Gamma Ray Bursts are detectable in the gamma-ray band if their jets are oriented towards the observer. However, for each GRB with a typical theta_jet, there should be ~2/theta_jet^2 bursts whose emission cone is oriented elsewhere in space. These off
-axis bursts can be eventually detected when, due to the deceleration of their relativistic jets, the beaming angle becomes comparable to the viewing angle. Orphan Afterglows (OA) should outnumber the current population of bursts detected in the gamma-ray band even if they have not been conclusively observed so far at any frequency. We compute the expected flux of the population of orphan afterglows in the mm, optical and X-ray bands through a population synthesis code of GRBs and the standard afterglow emission model. We estimate the detection rate of OA by on-going and forthcoming surveys. The average duration of OA as transients above a given limiting flux is derived and described with analytical expressions: in general OA should appear as daily transients in optical surveys and as monthly/yearly transients in the mm/radio band. We find that ~ 2 OA yr^-1 could already be detected by Gaia and up to 20 OA yr^-1 could be observed by the ZTF survey. A larger number of 50 OA yr^-1 should be detected by LSST in the optical band. For the X-ray band, ~ 26 OA yr^-1 could be detected by the eROSITA. For the large population of OA detectable by LSST, the X-ray and optical follow up of the light curve (for the brightest cases) and/or the extensive follow up of their emission in the mm and radio band could be the key to disentangle their GRB nature from other extragalactic transients of comparable flux density.
Gamma Ray Bursts (GRBs) are a powerful probe of the high redshift Universe. We present a tool to estimate the detection rate of high-z GRBs by a generic detector with defined energy band and sensitivity. We base this on a population model that reprod
uces the observed properties of GRBs detected by Swift, Fermi and CGRO in the hard X-ray and gamma-ray bands. We provide the expected cumulative distributions of the flux and fluence of simulated GRBs in different energy bands. We show that scintillator detectors, operating at relatively high energies (e.g. tens of keV to the MeV), can detect only the most luminous GRBs at high redshifts due to the link between the peak spectral energy and the luminosity (Ep-Liso) of GRBs. We show that the best strategy for catching the largest number of high-z bursts is to go softer (e.g. in the soft X-ray band) but with a very high sensitivity. For instance, an imaging soft X-ray detector operating in the 0.2-5 keV energy band reaching a sensitivity, corresponding to a fluence of ~10^-8 erg cm^-2, is expected to detect ~40 GRBs yr^-1 sr^-1 at z>5 (~3 GRBs yr^-1 sr^-1 at z>10). Once high-z GRBs are detected the principal issue is to secure their redshift. To this aim we estimate their NIR afterglow flux at relatively early times and evaluate the effectiveness of following them up and construct usable samples of events with any forthcoming GRB mission dedicated to explore the high-z Universe.
We investigated the rest frame spectral lags of two complete samples of bright long (50) and short (6) gamma-ray bursts (GRB) detected by Swift. We analysed the Swift/BAT data through a discrete cross-correlation function (CCF) fitted with an asymmet
ric Gaussian function to estimate the lag and the associated uncertainty. We find that half of the long GRBs have a positive lag and half a lag consistent with zero. All short GRBs have lags consistent with zero. The distributions of the spectral lags for short and long GRBs have different average values. Limited by the small number of short GRBs, we cannot exclude at more than 2 sigma significance level that the two distributions of lags are drawn from the same parent population. If we consider the entire sample of long GRBs, we do not find evidence for a lag-luminosity correlation, rather the lag-luminosity plane appears filled on the left hand side, thus suggesting that the lag-luminosity correlation could be a boundary. Short GRBs are consistent with the long ones in the lag-luminosity plane.
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.
Orphan Afterglows (OA) are slow transients produced by Gamma Ray Bursts seen off-axis that become visible on timescales of days/years at optical/NIR and radio frequencies, when the prompt emission at high energies (X and gamma rays) has already cease
d. Given the typically estimated jet opening angle of GRBs theta_jet ~ 3 deg, for each burst pointing to the Earth there should be a factor ~ 700 more GRBs pointing in other directions. Despite this, no secure OAs have been detected so far. Through a population synthesis code we study the emission properties of the population of OA at radio frequencies. OAs reach their emission peak on year-timescales and they last for a comparable amount of time. The typical peak fluxes (which depend on the observing frequency) are of few micro Jy in the radio band with only a few OA reaching the mJy level. These values are consistent with the upper limits on the radio flux of SN Ib/c observed at late times. We find that the OA radio number count distribution has a typical slope -1.7 at high fluxes and a flatter (-0.4) slope at low fluxes with a break at a frequency-dependent flux. Our predictions of the OA rates are consistent with the (upper) limits of recent radio surveys and archive searches for radio transients. Future radio surveys like VAST/ASKAP at 1.4 GHz should detect ~ 3x10^-3 OA deg^-2 yr-1, MeerKAT and EVLA at 8.4 GHz should see ~ 3x10^-1 OA deg-2 yr-1. The SKA, reaching the micro Jy flux limit, could see up to ~ 0.2-1.5 OA deg^-2 yr^-1. These rates also depend on the duration of the OA above a certain flux limit and we discuss this effect with respect to the survey cadence.
