How Special Is GRB 170817A?

In Wang et al. (2017a), we have compared GRB 170817A, the first short event unambiguously powered by neutron star mergers, with other sGRBs with the well-measured spectra and redshifts, and found out that GRB 170817A is the weakest sGRB detected so far and its isotropic equivalent energy (${E}_{\mathrm{iso}}$) and luminosity (L_γ) of the prompt emission are at least tens of times lower than the majority recorded before. However, its spectral peak energy, ${E}_{{\rm{p}},\mathrm{rest}}=187\pm 63\,\mathrm{keV}$ (Goldstein et al. 2017), is comparable to quite a few sGRBs, where the subscript "rest" represents the property in the rest frame. Therefore, GRB 170817A does not follow the regular ${E}_{{\rm{p}},\mathrm{rest}}\mbox{--}{E}_{\mathrm{iso}}$ and ${E}_{{\rm{p}},\mathrm{rest}}\mbox{--}{L}_{\gamma }$ correlations presented, for example, in Zhang et al. (2012), Tsutsui et al. (2013), and D'Avanzo et al. (2014). One possibility is that GRB 170817A is an off-axis event, which satisfies the following relations

$$\begin{eqnarray}&&{E}_{\mathrm{iso}}\approx {a}_{0}^{-3}{E}_{\mathrm{iso},\mathrm{int}},\,\,{L}_{\gamma }\approx {a}_{0}^{-4}{L}_{\gamma ,\mathrm{int}},\,\,{T}_{90}\sim {a}_{0}{T}_{90,\mathrm{int}},\\ &&\quad \mathrm{and}\,\,{E}_{{\rm{p}}}\sim {a}_{0}^{-1}{E}_{{\rm{p}},\mathrm{int}},\end{eqnarray} \tag{ 1 }$$

where ${a}_{0}=1+{(\eta {\rm{\Delta }}\theta )}^{2}$, η is the initial Lorentz factor of the GRB outflow, ${\rm{\Delta }}\theta ={\theta }_{{\rm{v}}}\mbox{--}{\theta }_{{\rm{j}}}\geqslant 0$, where ${\theta }_{{\rm{v}}}$ is the viewing angle and ${\theta }_{{\rm{j}}}$ is the half-opening angle, T₉₀ is the duration of the GRB, and the subscript "int" represents the parameters of the event if viewed on-axis (e.g., Yamazaki et al. 2002). Since ${E}_{{\rm{p}}}$ declines much shallower than either ${E}_{\mathrm{iso}}$ or ${L}_{\gamma }$, the regular ${E}_{{\rm{p}},\mathrm{rest}}\mbox{--}{E}_{\mathrm{iso}}$ and ${E}_{{\rm{p}},\mathrm{rest}}\mbox{--}{L}_{\gamma }$ correlations are thus violated. The main purpose of this subsection is to examine whether there are any proper candidates that can serve as the "on-axis" analogs of GRB 170817A.

We have collected the bright sGRBs (i.e., the observed ${L}_{\gamma }\gt {10}^{51}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, which is denoted as ${L}_{\gamma ,\mathrm{int}}$) detected so far (Zhang et al. 2012; D'Avanzo et al. 2014; Wang et al. 2017a). Then, we calculate ${a}_{0}={({L}_{\gamma ,\mathrm{int}}/{10}^{47}\mathrm{erg}{{\rm{s}}}^{-1})}^{1/4}$ (i.e., we take the isotropic luminosity of GRB 170817A, which is $\sim {10}^{47}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, Goldstein et al. 2017, as a fiducial value) and then get the T₉₀ and ${E}_{{\rm{p}}}$ of these "off-axis" events. The results are shown in the left panel of Figure 1. For comparison, GRB 170817A is also presented (but without any change of the parameters since it is speculated to be an off-axis event). As expected, almost all of these "off-axis" events peak in soft gamma-rays with a duration that should be classified in the long-duration group (except that the prompt emission pulses are so short that with the enhancement by a factor of a₀ it is still shorter than the central engine activity interval), indicating that some long-duration GRBs that have no associated supernovae (also known as the SN-less long GRBs or the hybrid GRBs) might be actually the "off-axis" sGRBs and thus associated with strong GW radiation (Wang et al. 2017b). Nevertheless, a few events (for example, GRB 100206A, GRB 100117A, and GRB 130603B if viewed off-axis) have parameters similar to GRB 170817A. Note that GRB 130603B is a short event with a macronova signal (Berger et al. 2013; Tanvir et al. 2013). In the double neutron star merger model, the late-time macronova emission is largely isotropic,⁷ which is remarkably different from the prompt X-/γ-ray emission. Though such a macronova signature has just one data point, it indeed reasonably matches the J-band emission of AT 2017gfo, strengthening the potential "connection" between GRB 170817A and GRB 130603B (see the right panel of Figure 1).

