Secondary Star Formation in a Population III Object

We explore the possibility of subsequent star formation after a first star forms in a Pop III object, by focusing on the radiation hydrodynamic (RHD) feedback brought by ionizing photons as well as H2 dissociating photons. For the purpose, we perform three-dimensional RHD simulations, where the radiative transfer of ionizing photons and H2 dissociating photons from a first star is self-consistently coupled with hydrodynamics based on a smoothed particle hydrodynamics method. As a result, it is shown that density peaks above a threshold density can keep collapsing owing to the shielding of H2 dissociating radiation by an H2 shell formed ahead of a D-type ionization front. But, below the threshold density, an M-type ionization front accompanied by a shock propagates, and density peaks are radiation hydrodynamically evaporated by the shock. The threshold density is dependent on the distance from a source star, which is $\approx 10^2 cm^{-3}$ for the source distance of 30pc. Taking into consideration that the extent of a Pop III object is $\approx 100$pc and density peaks within it have the density of $10^{2-4}$cm$^{-3}$, it is concluded that the secondary star formation is allowed in the broad regions in a Pop III object.Comment: 4pages, 2 figures, submitted to Ap

Merger of Multiple Accreting Black Holes Concordant with Gravitational-wave Events

Recently, the advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) has detected black hole (BH) merger events, most of which are sourced by BHs more massive than 30 M-circle dot. Especially, the observation of GW170104 suggests dynamically assembled binaries favoring a distribution of misaligned spins. It has been argued that mergers of unassociated BHs can be engendered through a chance meeting in a multiple BH system under gas-rich environments. In this paper, we consider the merger of unassociated BHs, concordant with the massive BH merger events. To that end, we simulate a multiple BH system with a post-Newtonian N-body code incorporating gas accretion and general relativistic effects. As a result, we find that gas dynamical friction effectively promotes a three-body interaction of BHs in dense gas of n(gas) greater than or similar to 10(6) cm(-3), so that BH mergers can take place within 30 Myr. This scenario predicts an isotropic distribution of spin tilts. In the concordant models with GW150914, the masses of seed BHs are required to be greater than or similar to 25 M-circle dot. The potential sites of such chance meeting BH mergers are active galactic nucleus (AGN) disks and dense interstellar clouds. Assuming the LIGO O1, we roughly estimate the event rates for PopI BHs and PopIII BHs in AGN disks to be similar or equal to 1-2 yr(-1) and similar or equal to 1 yr(-1), respectively. Multiple episodes of AGNs may enhance the rates by roughly an order of magnitude. For massive PopI BHs in dense interstellar clouds the rate is similar or equal to 0.02 yr(-1). Hence, high-density AGN disks are a more plausible site for mergers of chance meeting BHs

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

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

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.