The GW170817/GRB 170817A/AT 2017gfo Association: Some Implications for Physics and Astrophysics

The mergers of close compact object binaries are promising gravitational-wave (GW) sources (Clark & Eardley 1977), as demonstrated by the successful detection of the mergers of three massive black hole binaries (Abbott et al. 2016a, 2016b, 2017a). Usually no electromagnetic counterparts are expected from the binary black hole mergers unless some pre-merger objects have massive accretion disks. Therefore, the information that can be directly inferred is limited. For the compact object mergers involving at least one neutron star, the situation is dramatically different. These mergers are expected to launch ultra-relativistic ejecta and neutron-rich subrelativistic outflows. The ultra-relativistic ejecta can give rise to short gamma-ray bursts (sGRBs; Eichler et al. 1989; Kouveliotou et al. 1993; Piran 2004; Zhang & Mészáros 2004) while the r-process nucleosynthesis takes place in the neutron-rich subrelativistic outflows and then generates optical/infrared transients (i.e., the so-called marconova or kilonova; see Li & Paczyński 1998; Kulkarni 2005; Metzger et al. 2010; Barnes & Kasen 2013; Kasen et al. 2013; Tanaka & Hotokezaka 2013; Metzger 2017). After the historical detection of the GW emission from binary black holes, people are looking forward to catching the neutron star mergers with the Advanced LIGO/Virgo. The first electromagnetic counterpart of such GW events is widely believed to be macronova/kilonova since its emission is almost isotropic (Metzger & Berger 2012) and, moreover, a few candidates have already been reported in GRB 130603B (Berger et al. 2013; Tanvir et al. 2013), GRB 060614 (Jin et al. 2015; Yang et al. 2015), and GRB 050709 (Jin et al. 2016). The sGRBs are widely known to be beamed with a typical half-opening angle of ∼0.1 rad, which will suppress the GRB/GW association very effectively. Therefore, it is widely suspected that the first GRB/GW association will not be established in the 2020s when the Advanced LIGO/Virgo are running at their full sensitivity (Clark et al. 2015; Li et al. 2016b). Very recently it has been noticed that the GRB/GW association possibility can be high up to ∼10% since the neutron star merger events detectable for Advanced LIGO/Virgo are nearby and hence some off-beam events (if the ejecta are uniform) or off-axis events (if the ejecta are structured) can still be detectable (Jin et al. 2017). Even so, it is still less likely that the first neutron star merger GW event would be accompanied by an sGRB.

On 2017 August 17, the LIGO and Virgo detectors simultaneously detected a transient GW signal that is consistent with the merger of a pair of neutron stars (Abbott et al. 2017b). Surprisingly, at 12:41:06.47 UT on 2017 August 17, the Fermi Gamma-ray Burst Monitor (GBM) triggered and located GRB 170817A (von Kienlin et al. 2017), which is just about 1.7 s after the GW signal, and the location also overlaps with the GW event (Blackburn et al. 2017). The optical/infrared/ultraviolet follow-up observations (e.g., Coulter et al. 2017; Pian et al. 2017) found a bright unpolarized source (Covino et al. 2017), and the high-quality spectra are well consistent with the macronova/kilonova model (initially it was dominated by the lanthanide-free outflow region that may be mainly contributed by the accretion disk wind or the neutrino-driven mass loss of the hypermassive neutron star formed in the merger, and at late times it was dominated by the emission from the lanthanide-rich region). To the surprise of the community, a remarkable GW/GRB/macronova association is firmly established in the first GW event involving neutron star(s). The long-standing prediction that neutron star mergers are the sources of short-duration GRBs (Eichler et al. 1989) has thus been directly confirmed. Moreover, the GW/GRB/macronova association has some far-reaching implications for both physics and astrophysics, which are the focus of this work.

