The Gamma-ray Burst Monitor (GBM) (Meegan et al., 2009) onboard Fermi triggered on a burst-like transient on August 17, 2017 at 12:41:06.5 UT (trigger 524666471/170817529) (Connaughton et al., 2017; von Kienlin et al., 2017). With a GBM localization (Connaughton et al., 2017; von Kienlin et al., 2017) consistent with that of the LIGO/Virgo trigger (The LIGO Scientific Collaboration and Virgo Collaboration, 2017a) about 2 s earlier, there is little doubt that these two triggers are from the same event, a neutron star binary coalescence (Abbott et al., 2017a; The LIGO Scientific Collaboration and Virgo Collaboration, 2017b). It is possible that the LIGO and Fermi-GBM events are not related, however, the combination of observations across many wavelengths (e.g., Goldstein et al., 2017; Troja et al., 2017, 2018; Gottlieb et al., 2019), and the previous predictions falling perfectly inline with these observations push even the most pessimistic observers to accept the relation between the two events.

To obtain the spectral properties of the GRB associated to GW 170817, the temporal off-source photon event light curve was fitted with a polynomial via an unbinned Poisson likelihood. This polynomial was used to estimate the background counts during the source temporal interval. The on-source interval was derived by choosing bins via the Bayesian blocks method (Scargle et al., 2013) and selecting bins with a 3σ excess over the estimated background. This resulted in a single bin lasting 0.65 s (Figure 1). After the initial spike, there is no statistically significant emission from which to perform spectral analysis. The count spectra covering 10 keV to 40 MeV of this bin were fit via a Poisson-Gaussian likelihood to an exponentially cutoff power law. The spectral parameters were estimated by computing the posterior of the priors and likelihood with the Multinest (Feroz et al., 2009) nested sampling algorithm. The fits resulted in a photon index of α = −1.00±0.23 and a cutoff energy of E_c = 230 ± 100 keV. The event fluence during the ~0.65 s prime emission time interval in the 10–1,000 keV energy range is (2.45 ± 0.4) × 10⁻⁷ erg cm⁻². Combined with the LIGO distance estimate of 40 Mpc (Abbott et al., 2017a; The LIGO Scientific Collaboration and Virgo Collaboration, 2017c) this implies an isotropic equivalent energy of 5.2 × 10⁴⁶ erg in the 1 keV–10 MeV band (this energy band is given for comparability; no photons above 400 keV are measured for this event). Comparing the spectral properties of GRB 170817A to the sample of previously detected GRBs (Bhat et al., 2016) by Fermi-GBM shows that it is not a typical short GRB. The event resides on the boundary of the α-flux, α-E_c plane and temporal smoothness (see below), but is accompanied by a few sGRBs with similar properties (Figure 2). Spectral and temporal analyses were performed with the Multi-Mission Maximum Likelihood framework (3ML) (Vianello et al., 2015).

All Fermi-GBM GRBs with a reported duration <2 s were reanalyzed with the method described in Greiner et al. (2016) and temporal bins were selected for spectral analysis if they exceeded a threshold of 3σ above background. To study the peak flux spectral properties of the population, we discarded events with errors >50% on the photon spectral index and 60% on the cutoff energy to eliminate poorly fit spectra while simultaneously retaining those with constraints as good as those for GRB 170817A. The durations of the events were calculated by taking the start of the first significant bin to the end of the last significant bin which could include bins in between that were not significant.

Fermi-GBM has observed 355 sGRBs until mid-2014 (Bhat et al., 2016). After removal of poor fits and sGRB with badly modeled background in the GBM catalogs, we were left with 248 GRBs. Our cut on parameter constraints reduced the sample to 68 sGRBs. The choice of a cutoff power law for the spectral function does introduce a bias for low flux GRBs that would only be fit by a power law. These would not have proper flux estimates due to a lack of a measurable energy cutoff and are the main contribution to sGRBs that were removed from the sample due to poor constraints on the spectral parameters. Since these GRBs have low flux, our rate estimates are conservative.

