A peculiar low-luminosity short gamma-ray burst from a double neutron star merger progenitor

Double neutron star (DNS) merger events are promising candidates of short gamma-ray burst (sGRB) progenitors as well as high-frequency gravitational wave (GW) emitters. On August 17, 2017, such a coinciding event was detected by both the LIGO-Virgo gravitational wave detector network as GW170817 and Gamma-Ray Monitor on board NASA’s Fermi Space Telescope as GRB 170817A. Here, we show that the fluence and spectral peak energy of this sGRB fall into the lower portion of the distributions of known sGRBs. Its peak isotropic luminosity is abnormally low. The estimated event rate density above this luminosity is at least \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$190_{ - 160}^{ + 440}$$\end{document}190-160+440 Gpc−3 yr−1, which is close to but still below the DNS merger event rate density. This event likely originates from a structured jet viewed from a large viewing angle. There are similar faint soft GRBs in the Fermi archival data, a small fraction of which might belong to this new population of nearby, low-luminosity sGRBs.

S hort-duration gamma-ray bursts (sGRBs) have long been proposed to be produced in systems involving the coalescence of double neutron stars (DNS) 1 , and the observations of sGRB afterglows and host galaxies are consistent with such a conjecture [2][3][4] . Based on the estimated event rate density derived from previously observed sGRBs at cosmological distances 5,6 , the chance of detecting an sGRB within a small volume for detectable DNS mergers by advanced LIGO is very low 7 . Thus, GRB 170817A 8 /GW 170817 9 , as the first event in history showing a GRB associated with a gravitation wave signal from a compact binary merger, provides a unique opportunity to study its event rate, merger product, and implications of the GRB physics.
In this work, we performed a comprehensive analysis on GRB 170817A, mainly focusing on its prompt emission data in γ-ray energy band. Taking NGC 4993 as its host galaxy 10 , we find that its luminosity is abnormally low. We calculate the event rate of such sGRB event rate density and performed a comparison between such a rate density and the NS-NS merger event rate density. We also discussed the possible jet geometries, the physical implication of the time delay between GW signal and GRB signal, and the possible merger products of the event.

Results
Light curve structure. GRB 170817A (Fermi Trigger number 170817529) triggered Fermi GBM (8 keV-40 MeV) 11 at T 0 = 12:41:06.474598 UT on 17 August 2017 8 . We processed the public Fermi/GBM data using the procedure as described in ref. 12 . We selected two GBM/NaI detectors, n1 and n2, on board Fermi that are in good geometric configurations (e.g., angle <60°) with respect to the source position. By extracting the photon events from the Time-Tagged Event (TTE) data detected by these two detectors, we noticed that a sharp peak is present in the light curve between T 0 − 0.26 s and T 0 + 0.57 s with a signal-to-noise ratio (S/N) >5 (Methods). Such a signal is clearly identified in the two-dimensional (2-D) count map presented in Fig. 1. A weaker tail, which is also significant above the background with S/N >5, appears between T 0 + 0.95 s and T 0 + 1.79 s. The total span of GRB 170817A is about 2.05 s with a 0.38-s gap consistent with the background. The burst was also detected in the data of the SPI Anti-Coincidence System (ACS) on-board International Gamma-Ray Astrophysics Laboratory (INTEGRAL) 13 . We downloaded the pre-binned (50-ms bin) SPI-ACS light curve from http://isdc. unige.ch/Soft/ibas/ibas_acs_web.cgi, which is derived from 91 independent detectors with different lower energy thresholds (from 60 to 120 keV) and an upper threshold of~10 MeV. The multi-channel GBM light curves and the SPI-ACS light curves are presented in Supplementary Fig. 1. We performed an extended search for signals before and after the burst using GBM data and no significant emission was found (Supplementary Note 5; Supplementary Figs. 9 and 10).
