Late afterglow emission statistics: a clear link between GW170817 and bright short GRBs

TL;DR

This study compares the afterglow emissions of GW170817 and other short GRBs, revealing a continuous sequence and supporting the link between neutron star mergers and bright short GRBs, with implications for future detections.

Contribution

It demonstrates a clear connection between GW170817-like mergers and bright short GRBs through afterglow emission analysis, highlighting observational challenges.

Findings

GW170817's afterglow aligns with bright short GRBs in decay phase

On-axis viewing makes GW170817's afterglow among the brightest

Most neutron star mergers' afterglows are harder to detect due to distance and viewing angles

Abstract

GW170817, the first neutron star merger event detected by advanced LIGO/Virgo detectors, was associated with an underluminous short duration GRB 170817A. In this work we compare the forward shock afterglow emission of GW170817/GRB 170817A to other luminous short GRBs (sGRBs) with both a known redshift and an afterglow emission lasting at least one day after the burst. In the rapid decay phase, the afterglow emission of the bright sGRBs and GW170817/GRB 170817A form a natural and continuous sequence, though separated by an observation time gap. If viewed on-axis, the forward shock afterglow emission of GW170817/GRB 170817A would be among the brightest ones detected so far. This provides a strong evidence for the GW170817-like merger origin of bright sGRBs, and suggests that the detection of the forward shock afterglow emission of most neutron star merger events are more challenging than the case of GW170817 since usually the mergers will be more distant and the viewing angles are plausibly higher.

Full text

The mergers of double neutron star systems or the neutron star-black hole binaries generate strong gravitational wave radiation as well as short duration gamma-ray bursts (sGRBs; including the so-called long-short GRBs) Eichler1989 ; Piran2004 ; Berger2014 . Before 2017, it was widely believed that the GW/sGRB association rate is low since the sGRB outflows are highly collimated with a typical half-opening angle of $\sim 0.1$ radClark2015 . Surprisingly, on 2017 August 17, the gamma-ray monitor onboard the Fermi $\gamma-$ray space telescope had successfully detected a weak short GRB 170817AGoldstein2017 that is spatially and temporally correlated with GW170817, the first neutron star merger event detected by advanced LIGO/VirgoAbbott2017 . The GW/sGRB association has been formally established. However, with a low fluence as well as a short distance ($D\sim 40$ Mpc), the isotropic-equivalent gamma-ray radiation energy of GRB 170817A is just $\sim 3\times 10^{46}$ erg, which is at least 100 times dimmer than that of the typical sGRBs. An under-luminous sGRB could either result from the breakout of the mildly relativistic shock from the leading edge of the merger-driven quasi-isotropic sub-relativistic ejectaKasliwal2017 or be the faint prompt emission of a highly structured relativistic ejecta viewed at a large polar angleJin2018 . The puzzling fact that GRB 170817A and the long duration GRB 980425 (at a distance of $D\sim 36$ Mpc and has been suggested to be the shock breakout signalKulkarni1998 ), the closet two events with remarkably different progenitors, have rather similar luminosity and spectral peak energyWangH2017 , may favor the shock breakout model. It is thus unclear whether GW170817-like mergers are indeed the sources of the bright sGRBs or not. The forward shock afterglow observations of GW170817/GRB 170817A are helpful in answering such a question. Though the “early” rising X-ray and radio afterglow emission could be reproduced by a cocoon-like mildly relativistic ejectaKasliwal2017 , the late time afterglow data modelings strongly favor the presence of an off-axis relativistic (structured) outflow component Yue2018 ; D'Avanzo2018 ; Lamb2018 ; Mooley2018b . Particularly, the off-axis relativistic outflow component at a viewing angle of $\theta_{\rm v}\sim 0.35$ rad has been convincingly identified/measured in the radio image Mooley2018 . Nevertheless, a direct “observational” link between GW170817/GRB 170817A and bright sGRBs is still lack. In this work, we carry out statistical studies of the sGRB afterglow data and aim to establish such a connection.