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The prompt emission and the macronova emission are respectively governed by the relativistic and sub-relativistic outflows launched during the merger of the binary compact objects, which are independent of the density of the circumburst medium (e.g., Li & Paczyński 1998; Kasen et al. 2013; Tanaka & Hotokezaka 2013; Fernández et al. 2017; Metzger 2017). The afterglow emission is instead generated by the electrons accelerated in the blast wave expanding into the medium. Therefore, its flux depends on the medium density (n) sensitively, except that the observer's frequency is above both the cooling frequency and the typical synchrotron radiation frequency of the electrons, for which the flux is proportional to n⁰ (Sari et al. 1998). If GRB 170817A is an off-axis analog of GRB 130603B but within the medium with a significantly lower n (note that for GRB 130603B the afterglow modeling fit suggests an $n\sim 0.15\,{\mathrm{cm}}^{-3}$, Fan et al. 2013, which is higher than that for typical sGRBs; Fong et al. 2015), the afterglow emission would be further suppressed (in the off-axis jet scenario, the early time afterglow should rise rather than decay until the ejecta has got decelerated to a Lorentz factor that is already smaller than $1/{\theta }_{{\rm{v}}}$, where ${\theta }_{{\rm{v}}}$ is the observer's viewing angle; Granot et al. 2002; Wei & Jin 2003).

The afterglow emission of GRB 130603B (e.g., Berger et al. 2013; Tanvir et al. 2013; de Ugarte Postigo et al. 2014; Fong et al. 2014) has been reasonably fitted (Fan et al. 2013). We adopt the same set of physical parameters (including the energy injection process assumed in Fan et al. 2013) to estimate the off-axis afterglow radiation. The physical parameters include ${\epsilon }_{{\rm{e}}}=0.15$ and ${\epsilon }_{{\rm{B}}}=0.03$ (i.e., the fractions of shock energy given to electrons and magnetic field); ${\theta }_{{\rm{j}}}=0.085$, the initial kinetic energy of the GRB ejecta, is adopted to be $2\times {10}^{50}$ erg; and the power-law spectral index of electrons p = 2.3. The energy injection into the blast wave has been assumed to be $\approx 1.6\times {10}^{48}\,\mathrm{erg}\,{{\rm{s}}}^{-1}{(1+t/680{\rm{s}})}^{-1}$ for $t\leqslant 680\,{\rm{s}}$, otherwise it is zero (i.e., after the energy injection, the total isotropic equivalent kinetic energy is $\sim 1.2\times {10}^{51}$ erg). The initial Lorentz factor (${{\rm{\Gamma }}}_{0}$) is unknown. The empirical correlation between the prompt emission luminosity and the bulk Lorentz factor (Liang et al. 2010; Fan et al. 2012; Lü et al. 2012) suggests a typical value ${{\rm{\Gamma }}}_{0}\sim 100$, while a value lowered by a factor of a few is allowed. In this work, we take ${{\rm{\Gamma }}}_{0}\approx 50$ and then estimate ${\theta }_{{\rm{v}}}$ as $\sim {\theta }_{{\rm{j}}}+{({L}_{\gamma ,\mathrm{int}}/{10}^{47})}^{1/8}{{\rm{\Gamma }}}_{0}^{-1}\sim 0.185\,\mathrm{rad}$. With such a set of parameters, we calculated the afterglow emission with the same code adopted by Fan et al. (2013) but move the source to a redshift of 0.0097. The resulting afterglow emission is far brighter than that observed in GRB 170817 (see the dotted lines in Figure 2). In order to match the afterglow data (or upper limits) of GRB 170817A collected in the first month after the burst, the physical parameters are adjusted to be $n\sim 2.5\times {10}^{-5}\,{\mathrm{cm}}^{-3}$, $p\sim 2.15$, and ${\epsilon }_{{\rm{B}}}\sim 3.0\times {10}^{-4}$ (see the solid lines in Figure 2). To reasonably address the latest (i.e., $t\sim 100$ days) afterglow data, an additional energetic/narrow core, with the isotropic equivalent kinetic energy $\sim 1.3\times {10}^{52}\,\mathrm{erg}$ and the half-opening angle $\sim 0.5\,{\theta }_{{\rm{j}}}$, is likely needed (see Jin et al. 2017 and the references therein for more discussion on the structured outflows of short GRBs). Such an energetic jet component is expected to have a bulk Lorentz factor of hundreds, hence its contribution to the prompt emission can be ignored. Other possible interpretations can be found in Mooley et al. (2017) and Pooley et al. (2017). Finally, we would like to point out that both n and ${\epsilon }_{{\rm{B}}}$ are in the low end of the distribution of the physical parameters for short GRB afterglows (see Fong et al. 2015), implying brighter afterglow emission in some other neutron star merger events.

