Jet-driven and jet-less fireballs from compact binary mergers

During a compact binary merger involving at least one neutron star, a small fraction of the gravitational energy could be liberated in such a way to accelerate a small fraction (~ 10^-6) of the neutron star mass in an isotropic or quasi-isotropic way. In presence of certain conditions, a pair-loaded fireball can form, which undergoes accelerated expansion reaching relativistic velocities. As in the standard fireball scenario, internal energy is partly transformed into kinetic energy. At the photospheric radius, the internal radiation can escape, giving rise to a pulse that lasts for a time equal to the delay time since the merger. The subsequent interaction with the interstellar medium can then convert part of the remaining kinetic energy back into radiation in a weak isotropic afterglow at all wavelengths. This scenario does not require the presence of a jet: the associated isotropic prompt and afterglow emission should be visible for all NS-NS and BH-NS mergers within 90 Mpc, independent of their inclination. The prompt emission is similar to that expected from an off-axis jet, either structured or much slower than usually assumed (Gamma ~ 10), or from the jet cocoon. The predicted afterglow emission properties can discriminate among these scenarios.Comment: 5 pages, 1 figure, revised version submitted to MNRAS Letter

The on-axis view of GRB 170817A

The peculiar short gamma-ray burst GRB 170817A has been firmly associated to the gravitational wave event GW170817, which has been unaninmously interpreted as due to the coalescence of a double neutron star binary. The unprecedented behaviour of the non-thermal afterglow led to a debate about its nature, which was eventually settled by high-resolution VLBI observations, which strongly support the off-axis structured jet scenario. Using information on the jet structure derived from multi-wavelength fitting of the afterglow emission and of the apparent VLBI image centroid motion, we compute the appearance of a GRB 170817A-like jet as seen by an on-axis observer and we compare it to the previously observed population of SGRB afterglows and prompt emission events. We find that the intrinsic properties of the GRB 170817A jet are representative of a typical event in the SGRB population, hinting at a quasi-universal jet structure. The diversity in the SGRB afterglow population could therefore be ascribed in large part to extrinsic (redshift, density of the surrounding medium, viewing angle) rather than intrinsic properties. Although more uncertain, the comparison can be extended to the prompt emission properties, leading to similar conclusions.Comment: 9 pages, 3 figures, submitted to A&A. Comments and suggestions are welcom

Interpreting GRB170817A as a giant flare from a jet-less double neutron-star merger

We show that the delay between GRB170817A and GW170817 is incompatible with de-beamed emission from an off-axis relativistic jet. The prompt emission and the subsequent radio and X-ray observations can instead be interpreted within a giant-flare-like scenario, being the result of a relativistic outflow driven by the ultra-strong magnetic field produced by magnetohydrodynamic amplification during the merger of the progenitor double neutron-star binary. Within such picture, the data indicate that the outflow must be endowed with a steep velocity profile, with a relatively fast tail extending to Gamma~8. Since the conditions for the launch of such an outflow are quite general, and the presence of a velocity profile is a natural expectation of the acceleration process, most neutron star binary mergers should feature this quasi-isotropic, hard X-ray emission component, that can be a powerful guide to the discovery of additional kilonovae associated to relatively nearby gravitational wave events.Comment: 6 pages, 2 figures, accepted by Astronomy and Astrophysic

Light curves and spectra from off-axis gamma-ray bursts

If gamma-ray burst prompt emission originates at a typical radius, and if material producing the emission moves at relativistic speed, then the variability of the resulting light curve depends on the viewing angle. This is due to the fact that the pulse evolution time scale is Doppler contracted, while the pulse separation is not. For off-axis viewing angles $\theta_{\rm view} \gtrsim \theta_{\rm jet} + \Gamma^{-1}$, the pulse broadening significantly smears out the light curve variability. This is largely independent of geometry and emission processes. To explore a specific case, we set up a simple model of a single pulse under the assumption that the pulse rise and decay are dominated by the shell curvature effect. We show that such a pulse observed off-axis is (i) broader, (ii) softer and (iii) displays a different hardness-intensity correlation with respect to the same pulse seen on-axis. For each of these effects, we provide an intuitive physical explanation. We then show how a synthetic light curve made by a superposition of pulses changes with increasing viewing angle. We find that a highly variable light curve, (as seen on-axis) becomes smooth and apparently single-pulsed (when seen off-axis) because of pulse overlap. To test the relevance of this fact, we estimate the fraction of off-axis gamma-ray bursts detectable by \textit{Swift} as a function of redshift, finding that a sizable fraction (between 10\% and 80\%) of nearby ($z<0.1$) bursts are observed with $\theta_{\rm view} \gtrsim \theta_{\rm jet} + \Gamma^{-1}$. Based on these results, we argue that low luminosity gamma-ray bursts are consistent with being ordinary bursts seen off-axis.Comment: 13 pages, 17 figures, submitted to MNRAS main journal; updated estimate of the fraction of off-axis grbs seen by Swif

