The Solar Optical Telescope (SOT) on board Hinode satellite observed an X3.4 class flare on 2006 December 13. Typical two-ribbon structure was observed, not only in the chromospheric Ca II H line but also in G-band and Fe I 6302Å line. The high-resolution, seeing-free images achieved by SOT revealed, for the first time, the sub-arcsec fine structures of the "white light" flare. The G-band flare ribbons on sunspot umbrae showed a sharp leading edge followed by a diffuse inside, as well as previously known core-halo structure. The underlying structures such as umbral dots, penumbral filaments and granules were visible in the flare ribbons. Assuming that the sharp leading edge was directly heated by particle beam and the diffuse parts were heated by radiative back-warming, we estimate the depth of the diffuse flare emission using the intensity profile of the flare ribbon. We found that the depth of the diffuse emission is about 100 km or less from the height of the source of radiative back-warming. The flare ribbons were also visible in the Stokes-V images of Fe I 6302 A as a transient polarity reversal. This is probably related to "magnetic transient" reported in the literature. The intensity increase in Stokes-I images indicates that 1 the Fe I 6302Å line was significantly deformed by the flare, which may cause such a magnetic transient.

We present a new magnetohydrodynamic (MHD) simulation code with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements the HLLD approximate Riemann solver, the fifth-order-monotonicity-preserving interpolation (MP5) scheme, and the hyperbolic divergence cleaning method for a magnetic field. This choice of schemes significantly improved numerical accuracy and stability, and saved computational costs in multidimensional problems. Numerical tests of one-and two-dimensional problems showed the advantages of using the high-order scheme by comparing with results from a standard secondorder TVD MUSCL scheme. The present code enabled us to explore long-term evolution of a three-dimensional accretion disk around a black hole, in which compressible MHD turbulence caused continuous mass accretion via nonlinear growth of the magneto-rotational instability (MRI). Numerical tests with various computational cell sizes exhibited a convergent picture of the early nonlinear growth of the MRI in a global model, and indicated that the MP5 scheme has more than twice the resolution of the MUSCL scheme in practical applications.

We develop new numerical schemes for Vlasov-Poisson equations with high-order accuracy. Our methods are based on a spatially monotonicity-preserving (MP) scheme and are modified suitably so that positivity of the distribution function is also preserved. We adopt an efficient semi-Lagrangian time integration scheme that is more accurate and computationally less expensive than the threestage TVD Runge-Kutta integration. We apply our spatially fifth-and seventh-order schemes to a suite of simulations of collisionless self-gravitating systems and electrostatic plasma simulations, including linear and nonlinear Landau damping in one dimension and Vlasov-Poisson simulations in a six-dimensional phase space. The high-order schemes achieve a significantly improved accuracy in comparison with the third-order positive-flux-conserved scheme adopted in our previous study. With the semi-Lagrangian time integration, the computational cost of our high-order schemes does not significantly increase, but remains roughly the same as that of the third-order scheme. Vlasov-Poisson simulations on 128 3 ×128 3 mesh grids have been successfully performed on a massively parallel computer.

A large set of numerical simulations of MHD turbulence induced by the magnetorotational instability is presented. Revisiting the previous survey conducted by Sano et al., we investigate the gas pressure dependence of the saturation level. In ideal MHD simulations, the gas pressure dependence is found to be very sensitive to the choice of numerical scheme. This is because the numerical magnetic Prandtl number varies according to the scheme as well as the pressure, which considerably affects the results. The saturation level is more sensitive to the numerical magnetic Prandtl number than the pressure. In MHD simulations with explicit viscosity and resistivity, the saturation level increases with the physical magnetic Prandtl number, and it is almost independent of the gas pressure when the magnetic Prandtl number is constant. This is indicative of the incompressible turbulence saturated by the secondary tearing instability.

We study nonthermal emission in a solar flare occurring on 2003 May 29 using RHESSI hard X-ray ( HXR) and Nobeyama microwave observations. This flare shows several typical behaviors of HXR and microwave emission: time delay of microwave peaks relative to HXR peaks, loop-top microwave and footpoint HXR sources, and a harder electron energy distribution from the microwave spectrum than from the HXR spectrum. In addition, we found that the time profile of the spectral index of the higher energy (k100 keV ) HXRs is similar to that of the microwaves, and is delayed relative to that of the lower energy (P100 keV ) HXRs. We interpret these observations in terms of an electron transport model called trap-plus-precipitation. We numerically solved the spatially homogeneous FokkerPlanck equation to determine electron evolution in energy and pitch-angle space. By comparing observations with the behavior of HXR and microwave emission predicted by the model, we examine the pitch-angle distribution of the electrons injected into the flare site. We find that the observed spectral variations can be qualitatively explained if the injected electrons have a pitch-angle distribution concentrated perpendicular to the magnetic field lines rather than an isotropic distribution.