We estimate the initial bulk Lorentz factors Gamma_0 for GRBs that show the onset of the afterglow in their optical light curves. We find that Gamma_0 is strongly correlated with both the isotropic equivalent luminosity L_iso and energy E_iso and, wi
th a larger scatter, also with the rest frame peak energy E_peak. These new correlations allow us to interpret the spectral energy correlations E_peak-L_iso (-E_iso) as a sequence of Gamma_0 factors. By accounting for the beaming effects, we find that the comoving frame properties of GRBs result clustered around typical values (e.g. L_iso~5x10^48 erg/s). Moreover, it is theoretically predicted that there should be a link between the jet dynamics (Gamma_0) and its geometry (theta_jet). Through a population synthesis code we reconstruct the Gamma_0 and theta_jet distributions and search for a possible link between them. We find that Gamma_0 and theta_jet in GRBs should have log-normal distributions and they should be anti correlated (i.e. theta_jet^2*Gamma_0=const).
Radio observations of Gamma Ray Bursts afterglows are fundamental in providing insights into their physics and environment, and in constraining the true energetics of these sources. Nonetheless, radio observations of GRB afterglows are presently spar
se in the time/frequency domain. Starting from a complete sample of 58 bright Swift long bursts (BAT6), we constructed a homogeneous sub-sample of 38 radio detections/upper limits which preserves all the properties of the parent sample. One half of the bursts have detections between 1 and 5 days after the explosion with typical fluxes F>100 muJy at 8.4 GHz. Through a Population SYnthesis Code coupled with the standard afterglow Hydrodynamical Emission model (PSYCHE) we reproduce the radio flux distribution of the radio sub-sample. Based on these results we study the detectability in the time/frequency domain of the entire long GRB population by present and future radio facilities. We find that the GRBs that typically trigger Swift can be detected at 8.4 GHz by JVLA within few days with modest exposures even at high redshifts. The final SKA can potentially observe the whole GRB population provided that there will be a dedicated GRB gamma-ray detector more sensitive than Swift. For a sizable fraction (50%) of these bursts, SKA will allow us to perform radio-calorimetry, after the trans-relativistic transition (occurring ~100 d), providing an estimate of the true (collimation corrected) energetics of GRBs.
We recently found that Gamma Ray Burst energies and luminosities, in their comoving frame, are remarkably similar. This, coupled with the clustering of energetics once corrected for the collimation factor, suggests the possibility that all bursts, in
their comoving frame, have the same peak energy Epeak (of the order of a few keV) and the same energetics of the prompt emission Egamma (of the order of 2e48 erg). The large diversity of bursts energies is then due to the different bulk Lorentz factor Gamma and jet aperture angle theta_jet. We investigated, through a population synthesis code, what are the distributions of Gamma and theta_jet compatible with the observations. Both quantities must have preferred values, with log-normal best fitting distributions and <Gamma0> ~ 275 and <theta_jet> ~ 8.7 degree. Moreover, the peak values of the Gamma and theta_jet distributions must be related - theta_jet^2.5 Gamma =const: the narrower the jet angle, the larger the bulk Lorentz factor. We predict that ~6% of the bursts that point to us should not show any jet break in their afterglow light curve since they have sin(theta_jet)<1/Gamma. Finally, we estimate that the local rate of GRBs is ~0.3% of all local SNIb/c and ~2.5% of local hypernovae, i.e. SNIb/c with broad absorption lines.
The jet opening angle theta_jet and the bulk Lorentz factor Gamma_0 are crucial parameters for the computation of the energetics of Gamma Ray Bursts (GRBs). From the ~30 GRBs with measured theta_jet or Gamma_0 it is known that: (i) the real energetic
E_gamma, obtained by correcting the isotropic equivalent energy E_iso for the collimation factor ~theta_jet^2, is clustered around 10^50-10^51 erg and it is correlated with the peak energy E_p of the prompt emission and (ii) the comoving frame E_p and E_gamma are clustered around typical values. Current estimates of Gamma_0 and theta_jet are based on incomplete data samples and their observed distributions could be subject to biases. Through a population synthesis code we investigate whether different assumed intrinsic distributions of Gamma_0 and theta_jet can reproduce a set of observational constraints. Assuming that all bursts have the same E_p and E_gamma in the comoving frame, we find that Gamma_0 and theta_jet cannot be distributed as single power-laws. The best agreement between our simulation and the available data is obtained assuming (a) log-normal distributions for theta_jet and Gamma_0 and (b) an intrinsic relation between the peak values of their distributions, i.e theta_jet^2.5*Gamma_0=const. On average, larger values of Gamma_0 (i.e. the faster bursts) correspond to smaller values of theta_jet (i.e. the narrower). We predict that ~6% of the bursts that point to us should not show any jet break in their afterglow light curve since they have sin(theta_jet)<1/Gamma_0. Finally, we estimate that the local rate of GRBs is ~0.3% of all local SNIb/c and ~4.3% of local hypernovae, i.e. SNIb/c with broad-lines.
We study the possible effects of selection biases on the Ep-Liso correlation caused by the unavoidable presence of flux-limits in the existing samples of Gamma Ray Bursts (GRBs). We consider a well defined complete sample of Swift GRBs and perform Mo
nte Carlo simulations of the GRB population under different assumptions for their luminosity functions. If we assume that there is no correlation between the peak energy Ep and the isotropic luminosity Liso, we are unable to reproduce it as due to the flux limit threshold of the Swift complete sample. We can reject the null hypothesis that there is no intrinsic correlation between Ep and Liso at more than 2.7 sigma level of confidence. This result is robust against the assumptions of our simulations and it is confirmed if we consider, instead of Swift, the trigger threshold of the Batse instrument. Therefore, there must be a physical relation between these two quantities. Our simulations seem to exclude, at a lower confidence level of 1.6 sigma, the possibility that the observed Ep-Liso correlation among different bursts is caused by a boundary, i.e. such that for any given Ep, we see only the largest Liso, which has a flux above the threshold of the current instruments.
