A search for thermal X-ray signatures in Gamma-Ray Bursts II: The Swift sample

In several gamma-ray bursts (GRBs) excess emission, in addition to the standard synchrotron afterglow spectrum, has been discovered in the early time X-ray observations. It has been proposed that this excess comes from black body emission, which may be related to the shock break-out of a supernova in the GRBs progenitor star. This hypothesis is supported by the discovery of excess emission in several GRBs with an associated supernova. Using mock spectra we show that it is only likely to detect such a component, similar to the one proposed in GRB 101219B, at low redshift and in low absorption environments. We also perform a systematic search for black body components in all the GRBs observed with the Swift satellite and find six bursts (GRB 061021, 061110A, 081109, 090814A, 100621A and 110715A) with possible black body components. Under the assumption that their excess emission is due to a black body component we present radii, temperatures and luminosities of the emitting components. We also show that detection of black body components only is possible in a fraction of the Swift bursts.Comment: 11 pages, 8 figures, accepted for MNRA

Time-Dependent Random Walks and the Theory of Complex Adaptive Systems

Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing boundary. For an unbiased walk the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities. On the other hand, a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability. We use the results to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clustering observed in the evolutionary minority game.Comment: 5 pages, 2 figure

Driven particle in a random landscape: disorder correlator, avalanche distribution and extreme value statistics of records

We review how the renormalized force correlator Delta(u), the function computed in the functional RG field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in presence of pinning disorder. We show how this function can be computed analytically for a particle dragged through a 1-dimensional random-force landscape. The limit of small velocity allows to access the critical behavior at the depinning transition. For uncorrelated forces one finds three universality classes, corresponding to the three extreme value statistics, Gumbel, Weibull, and Frechet. For each class we obtain analytically the universal function Delta(u), the corrections to the critical force, and the joint probability distribution of avalanche sizes s and waiting times w. We find P(s)=P(w) for all three cases. All results are checked numerically. For a Brownian force landscape, known as the ABBM model, avalanche distributions and Delta(u) can be computed for any velocity. For 2-dimensional disorder, we perform large-scale numerical simulations to calculate the renormalized force correlator tensor Delta_{ij}(u), and to extract the anisotropic scaling exponents zeta_x > zeta_y. We also show how the Middleton theorem is violated. Our results are relevant for the record statistics of random sequences with linear trends, as encountered e.g. in some models of global warming. We give the joint distribution of the time s between two successive records and their difference in value w.Comment: 41 pages, 35 figure

First passage time exponent for higher-order random walks:Using Levy flights

We present a heuristic derivation of the first passage time exponent for the integral of a random walk [Y. G. Sinai, Theor. Math. Phys. {\bf 90}, 219 (1992)]. Building on this derivation, we construct an estimation scheme to understand the first passage time exponent for the integral of the integral of a random walk, which is numerically observed to be $0.220\pm0.001$. We discuss the implications of this estimation scheme for the $n{\rm th}$ integral of a random walk. For completeness, we also address the $n=\infty$ case. Finally, we explore an application of these processes to an extended, elastic object being pulled through a random potential by a uniform applied force. In so doing, we demonstrate a time reparameterization freedom in the Langevin equation that maps nonlinear stochastic processes into linear ones.Comment: 4 figures, submitted to PR

Comment on "Mean First Passage Time for Anomalous Diffusion"

We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)] of the mean first passage time of a subdiffusive process to reach either end of a finite interval in one dimension. The mean first passage time is in fact infinite.Comment: To appear in Phys. Rev.

Survival of a Diffusing Particle in a Transverse Shear Flow: A First-Passage Problem with Continuously Varying Persistence Exponent

We consider a particle diffusing in the y-direction, dy/dt=\eta(t), subject to a transverse shear flow in the x-direction, dx/dt=f(y), where x \ge 0 and x=0 is an absorbing boundary. We treat the class of models defined by f(y) = \pm v_{\pm}(\pm y)^\alpha where the upper (lower) sign refers to y>0 (y<0). We show that the particle survives with probability Q(t) \sim t^{-\theta} with \theta = 1/4, independent of \alpha, if v_{+}=v_{-}. If v_{+} \ne v_{-}, however, we show that \theta depends on both \alpha and the ratio v_{+}/v_{-}, and we determine this dependence.Comment: 4 page

Constraining SIDM with halo shapes: Revisited predictions from realistic simulations of early-type galaxies

We study the effect of self-interacting dark matter (SIDM) and baryons on the shape of early-type galaxies (ETGs) and their dark matter haloes, comparing them to the predictions of the cold dark matter (CDM) scenario. We use five hydrodynamical zoom-in simulations of haloes hosting ETGs (Mvir sim 10 13 , M ⊙ and M ∗ ∼ 10 11 , M ⊙), simulated in CDM and a SIDM model with constant cross-section of σT/mχ = 1 cm2g-1. We measure the 3D and projected shapes of the dark matter haloes and their baryonic content using the inertia tensor and compare our measurements to the results of three HST samples of gravitational lenses and Chandra and XMM-Newton X-ray observations. We find that the inclusion of baryons greatly reduces the differences between CDM and a SIDM, together with the ability to draw constraints based on shapes. Lensing measurements reject the predictions of CDM dark-matter-only simulations and prefer one of the hydro scenarios. When we consider the total sample of lenses, observational data prefer the CDM hydro scenario. The shapes of the X-ray emitting gas are compatible with observational results in both hydro runs, with CDM predicting higher elongations only in the very centre. Contrary to previous claims at the scale of elliptical galaxies, we conclude that both CDM and our SIDM model can still explain observed shapes once we include baryons in the simulations. Our results demonstrate that this is essential to derive realistic constraints and that new simulations are needed to confirm and extend our findings

Anomalous diffusion and generalized Sparre-Andersen scaling

We are discussing long-time, scaling limit for the anomalous diffusion composed of the subordinated L\'evy-Wiener process. The limiting anomalous diffusion is in general non-Markov, even in the regime, where ensemble averages of a mean-square displacement or quantiles representing the group spread of the distribution follow the scaling characteristic for an ordinary stochastic diffusion. To discriminate between truly memory-less process and the non-Markov one, we are analyzing deviation of the survival probability from the (standard) Sparre-Andersen scaling.Comment: 5 pages, 3 figure