In order to assess temporal smoothness of the light curves, the pulse structure was determined by dividing the observed significant intervals into three categories (which are color-coded in Figure 2): (1) single bin, (2) contiguous bins with monotonic increase/decrease or rise and decay pulse shape and, (3) complex which including non-contiguous bins.

We searched our GBM GRB database for events with similar spectral and temporal characteristics. On December 24, 2010, at 05:26:57.5 UTC, both Swift-BAT and Fermi-GBM triggered on the short GRB 101224A (McBreen, 2010), lasting 0.36 s. Our analysis of its temporal and spectral properties shows that the event is remarkably similar to GRB 170817A (Figures 2, 3), including its light curve structure. As noted earlier (Krimm et al., 2017), there is the galaxy pair MCG+08-34-033 nearby, at a distance of 75 Mpc. The offset of this GRB to the center of MCG+08-34-033 is <135 kpc, not unusual for sGRBs (Berger, 2010). Assuming this to be the distance of GRB 101224A, we calculate a fluence of 2.8 × 10⁴⁷ erg in the 1 keV–10 MeV band. For comparison, assuming standard ΛCDM cosmological parameters (Planck Collaboration, 2015), the short GRB 090510A (Rau, 2009) at luminosity distance of 5,990 Mpc has an energy of 2.7 × 10⁵³ erg and GRB 100625A (Bhat, 2010) at a luminosity distance of 2,590 Mpc has an energy of 2.3 × 10⁵³ erg, making them markedly dissimilar from the two local events we identify (Figure 4). In Figure 2, the two candidate off-axis GRBs are spectrally weak and soft in comparison to the population, however, they do not deviate from the typical cutoff energy distribution. In contrast, GRB 0090510A and GRB 100625A are spectrally harder and brighter while being two orders of magnitude further away.

While there is only one published prediction of the properties of off-axis emission (Janka et al., 2006), the generic expectations are a decreased luminosity and non-complex observed light curve structure due to the relativistic smoothing of the internal emission episodes (Salafia et al., 2016). Similarly, the stacking of spectra observed over the profile of the jet leads to an observed increase in low-energy photons and thus a softer spectrum below the νF_ν peak (Yamazaki et al., 2002). These are exactly the properties of GRB 170817A. Recently, studies have attempted to advance these predictions in light of more of these events (e.g., Eichler, 2018; Gottlieb et al., 2019; Kathirgamaraju et al., 2019). Moreover, many of these newer observations confirm that the jet is indeed beamed implying that the emission was observed off-axis. Conversely, observed on-axis emission probes the internal Lorentz profile for the jet allowing the observer to see multi-episodic emission as well as the direct spectral (harder) shape of the spectrum. Given this separation into two populations, with a coincidence of expected and observed properties, our working hypothesis below is that GRB 170817A and the likes are members of the same population but observed off-axis. This is observationally supported also by the measurement of superluminal motion of the radio jet of GRB 170817A from which an off-axis angle of 20 ± 5° is inferred (Mooley et al., 2018). The alternative, a low-luminosity population has the additional problem that a luminosity difference of a factor 10⁵ would have to be accommodated with the same emission mechanism which is challenging (Begue et al., 2017). Instead, several other explanations have been proposed, the most popular being emission from mildly relativistic cocoon (Kasliwal et al., 2017; Lazzati et al., 2017; Kathirgamaraju et al., 2018) or emission from shock-breakout (Gottlieb et al., 2018).

With another promising off-axis sGRB identified, and a third one suggested recently (Troja et al., 2018), we can ask the question: how many of these events we have detected with Fermi-GBM in the past without recognizing them as being nearby and off-axis?

