Fermi and Swift observations of the bright short GRB 090510

The spectral analysis of the prompt emission was performed with RMfit, combining GBM and LAT data (fig. 2).

The time-integrated spectrum shows a significant additional high-energy power-law component ($N_{\sigma}=5.6$, $\beta_{PL}=0.62\pm 0.03$), which carries 37% of the total $\gamma$-ray fluence.

The time-resolved spectroscopy shows the late arrival of the LAT emission and of the additional component. In bin ’a’ (0.5s – 0.6s after Fermi trigger), a Band function with steep $\beta_{Band}>$ 4 is fitted. In bin ’b’ (0.6s – 0.8s), a significant additional power-law component is found ($\beta_{PL}=0.66\pm 0.04$). In bin ’c’ (0.8s – 0.9s) this high-energy component can be fitted but not significantly. In bin ’d’ (0.9s – 1.0s) the LAT data only are fitted by a power-law ($\beta_{PL}=0.9\pm 0.2$).

The observation of high-energy events allows to constrain the jet’s initial bulk Lorentz factor $\Gamma_{0}$. Low- and high-energy photons emitted in the same physical region of the jet can interact to produce $e^{\pm}$ pairs. The opacity to pair-production is strongly reduced if the emission region moves towards the observer with a high bulk Lorentz factor. The optical depth to $e^{\pm}$-pair production at a given photon energy $\tau_{\gamma\gamma}(E)$ depends on the $\gamma$-ray emission spectral shape and variability time scale $t_{v}$, the GRB redshift and the jet’s bulk Lorentz factor. The condition $\tau_{\gamma\gamma}(E<E_{max})<1$, where $E_{max}$ is the maximal observed photon energy, yields a lower limit on $\Gamma_{0}$.

For different epochs of the LAT emission, estimates of $t_{v}$ and spectral models lead to several possible lower limits, all of order $\Gamma_{0,min}\sim 10^{3}$ (see table 2). This is the highest lower limit ever set on a GRB, and the most rapid ejection ever observed from a short GRB.

The physical interpretation of the high-energy prompt spectrum of GRB 090510 is described in detail in ApJ090510 . The lower-energy part of the prompt emission spectrum ($<$ 10 MeV) can be explained by non-thermal synchrotron processes, as well as photospheric thermal emission.

In a non-thermal leptonic model framework, Synchrotron Self-Compton (SSC) emission is expected at GeV-TeV energies and can result in the observed additional power-law component. Detailed simulations of SSC emission have been performed, using the observed Band component as the seed population, taking into account internal $\gamma\gamma$ opacity, self-absorption, radiative escapes, and considering either Thomson or Klein-Nishina scattering regimes. A low magnetic field ($B<<10^{3}G$) favors Compton scattering and can explain the observed bright and hard high-energy component. It would also slow down the cascade formation which could explain the late onset of the high-energy emission. The interpretation of the high-energy emission as forward shock emission from an early afterglow was also considered to explain the delayed onset of the high-energy emission. However, this scenario assumes a very rapid ejection ($\Gamma\simeq$ 2000 – 4000), and implies a high-energy component spectral index of $\beta_{PL}\simeq 1$. This spectrum is consistent with the long-lived spectrum, but not with the additional component found in bin ’b’ ($\beta_{PL}=0.66$). In both cases, the hard spectral index of the soft photons ($\alpha_{Band}=-0.48$) is not explained by the standard synchrotron mechanism.

In hadronic models, secondary $e^{\pm}$ pairs come from the decay of pions formed through photohadronic processes and by the $\gamma-\gamma$ attenuation of synchrotron photons radiated by protons and ions. Synchrotron radiation or inverse Compton scattering from these pairs can produce the observed high-energy $\gamma$-ray emission. In the case of photohadronic models, a stronger magnetic field makes secondary pion production more efficient through more rapid hadronic acceleration, but results in a high-energy component spectral index $\beta_{PL}\simeq 1$, significantly softer than observed. On the other hand, inverse Compton scattering of secondary pairs can produce a high-energy component as hard as the one observed, but this scenario requires a very high isotropic-equivalent power $P_{iso}\sim 10^{55}erg.s^{-1}$. Proton synchrotron models also require a high isotropic equivalent energy, and a high magnetic field. However, the apparent $E_{iso}$ problem can be solved if the jet is strongly collimated or if the true Lorentz factor $\Gamma$ is a factor $\simeq$2 less than the minimum values $\Gamma_{0,min}$ estimated through the $\gamma-\gamma$ opacity constraint. If $\Gamma>\Gamma_{0,min}$, then a proton synchrotron model is strongly disfavored, though note that GRBs with a very high isotropic energy have been observed.

Some quantum gravity models allow for a dependence of the photons speed $v_{ph}$ on their energy, i.e. their arrival time can be written as a development in their energy. In this framework, a low-energy ($E_{\ell}$) and a high-energy ($E_{h}$) photons emitted together would arrive at different times, with the dominant LIV delay term :

where $z$ is the GRB redshift, and n = 1 or 2. A standard cosmology $(h,\,\Omega_{m},\,\Omega_{\Lambda})=(0.71,\,0.27,\,0.73)$ has been assumed for the computations. The difference in arrival times can be of any sign $s_{n}$, depending on the models. The observation of high-energy photons from distant sources allows to put constraints on the energy scales $M_{QG,n}$ that appear in the development.

