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Register a new userTail Emission of Prompt Gamma-Ray Burst Jets
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Ryo Yamazaki
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Tail emission of the prompt gamma-ray burst (GRB) is discussed using a multiple emitting sub-shell (inhomogeneous jet, sub-jets or mini-jets) model, where the whole GRB jet consists of many emitting sub-shells. One may expect that such a jet with angular inhomogeneity should produce spiky tail emission. However, we found that the tail is not spiky but is decaying roughly monotonically. The global decay slope of the tail is not so much affected by the local angular inhomogeneity but affected by the global sub-shell energy distribution. The fact that steepening breaks appeared in some events prefers the structured jets. If the angular size of the emitting sub-shell is around 0.01-0.02 rad, some bumps or fluctuations appear in the tail emission observed frequently in long GRBs. If the parameter differences of sub-shell properties are large, the tail has frequent changes of the temporal slope observed in a few bursts. Therefore, the multiple emitting sub-shell model has the advantage of explaining the small-scale structure in the observed rapid decay phase.
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We aim to obtain a measure of the curvature of time-resolved spectra that can be compared directly to theory. This tests the ability of models such as synchrotron emission to explain the peaks or breaks of GBM prompt emission spectra. We take the burst sample from the official Fermi GBM GRB time-resolved spectral catalog. We re-fit all spectra with a measured peak or break energy in the catalog best-fit models in various energy ranges, which cover the curvature around the spectral peak or break, resulting in a total of 1,113 spectra being analysed. We compute the sharpness angles under the peak or break of the triangle constructed under the model fit curves and compare to the values obtained from various representative emission models: blackbody, single-electron synchrotron, synchrotron emission from a Maxwellian or power-law electron distribution. We find that 35% of the time-resolved spectra are inconsistent with the single-electron synchrotron function, and 91% are inconsistent with the Maxwellian synchrotron function. The single temperature, single emission time and location blackbody function is found to be sharper than all the spectra. No general evolutionary trend of the sharpness angle is observed, neither per burst nor for the whole population. It is found that the limiting case, a single temperature Maxwellian synchrotron function, can only contribute up to $58^{+23}_{-18}$% of the peak flux. Our results show that even the sharpest but non-realistic case, the single-electron synchrotron function, cannot explain a large fraction of the observed GRB prompt spectra. Because of the fact that any combination of physically possible synchrotron spectra added together will always further broaden the spectrum, emission mechanisms other than optically thin synchrotron radiation are likely required in a full explanation of the spectral peaks or breaks of the GRB prompt emission phase.
Recently, a tight correlation among three quantities that characterize the prompt emission of long Gamma-Ray Bursts (GRBs) with known redshift z, was discovered (Firmani et al. 2006). We use this correlation to construct the Hubble diagram (HD) with a sample of 19 GRBs in the broad range of z=0.17-4.5, and carry out a full statistical analysis to constrain cosmological parameters (CPs). To optimally solve the problem of circularity, a Bayesian approach is applied. The main result is that the concordance LambdaCDM cosmology is fully consistent with the GRB data at the level of several tests. If we assume the Lambda cosmology, then we find Om_M=0.31^{+0.09}_{-0.08} and Om_Lambda=0.80^{+0.20}_{-0.30}$ (1sigma); the flat-geometry case is within 1sigma. Assuming flatness, we find Om_M=0.29^{+0.08}_{-0.06}, and fixing Om_M=0.28, we obtain a dark energy equation of state parameter w=-1.07^{+0.25}_{-0.38}, i.e. the ambdaCDM model (w=-1) is within 1sigma. Given the low number of usable GRBs we cannot yet constrain well the possible evolution of w=w(z). However, the case w(z)=-1 (LambdaCDM) is consistent at the 68.3% CL with GRBs. It is shown also how a broad range of zs in the used sample improves the determination of CPs from the HD, which is the case of GRBs as distance indicators.
