Simulations of GRB Jets in a Stratified External Medium: Dynamics, Afterglow Lightcurves, Jet Breaks and Radio Calorimetry

The dynamics of GRB jets during the afterglow phase is most reliably and accurately modelled using hydrodynamic simulations. All published simulations, however, have considered only a uniform external medium, while a stratified external medium is expected around long duration GRB progenitors. Here we present simulations of the dynamics of GRB jets and the resulting afterglow emission for both uniform and stratified external media with $\rho \propto r^{-k}$ for k = 0, 1, 2. The simulations are performed in 2D using the special relativistic version of the Mezcal code. The dynamics for stratified external media are broadly similar to those derived for expansion into a uniform external medium. The jet half-opening angle start increasing logarithmically with time once the Lorentz factor drops below 1/theta_0. For larger k values the lateral expansion is faster at early times and slower at late times with the jet expansion becoming Newtonian and slowly approaching spherical symmetry over progressively longer timescales. We find that contrary to analytic expectations, there is a reasonably sharp jet break in the lightcurve for k = 2 although the shape of the break is affected more by the viewing angle than by the slope of the external density profile. Steeper density profiles are found to produce more gradual jet breaks while larger viewing angles cause smoother and later appearing jet breaks. The counter-jet becomes visible as it becomes sub-relativistic, and for k=0 this results in a clear bump-like feature in the light curve. However, for larger k values the jet decelerates more gradually, causing only a mild flattening in the radio light curve that might be hard to discern when k=2. Late time radio calorimetry is likely to consistently over-estimate the true energy by up to a factor of a few for k=2, and either over-predict or under-predict it by a smaller factor for k = 0,1.Comment: 10 pages, 13 figures, submitted to Ap

Diversity Of Short Gamma-Ray Burst Afterglows From Compact Binary Mergers Hosting Pulsars

Short gamma-ray bursts (sGRBs) are widely believed to result from the mergers of compact binaries. This model predicts an afterglow that bears the characteristic signatures of a constant, low density medium, including a smooth prompt-afterglow transition, and a simple temporal evolution. However, these expectations are in conflict with observations for a non-negligible fraction of sGRB afterglows. In particular, the onset of the afterglow phase for some of these events appears to be delayed and, in addition, a few of them exhibit late- time rapid fading in their lightcurves. We show that these peculiar observations can be explained independently of ongoing central engine activity if some sGRB progenitors are compact binaries hosting at least one pulsar. The Poynting flux emanating from the pulsar companion can excavate a bow-shock cavity surround- ing the binary. If this cavity is larger than the shock deceleration length scale in the undisturbed interstellar medium, then the onset of the afterglow will be delayed. Should the deceleration occur entirely within the swept-up thin shell, a rapid fade in the lightcurve will ensue. We identify two types of pulsar that can achieve the conditions necessary for altering the afterglow: low field, long lived pulsars, and high field pulsars. We find that a sizable fraction (~20-50%) of low field pulsars are likely to reside in neutron star binaries based on observations, while their high field counterparts are not. Hydrodynamical calculations motivated by this model are shown to be in good agreement with observations of sGRB afterglow lightcurves.Comment: Accepted to ApjL. Direct comparison to observed X-Ray afterglows now included. 5 Figure

What determines the structure of short gamma-ray burst jets?

The discovery of GRB 170817A, the first unambiguous off-axis short gamma-ray burst arising from a neutron star merger, has challenged our understanding of the angular structure of relativistic jets. Studies of the jet propagation usually assume that the jet is ejected from the central engine with a top-hat structure and its final structure, which determines the observed light curve and spectra, is primarily regulated by the interaction with the nearby environment. However, jets are expected to be produced with a structure that is more complex than a simple top-hat, as shown by global accretion simulations. We present numerical simulations of short GRBs launched with a wide range of initial structures, durations and luminosities. We follow the jet interaction with the merger remnant wind and compute its final structure at distances $\gtrsim 10^{11}$~cm from the central engine. We show that the final jet structure, as well as the resulting afterglow emission, depend strongly on the initial structure of the jet, its luminosity and duration. While the initial structure at the jet is preserved for long-lasting SGRBs, it is strongly modified for jets barely making their way through the wind. This illustrates the importance of combining the results of global simulations with propagation studies in order to better predict the expected afterglow signatures from neutron star mergers. Structured jets provide a reasonable description of the GRB 170817A afterglow emission with an off-axis angle $\theta_{\rm obs} \approx 22.5^\circ$.Comment: 9 pages, 7 Figures; Added discussion; Accepted for publication in MNRA

The dynamics, appearance and demographics of relativistic jets triggered by tidal disruption of stars in quiescent supermassive black holes