Spectral analysis. We first extract the time integrated spectrum in the first peak region (i.e., from T 0 − 0.26 to T 0 + 0.57 s). We select the NaI detectors n1 & n2 and BGO detector b0. The total number of photon counts is significantly above the background counts in NaI detectors ( Supplementary Fig. 11). We used a software package developed by the first author, McSpecFit 14 , to perform spectral fitting. The energy channels at and around the iodine K-edge at 33.17 keV 15 were excluded to better assess the quality of the fitting of spectral models. We find that the net spectrum can be successfully fitted by a power law function with an exponential high-energy cutoff (hereafter, cutoff power law or parameterized as E p , is 149:1 þ229:4 À24:2 keV. The corresponding average flux in this time interval is 2:19 þ3:76 À0:62 10 À7 erg cm −2 s −1 between 10 keV and 10 MeV. The fluence is 1:81 þ3:11 À0:51 10 À7 erg cm −2 . For the second peak between T 0 + 0.95 s and T 0 + 1.79 s, we find that the net spectrum can be preferably fitted by a blackbody model with kT ¼ 11:3 þ3:8 À2:4 keV (PGSTAT/DOF = 236.4/352) although we cannot rule out its non-thermal origin due to the large uncertainty of the lower spectral index when fitted by a CPL model (Supplementary Table 1). The corresponding average flux in this time interval is 5:2 þ4:7 À2:4 10 À8 erg cm −2 s −1 between 10 keV and 10 MeV. The fluence in the same energy range is 4:33 þ3:95 À1:99 10 À8 erg cm −2 . Including both peaks, the total fluence is 2:24 þ3:51 À0:53 10 À7 erg cm −2 , corresponding to an isotropic energy of 4:17 þ6:54 À0:99 10 46 erg. Using a 50-ms time resolution light curve, the peak luminosity at T 0 ≃ −0.07 s is derived as 1:6 þ2:5 À0:4 10 47 erg s −1 . The best-fit parameters are presented in Supplementary  Table 1. The spectral fitting plots as well as the parameter constraints are presented in Supplementary Figs. 2-4. No significant spectral evolution is observed ( Supplementary Fig. 5).
Spectral lag analysis. Using the cross correlation function (CCF) method, we also calculate the spectral lag of the GRB between (25-50) keV and (50-100) keV, which is 0.03 ± 0.05 s, consistent with zero. This is consistent with the spectral lag distribution of sGRBs 16 .
Comparison with other GRBs. With the observed and derivative properties summarized in Table 1, one can compare GRB 170817A with other sGRBs. The following samples extracted from the Fermi/GBM catalog 17 are considered for comparison: (a) the long GRB sample with E p measured (1679 GRBs); (b) the short GRB sample (T 90 < 2 s) with E p measured (317 GRBs); and (c) the short GRB sample with S/N < 6 and E p measured (66 "faint & short" GRBs). The latter is the faint sGRB sample to which GRB 170817A belongs (Supplementary Note 2 and Supplementary Fig. 6).
We first compare the observed properties of GRB 170817A with other GRBs. Figure 2 upper panel is the standard T 90 − HR (hardness ratio) plot for GRBs. One can see that GRB 170817A falls in the boundary between short and long GRB populations. Since evidence has suggested that majority of sGRBs are consistent with the compact star merger origin, GRB 170817A, being associated with GW170817, belongs to the long and soft regime of this population. Figure 2 lower panel compares GRB 170817A and other GRBs in the fluence vs. E p diagram. GRB 170817A seems to lie far away from the majority of the long GRBs. Based on γ-ray information only, this burst would be more likely regarded as one of those normal (but faint and soft) short GRBs if there was no gravitational wave trigger. Comparing the host galaxy NGC 4993 of GRB 170817A with the host galaxies of other sGRBs 3, 18 , we find that NGC 4993 falls into the distribution of sGRB hosts in terms of half-light radius, stellar mass, and afterglow offset from the host galaxy (Supplementary Note 3; Supplementary Fig. 7).