GRB 090510 has a redshift of $z=0.903\pm 0.03$, and its emission in the LAT energy range includes a photon of energy $E_{h}=30.5^{+5.8}_{-2.6}$ GeV detected 0.829 s after the GBM trigger. This event’s topology makes it a very good photon candidate. The expected background rate and this event’s direction proximity to GRB 090510 location allowed us to associate this event to the burst with high confidence ($N_{\sigma}=$4.4 to 5.6 depending on the selections used).

The observed lightcurve allows different measurements of the temporal delay for this event, depending on which part of the lower energy emission it is associated to. As described in detail in Nat090510 , several lower limits on the linear term’s energy scale $M_{QG,1}$ could be derived (see table 3). All require $M_{QG,1}>M_{Planck}$, which is a strong constraint on linear LIV models.

Lower limits on $M_{QG,2}$ were also derived, but they are much less constraining. For more details on LIV limits derivation, see Vlasios .

The fast repoint by Swift and the ARR performed by Fermi provided a long-lasting observation of GRB 090510 afterglow, from the optical range to several GeV, interrupted by Earth occultation of the GRB to both observatories. The fluxes observed by all instruments are reported in fig. 3.

UVOT and XRT observations of the afterglow started $\sim$ 100 s after the prompt emission trigger, and lasted over 2 days. The optical and UV lightcurve is best fit by a smoothly broken power-law with an initial rise : $\alpha_{Opt,1}=-0.50^{+0.11}_{-0.13}$. The smooth break at $t_{Opt}=1.58^{+0.46}_{-0.37}$ ks is followed by a shallow decay $\alpha_{Opt,2}=1.13^{+0.11}_{-0.10}$. The X-ray lightcurve is best fit by a broken power-law, with an initial shallow decay $\alpha_{X,1}=0.74\pm 0.03$, a break at $t_{X}=1.43^{+0.09}_{-0.15}$ ks and a steep late decay $\alpha_{X,2}=2.18\pm 0.10$.

The beginning of the temporally-extended emission in the LAT has been chosen as the end of the prompt emission seen by the GBM (0.9 s after GBM trigger, i.e. 0.38 s after BAT trigger). A significant emission was detected up to 200s after trigger and up to 4 GeV. This observation was divided in time bins, in all of them an unbinned likelihood spectral analysis was performed using diffuse class events ApJ080825C . The flux decay is best fit by a simple power-law of index $\alpha_{\gamma}=1.38\pm 0.07$, with no significant feature or break. The power-law spectrum shows no significant evolution over time and has an average index $\beta_{\gamma}=1.1\pm 0.1$.

The interpretation of the long-lasting multi-waveband emission fron GRB 090510 is discussed in detail in MW090510 . Two scenarios are considered in the fireball model frame.

In the first scenario, X-ray and $\gamma$-ray emissions are due to internal shocks, and the optical and UV emission to the forward shock. The fluxes measured at 100 s after trigger in the X-ray and $\gamma$-ray ranges are consistent with an internal shock origin, with some fine tuning required. For instance this scenario assumes that the initial rise of the optical emission is due to the forward shock onset, and therefore is steeper than what was observed. But the observation may have caught the end of the steep rise phase. This interpretation also requires a very low ambient density $n\sim 10^{-6}cm^{-3}$, which is low, even for short GRBs. The assumed initial bulk Lorentz factor $\Gamma_{0}\sim 10^{3}$ is consistent with the prompt emission analysis (see section II.2).

Another possibility is that the full long-lasting emission comes from the forward shock region. This model predicts a broad spectrum with a doubly-broken power-law shape and constraints on the indices : $\beta_{1}=-1/3$, $\beta_{3}=\beta_{2}+1/2$. Five successive Spectral Energy Distributions (SED) have been built for 5 different observation dates (100 s, 150 s, 700 s, 1000 s, 1400 s after trigger), including X-ray and UV data, as well as LAT data for the SED at 150 s (see fig. 4). A fit of these data yields a good agreement with the aforementioned model, with $\beta_{2}=0.78\pm 0.04$. The low-energy break decreases with time, from 0.43 keV to $<$0.01 keV. The high-energy break is poorly constrained ($\in[10-130]$ MeV) but is confirmed by a fit of the 100 s SED alone ($N_{\sigma}>4.8$) where the constraint on $\beta_{2}$ and $\beta_{3}$ is relaxed but still holds within error bars. As a result, the afterglow emission spectrum is well described by the forward shock model over 9 energy decades. The lightcurves observed before 1 ks after trigger are also consistent with this model. However, the early onset of the forward shock emission requires a very high bulk Lorentz factor $\Gamma_{0}>5800$, and some temporal emission properties are not well explained, e.g. $\alpha_{X,1}$ is too shallow and $\alpha_{Opt,2}\neq\alpha_{X,2}$. Theoretical extensions of the model can alleviate these problems. E.g., a phase of energy injection or an evolution of the microphysical parameters of the blast wave may cause an early shallow decay of the X-ray flux ; also the difference between X-ray and optical late decay slopes could be explained by dynamical effects.