We base our simple estimates of the rate of sGRBs on the method proposed previously (Guetta and Piran, 2005; Coward et al., 2012). We assume that the peak energy flux limit for detection by the GBM detector is 10⁻⁷ erg s⁻¹ cm⁻². Knowing the spectrum and the redshift, the maximum distance d_max at which a given GRB is visible can be estimated (after k-correction). This maximum distance corresponds to a maximum volume V_max. Then the rate is estimated as

where Ω = 0.5 is the fraction of the sky seen by GBM and T = 9 years is the duration of the mission. This leads to a rate of GRB 170817A and GRB 101224A of ~170 and ~2 Gpc⁻³ yr⁻¹. This is far more than the rate of individual other short GRBs, being around 0.03 Gpc⁻³ yr⁻¹, with the exception of GRB 080905 which has high individually derived rate compared with other sGRBs (Coward et al., 2012). While the rates given above are strongly sensitive to the chosen value of the flux limit, the ratio between rates does not depend on this flux limit, provided that the k-correction can be neglected, as is the case for bursts at small redshift.

We estimate the ratio of sGRBs seen on- and off-axis as a function of redshift. The ratio of such off-axis bursts to on-axis bursts strongly depends on the structure of the jet and on the luminosity function; both poorly understood. We assume that the angular-dependent, emitted, co-moving luminosity of a burst can be expressed as a step function

where L₀ is the luminosity emitted in the direction of the jet, θ₀ is the opening angle, θ_obs is the angle between the jet's direction and the observer direction, and L~ is a reduction factor, taken to be 100 (we note that this is conceptually different from off-axis afterglow emission, where due to sideways expansion θ₀ is growing, from originally θ₀ < θ_obs toward θ₀>θ_obs at late stages). We further assume that if θ_obs is larger than 45°, the sGRB is not seen.

The distribution of emitted luminosity can be obtained by

where Ψ(L₀) and ξ(θ₀) are the distributions of the jet's luminosity, L₀, and of the opening angle. We can take those distributions in the form

where Θ is the Heaviside function, L_b is the break luminosity which can be taken at few 10⁵³ erg s⁻¹, β = 0.5 describes the decay of the luminosity distribution (Ghirlanda et al., 2016) and Llim=5×1050 erg s⁻¹ is the minimum luminosity of an on-axis burst. The opening angle distribution function is taken to be a log normal distribution centered on θ_ref = 7° with width σ = 0.1. These forms and values are taken to mimic values and general shapes derived from the simulations of Janka et al. (2006).

We further assume that the rate of sGRBs follows the retarded star formation rate (Li, 2008)

where S_FR is the star formation rate at a given redshift and f is the distribution of delay τ, taken to be a log-normal distribution (Wanderman and Piran, 2015; Beniamini and Piran, 2019) centered on 3 Gyr with a deviation of 0.2 Gyr. The star formation rate is taken to be the form

via work of Hopkins and Beacom (2006), though it is possible to adapt the calculations to other forms since knowledge of the true SFR is uncertain.

The rate of short GRBs between two given fluxes F₁ and F₂ up to a given redshift z can therefore be estimated as

where ρ₀ is the local rate of short GRBs, dV/dz is the comoving volume and d_L is the luminosity distance. Overall, the rate is a 5-fold integral computed numerically with parallel processing on a GPU using CUDA. The results are shown in Figure 5: on and off-axis emission rates are separated to show where each component of the total rate would dominate. For the local Universe at redshift smaller than 0.02, off-axis emission would dominate. Conversely, on-axis sGRBs dominate the observed rate at high redshift. Notably, even after integrating deep into the Universe, the low end of the observed flux distribution would be dominated by off-axis events. Even if this computation needs to be refined, it indicates that for the future LIGO/Virgo observing runs we can expect to detect faint short GRBs until their horizon exceeds 300 Mpc. While on-axis sGRBs, beamed at us, are visible to a redshift of about 1.5 (the highest redshift sGRBs are 1.4, 1.7, and 2.6, the last one being highly debated); off-axis GRBs are unbeamed, and with the same instrument sensitivity can only be seen to about 1/30 of those distances, i.e., about 300 Mpc. Our analysis of Fermi-GBM data suggests that at least a few percent (for an off-axis flux reduction factor L~ = 1,000), if not up to 30% (L~ = 100) of sGRBs are local (Figure 5). We note that this fraction also depends on the parametrization of the jet profile, on the merger delay and on the luminosity distribution. This range of the local sGRB rate is consistent with the detection of one such event during LIGO run O2 with a distance threshold of 100 Mpc.