Toda Lattice and Tomimatsu-Sato Solutions

We discuss an analytic proof of a conjecture (Nakamura) that solutions of Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl solutions completely and for generic cases partially.Comment: LaTeX 8 page

Downward auroral currents from the reconnection Hall-region

We present a simple (stationary) mechanism capable of generating the auroral downward field-aligned electric field {that is} needed for {accelerating the ionospheric electron component up into the magnetosphere and confining the ionospheric ions at low latitudes (as is required by observation of an ionospheric cavity in the downward auroral current region). The lifted ionospheric electrons carry the downward auroral current. Our model is based on the assumption of collisionless reconnection in the tail current sheet. It makes use of the dynamical difference between electrons and ions in the ion inertial region surrounding the reconnection {\sf X}-line which causes Hall currents to flow. We show that the spatial confinement of the Hall magnetic field and flux to the ion inertial region centred on the {\sf X}-point generates a spatially variable electromotive force which is positive near the outer inflow boundaries of the ion inertial region and negative in the central inflow region. Looked {at} from the ionosphere it functions like a localised meso-scale electric potential.} The positive electromotive force gives rise to upward electron flow from the ionosphere {during substorms (causing `black aurorae')}. A similar positive potential is identified on the earthward side of the fast reconnection outflow region which has the same effect, explaining the observation that auroral upward currents are flanked from both sides by narrow downward currents. keywords{Field-aligned auroral currents, parallel fields, Hall field in reconnection, substorms}Comment: 5 figures, 7 printed Journal pages, revised, extended and 3 figures adde

Magnetically Regulated Star Formation in Turbulent Clouds

We investigate numerically the combined effects of supersonic turbulence, strong magnetic fields and ambipolar diffusion on cloud evolution leading to star formation. We find that, in clouds that are initially magnetically subcritical, supersonic turbulence can speed up star formation, through enhanced ambipolar diffusion in shocks. The speedup overcomes a major objection to the standard scenario of low-mass star formation involving ambipolar diffusion, since the diffusion time scale at the average density of a molecular cloud is typically longer than the cloud life time. At the same time, the strong magnetic field can prevent the large-scale supersonic turbulence from converting most of the cloud mass into stars in one (short) turbulence crossing time, and thus alleviate the high efficiency problem associated with the turbulence-controlled picture for low-mass star formation. We propose that relatively rapid but inefficient star formation results from supersonic collisions of somewhat subcritical gas in strongly magnetized, turbulent clouds. The salient features of this shock-accelerated, ambipolar diffusion-regulated scenario are demonstrated with numerical experiments.Comment: 10 pages, 3 figures, accepted for publication in ApJ

Perturbations of Matter Fields in the Second-order Gauge-invariant Cosmological Perturbation Theory

Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in the papers [K.Nakamura, Prog.Theor.Phys., 117 (2007), 17.]. We derive the formulae for the perturbations of the energy momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a signle scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing.Comment: (v1) 76 pages, no figure; (v2) minor revision, typos are corrected, references are added; (v3) Title is changed, Compactified into 55 pages, Comment on the comparison with the other work is added; (v4)typos are correcte