Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)

The critical and asymptotic behaviors of solutions of the sixth Painlev\'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated.Comment: 30 pages, 1 figure; Nonlinearity 201

The Nature of Lya Blobs: Supernova-Dominated Primordial Galaxies

We consider a forming galaxy undergoing multitudinous supernova (SN) explosions, as a possible model of \lya blobs (LABs). For this purpose, an ultra--high resolution hydrodynamic simulation is performed using $1024^3$ grid points, where SN remnants are resolved with sufficient accuracy. It is found that multiple SN explosions produce kpc--size expanding hot bubbles, which drive cool, dense shells by strong shock. The colliding high--density cooling shells radiate intensive \lya emission, resulting in a high \lya luminosity of $\sim10^{43}$ erg s$^{-1}$, comparable to the observed level in LABs. Also, recently discovered bubbly features in some LABs are quite similar to the structure predicted in the present simulation. Furthermore, the result demonstrates that LABs are representative of evolving primordial galaxies; they could hold direct information on the early chemical enrichment of galaxies, contrary to present--day galaxies which have undergone intense recycling of interstellar matter, thus erasing most of the early chemical history. It turns out that the metal mixing proceeds in a very inhomogeneous fashion, so that there appears a large spread of metallicity, that is,$[{\rm Fe/H}] \approx 0 {\rm ~to} -5$ or $[{\rm O/H}] \approx 1 {\rm ~to} -4$. Hence, the early galactic chemical evolution may have proceeded in a different manner from that hitherto considered in one--zone models.Comment: 4 pages, 2 figures, accepted fot publicatin in ApJ

Rational Solutions of the Painleve' VI Equation

In this paper, we classify all values of the parameters $\alpha$, $\beta$, $\gamma$ and $\delta$ of the Painlev\'e VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlev\'e VI equation.Comment: 13 pages, 1 Postscript figure Typos fixe

Determinant Structure of the Rational Solutions for the Painlev\'e IV Equation

Rational solutions for the Painlev\'e IV equation are investigated by Hirota bilinear formalism. It is shown that the solutions in one hierarchy are expressed by 3-reduced Schur functions, and those in another two hierarchies by Casorati determinant of the Hermite polynomials, or by special case of the Schur polynomials.Comment: 19 pages, Latex, using theorem.st

Ultrafast outflows: Galaxy-scale active galactic nucleus feedback

We show, using global three-dimensional grid-based hydrodynamical simulations, that ultrafast outflows (UFOs) from active galactic nuclei (AGNs) result in considerable feedback of energy and momentum into the interstellar medium (ISM) of the host galaxy

Early Cosmic Formation of Massive Black Holes

The evolution of nonlinear density fluctuations around the Jeans mass shortly after cosmological recombination is analyzed using a 3D hydrodynamics/dark--matter code. The Cosmic Background Radiation (CBR) exerts Compton friction on free electrons due to peculiar velocities. The dynamics therefore depends strongly on the gas ionization history. Under a variety of ionization conditions and in systems with or without non-baryonic components, the baryons lose angular momentum efficiently and collapse to form a compact optically--thick object which would probably quickly evolve into a massive black hole. Attention is concentrated on elucidating some of the novel physical effects in early cosmological collapses, but ways in which more realistic calculations might be made and in which the scenario could be incorporated into a more complete cosmogonic model are discussed.Comment: LaTeX file, figures not included. For hardcopy of figures contact [email protected]. Institute for Advanced Study number AST 93/11-

Existence and Uniqueness of Tri-tronqu\'ee Solutions of the second Painlev\'e hierarchy

The first five classical Painlev\'e equations are known to have solutions described by divergent asymptotic power series near infinity. Here we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlev\'e equation. Moreover we prove that these are unique in certain sectors near infinity.Comment: 13 pages, Late

A generalization of determinant formulas for the solutions of Painlev\'e II and XXXIV equations

A generalization of determinant formulas for the classical solutions of Painlev\'e XXXIV and Painlev\'e II equations are constructed using the technique of Darboux transformation and Hirota's bilinear formalism. It is shown that the solutions admit determinant formulas even for the transcendental case.Comment: 20 pages, LaTeX 2.09(IOP style), submitted to J. Phys.