In the fireball afterglow model, the emission arises from the shock-accelerated electrons (with an energy distribution power law index $p$) moving in the shock-generated magnetic fields Piran2004 . A simplified uniform energy distribution with an abrupt energy depletion of a conical ejecta has been assumed in most studies. In reality, the energy distribution function could be more complicated and several empirical structured jet models have been proposed in the literature Dai2001 ; Rossi2002 ; Berger2003 ; Zhang2004 ; Jin2007 . Usually the energy distribution is insensitive on the polar angle for $\theta\leq\theta_{\rm c}$ but drops rapidly outward, where $\theta_{\rm c}$ is the half opening angle of the energetic core. The GRBs viewed at the angles of $\theta_{\rm v}\leq\theta_{\rm c}$ are called as the on-axis events and otherwise the off-axis events. The afterglow emission of structured jets have been extensively calculated in the literature. If viewed off-axis, it is found that the early afterglow emission are sensitively dependent on the viewing angle $\theta_{\rm v}$ (the larger $\theta_{\rm v}$, the much weaker the emission), while at late times with the considerably decreased bulk Lorentz factor the viewing angle effect will be significantly suppressed Wei2003 ; Kumar2003 ; Lamb2017 . In particular, a quick decline ($t^{-p}$) phase will appear in the afterglow lightcurve when the bulk Lorentz factor of the ejecta drops to $\sim 1/(\theta_{\rm v}+\theta_{\rm c})^{-1}$, after which the afterglow emission viewed at different $\theta_{\rm v}$ will be similarWei2003 ; Kumar2003 ; Lamb2017 . This conclusion holds for the off-axis uniform ejecta as well. Therefore we can “extrapolate” the very-late quick-decaying X-ray and optical afterglow emission of GW170817/GRB 170817A to $t_{\rm com}\sim 2$ days (i.e., if viewed on-axis) after the burst and then compare them to other distant sGRBs (Please see Fong et al.Fong2017 instead for a direct comparison of the “early” emerging forward shock emission of GW170817/GRB 170817A to the afterglow emission of other sGRBs). The choice of such a $t_{\rm com}$ is for two reasons. One is that at such a late time the forward shock emission is usually in the post-jet-break phase if viewed on-axis (i.e., the bulk Lorentz factor of the decelerated ejecta $\Gamma$ drops below $1/\theta_{\rm c}$ for $\theta_{\rm c}\sim 0.1$. Note that the energetic core of the relativistic outflow driven by GW170817 has an $\theta_{\rm c}\approx 0.08$ rad Mooley2018 ). The other is that the afterglow lightcurves of some sGRBs do not cover a longer time. For the radio emission, $t_{\rm com}\sim 10$ days is needed otherwise the typical synchrotron radiation frequency of the forward shock electrons ($\nu_{\rm m}$, which is independent of the number density of circum-burst medium) is still above the observer’s frequency and the flux will not drop with time quickly Piran2004 . If the burst was born in a dense circum-burst medium, the synchrotron self-absorption plays an important role in suppressing the radio emission, too. Fortunately, for the sGRBs, usually the medium density is low and the self-absorption correction is ignorable.

For our purpose, we select the events with both a known redshift and an afterglow emission lasting at least one day after the burst. In comparison to the long-duration GRBs, sGRBs have smaller $E_{\rm k}$ mainly due to the shorter durations. The number density of the medium surrounding the sGRBs is also expected to be lower. That is why usually the sGRB forward shock afterglow emission is faint and can not be detected in a long term Fong2015 . Most X-ray data were recorded by the Swift X-ray Telescope (XRT) and are available at http://www.swift.ac.uk/xrt*-*curves/ and http://www.swift.ac.uk/xrt*-*spectra/ Evans2009 . For GRB 050709, GRB 050724, GRB 051221A, GRB 060505, GRB 120804A, GRB 130603B, GRB 140903A and GRB 150101B, the X-ray data from Chandra or XMM-Newton satellites are availableFong2015 . The optical observations were performed by various telescopes, while at late times only a few very-large ($\sim 8-10$m) ground-based telescopes and the Hubble Space Telescope (HST) are able to contribute. Our X-ray sample consists of $19$ bursts. While in optical and radio bands, there are just $7$ and $3$ bursts in our samples, respectively. The details of our samples and the data sources (references) are introduced in the Appendix.