We next investigate the intrinsic property of the burst. Taking into consideration the very small distance D L~4 0 Mpc of the host galaxy NGC 4993 19 , this burst is abnormally low in terms of luminosity and energy (throughout the paper, luminosity and energy are the isotropic-equivalent ones). The peak isotropic luminosity with 50 ms bin size is 1:6 þ2:5 À0:4 10 47 erg s −1 , and the isotropic energy is E iso ¼ 4:17 þ6:54 À0:99 10 46 erg. Such lowluminosity sGRBs have never been observed before. Plotting it onto the intrinsic peak energy E p,z = E p (1 + z) vs. isotropic energy E iso plane 20, 21 , we find that it is within the 2σ of the track of the sGRB population, but slightly deviates from the 1σ region of the track into the hard regime even if its E p error is included (Fig. 3). The burst would be more normal if its isotropic luminosity was somewhat higher.  Event rate density of the 170817A-like GRBs. Based on previously known sGRBs, the event rate density (also called volumetric event rate) of sGRBs above then-minimum luminosity (~10 50 erg s −1 ) is a few Gpc −3 yr −1 5, 6 . For example, for a Gaussian distribution of the merger delay time 22 , the event rate density of sGRBs is 4:2 þ1:3 À1:0 Gpc −3 yr −1 above 7 × 10 49 erg s −1 6 . This was significantly lower than the estimated DNS merger event rate density (ref. 9 , see below). The discrepancy may be removed if one considers the beaming correction of sGRBs within the top-hat uniform jet model. Using the beaming factor f b~0 .04 inferred from the sparse sGRB jet break data collected in the past 23 , the beaming-corrected event rate density (counting for sGRBs not beaming toward us) was~100 Gpc −3 yr −1 . With the detection of GRB 170817A, the distribution of the sGRB isotropic peak luminosity extended down by~three orders of magnitude. The revised event rate density of sGRB above 1.6 × 10 47 erg s −1 becomes (Methods) ρ 0;sGRB L iso >1:6 10 47 erg s À1 if one assumes only one such event within the GBM archives. This is comparable to (or somewhat higher than) the previously derived beaming-corrected sGRB event rate density, but could be still up to a factor of a few smaller than the DNS merger event rate density derived based on the detection of GW 170817A 9 , which is (Methods) ρ 0;DNS ¼ 1100 þ2500 À910 Gpc À3 yr À1 : ð2Þ Figure 4 upper panel shows the sGRB event rate density as a function of luminosity threshold. The black power-law (PL) line with an index −0.7 was derived from the Swift sGRBs (black crosses with error included, peak luminosity derived with 64 ms time bin) with redshift measurements 6 . GRB 170817A (orange) extends the sGRB luminosity by three orders of magnitude in the low-L iso regime. Interestingly, the revised event rate density above 1.6 × 10 47 erg s −1 follows the extension of the PL distribution derived by ref. 6 . If one considers that there might be some sGRBs similar to GRB 170817A hidden in the GBM archives, the true event rate density could be higher, but has to be limited by the DNS merger event rate density (blue symbol). In Fig. 4 lower panel, we derive a new sGRB luminosity function across a wide range of luminosity, which is consistent with the extrapolation of the previous results that show a power law with L À1:7 iso 6 .

Discussion
There are in principle two possibilities to produce a lowluminosity sGRB from a DNS merger. The first possibility is a bright sGRB jet viewed off-axis. Within this picture, the main jet (similar to the one observed from a more distant sGRB) beams toward a different direction. However, within such a scenario, one cannot have a sharp-edge conical jet viewed outside the jet cone. This is because the observed duration would be longer than the central engine activity time scale, inconsistent with its typical sGRB duration (Supplementary Note 6). Rather, one requires a The orange symbol with error denotes the event rate density derived from GRB 170817A and the blue symbol with error denotes the DNS merger event rate density derived from GW170817. The black power-law line and other data points were derived from the Swift sGRB sample 6 . The vertical error bar represents the 1σ Gaussian errors derived from ref. 35 . b Luminosity function distribution of sGRBs including GRB 170817A, with labels same as the upper panel. All error bars represent 1−σ uncertainties structured jet viewed from a large wing 24,25 with emission powered by the low-luminosity wind along the line of sight.
Within the sGRB context, such a jet configuration has been discussed in terms of a jet-cocoon geometry 26,27 . A viewing angle θ v ≤ 28°(or ≤36°depending on the assumed value of the Hubble constant 28 ) has been inferred from the gravitational wave data. This is consistent with such a scenario. The second possibility is that the outflow of GRB 170817A may have an intrinsically low luminosity. However, the late rise of X-ray and radio flux 29,30 from the source suggests that the total energy budget of the source is higher. It disfavors this second possibility but favors the off-axis structured jet scenario (Supplementary Note 9). The short duration of the burst is consistent with a prompt black hole or a hyper-massive neutron star that survived for a short (e.g.,~100 ms) period of time before collapsing to a black hole. We conduct a search of precursor or extended emission before and after the GRB trigger time and give a negative result (Supplementary Note 5). Even though the possibility of a longlive post-merger neutron star product cannot be ruled out from the GW 31 and EM data, our non-detection of extended γ-ray emission is consistent with a BH post-merger product (Supplementary Note 7).
The It is intriguing that this delay time scale has the same order as the burst duration itself. Such a delay offers a diagnostic of the emission site and energy dissipation process of GRBs. In particular, a scenario that invokes a magnetized jet dissipating in an optically thin region can interpret both time scales simultaneously without introducing an ad hoc jet-launching delay time as most other models do (Supplementary Note 8).