After the claim of the possible detection of a transient associated with GW150914 by Fermi-GBM (Connaughton et al. 2016), we discussed some implications of the transient/GW association (Li et al. 2016b). This work extends our previous approaches significantly. In addition to comparing GRB 170817A to other sGRBs and measuring the velocity of the GW, we further test the Einstein Equal Principle (i.e., for the specific scenario that the photons and GWs may not follow the same trajectories in the gravitational field), and rule out "the Dark Matter Emulators and some dark energy models." Moreover, with the unambiguous detection of a large amount of the r-process elements in the macronova associated with GW170817, we show that the neutron star mergers are indeed the main sites of the very heavy elements in the universe and the binary strange star merger model for GRB 170817A is ruled out.

Li et al. (2016b) suggested testing the merger origin of old sGRBs via the comparison with the newly detected GRBs/GW events. If these GW-associated GRB events are found to be similar to the (old) events without GW observation data in many aspects, the merger scenario for sGRBs may be supported. Though such a test is likely non-trivial, one of the cautions is that the Advanced LIGO/Virgo can only reach $z\leqslant 0.1$ for neutron star mergers. For such local events, some merger-driven GRBs can be detectable even when our line of sight is outside the cone of the "uniform" relativistic ejecta or a bit far from the symmetric axis of the structured outflow (e.g., Yamazaki et al. 2002; Jin et al. 2017; Kathirgamaraju et al. 2017). The shock breakout of relativistic ejecta from surrounding subrelativistic outflow launched during the merger may also generate some underluminous GRBs (e.g., Kasliwal et al. 2017). Therefore, the GW-associated GRBs are likely dominated by an apparently "underluminous" group, and the goal outlined in Li et al. (2016b) may be potentially achievable only when a subgroup of bright local sGRBs have been detected.

Since GRB 170817A is the first short burst unambiguously associated with a GW event, it is necessary that it is compared with other sGRBs. Following Li et al. (2016b) we present the ${E}_{{\rm{p}},\mathrm{rest}}-{E}_{\mathrm{iso}}$ and ${E}_{{\rm{p}},\mathrm{rest}}-{L}_{\gamma }$ diagrams, where $({E}_{{\rm{p}}},\,{E}_{\mathrm{iso}},\,{L}_{\gamma })$ are the spectral peak energy, isotropic equivalent energy, and luminosity of the prompt emission, respectively, and the subscript $\mathrm{rest}$ represents the parameter(s) measured in the host galaxy frame of the burster. Only the sGRBs with the well-measured spectra are included. As shown in the Figure 1, GRB 170817A is the weakest sGRB detected so far and its ${E}_{\mathrm{iso}}$ and L_γ are more than two orders of magnitude lower than those recorded before. However, its ${E}_{{\rm{p}},\mathrm{rest}}=187\pm 63\,\mathrm{keV}$ (Goldstein et al. 2017) is comparable to quite a few sGRBs (Goldstein et al. 2017). Therefore, GRB 170817A does not follow the regular correlations (see the solid lines in Figure 1). One possible interpretation is that GRB 170817A is an off-beam/off-axis event or a shock breakout event. In Figure 1, we also compare sGRB 170817A and long-event GRB 980425, the closest bursts in each group. Surprisingly, sGRB 170817A and GRB 980425, two events with completely different progenitors, have rather similar L_γ and ${E}_{{\rm{p}},\mathrm{rest}}$ (see Figure 1). If not just a coincidence, this might indicate similar radiation processes. The progenitor of GRB 980425 is known to be a massive star. Its prompt radiation process is still unclear, and an attractive model is the shock breakout of relativistic outflow from the stellar envelope with a significant density gradient (Kulkarni et al. 1998). For sGRB 170817A, which originated from a neutron star binary merger, there was certainly no stellar envelope. The numerical simulation suggests that the subrelativistic outflow launched during the merger can play a similar role and GRB 170817A could be a shock breakout event (Kasliwal et al. 2017).

