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Register a new userGRBs have preferred jet opening angles and bulk Lorentz factors
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Added by
Gabriele Ghisellini
Publication date
2012
fields
Physics
and research's language is
English
Authors
G. Ghisellini
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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.
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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.
Knowledge of the bulk Lorentz factor $Gamma_{0}$ of GRBs allows us to compute their comoving frame properties shedding light on their physics. Upon collisions with the circumburst matter, the fireball of a GRB starts to decelerate, producing a peak or a break (depending on the circumburst density profile) in the light curve of the afterglow. Considering all bursts with known redshift and with an early coverage of their emission, we find 67 GRBs with a peak in their optical or GeV light curves at a time $t_{rm p}$. For another 106 GRBs we set an upper limit $t_{rm p}^{rm UL}$. We show that $t_{rm p}$ is due to the dynamics of the fireball deceleration and not to the passage of a characteristic frequency of the synchrotron spectrum across the optical band. Considering the $t_{rm p}$ of 66 long GRBs and the 85 most constraining upper limits, using censored data analysis methods, we reconstruct the most likely distribution of $t_{rm p}$. All $t_{rm p}$ are larger than the time $t_{rm p,g}$ when the prompt emission peaks, and are much larger than the time $t_{rm ph}$ when the fireball becomes transparent. The reconstructed distribution of $Gamma_0$ has median value $sim$300 (150) for a uniform (wind) circumburst density profile. In the comoving frame, long GRBs have typical isotropic energy, luminosity, and peak energy $langle E_{rm iso}rangle=3(8)times 10^{50}$ erg, $langle L_{rm iso}rangle=3(15) times 10^{47}$ erg s$^{-1}$ , and $langle E_{rm peak}rangle =1(2)$ keV in the homogeneous (wind) case. We confirm that the significant correlations between $Gamma$ and the rest frame isotropic energy ($E_{rm iso}$), luminosity ($L_{rm iso}$) and peak energy ($E_{rm peak}$) are not due to selection effects. Assuming a typical opening angle of 5 degrees, we derive the distribution of the jet baryon loading which is centered around a few $10^{-6} {rm M_{odot}}$.
The jet breaks in the afterglow lightcurves of short gamma-ray bursts (SGRBs), rarely detected so far, are crucial for estimating the half-opening angles of the ejecta ($theta_{rm j}$) and hence the neutron star merger rate. In this work we report the detection of jet decline behaviors in GRB 150424A and GRB 160821B and find $theta_{rm j}sim 0.1$ rad. Together with five events reported before 2015 and other three identified recently (GRB 050709, GRB 060614 and GRB 140903A), we have a sample consisting of nine SGRBs and one long-short GRB with reasonably estimated $theta_{rm j}$. In particular, three {it Swift} bursts in the sample have redshifts $zleq 0.2$, with which we estimate the local neutron star merger rate density {to be $sim 1109^{+1432}_{-657}~{rm Gpc^{-3}~yr^{-1}}$ or $162^{+140}_{-83} {rm Gpc^{-3}yr^{-1}}$ if the narrowly-beamed GRB 061201 is excluded}. Inspired by the typical $theta_{rm j}sim 0.1$ rad found currently, we further investigate whether the off-beam GRBs (in the uniform jet model) or the off-axis events (in the structured jet model) can significantly enhance the GRB/GW association or not. For the former the enhancement is at most moderate, while for the latter the enhancement can be much greater and a high GRB/GW association probability of $sim 10%$ is possible. We also show that the data of GRB 160821B may contain a macronova/kilonova emission component with a temperature of $sim 3100$ K at $sim 3.6$ days after the burst and more data are needed to ultimately clarify.
We present 15 GHz stacked VLBA images of 373 jets associated with active galactic nuclei (AGN) having at least five observing epochs within a 20 yr time interval 1994-2015 from the MOJAVE programme and/or its precursor, the 2 cm VLBA Survey. These data are supplemented by 1.4 GHz single-epoch VLBA observations of 135 MOJAVE AGNs to probe larger scale jet structures. The typical jet geometry is found to be close to conical on scales from hundreds to thousands of parsecs, while a number of galaxies show quasi-parabolic streamlines on smaller scales. A true jet geometry in a considerable fraction of AGNs appears only after stacking epochs over several years. The jets with significant radial accelerated motion undergo more active collimation. We have analysed total intensity jet profiles transverse to the local jet ridgeline and derived both apparent and intrinsic opening angles of the flows, with medians of $21.5deg$ and $1.3deg$, respectively. The Fermi LAT-detected gamma-ray AGNs in our sample have, on average, wider apparent and narrower intrinsic opening angle, and smaller viewing angle than non LAT-detected AGNs. We have established a highly significant correlation between the apparent opening angle and gamma-ray luminosity, driven by Doppler beaming and projection effects.
We intend to determine the type of circumburst medium and measure directly the initial Lorentz factor $Gamma_0$ of GRB outflows. If the early X-ray afterglow lightcurve has a peak and the whole profile across the peak is consistent with the standard external shock model, the early rise profile of light curves can be used to differentiate whether the burst was born in interstellar medium (ISM) or in stellar wind. In the thin shell case, related to a sub-relativistic reverse shock, the peak time occurring after the end of the prompt emission, can be used to derive an accurate $Gamma_0$, especially for the ISM case. The afterglow lightcurves for a flat electron spectrum $1<p<2$ have been derived analytically. In our GRB sample, we obtain $Gamma_0 sim 300$ for the bursts born in ISM. We did not find any good case for bursts born in stellar wind and behaving as a thin shell that can be used to constrain $Gamma_0$ reliably.
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