Assuming a standard radiative efficiency and standard shock microphysics parameters, the low isotropic energy of GRB 170817A suggests that the multi-wavelength afterglows of the burst should be very faint (Supplementary Note 6). We used the Javier Gorosabel 0.6 m robotic telescope at the BOOTES-5 station at Observatorio Nacional de San Pedro Martir (Mexico) to image the 15 galaxies in the GLADE Catalogue starting on Aug 18.21 UT. The optical counterpart (SSS17a) of GW 170817 was detected in the outskirts of the NGC 4993 galaxy, with a magnitude R = 18.20 ± 0.45, in agreement with other contemporaneous measurements. This is much brighter than the predicted flux of optical afterglow. As a result, this optical transient originates from a quasi-thermal kilonova 32,33 , as suggested by independent modeling of many authors (e.g., ref. 34 ).
Within the Fermi GBM soft faint sGRB sample, there might be at most GRB 170817A-like events limited by the DNS merger rate. Some short, faint sGRB events are presented in Supplementary Fig. 6. However, identifying them turns out difficult without gravitational wave detections (Supplementary Note 10).

Methods
Determining GRB duration using 2-D energy vs. time count map. The GRB duration is usually defined by T 90 , which is the time span over which 5-95% of its total measured counts are measured 17 . The calculation of T 90 is subject to the selection of energy band, the bin-size as well as the assumption of the model background (e.g., a 2nd or 3rd order polynomial function) of the GRB light curve. To minimize such an artificial effect for a faint GRB like GRB 170817A, we utilize the 2-D count map of the photon energy and photon arrival time directly from the Fermi/GBM TTE data and calculate the GRB duration. Our procedure is the following: (1) (2) and (3) to get two 2-D count maps for the pre-burst and after-burst backgrounds. (5) Perform interpolation between those two background count maps to calculate the source-normalized background count map within [t1, t2] (middle panel of Fig. 2). Such a normalized and interpolated background within the source region can be used to calculate the standard derivation (STD) of the background. (6) Subtract the background count map from the source count map to get the net count map (bottom panel of Fig. 1). For each bin in the count map, define its signal-to-noise ratio as S/N = (net count)/STD. Overplotting the S/N = 1, 3, 5 in the net count map, we then define the burst duration region as where S/N ≥ 5.0 is satisfied.
sGRB event rate density. The abnormally low luminosity and extremely small distance of GRB 170817A suggest that the actual event rate density of short GRBs is large. With one detection, one can estimate the local event rate density ρ 0,sGRB of short GRBs through The field of view of GBM is approximatively taken as full sky with Ω GBM ' 4π. The working time of GBM is taken since 2008 with a duty cycle of~50%, so that T GBM ' 4:5 yrs. The maximum volume a telescope can detect for this lowluminosity event is V max ¼ 4πD 3 L;max =3. We simulate a set of pseudo-GRBs by placing GRB 170817A to progressively larger distances, and find that the signal would not be detectable at 65 Mpc (Supplementary Note 4; Supplementary Fig. 8). Taking this distance as D L,max , we derive the event rate density of sGRBs 6 ρ 0;sGRB L iso >1:6 10 47 erg s À1 assuming only one such sGRB exists in the GBM archives. This number may be regarded as a lower limit if in reality there are other hidden ones. The event rate density of DNS mergers may be also estimated based on one detection by aLIGO during O1 and O2. Since only one DNS merger event was detected 9 , one may write Noticing Ω = 4π for GW detectors, taking DNS merger horizon~60 and~80 Mpc for O1 and O2, respectively, and adopting a duty cycle of~40% for both O1 and O2, we estimate ρ 0;DNS ¼ 1100 þ2500 À910 Gpc À3 yr À1 : This is consistent with the DNS merger event rate density derived by the LIGO-VIRGO team using more sophisticated simulations 9 . The error bars in both Eqs. (4) and (6) show the 1σ Gaussian errors derived from ref. 35 by taking only one observational event into account. Comparing the two equations, one can see that even though the sGRB rate density may be consistent with the DNS merger rate density, it can be smaller than the latter by up to a factor of a few. This either suggests that there might be even less luminous sGRBs than GRB 170817A, or there might be GRB 170817A-like sGRBs hidden in the GBM archives. The number of these events is at most a few.
Data availability. The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.