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3.1. The Astrophysical Implications of the ∼1.7 s Time Lag between the GW and GRB Signals

3.2. Measuring the GW Velocity, Testing the Equivalence Principle, and Ruling Out Some Modified Gravity Models for Dark Matter and Dark Energy

3.2.1. Measuring the GW Velocity

In some modified gravity theories that amazingly explain away dark matter or dark energy, GW travels in the vacuum at velocities that can be different from the speed of light (i.e., $\varsigma \equiv (c-{v}_{g})/c\ne 0;$ see, e.g., Clifton et al. 2012; Joyce et al. 2015, for reviews). In this work, we assume a constant ς. The subluminal movement of gravitons (i.e., $\varsigma \gt 0$) has already been tightly constrained by the absence of gravitational Cerenkov radiation of ultra-high-energy cosmic rays (Moore & Nelson 2001).⁶ The superluminal constraints of gravitons (i.e., $\varsigma \lt 0$) are weak and model-dependent (Yagi et al. 2014; Audren et al. 2015; Bellini et al. 2016; Beltrán Jiménez et al. 2016). The simultaneously radiated GW and electromagnetic signals can set stringent/robust constraints on ς (Will 1998; Nishizawa & Nakamura 2014; Li et al. 2016a), because after traveling a distance of $D\sim {10}^{2}$ Mpc, even a very tiny ς will induce a time delay of ${\rm{\Delta }}{t}_{\varsigma }\approx 1\,{\rm{s}}\,(\tfrac{\varsigma }{{10}^{-16}})(\tfrac{D}{100\,\mathrm{Mpc}})$. Note that in the absence of an equivalence principle violation, ${\rm{\Delta }}{t}_{\mathrm{GW}-\mathrm{GRB}}={\rm{\Delta }}{t}_{\varsigma }+{\rm{\Delta }}{t}_{{\rm{e}}}$, where ${\rm{\Delta }}{t}_{{\rm{e}}}$ represents the intrinsic delay of the emitting times of the GW signal and the GRB. In the merger-driven scenario, the GW single always precedes the GRB emission, and we have ${\rm{\Delta }}{t}_{{\rm{e}}}\geqslant 0$ and hence ${\rm{\Delta }}{t}_{\mathrm{GW}-\mathrm{GRB}}\,\geqslant {\rm{\Delta }}{t}_{\varsigma }$. For GW170817/GRB 170817A with ${\rm{\Delta }}{t}_{\mathrm{GW}-\mathrm{GRB}}\sim 1.7\,{\rm{s}}$ and $D\sim 40$ Mpc, the constraint reads (see also Abbott et al. 2017c)

$$\begin{eqnarray}&&-4.3\times {10}^{-16}\leqslant \varsigma \leqslant 0.\end{eqnarray} \tag{ 1 }$$

Such results imply that the superluminal movement of gravitons, if any, should not exceed the speed of light by a velocity of $1.3\times {10}^{-5}\,\mathrm{cm}\,{{\rm{s}}}^{-1}$.

A reliable constraint on the subluminal movement of GWs with ${\rm{\Delta }}{t}_{\mathrm{GW}-\mathrm{GRB}}$ for a single GW/GRB association event is less straightforward. This is because ${\rm{\Delta }}{t}_{{\rm{e}}}$ could be long (for instance $\sim {10}^{2}\mbox{--}{10}^{4}$ s or even longer, as speculated in Rezzolla & Kumar 2015), which hampers a reliable constraint on ς. The problem can be solved in the (near) future when an NS–BH merger-driven GW/GRB event has been successfully detected, for which a small ${\rm{\Delta }}{t}_{{\rm{e}}}\lt {T}_{90}$ is predicted, where T₉₀ is the duration of the prompt emission of the GRB (Li et al. 2016a). In the current case, the constraint on the subluminal movement of GWs is still possible since the optical emission of macronova/kilonova is known to be present within 1 day after the merger (Barnes & Kasen 2013; Kasen et al. 2013). As the successful detection of macronova/kilonova emission at ${t}_{\mathrm{mn},\det }\sim 0.5$ days suggests that the time delay of the arrival of the GW signal due to its subluminal movement cannot be longer than ∼0.5 days, we then have

$$\begin{eqnarray}&&0\leqslant \varsigma \leqslant {10}^{-11}({t}_{\mathrm{mn},\det }/4\times {10}^{4}\,{\rm{s}}).\end{eqnarray} \tag{ 2 }$$

Abbott et al. (2017c) reported a much tighter constraint on the subluminal movement of gravitons by (arbitrarily) assuming a ∼10 s intrinsic delay between the merger and the prompt GRB emission. Our constraint is weaker but less assumption-dependent. In Figure 2, we show our bound in comparison to some previous constraints.

