arXiv subjects
Publications and source records attributed to Elena Rossi.
The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in Bardos, Leroux and Nédélec (1979), striving to provide a rigorous treatment and detailed references.
We present a nonlinear predator-prey system consisting of a nonlocal conservation law for predators coupled with a parabolic equation for preys. The drift term in the predators' equation is a nonlocal function of the prey density, so that the movement of predators can be directed towards region with high prey density. Moreover, Lotka-Volterra type right hand sides describe the feeding. A theorem ensuring existence, uniqueness, continuous dependence of weak solutions and various stability estimates is proved, in any space dimension. Numerical integrations show a few qualitative features of the solutions.
Unambiguous detection of the tidal disruption of a star would allow an assessment of the presence and masses of supermassive black holes in quiescent galaxies. It would also provide invaluable information on bulge scale stellar processes (such as two-body relaxation) via the rate at which stars are injected into the tidal sphere of influence of the black holes. This rate, in turn, is essential to predict gravitational radiation emission by compact object inspirals. The signature of a tidal disruption event is thought to be a fallback rate for the stellar debris onto the black hole that decreases as $t^{-5/3}$. This mass flux is often assumed to yield a luminous signal that decreases in time at the same rate. In this paper, we calculate the monochromatic lightcurves arising from such an accretion event. Differently from previous studies, we adopt a more realistic description of the fallback rate and of the super-Eddigton accretion physics. We also provide simultaneous lightcurves in optical, UV and X-rays. We show that, after a few months, optical and UV lightcurves scale as $t^{-5/12}$, and are thus substantially flatter than the $t^{-5/3}$ behaviour, which is a prerogative of the bolometric lightcurve, only. At earlier times and for black hole masses $< 10^7 M_{\sun}$, the wind emission dominates: after reaching a peak of $10^{41}-10^{43}$ erg/s at roughly a month, the lightcurve decreases steeply as $\sim t^{-2.6}$, until the disc contribution takes over. The X-ray band, instead, is the best place to detect the $t^{-5/3}$ "smoking gun" behaviour, although it is displayed only for roughly a year, before the emission steepens exponentially.
Polarimetry of Gamma-Ray Burst (GRB) afterglows in the last few years has been considered one of the most effective tool to probe the geometry, energetic, dynamics and the environment of GRBs. We report some of the most recent results and discuss their implications and future perspectives.
The recent claim by Coburn & Boggs to have detected a very high degree of linear polarization in the prompt emission of GRB 021206 has stimulated interest in how much polarization could arise in gamma-ray bursts from synchrotron emission. Alternatively, as Shaviv & Dar have shown, GRB polarization could be produced by inverse Compton scattering in the point-source limit. We discuss polarization from a fireball that upscatters a soft radiation field. We show that, after the proper angular integration, the residual polarization can be large, in some cases approaching the point-source limit. We discuss the probability of realizing the geometrical conditions in which a large polarization is obtained showing that, for a particularly bright burst as GRB 021206, the detection of polarization at the first attempt in the Compton drag scenario is not unlikely.
In models for gamma ray burst afterglows, it is normally assumed that the external shock strongly amplifies the magnetic field and that this field maintains a steady value throughout the shocked region. We discuss the effects of modifying this (probably simplistic) assumption by allowing for a short decay time. The observations are incompatible with a post-shock field that decays too rapidly. However if the field pervades only a few percent of the total thickness of the shocked shell (and the electrons undergo only inverse Compton losses in the remainder) the model could be compatible with data. This would suggest a strong dependence of model parameters on the uncertainties of shock physics, therefore calling for independent external density estimates. We claim that afterglow emission should be instead seen as a laboratory where we can understand relativistic shock physics. The model we propose here together with afterglow observations in all wavebands could help to pin down the field structure.