In Fig.1 and Fig.2 we show the X-ray (1.732 keV), optical ($R-$band) and radio (6 GHz) fluxes if observed at a distance of $200$ Mpc, motivated by the fact that the averaged sensitive range of the advanced LIGO/Virgo detectors in their full-sensitivity run is about 210 Mpc, for the current samples, respectively. Due to the faintness of the sGRB afterglow emission, there are gaps of the data between the previous more-distant events and GW170817/GRB 170817A (please note that for the latter we only consider the quick decline phase since the early part is significantly influenced by the beam effect of the off-axis outflow). Therefore we extrapolate the very late ($t>200$ day) X-ray and optical afterglow data of GRB 170817A to $t\sim 2$ day after the burst and then compare them to other events. The radio to X-ray spectrum of the forward shock afterglow emission of GW170817/GRB 170817A is $f_{\nu}\propto\nu^{-0.6}$, which yields a $p=2.2$ in the slow-cooling synchrotron radiation scenario Lamb2018 ; Troja2018 . In the jet model, such a $p$ can also reasonably account for the very late flux decline ofLamb2018 $f\propto t^{-2.42\pm 0.2}$. The extrapolation function of the forward shock emission of GRB 170817A to early times is thus taken as $f\propto t^{-2.2}$. Surprisingly, the forward shock afterglow emission of GW170817/GRB 170817A, the first neutron star merger event detected by advanced LIGO/Virgo, are among the brightest ones for all short GRBs detected so far. Just a few events have X-ray afterglow emission brighter than that of GRB 170817A, as demonstrated in the right panels of Fig.1. The same conclusion holds for the optical and radio afterglow data as well, though these two samples are rather limited. We have also compared the distribution of the isotropic gamma-ray energy $E_{\rm iso}$, calculated in the rest frame energy band of $1-10^{4}$ keV, for the sGRBs with well measured spectra and found no significant difference for the sGRBs with and without “long-lasting” afterglow emission (see Fig.3; where the number of events for the X-ray sample are smaller than that presented in Fig.1 because some bursts are lack of reliable spectral measurements). GRB170817A and GRB 150101B, two short events with the weakest detected prompt emission, have “bright” late time afterglow emission because of their off-axis nature.

The above results have two intriguing implications. One is that there is a tight connection between GW170817-like mergers and the bright sGRBs though the physical process giving rise to GRB 170817A is still to be pined down. The other is that the detection of the forward shock afterglow emission of most (though not all) neutron star merger events is likely more challenging than in the case of GW170817 since usually the mergers will be more distant and the viewing angles will be larger Lamb2017 .

In both Fig.1 and Fig.2, there are observation time gaps (roughly from $\sim 10-30$ days to $\sim 150$ days) between the sharp decline phases of the forward shock afterglow emission of GW170817/GRB 170817A and those of the much more distant events (note that the second nearest short/long-short burst has a redshift about ten times that of GRB170817A). Such gaps are expected to be bridged as some other off-axis GW/GRB events, but less extreme than GW170817/GRB 170817A (i.e., $\theta_{v}\gtrsim\theta_{\rm c}$, which we call the quasi on-axis events), have been discovered and densely followed. The quasi on-axis events are less frequent than GW170817/GRB 170817A plausibly by a factor of $\lesssim 10$, but statistically the forward shock peak time will be earlier and the afterglow emission are brighter, which can be well recorded. This would be particularly the case in X-ray and radio bands, for which the contamination by the macronova/kilonova are negligible.

With a local neutron star merger rate of $\sim 10^{3}~{}{\rm Gpc^{-3}}~{}{\rm yr^{-1}}$, as inferred from both the gravitational wave data Abbott2017 and the sGRB observations Fong2015 ; Jin2018 , in the era of the full-sensitivity run of the second generation gravitational wave detectors, a sample consisting of $\sim 10^{2}-10^{3}$ neutron star mergers will be available. Some of them may generate detectable very-late forward shock afterglow emission. With a reasonably large sample, the luminosity function of the quickly decaying (i.e., post jet-break) forward shock afterglow emission driven by the neutron star mergers will be reconstructed. Intriguing difference between the double neutron star merger events and the neutron star-black hole merger events may be identified in the afterglow data. As for the double neutron star merger events, special attention may be paid on probing the possible correlations between the total mass ($M_{\rm tot}$) or the mass asymmetry ($q$) of the progenitor stars and the luminosity of the very-late afterglow emission. GW170817 has a $M_{\rm tot}\approx 2.74M_{\odot}$ ($q\approx 0.86$), which seems to be in the high total mass (high mass asymmetry) part of the double neutron star binary systems detected in the Galaxy, while the absence of $M_{\rm tot}$ and $q$ of the progenitor stars for all other sGRBs hamper us to go further. The situation will change dramatically in the next decade and the roles of properties of the progenitor stars on launching the relativistic outflows and generating the (very late) forward shock afterglow emission will be revealed.

Acknowledgments. This work was supported in part by NSFC under grants of No. 11525313 (i.e., Funds for Distinguished Young Scholars), No. 11433009, No. 11773078 and 11763003, the Foundation for Distinguished Young Scholars of Jiangsu Province (No. BK20180050), the Chinese Academy of Sciences via the Strategic Priority Research Program (Grant No. XDB09000000) and and the International Partnership Program of Chinese Academy of Sciences (114332KYSB20170008). F.-W.Z. also acknowledges the support by the Guangxi Natural Science Foundation (No. 2017GXNSFAA198094)

∗Email: jin@pmo.ac.cn (Z.P.J), xiangli@pmo.ac.cn (X.L), yzfan@pmo.ac.cn (Y.Z.F).