The radiative process responsible for gamma-Ray Burst (GRB) prompt emission has not been identified yet. If dominated by fast-cooling synchrotron radiation, the part of the spectrum immediately below the $ u F_ u$ peak energy should display a power-law behavior with slope $alpha_2=-3/2$, which breaks to a higher value $alpha_1=-2/3$ (i.e. to a harder spectral shape) at lower energies. Prompt emission spectral data (usually available down to $sim10-20,$keV) are consistent with one single power-law behavior below the peak, with typical slope $langlealpharangle=-1$, higher than (and then inconsistent with) the expected value $alpha_2=-3/2$. To better characterize the spectral shape at low energy, we analyzed 14 GRBs for which the Swift X-ray Telescope started observations during the prompt. When available, Fermi-GBM observations have been included in the analysis. For 67% of the spectra, models that usually give a satisfactory description of the prompt (e.g., the Band model) fail in reproducing the $0.5-1000,$keV spectra: low-energy data outline the presence of a spectral break around a few keV.We then introduce an empirical fitting function that includes a low-energy power law $alpha_1$, a break energy $E_{rm break}$, a second power law $alpha_2$, and a peak energy $E_{rm peak}$. We find $langlealpha_1rangle=-0.66$ ($ rm sigma=0.35$), $langle log (E_{rm break}/rm keV)rangle=0.63$ ($ rm sigma=0.20$), $langlealpha_2rangle=-1.46$ ($rm sigma=0.31$), and $langle log (E_{rm peak}/rm keV)rangle=2.1$ ($ rm sigma=0.56$).The values $langlealpha_1rangle$ and $langlealpha_2rangle$ are very close to expectations from synchrotron radiation. In this context, $E_{rm break}$ corresponds to the cooling break frequency.
The counter jet of a short gamma-ray burst (sGRB) has not yet been observed, while recent discoveries of gravitational waves (GWs) from a binary neutron star (NS) merger GW170817 and the associated sGRB 170817A have demonstrated that off-axis sGRB jets are detectable. We calculate the prompt emission from the counter jet of an sGRB and show that it is typically 23-26 mag in the optical-infrared band 10-10^3 sec after the GWs for an sGRB 170817A-like event, which is brighter than the early macronova (or kilonova) emission and detectable by LSST in the near future. We also propose a new method to constrain the unknown jet properties, such as the Lorentz factor, opening angle, emission radii, and jet launch time, by observing both the forward and counter jets. To scrutinize the counter jets, space GW detectors like DECIGO are powerful in forecasting the merger time (<~ 1 sec) and position (<~ 1 arcmin) (~ a week) before the merger.
Gamma-ray Bursts (GRBs) prompt emission spectra are often fitted with the empirical Band function, namely two power laws smoothly connected. The typical slope of the low energy (sub-MeV) power law is $alpha_{B}simeq -1$. In a small fraction of long GRBs this power law splits into two components such that the spectrum presents, in addition to the typical $sim$ MeV $ u F_{ u}$ peak, a break at the order of a few keV or hundreds keV. The typical power law slopes below and above the break are -0.6 and -1.5 respectively. If the break is a common feature, the value of $alpha_{B}$ could be an average of the spectral slopes below and above the break in GRBs fitted with Band function. We analyze the spectra of 27 (9) bright long (short) GRBs detected by the Fermi satellite finding a low energy break between 80 keV and 280 keV in 12 long GRBs, but in none of the short events. Through spectral simulations we show that if the break is moved closer (farther) to the peak energy a relatively harder (softer) $alpha_{B}$ is found by fitting the simulated spectra with the Band function. The hard average slope $alpha_{B}simeq-0.38$ found in short GRBs suggests that the break is close to the peak energy. We show that for 15 long GRBs best fitted by the Band function only, the break could be present, but it is not identifiable in the Fermi/GBM spectrum, because either at low energies, close to the detector limit for relatively soft $alpha_{B}lesssim-1$, or in the proximity of the energy peak for relatively hard $alpha_{B}gtrsim-1$. A spectrum with two breaks could be typical of GRB prompt emission, though hard to identify with current detectors. Instrumental design such that conceived for the THESEUS space mission, extending from 0.3 keV to several MeV and featuring a larger effective area with respect to Fermi/GBM, can reveal a larger fraction of GRBs with a spectral energy break.
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