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

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.

Imprint of Gravitational Lensing by Population III Stars in Gamma Ray Burst Light Curves

We propose a novel method to extract the imprint of gravitational lensing by Pop III stars in the light curves of Gamma Ray Bursts (GRBs). Significant portions of GRBs can originate in hypernovae of Pop III stars and be gravitationally lensed by foreground Pop III stars or their remnants. If the lens mass is on the order of $10^2-10^3M_\odot$ and the lens redshift is greater than 10, the time delay between two lensed images of a GRB is $\approx 1$s and the image separation is $\approx 10 \mu$as. Although it is difficult to resolve the two lensed images spatially with current facilities, the light curves of two images are superimposed with a delay of $\approx 1$ s. GRB light curves usually exhibit noticeable variability, where each spike is less than 1s. If a GRB is lensed, all spikes are superimposed with the same time delay. Hence, if the autocorrelation of light curve with changing time interval is calculated, it should show the resonance at the time delay of lensed images. Applying this autocorrelation method to GRB light curves which are archived as the {\it BATSE} catalogue, we demonstrate that more than half light curves can show the recognizable resonance, if they are lensed. Furthermore, in 1821 GRBs we actually find one candidate of GRB lensed by a Pop III star, which may be located at redshift 20-200. The present method is quite straightforward and therefore provides an effective tool to search for Pop III stars at redshift greater than 10. Using this method, we may find more candidates of GRBs lensed by Pop III stars in the data by the {\it Swift} satellite.Comment: 13 pages, 13 figures, accepted for publication in Ap