3.2.2. Testing the Einstein Equivalence Principle

Another scenario yielding a different arrival time of "simultaneous" emitted GWs and photons, two different types of massless particles, is the violation of the Einstein equivalence principle (EEP). In the framework of parameterized post-Newtonian approximation, deviations from EEP can be described by a parameter γ, which is 1 in general relativity. Therefore, the GW/GRB association is very suitable to test the EEP violation (Sivaram 1999; Li et al. 2016a; Wu et al. 2016). The Shapiro delay is generally calculated as ${\rm{\Delta }}{t}_{\mathrm{gra}}\,=-\tfrac{{\rm{\Delta }}\gamma }{{c}^{3}}{\int }_{{r}_{{\rm{o}}}}^{{r}_{{\rm{e}}}}U(r(t);t)$ (Shapiro 1964; Krauss & Tremaine 1988; Longo 1988), where the integral is along the traveling path of photons and $U(r(t);t)$ is the gravitational potential. The time delay caused by the Milky Way can be calculated by ${\rm{\Delta }}{t}_{\mathrm{gra}}=1.7\times {10}^{7}\,{\rm{s}}\,{\rm{\Delta }}\gamma ({M}_{\mathrm{MW}}/6\times {10}^{11}\,{M}_{\odot })$ $(\mathrm{log}(D/b)/4\mathrm{log}10)$ (Misner et al. 1973; Longo 1988), where ${\rm{\Delta }}\gamma \equiv {\gamma }_{\mathrm{photon}}-{\gamma }_{\mathrm{GW}}$ (if ${\rm{\Delta }}\gamma \ne 0$, it would mean that the photons and GWs do not follow the same trajectories in the gravitational field of the galaxy and the EEP is violated), ${M}_{\mathrm{MW}}$ is the total mass of Milky Way, and b is the impact parameter of the particle paths relative to the center of the Milky Way. Now the observed ${\rm{\Delta }}{t}_{\mathrm{GW}-\mathrm{GRB}}$ should be expressed as ${\rm{\Delta }}{t}_{\mathrm{GW}-\mathrm{GRB}}={\rm{\Delta }}{t}_{{\rm{e}}}-{\rm{\Delta }}{t}_{\varsigma }+{\rm{\Delta }}{t}_{\mathrm{gra}}$. We thus need a group of GW/GRB events, in particular those driven by NS–BH mergers, at different D to self-consistently constrain ς and ${\rm{\Delta }}\gamma$. This is because for NS–BH merger-driven GW/GRB events it is generally expected that ${\rm{\Delta }}{t}_{{\rm{e}}}\leqslant {T}_{90}$ (please see Li et al. 2016a for more extensive discussion). For the current data and under the assumptions of $\varsigma =0$ (i.e., in the vacuum the GW velocity is equal to the speed of light) and ${\rm{\Delta }}{t}_{{\rm{e}}}=0$ (i.e., ${\rm{\Delta }}{t}_{\mathrm{GW}-\mathrm{GRB}}={\rm{\Delta }}{t}_{\mathrm{gra}}$), a rough constraint on ${\rm{\Delta }}\gamma$ reads

$$\begin{eqnarray}&&{\rm{\Delta }}\gamma \leqslant {10}^{-7}\,\left(\displaystyle \frac{{\rm{\Delta }}{t}_{\mathrm{GW}-\mathrm{GRB}}}{1.7\,{\rm{s}}}\right){\left(\displaystyle \frac{{M}_{{MW}}}{6\times {10}^{11}{M}_{\odot }}\right)}^{-1}{\left[\displaystyle \frac{\mathrm{log}(D/b)}{4\mathrm{log}10}\right]}^{-1}.\end{eqnarray} \tag{ 3 }$$

