On inferring extinction laws in z~6 quasars as signatures of supernova dust

Unusual extinction curves of high-redshift QSOs have been taken as evidence that dust is primarily produced by supernovae at high redshift. In particular, the 3000 A Todini-Ferrara-Maiolino kink in the extinction curve of the z = 6.20 SDSS J1048+4637 has been attributed to supernova dust. Here we discuss the challenges in inferring robust extinction curves of high-redshift QSOs and critically assess previous claims of detection of supernova dust. In particular, we address the sensitivity to the choice of intrinsic QSO spectrum, the need for a long wavelength baseline, and the drawbacks in fitting theoretical extinction curves. In a sample of 21 QSOs at z ~ 6 we detect significant ultraviolet extinction using existing broad-band optical, near-infrared, and Spitzer photometry. The median extinction curve is consistent with a Small Magellanic Cloud curve with A_1450 ~ 0.7 mag and does not exhibit any conspicuous (restframe) 2175 A or 3000 A features. For two QSOs, SDSS J1044-0125 at z = 5.78 and SDSS J1030+0524 at z = 6.31, we further present X-shooter spectra covering the wavelength range 0.9-2.5 um. The resulting non-parametric extinction curves do not exhibit the 3000 A kink. Finally, in a re-analysis of literature spectra of SDSS J1048+4637, we do not find evidence for a conspicuous kink. We conclude that the existing evidence for a 3000 A feature is weak and that the overall dust properties at high and low redshift show no significant differences. This, however, does not preclude supernovae from dominating the dust budget at high redshift.Comment: 13 pages, 13 figures, ApJ, in pres

An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model

Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings subject to white noises, has been studied by using both direct simulations and a semi-analytical augmented moment method (AMM) which has been proposed in a recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For $N$-unit FN neuron ensembles, AMM transforms original $2N$-dimensional {\it stochastic} delay differential equations (SDDEs) to infinite-dimensional {\it deterministic} DEs for means and correlation functions of local and global variables. Infinite-order recursive DEs are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), yielding $8(m+1)$-dimensional deterministic DEs. When a single spike is applied, the oscillation may be induced if parameters of coupling strength, delay, noise intensity and/or ensemble size are appropriate. Effects of these parameters on the emergence of the oscillation and on the synchronization in FN neuron ensembles have been studied. The synchronization shows the {\it fluctuation-induced} enhancement at the transition between non-oscillating and oscillating states. Results calculated by AMM5 are in fairly good agreement with those obtained by direct simulations.Comment: 15 pages, 3 figures; changed the title with correcting typos, accepted in Phys. Rev. E with some change

Photometric Variability in the Faint Sky Variability Survey

The Faint Sky Variability Survey (FSVS) is aimed at finding photometric and/or astrometric variable objects between 16th and 24th mag on time-scales between tens of minutes and years with photometric precisions ranging from 3 millimag to 0.2 mag. An area of 23 deg$^2$, located at mid and high Galactic latitudes, was covered using the Wide Field Camera (WFC) on the 2.5-m Isaac Newton Telescope (INT) on La Palma. Here we present some preliminary results on the variability of sources in the FSVS.Comment: 4 pages, 3 figures, to appear in 14th European Workshop on White Dwarfs, ASP Conference Series, eds. D. Koester, S. Moehle

The host galaxy of GRB010222: The strongest damped Lyman-alpha system known

Analysis of the absorption lines in the afterglow spectrum of the gamma-ray burst GRB010222 indicates that its host galaxy (at a redshift of z=1.476) is the strongest damped Lyman-alpha (DLA) system known, having a very low metallicity and modest dust content. This conclusion is based on the detection of the red wing of Lyman-alpha plus a comparison of the equivalent widths of ultraviolet Mg I, Mg II, and Fe II lines with those in other DLAs. The column density of H I, deduced from a fit to the wing of Lyman-alpha, is (5 +/- 2) 10^22 cm^-2. The ratio of the column densities of Zn and Cr lines suggests that the dust content in our line of sight through the galaxy is low. This could be due to either dust destruction by the ultraviolet emission of the afterglow or to an initial dust composition different to that of the diffuse interstellar material, or a combination of both.Comment: Submitted to MNRAS 12 page