We examine the consequences of a model in which relativistic jets can be triggered in quiescent massive black holes when a geometrically thick and hot accretion disk forms as a result of the tidal disruption of a star. To estimate the power, thrust and lifetime of the jet, we use the mass accretion history onto the black hole as calculated by detailed hydrodynamic simulations of the tidal disruption of stars. We go on to determine the states of the interstellar medium in various types of quiescent galactic nuclei, and describe how this external matter can affect jets propagating through it. We use this information, together with a two-dimensional hydrodynamic model of the structure of the relativistic flow, to study the dynamics of the jet, the propagation of which is regulated by the density stratification of the environment and by its injection history. The breaking of symmetry involved in transitioning from one to two dimensions is crucial and leads to qualitatively new phenomena. Many of the observed properties of the Swift 1644+57/GRB 110328A event can be understood as resulting from accretion onto and jets driven by a $10^6 M_\odot$ central mass black hole following the disruption of sun-like star. With the inclusion of a stochastic contribution to the luminosity due to variations in the feeding rate driven by instabilities near the tidal radius, we find that our model can explain the X-ray light curve without invoking a rarely-occurring deep encounter. In conjunction with the number density of black holes in the local universe, we hypothesize that the conditions required to produce the Swift event are not anomalous, but are in fact representative of the jet-driven flare population arising from tidal disruptions. [abridged]Comment: 16 pages, 16 figures, submitted to Ap

The Fate of the Merger Remnant in GW170817 and its Imprint on the Jet Structure

The first neutron star binary merger detected in gravitational waves, GW170817 and the subsequent detection of its emission across the electromagnetic spectrum showed that these systems are viable progenitors of short $\gamma$-ray bursts (sGRB). The afterglow signal of GW170817 has been found to be consistent with a structured GRB jet seen off-axis, requiring significant amounts of relativistic material at large angles. This trait can be attributed to the interaction of the relativistic jet with the external wind medium. Here we perform numerical simulations of relativistic jets interacting with realistic wind environments in order to explore how the properties of the wind and central engine affect the structure of successful jets. We find that the angular energy distribution of the jet depends primarily on the ratio between the lifetime of the jet and the time it takes the merger remnant to collapse. We make use of these simulations to constrain the time it took for the merger remnant in GW170817 to collapse into a black hole based on the angular structure of the jet as inferred from afterglow observations. We conclude that the lifetime of the merger remnant in GW170817 was $\approx 1-1.7$s, which, after collapse, triggered the formation of the jet.Comment: 13 figures, 15 pages, accepted in Ap

Hydrodynamical Simulations to Determine the Feeding Rate of Black Holes by the Tidal Disruption of Stars: The Importance of the Impact Parameter and Stellar Structure

The disruption of stars by supermassive black holes has been linked to more than a dozen flares in the cores of galaxies out to redshift $z \sim 0.4$. Modeling these flares properly requires a prediction of the rate of mass return to the black hole after a disruption. Through hydrodynamical simulation, we show that aside from the full disruption of a solar mass star at the exact limit where the star is destroyed, the common assumptions used to estimate $\dot{M}(t)$, the rate of mass return to the black hole, are largely invalid. While the analytical approximation to tidal disruption predicts that the least-centrally concentrated stars and the deepest encounters should have more quickly-peaked flares, we find that the most-centrally concentrated stars have the quickest-peaking flares, and the trend between the time of peak and the impact parameter for deeply-penetrating encounters reverses beyond the critical distance at which the star is completely destroyed. We also show that the most-centrally concentrated stars produced a characteristic drop in $\dot{M}(t)$ shortly after peak when a star is only partially disrupted, with the power law index $n$ being as extreme as -4 in the months immediately following the peak of a flare. Additionally, we find that $n$ asymptotes to $\simeq -2.2$ for both low- and high-mass stars for approximately half of all stellar disruptions. Both of these results are significantly steeper than the typically assumed $n = -5/3$. As these precipitous decay rates are only seen for events in which a stellar core survives the disruption, they can be used to determine if an observed tidal disruption flare produced a surviving remnant. These results should be taken into consideration when flares arising from tidal disruptions are modeled. [abridged]Comment: 16 pages, 13 figures (2 new figures in revised version). Published in ApJ. Latest version incorporates erratum that fixes issue with fitting formulae not including enough significant digit

Private equity and venture capital in Italy

This paper examines private equity and venture capital in Italy. The first part looks at the main features of the Italian market and its recent evolution; the second part considers the results of a survey of firms and intermediaries designed to gather information regarding contract features and the characteristics of investee firms and investing intermediaries. Finally, the paper discusses the main obstacles to the development of the sector using information from the survey of intermediaries.private equity, venture capital