Such a constraint can be further improved. As noticed in Nusser (2016), the potential fluctuations from the large-scale structure, which can be found from the observed peculiar velocities (deviations from a pure Hubble flow; ${v}_{{\rm{p}}}$) of galaxies, are significantly larger than the gravitational potential of the Milky Way (${U}_{\mathrm{MW}}$). Peculiar velocity data yield a bulk peculiar velocity of ${v}_{{\rm{p}}}\sim 300\,\mathrm{km}\,{{\rm{s}}}^{-1}$ for the sphere of radius $R\sim 50$ Mpc around us (Ma & Pan 2014), suggesting a gravitational potential $U\sim {v}_{{\rm{p}}}{{RH}}_{0}\sim 25{U}_{\mathrm{MW}}$ at the site of GW170817/GRB 170817A, where H₀ is the Hubble's constant. Therefore, for the current data we have the constraint

$$\begin{eqnarray}&&{\rm{\Delta }}\gamma \leqslant 4\times {10}^{-9}.\end{eqnarray} \tag{ 4 }$$

Such a constraint has taken into account the contribution of the gravitational potential of the large-scale structure, which is thus stronger than the bound inferred from the better measured Milky Way gravitational potential alone (see also Abbott et al. 2017c; Wei et al. 2017).

Here, we simply adopt the GW/GRB association to set the bound. In the future, if the strong gravitational lensing of GW/GRB association events can be detected as well, one can use the delay times of the GW/GRB signals and their corresponding lensing "counterparts" to set stringent constraints on ${\rm{\Delta }}\gamma$. This is because the gravitational-wave potential of the lens (in particular the galaxy clusters) will induce an additional Shapiro delay if ${\rm{\Delta }}\gamma \ne 0$. The main challenge for such an approach is, however, the absence/rarity of such events in the foreseeable future.

3.2.3. Ruling Out Dark Matter Emulators and Some Dark Energy Models

In general relativity, the GW velocity is the same as the speed of light. However, major outstanding theoretical issues such as the nature of dark energy and dark matter have led to consider the possibility that gravity differs from GR in some regimes (see Clifton et al. 2012; Joyce et al. 2015, for reviews). Some of these models predict very different arrival times of the simultaneously radiated GW/GRB signals and hence can be accurately tested.

For example, motivated by the non-detection of dark matter particles so far, there are a group of modified gravity theories, known as Dark Matter Emulators, which dispense with the need for dark matter. These models have the property that weak GWs couple to the metric that would follow from general relativity without dark matter, whereas ordinary particles couple to a combination of the metric and other fields that reproduces the result of general relativity with dark matter. The absence of reliable detection of dark matter particles so far renders such a possibility attractive. Desai et al. (2008) show that there is an appreciable difference in the Shapiro delays of GWs and photons from the same source, with the GWs always arriving first. Even for the very nearby extragalactic sources, the predicted time lags between the GW signals and the electromagnetic counterparts (${\rm{\Delta }}{t}_{\mathrm{DME}}$) are several hundreds of days. An additional comparable time lag arises during propagation in the host galaxy of the source. If this is indeed the case, in extragalactic space the GW should move subluminally to yield an almost simultaneous arrival of GW170817 and GRB 170817A, i.e., ${\rm{\Delta }}{t}_{\varsigma }+{\rm{\Delta }}{t}_{\mathrm{DME}}\approx 0$, which then yields

$$\begin{eqnarray}&&\varsigma \sim 2.1\times {10}^{-8}\left(\displaystyle \frac{D}{40\,\mathrm{Mpc}}\right)\left(\displaystyle \frac{{\rm{\Delta }}{t}_{\mathrm{DME}}}{{10}^{3}\,\mathrm{days}}\right).\end{eqnarray} \tag{ 5 }$$

Such a ς, however, is already about 3 orders of magnitude larger than our subluminal bound set by GW170817/AT 2017gfo in Equation (2). The tension is far stronger (i.e., the divergency is by a factor of $\sim {10}^{7}$ or more) if the subluminal movement constraints set by ultra-high-energy cosmic rays apply (however, see footnote ⁶). We therefore conclude that the Dark Matter Emulators have been ruled out and the dark matter model is favored (See Figure 2).