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Figure 3 shows the distribution of T₉₀ and ${E}_{\mathrm{iso}}$ (calculated in the rest frame in the energy range 1–10,000 keV) of sGRBs and long-short GRBs (including GRB 060505, GRB 060614, and GRB 111005A) that also could be from neutron star mergers. The data are taken from Zhang et al. (2012), D'Avanzo et al. (2014), Gruber et al. (2014), and Li et al. (2016b) and some are analyzed in this work. In the left side of the plot we find a few additional underluminous events (or candidates), including GRB 111005A (z = 0.0133; see Michałowski et al. 2017; Tanga et al. 2017), GRB 070923, GRB 080121, an GRB 090417A, which are at least a few tens of times smaller than the others. The caution is that for GRB 070923, GRB 080121, and GRB 090417A, the redshifts are not secure, simply because of the lack of quick follow-up observations (prompt Swift/XRT observations were not possible for these events due to the Sun constraint). Their tentative redshifts ∼ $(0.076,\,0.046,\,0.088)$ are based on the possible association of the bursts with nearby galaxies (Fox & Ofek 2007; Perley et al. 2008; Fox 2009). Though the galaxy NGC 3313 (z = 0.0124) in the direction of GRB 150906B (a very hard short GRB) has been proven to be just a coincidence (Abbott et al. 2017c), the possibility of having the whole sample (now consisting of four candidates) solely by chance is very small. Moreover, the presence of GRB 111005A, a long-short event at z = 0.0113 (Michałowski et al. 2017; Tanga et al. 2017), strongly favors the "emergence" of a group of underluminous merger-driven GRBs. In Wang et al. (2017b), we have estimated the rate density of a GRB 111005A-like event to be ${ \mathcal R }={58}_{-38}^{+219}\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$ (using the Uniform prior, the errors are reported in 90% confidence level) or ${29}_{-18}^{+199}\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$ (using the Poisson Jeffreys prior). Note that the jet-opening angle correction has not been taken into account and hence the intrinsic rate density could be much higher. The rate density of GRB 170817A is difficult to estimate since usually the Fermi-GBM GRBs have a very large localization error and it is rather challenging to carry out intense follow-up observations and then establish their connection with the "nearby" galaxies. Assuming that GRB 170817A was observed at a viewing angle of ∼0.4 rad, the corresponding GRB 170817A-like event rate is $\sim 16\mbox{--}640\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$, well consistent with ${ \mathcal R }$. Such a fact further strengthens the possible connection between GRB 170817A and GRB 111005A.

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GRB 170817A hosts the first spectroscopically identified macronova AT 2017gfo. While for GRB 111005A, GRB 070923, GRB 080121, and GRB 090417A, no reliable optical/infrared counterparts have been detected. There are just some upper limits, and we have compared to AT 2017gfo. (Note that all of these upper limits have been properly corrected to the redshift of GRB 170817A. For the observation data of GRB 111005A, the extinction correction with ${A}_{{\rm{v}}}=2$ mag also has been addressed.) As shown in Figure 4, the macronova associated with GRB 111005A should be dimmer than AT 2017gfo by 2–3 mag in the K band, which might imply that the macronova emission from neutron star mergers are diverse (see also Gompertz et al. 2017 and Fong et al. 2017 for similar conclusions, though GRB 111005A was not included in these analyses). For GRB 080121, the constraint is much looser due to its relatively high redshift, while for GRB 070923 and GRB 090417A there were no optical observations. The diversity of the macronova radiation may be caused by the different physical properties of the merger system as well as our lines of sight. In view of the high neutron star merger rate, tens of macronovae triggered by the gravitational-wave detection are expected to be annually detected in 2020s, and our speculation can be directly tested.

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