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Register a new userThe faster the narrower: characteristic bulk velocities and jet opening angles of Gamma Ray Bursts
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Added by
Giancarlo Ghirlanda
Publication date
2012
fields
Physics
and research's language is
English
Authors
G. Ghirlanda
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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.
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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.
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 $10^{-6} {rm M_{odot}}$.
For a sample of Swift and Fermi GRBs, we show that the minimum variability timescale and the spectral lag of the prompt emission is related to the bulk Lorentz factor in a complex manner: For small $Gamma$s, the variability timescale exhibits a shallow (plateau) region. For large $Gamma$s, the variability timescale declines steeply as a function of $Gamma$ ($delta TproptoGamma^{-4.05pm0.64}$). Evidence is also presented for an intriguing correlation between the peak times, t$_p$, of the afterglow emission and the prompt emission variability timescale.
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.
The gravitational wave (GW) memory from a radiating and decelerating point mass is studied in detail. It is found that for isotropic photon emission the memory generated from the photons is essentially the same with the memory from the point mass that radiated the photons so that it is anti-beamed. On the other hand, for anisotropic emission the memory from the photons may have a non-vanishing amplitude even if it is seen with small viewing angles. In the decelerating phases of gamma-ray burst (GRB) jets the kinetic energy of the jet is converted into the energy of gamma-ray photons. Then it would be possible to observe a variation in the GW memory associated with GRB jets on the timescale of the gamma-ray emission if the emission is partially anisotropic. Such an anisotropy in the gamma-ray emission has been suggested by the polarizations detected in recent observations of GRBs. The GW memory from GRB jets would provide clues to clarifying the geometry of the jets and the emission mechanism in GRBs. Thus it will be an interesting target for the next generation detectors of the GWs.
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