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There is also a large class of scalar-tensor theories that predict that GWs propagate with velocity different from the speed of light and a difference of ${ \mathcal O }(1)$ is possible for many models of dark energy. For example, in the model of "Covariant Galileon" (Deffayet et al. 2009; Barreira et al. 2014), the violation parameter is about $\varsigma \sim 10 \% \mbox{--}100 \%$, and the delay between GW and electromagnetic signals from distant events will run far beyond human timescales (Lombriser & Taylor 2016; Bettoni et al. 2017; Lombriser & Lima 2017), which is clearly not the case for GW170817/GRB 170817A. The first GW/GRB association event thus places very stringent constraints on theories allowing variations in the speed of GWs and eliminates many contender models for cosmic acceleration (See Figure 2).

4.1. Neutron Star Mergers as the Main Site of the r-process Element Production

The heavy elements origin, also known as nucleosynthesis, is one of the mysteries in the universe (Qian & Wasserburg 2007). The widely discussed sites include the core-collapse supernovae (Burbidge et al. 1957) and neutron star mergers (Lattimer & Schramm 1974; Eichler et al. 1989). Though there is increasing evidence that the neutron star mergers are a significant site of the heavy elements (e.g., Tanvir et al. 2013; Hotokezaka et al. 2015; Yang et al. 2015; Ji et al. 2016; Jin et al. 2016), the unambiguous detection of a large amount of r-process material in AT 2017gfo provides the most direct evidence (Chornock et al. 2017; Drout et al. 2017; Kasen et al. 2017; Pian et al. 2017). To account for the measured total mass of galactic heavy r-process elements (i.e., $A\gt 90$), the binary neutron star merger rate averaged over the galaxy age should be $\langle R\rangle \approx 50\,{\mathrm{Myr}}^{-1}\,{({M}_{\mathrm{ej},{\rm{A}}\gt 90}/0.01{M}_{\odot })}^{-1}$ (Hotokezaka et al. 2015), where ${M}_{\mathrm{ej},{\rm{A}}\gt 90}$ refers to the heavy element mass ejection for a single event. However, the merger rate is actually not a constant and the inferred merger rate at present time (${R}_{0}$) may be lower than the averaged one by a factor of a few (i.e., ${R}_{{\rm{o}}}\lt \langle R\rangle$). Thus, we draw the lines of ${R}_{0}=(1,\,0.5,\,0.2)\,\langle R\rangle$ in Figure 3.

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Based on four "nearby" sGRBs with reasonably estimated jet half-opening angles, a conservative estimate of the local ($z\leqslant 0.2$) neutron star merger rate is $\sim {583}_{-318}^{+923}\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$ (Jin et al. 2017). Such a (conservative) merger rate is well consistent with that ($\sim {1540}_{-1220}^{+3200}\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$) inferred from the successful detection of a neutron star merger event by Advanced LIGO/Virgo in their second observational run (Abbott et al. 2017b). Since the Milky Way Equivalence Galaxy density in the local universe is $\sim 1.16\times {10}^{-2}\,{\mathrm{Mpc}}^{-3}$ (Kopparapu et al. 2008), we can convert the number to the Milky Way merger rate $\sim {50}_{-27}^{+80}\,{\mathrm{Myr}}^{-1}$. On the other hand, the macronova spectrum modeling suggests the mass ejection of GRB170817 to be ${M}_{\mathrm{ej}}\sim 0.04\pm 0.01\,{M}_{\odot }$ and the heavy r-process material may consist of $\sim 1/2$ of the total (Pian et al. 2017). This information is presented in Figure 3. The "data point" is above the line of ${R}_{0}=\langle R\rangle$, which is in support of the neutron star merger origin of the r-process material (see also, e.g., Chornock et al. 2017; Drout et al. 2017; Kasen et al. 2017) and furthermore implies that either the "averaged" rate of neutron star mergers in the Milky Way is lower than that of the "local" universe or the "typical" mass ejection of such mergers is significantly smaller than $0.04\,{M}_{\odot }$. For the latter, one caveat is that the neutron-rich outflow mass estimated for GRB 130603B, GRB 060614, and GRB 050709 is in the range of $\sim 0.02\mbox{--}0.1\,{M}_{\odot }$ (Tanvir et al. 2013; Yang et al. 2015; Jin et al. 2016).

