On the anomalous X-ray afterglows of GRB 970508 and GRB 970828

Recently, BeppoSAX and ASCA have reported an unusual resurgence of soft X-ray emission during the afterglows of GRB 970508 and GRB 970828, together with marginal evidence for the existence of Fe-lines in both objects. We consider the implications of the existence of a torus of iron-rich material surrounding the sites of gamma ray bursts as would be expected in the SupraNova model; in particular, we show that the fireball will quickly hit this torus, and bring it to a temperature ~3x10^7 K. Bremsstrahlung emission from the heated up torus will cause a resurgence of the soft X-ray emission with all expected characteristics (flux level, duration and spectral hardening with time) identical to those observed during the reburst. Also, thermal emission from the torus will account for the observed iron line flux. These events are also observable, for instance by new missions such as SWIFT, when beaming away from our line sight makes us miss the main burst, as Fast (soft) X-ray Transients, with durations ~10^3 s, and fluences ~10^-7-10^-4 erg cm^-2. This model provides evidence in favor of the SupraNova model for Gamma Ray Bursts.Comment: To appear in MN Pink pages, MN-LateX, no figure

Topological and geometrical entanglement in a model of circular DNA undergoing denaturation

The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. The writhe of the two strands grows as the square root of N in both phases.Comment: 7 pages, 11 figures, revte

Ranking knots of random, globular polymer rings

An analysis of extensive simulations of interacting self-avoiding polygons on cubic lattice shows that the frequencies of different knots realized in a random, collapsed polymer ring decrease as a negative power of the ranking order, and suggests that the total number of different knots realized grows exponentially with the chain length. Relative frequencies of specific knots converge to definite values because the free energy per monomer, and its leading finite size corrections, do not depend on the ring topology, while a subleading correction only depends on the crossing number of the knots.Comment: 4 pages, 5 figure

On gravitomagnetic precession around black holes

We compute exactly the Lense-Thirring precession frequency for point masses in the Kerr metric, for arbitrary black hole mass and specific angular momentum. We show that this frequency, for point masses at or close to the innermost stable orbit, and for holes with moderate to extreme rotation, is less than, but comparable to the rotation frequency. Thus, if the quasi periodic oscillations (QPOs) observed in the modulation of the X-ray flux from some black holes candidates are due to Lense-Thirring precession of orbiting material, we predict that a separate, distinct QPO ought to be observed in each object.Comment: Accepted for publication in MNRAS. MN-Latex, 2 figure

Relativistic precession around rotating neutron stars: Effects due to frame-dragging and stellar oblateness

General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a non-equatorial orbit precesses about the body's symmetry axis. In this paper we compute the precession frequencies of circular orbits around rapidly rotating neutron stars for a variety of masses and equations of state. The precession frequencies computed are expressed as numerical functions of the orbital frequency observed at infinity. The post-Newtonian expansion of the exact precession formula is examined to identify the relative magnitudes of the precession caused by the Lense-Thirring effect, the usual Newtonian quadrupole effect and relativistic corrections. The first post-Newtonian correction to the Newtonian quadrupole precession is derived in the limit of slow rotation. We show that the post-Newtonian precession formula is a good approximation to the exact precession close to the neutron star in the slow rotation limit (up to \sim 400 Hz in the present context). The results are applied to recent RXTE observations of neutron star low-mass X-ray binaries, which display kHz quasi-periodic oscillations and, within the framework of beat frequency models, allow the measurement of both the neutron star spin frequency and the Keplerian frequency of the innermost ring of matter in the accretion disk around it. For a wide range of realistic equations of state, we find that the predicted precession frequency of this ring is close to one half of the low-frequency (\sim 20 - 35 Hz) quasi-periodic oscillations seen in several Atoll sources.Comment: 35 pages including 10 figures and 6 tables. To appear in the Astrophysical Journa

Robust non-adiabatic molecular dynamics for metals and insulators

We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can simulate models of non-adiabatic electronic transitions, and test it against exact integration of the time-dependent Schroedinger equation. Unlike previous formulations of CEID, the accuracy of this scheme depends on a single tunable parameter which sets the level of atomic fluctuations included. The convergence to the exact dynamics by increasing the tunable parameter is demonstrated for a model two level system. This algorithm provides a smooth description of the non-adiabatic electronic transitions which satisfies the kinematic constraints (energy and momentum conservation) and preserves quantum coherence. The applicability of this algorithm to more complex atomic systems is discussed.Comment: 36 pages, 5 figures. Accepted for publication in Journal of Chemical Physic

Analysis of X-ray flares in GRBs

We present a detailed study of the spectral and temporal properties of the X-ray flares emission of several GRBs. We select a sample of GRBs which X-ray light curve exhibits large amplitude variations with several rebrightenings superposed on the underlying three-segment broken powerlaw that is often seen in Swift GRBs. We try to understand the origin of these fluctuations giving some diagnostic in order to discriminate between refreshed shocks and late internal shocks. For some bursts our time-resolved spectral analysis supports the interpretation of a long-lived central engine, with rebrightenings consistent with energy injection in refreshed shocks as slower shells generated in the central engine prompt phase catch up with the afterglow shock at later times.Comment: 9 pages, 3 figures. Invited talk at the Swift-Venice 2006 meeting to be published by "Il Nuovo Cimento