Structure of Gamma-Ray Burst jets: intrinsic versus apparent properties

With this paper we introduce the concept of apparent structure of a GRB jet, as opposed to its intrinsic structure. The latter is customarily defined specifying the functions epsilon(theta) (the energy emitted per jet unit solid angle) and Gamma(theta) (the Lorentz factor of the emitting material); the apparent structure is instead defined by us as the isotropic equivalent energy E_iso(theta_v) as a function of the viewing angle theta_v. We show how to predict the apparent structure of a jet given its intrinsic structure. We find that a Gaussian intrinsic structure yields a power law apparent structure: this opens a new viewpoint on the Gaussian (which can be understood as a proxy for a realistic narrow, well collimated jet structure) as a possible candidate for a quasi-universal GRB jet structure. We show that such a model (a) is consistent with recent constraints on the observed luminosity function of GRBs; (b) implies fewer orphan afterglows with respect to the standard uniform model; (c) can break out the progenitor star (in the collapsar scenario) without wasting an unreasonable amount of energy; (d) is compatible with the explanation of the Amati correlation as a viewing angle effect; (e) can be very standard in energy content, and still yield a very wide range of observed isotropic equivalent energies.Comment: 10 pages, 8 figures, 1 table. Accepted by MNRA

Irreducible free energy expansion and overlaps locking in mean field spin glasses

We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra relationships (GG) (often called Aizenman-Contucci polynomials (AC)) in a very simple way. We show moreover how these constraints are "superimposed" by the symmetry of the model with respect to the restriction required by thermodynamic stability. Within this framework it is possible to expand the free energy in terms of these irreducible overlaps fluctuations and in a form that simply put in evidence how the complexity of the solution is related to the complexity of the entropy.Comment: 19 page

General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity

For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the overlaps among s replicas. Add one replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas, let us say a, and the added s+1 is either independent of the former ones, or it is identical to one of the overlaps q(a,b), with b running among the first s replicas, excluding a. Each of these cases has equal probability 1/s.Comment: LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical and General. Also available at http://rerumnatura.zool.su.se/stefano/ms/ghigu.p

Are GRB 980425 and GRB 031203 real outliers or twins of GRB 060218?

GRB 980425 and GRB 031203 are apparently two outliers with respect to the correlation between the isotropic equivalent energy E_iso emitted in the prompt radiation phase and the peak frequency E_peak of the spectrum in a vF(v) representation (the so-called Amati relation). We discuss if these two bursts are really different from the others or if their location in the E_iso-E_peak plane is the result of other effects, such as viewing them off-axis, or through a scattering screen, or a misinterpretation of their spectral properties. The latter case seems particularly interesting after GRB 060218, that, unlike GRB 031203 and GRB 980425, had a prompt emission detected both in hard and soft X-rays which lasted ~2800 seconds. This allowed to determine its E_peak and total emitted energy. Although it shares with GRB 031203 the total energetics, it is not an outlier with respect to the Amati correlation. We then investigate if a hard-to-soft spectral evolution in GRB 031203 and GRB 980425, consistent with all the observed properties, can give rise to a time integrated spectrum with an E_peak consistent with the Amati relation.Comment: 13 pages, 9 figures, 2 tables. Accepted for publication in MNRA

Luminosity function and jet structure of Gamma Ray Bursts

The structure of Gamma Ray Burst (GRB) jets impacts on their prompt and afterglow emission properties. The jet of GRBs could be uniform, with constant energy per unit solid angle within the jet aperture, or it could instead be structured, namely with energy and velocity that depend on the angular distance from the axis of the jet. We try to get some insight about the still unknown structure of GRBs by studying their luminosity function. We show that low (1e46-1e48 erg/s) and high (i.e. with L > 1e50 erg/s) luminosity GRBs can be described by a unique luminosity function, which is also consistent with current lower limits in the intermediate luminosity range (1e48-1e50} erg/s). We derive analytical expressions for the luminosity function of GRBs in uniform and structured jet models and compare them with the data. Uniform jets can reproduce the entire luminosity function with reasonable values of the free parameters. A structured jet can also fit adequately the current data, provided that the energy within the jet is relatively strongly structured, i.e. E propto theta^{-k} with k > 4. The classical E propto theta^{-2} structured jet model is excluded by the current data.Comment: 11 pages, 2 tables, 7 figures, submitted to MNRA