an initial and boundary value problem with the use of Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15 M progenitor model by Woosley & Heger (2007), which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically showed that the growth rate is proportional to l, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.

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