Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions

In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian Mean Field model and show that the life-time of quasi-stationary states resulting from the violent relaxation does not allow the system to reach a complete mixed state. We also discuss the applicability of a generalization of the central limit theorem. In this context, we show that no attractor exists in distribution space for the sum of velocities of a particle other than the Gaussian distribution. The long-range nature of the interaction leads in fact to a new instance of sluggish convergence to a Gaussian distribution.Comment: 13 pages,6 figure

A Search for Host Galaxies of 24 Gamma Ray Bursts

We report the results from observations of 24 gamma ray burst (GRB) fields from 2005 and 2006 undertaken at the Danish 1.54m telescope at ESO/La Silla. Photometry and positions for two previously unpublished host galaxy candidates (GRBs 050915 and 051021) are presented, as well as for eight other detected objects which are either known GRB hosts or candidate hosts. The candidates are suitable for spectroscopic follow-up in order to have their redshifts and other physical characteristics determined. In the cases where no likely host candidate is detected inside the refined Swift XRT error circle we are still able to put interesting and rather deep limits on the host magnitude. Based on our detections and upper limits we have performed simulations which suggest that the host galaxies are drawn from a fainter sample than previous (i.e. pre-Swift) studies

Supernova 2006aj and the associated X-Ray Flash 060218

Original article can be found at: http://www.aanda.org/--Copyright The European Southern Observatory (ESO)Peer reviewe

The nature of the x-ray flash of August 24 2005

Original article can be found at: http://www.aanda.org/--Copyright The European Southern Observatory DOI: 10.1051/0004-6361:20066683Peer reviewe

The nature of the X-ray flash of August 24 2005 Photometric evidence for an on-axis z = 0.83 burst with continuous energy injection and an associated supernova?

Aims.Our aim is to investigate the nature of the X-Ray Flash (XRF) of August 24, 2005. Methods.We present comprehensive photometric R-band observations of the fading optical afterglow of XRF 050824, from 11 min to 104 days after the burst. In addition we present observations taken during the first day in the $\it BRIK$ bands and two epochs of spectroscopy. We also analyse available X-ray data. Results.The R-band lightcurve of the afterglow resembles the lightcurves of long duration Gamma-Ray Bursts (GRBs), i.e., a power-law, albeit with a rather shallow slope of $\alpha=0.6$ ( $F_{\nu} \propto t^{-\alpha}$). Our late R-band images reveal the host galaxy. The rest-frame B-band luminosity is ~0.5 L*. The star-formation rate as determined from the [O II] emission line is ~ $1.8~M_{\odot}$ yr-1. When accounting for the host contribution, the slope is $\alpha=0.65$ $\pm$ 0.01 and a break in the lightcurve is suggested. A potential lightcurve bump at 2 weeks can be interpreted as a supernova only if this is a supernova with a fast rise and a fast decay. However, the overall fit still shows excess scatter in the lightcurve in the form of wiggles and bumps. The flat lightcurves in the optical and X-rays could be explained by a continuous energy injection scenario, with an on-axis viewing angle and a wide jet opening angle ( \theta_j \ga {10}^\circ). If the energy injections are episodic this could potentially help explain the bumps and wiggles. Spectroscopy of the afterglow gives a redshift of z=0.828 $\pm$ 0.005 from both absorption and emission lines. The spectral energy distribution (SED) of the afterglow has a power-law ( $F_{\nu} \propto \nu ^{-\beta}$) shape with slope ${\beta}=0.56$ $\pm$ 0.04. This can be compared to the X-ray spectral index which is ${\beta_{\rm X}}=1.0$ $\pm$ 0.1. The curvature of the SED constrains the dust reddening towards the burst to $A_{\rm v}<0.5$ mag