46,511 research outputs found
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
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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
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