Gas and dust properties in the afterglow spectra of GRB 050730

We present early WHT ISIS optical spectroscopy of the afterglow of gamma-ray burst GRB 050730. The spectrum shows a DLA system with the highest measured hydrogen column to date: N(HI) = 22.1 +/- 0.1 at the third-highest GRB redshift z = 3.968. Our analysis of the Swift XRT X-ray observations of the early afterglow show X-ray flares accompanied by decreasing X-ray absorption. From both the optical and the X-ray spectra we constrain the dust and gas properties of the host galaxy. We find the host to be a low metallicity galaxy, with low dust content. Much of the X-ray absorbing gas is situated close to the GRB, whilst the HI absorption causing the DLA is most likely located further out.Comment: 5 pages, 2 figures. Accepted for A&A Letter

Dynamically-Coupled Oscillators -- Cooperative Behavior via Dynamical Interaction --

We propose a theoretical framework to study the cooperative behavior of dynamically coupled oscillators (DCOs) that possess dynamical interactions. Then, to understand synchronization phenomena in networks of interneurons which possess inhibitory interactions, we propose a DCO model with dynamics of interactions that tend to cause 180-degree phase lags. Employing an approach developed here, we demonstrate that although our model displays synchronization at high frequencies, it does not exhibit synchronization at low frequencies because this dynamical interaction does not cause a phase lag sufficiently large to cancel the effect of the inhibition. We interpret the disappearance of synchronization in our model with decreasing frequency as describing the breakdown of synchronization in the interneuron network of the CA1 area below the critical frequency of 20 Hz.Comment: 10 pages, 3 figure

The star-formation rate in the host of GRB 990712

We have observed the host galaxy of GRB 990712 at 1.4 GHz with the Australia Telescope Compact Array, to obtain an estimate of its total star-formation rate. We do not detect a source at the position of the host. The 2 sigma upper limit of 70 microJy implies that the total star-formation rate is lower than 100 Msun/yr, using conservative values for the spectral index and cosmological parameters. This upper limit is in stark contrast with recent reports of radio/submillimeter-determined star-formation rates of roughly 500 Msun/yr for two other GRB host galaxies. Our observations present the deepest radio-determined star-formation rate limit on a GRB host galaxy yet, and show that also from the unobscured radio point-of-view, not every GRB host galaxy is a vigorous starburst.Comment: A&A Letters, in press, 5 pages; a high-resolution color gif version of the paper figure is also supplie

SCUBA sub-millimeter observations of gamma-ray bursters. I. GRB 970508, 971214, 980326, 980329, 980519, 980703

We discuss the first results of our ongoing program of Target of Opportunity observations of gamma-ray bursts (GRBs) using the SCUBA instrument on the James Clerk Maxwell Telescope. We present the results for GRB 970508, 971214, 980326, 980329, 980519, and 980703. Our most important result to date is the detection of a fading counterpart to GRB 980329 at 850 microns. Although it proved to be difficult to find the infrared counterpart to this burst, the sub-millimeter flux was relatively bright. This indicates that intrinsically the brightness of this counterpart was very similar to GRB 970508. The radio through sub-millimeter spectrum of GRB 980329 is well fit by a power law with index alpha = +0.9. However, we cannot exclude a nu^(1/3) power law attenuated by synchrotron self-absorption. An alpha = +1 VLA-SCUBA power law spectrum is definitely ruled out for GRB 980703, and possibly also for GRB 980519. We cannot rule out that part of the sub-millimeter flux from GRB 980329 comes from a dusty star-forming galaxy at high redshift, such as the ones recently discovered by SCUBA. Any quiescent dust contribution will be much larger at sub-millimeter than at radio wavelengths. Both a high redshift and large dust extinction would help explain the reddening of the counterpart to GRB 980329, and a redshift of z = 5 has been suggested. The large intensity of this burst might then indicate that beaming is important.Comment: 6 pages, 3 figures, submitted to Astronomy and Astrophysic

Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincar\'e map associated to the system. We show that for strong interactions the Poincar\'e map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincar\'e map under study, but also to a wide class of general n-dimensional piecewise contractive maps.Comment: 46 pages. In this version we added many comments suggested by the referees all along the paper, we changed the introduction and the section containing the conclusions. The final version will appear in Journal of Mathematical Biology of SPRINGER and will be available at http://www.springerlink.com/content/0303-681