4.2. Constraining the Double Strange Quark Star Merger Model for GRB 170817A

The GW/GRB/macronova association established in 2017 August directly confirms the long-standing suggestions that neutron star mergers do take place frequently and generate strong GWs, which further produce short gamma-ray flashes and launch r-process material. In this work, we have discussed some far-reaching additional physical and astrophysical implications. In particular, we show that:

• 1.  
  The short time delay between the GW and GRB signals set a very tight constraint on the possible superluminal movement of GWs and the difference between its velocity and the speed of light should be within a factor of $\sim 4.3\times {10}^{-16}$ (see also Abbott et al. 2017c). The GW/macronova association set an independent constraint on the possible subluminal movement of GWs and the difference between its velocity and the speed of light should be within a factor of $\sim {10}^{-11}$. The underlying assumption for these constraints is that the GW velocity is independent of the frequency (see Section 3.2.1). In the foreseeable future, these two constraints can be improved by (quite) a few orders of magnitude.
• 2.  
  The possible violation of weak equivalence principle is tightly constrained (the additional assumption is that in the vacuum the GW velocity equals to the speed of light) and the difference of the gamma-ray and GW trajectories in the gravitational field of the galaxy and the local universe should be within a factor of $\sim 3.4\times {10}^{-9}$ (see Section 3.2.2).
• 3.  
  The so-called Dark Matter Emulators and some contender models for cosmic acceleration, such as "Covariant Galileon," which predicted the long time delay of the arrival times of the simultaneously radiated GWs and photons from the same source, are ruled out (see Section 3.2.3 and Figure 2).
• 4.  
  The high neutron star merger rate (inferred from both the local sGRB data and the GW data) together with the significant ejected mass strongly suggests that such mergers are main sites of heavy r-process nucleosynthesis (see Section 4.1 and Figure 3 and also Kasen et al. 2017; Drout et al. 2017; Chornock et al. 2017). Moreover, it is likely that the "averaged" rate of neutron star mergers in the Milky Way is lower than that of the "local" universe.
• 5.  
  The successful identification of Lanthanide elements in the macronova/kilonova spectrum also excludes the possibility that the progenitors of GRB 170817A are a binary strange quark star system (see Section 4.2).

Finally, we'd like to mention the puzzling fact that sGRB 170817A ($D\sim 40$ Mpc) and GRB 980425 ($D\sim 36$ Mpc), two events with completely different progenitors, have almost the same L_γ and ${E}_{{\rm{p}},\mathrm{rest}}$ (see Figure 1), which might indicate similar prompt radiation processes if it is not just a coincidence.

We thank Yi-Ming Hu and Yi-Fan Wang for useful discussions and the anonymous referee for helpful suggestions. This work was supported in part by 973 Programme of China (No. 2014CB845800), by NSFC under grants 11525313 (the National Natural Fund for Distinguished Young Scholars), 11273063, and 11433009, by the Chinese Academy of Sciences via the Strategic Priority Research Program (No. XDB09000000), and the External Cooperation Program of BIC (No. 114332KYSB20160007).