A Spectrophotometric Method to Determine the Inclination of Class I Objects

A new method which enables us to estimate the inclination of Class I young stellar objects is proposed. Since Class I objects are not spherically symmetric, it is likely that the observed feature is sensitive to the inclination of the system. Thus, we construct a protostar model by carefully treating two-dimensional (2D) radiative transfer and radiative equilibrium. We show from the present 2D numerical simulations that the emergent luminosity L_SED,which is the frequency integration of spectral energy distribution (SED), depends strongly on the inclination of the system i, whereas the peak flux is insensitive to i. Based on this result, we introduce a novel indicator f_L, which is the ratio of L_SED to the peak flux, as a good measure for the inclination. By using f_L, we can determine the inclination regardless of the other physical parameters. The inclination would be determined by f_L within the accuracy of +- 5 degree, if the opening angle of bipolar outflows is specified by any other procedure. Since this spectrophotometric method is easier than a geometrical method or a full SED fitting method, this method could be a powerful tool to investigate the feature of protostars statistically with observational data which will be provided by future missions, such as SIRTF, ASTRO-F, and ALMA.Comment: 14 pages, 9 figures, accepted by Ap

The Reionization History and Early Metal Enrichment inferred from the Gamma-Ray Burst Rate

Based on the gamma-ray burst (GRB) event rate at redshifts of $4 \leq z \leq 12$, which is assessed by the spectral peak energy-to-luminosity relation recently found by Yonetoku et al., we observationally derive the star formation rate (SFR) for Pop III stars in a high redshift universe. As a result, we find that Pop III stars could form continuously at $4 \leq z \leq 12$. Using the derived Pop III SFR, we attempt to estimate the ultraviolet (UV) photon emission rate at $7 \leq z \leq 12$ in which redshift range no observational information has been hitherto obtained on ionizing radiation intensity. We find that the UV emissivity at $7 \leq z \leq 12$ can make a noticeable contribution to the early reionization. The maximal emissivity is higher than the level required to keep ionizing the intergalactic matter at $7 \leq z \leq 12$. However, if the escape fraction of ionizing photons from Pop III objects is smaller than 10%, then the IGM can be neutralized at some redshift, which may lead to the double reionization. As for the enrichment, the ejection of all metals synthesized in Pop III objects is marginally consistent with the IGM metallicity, although the confinement of metals in Pop III objects can reduce the enrichment significantly.Comment: 12 pages, 2 figures, ApJL accepte

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.

Formation of Large-Scale Obscuring Wall and AGN Evolution Regulated by Circumnuclear Starbursts

By considering the radiative force by a circumnuclear starburst as well as an AGN, we analyze the equilibrium configuration and the stability of dusty gas in the circumnuclear regions. It is found that the radiative force by an intensive starburst can support a stable gaseous wall with a scale-height of several hundred parsecs. Moreover, by taking the simple stellar evolution in the starburst into account, we find that the covering factor of the wall decreases on a time-scale of several $10^7$ yr. The large-scale wall, if formed, works to obscure the nucleus due to the dust opacity. Hence, it is anticipated that the index of AGN type tends to shift from higher to lower in several $10^7$ yr according as the circumnuclear starburst becomes dimmer. On the other hand, if the AGN itself is brighter than the circumnuclear starburst (e.g. quasar case), no stable large-scale wall forms. In that case, the AGN is highly probably identified as type 1. The present mechanism may provide a physical explanation for the putative correlation between AGN type and host properties that Sy2's are more frequently associated with circumnuclear starbursts than Sy1's, whereas quasars are mostly observed as type 1 regardless of star-forming activity in the host galaxies.Comment: 10 pages, 3 figures, ApJ Letters in pres

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

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

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

An X-Ray Microlensing Test of AU-Scale Accretion Disk Structure in Q2237+0305

The innermost regions of quasars can be resolved by a gravitational-lens {\lq}telescope{\rq} on scales down to a few AU. For the purpose, X-ray observations are most preferable, because X-rays originating from the innermost regions, can be selectively amplified by microlensing due to the so-called `caustic crossing'. If detected, X-ray variations will constrain the size of the X-ray emitting region down to a few AU. The maximum attainable resolution depends mainly on the monitoring intervals of lens events, which should be much shorter than the crossing time. On the basis of this idea, we performe numerical simulations of microlensing of an optically-thick, standard-type disk as well as an optically-thin, advection-dominated accretion flow (ADAF). Calculated spectral variations and light curves show distinct behaviors, depending on the photon energy. X-ray radiation which is produced in optically thin region, exhibits intensity variation over a few tens of days. In contrast, optical-UV fluxes, which are likely to come from optically thick region, exhibit more gradual light changes, which is consistent with the microlensing events so far observed in Q2237+0305. Currently, Q2237+0305 is being monitored in the optical range at Apache Point Observatory. Simultaneous multi-wavelength observations by X-ray sattelites (e.g., ASCA, AXAF, XMM) as well as HST at the moment of a microlens event enable us to reveal an AU scale structure of the central accretion disk around black hole.Comment: 10 pages LaTeX, 3 figures, accepted to ApJ Letter. e-mail: [email protected]

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