Prompt gamma-ray emission of GRB 170817A associated to GW 170817: A consistent picture
The short GRB 170817A associated to the first detection of gravitation waves from a Binary Neutron Star (BNS) merger was in many ways unusual. Possible explanations are emission from cocoon at its break out, off-axis view of an structured jet, and on-axis ultra-relativistic jet with reduced density and Lorentz factor. Here we use a phenomenological model for generation and evolution of gamma-ray bursts to simulate prompt emission of GRB 170817A and test above proposals. We find that mildly relativistic cocoon models with characteristics considered in the literature generates too soft, too long and too bright prompt emission. Off-axis view of an structured jet with a Lorentz factor of about 10 can reproduce observations, but needs a very efficient transfer of kinetic energy to electrons in internal shocks, which is disfavored by particle in cell simulations. A diluted jet with a Lorentz factor about 100 seems the most plausible model. This is an evidence for intrinsic faintness of GRB 170817A. Based on this result and findings of relativistic magnetohydrodynamics simulations of BNS merger in the literature, we discuss physical and astronomical conditions, which may lead to such faint short GRBs. We identify small mass difference of neutron star progenitors, their old age and reduced magnetic field, and anti-alignment of spin-orbit angular momentum induced by environmental gravitational disturbances during the lifetime of the BNS as causes for the faintness of GRB 170817A, and predict that BNS mergers at lower redshifts generate on average fainter GRBs.
a,b]Houri Ziaeepour \affiliation[a]Institut UTINAM, CNRS UMR 6213, Observatoire de Besançon, Université de Franche Compté, 41 bis ave. de l’Observatoire, BP 1615, 25010 Besançon, France \affiliation[b]Mullard Space Science Laboratory, University College London, Holmbury St. Mary, GU5 6NT, Dorking, UK \emailAddhouriziaeepour@gmail.com
The discovery of the Gravitational Wave (GW) event GW 170817  and accompanying electromagnetic transient GRB 170817A [49, 79], and its afterglow in X-ray [93, 31, 23] and other energy bands [84, 95, 12, 70, 2, 38, 37, 13, 32, 72, 1] are revolutionizing astronomy and fundamental physics. Association of GW 170817 to merger of a binary neutron star, based on the masses of the progenitors and the length of GW event, is the first direct evidence for formation of short GRBs by collision and merging of ultra-compact astronomical objects. Although observation of supernova-like behaviour of late time afterglow of long GRBs had confirmed the hypothesis of their formation during core collapse of massive stars, a direct evidence for the origin of short GRBs had to wait the historic detection of GW/GRB 170817A. Some
Despite excitements about its observation, GRB 170817A is very far from being a typical representative of hundreds of short GRB events detected during the past 3 decades or so by high energy spatial observatories such as BATSI, Neil Gehrels Swift Observatory, Fermi, Integral, Konus Wind, etc. It is much softer than most short GRBs, a few orders of magnitude fainter than short bursts with known redshift, and falls on the boundary of short-long GRB separation. The unusual characteristics of GRB 170817A are evidently noticed and widely discussed in the articles published immediately after the announcement of GW/GRB 170817 detection. The simplest explanation is an off-axis viewing angle of an ultra-relativistic jet similar to those of other short GRBs . Alternatively, the burst might be formed by a mildly relativistic magnetized cocoon  at the time its outbreak. However, it seems an extra-ordinary coincidence if we have detected an off-axis GRB or one generated by cocoon in the first detection of gravitational waves from a BNS merger. Such events were searched for a long time without success. Evidence for thermal emission from a cocoon is also very rare and mostly in low energies. Therefore, although with a statistical sample of one event it is not possible to rule out a coincidence, we should consider other possibilities.
In this work we first briefly review the properties of GRB 170817A in Sec. 2 and compare them with those of other short GRBs. This opens our discussion and arguments in Sec 3 about the small probability that faint soft short GRBs, such as GRB 170817A, be off-axis view of an otherwise normal GRBs. We raise other possibilities, which have their root in the physics of jet formation, acceleration, and production of GRB emission and may contribute to faintness and softness of some short GRBs. In Sec. 4 we use a phenomenological model for formation and evolution of GRB emission by internal shocks [100, 101] to simulate the prompt emission of GRB 170817A and compare simulation parameters with those of GRB 130603B - the only other short GRB with evidence for an accompanying kilonova [5, 91, 60]. The aim of this exercise is to have a quantitative estimation of physical properties of GRB producing processes and progenitor stars, notably jet density, Lorentz factor, and Poynting energy, which can be compared with findings of BNS merger simulations. Results of our simulations are discussed and interpreted in Sec. 5. In Sec. 6 we use conclusions of 3D General Relativistic Magneto-HydroDynamics (GRMHD) simulations from literature to investigated which configuration and properties of progenitors may lead to thin jet and relatively low Lorentz factor, as estimated for GRB 170817A. Implications of our findings are discussed in Sec. 7. We provide an overall qualitative picture of GW/GRB 170817 event and its difference with intrinsically brighter GRBs. Outlines and prospectives are presented in Sec. 8.
2 GRB and other electromagnetic emissions
GRB 170817A was detected by the GBM detector of the Fermi satellite about 1.7 sec after the end of gravitational wave event GW 170817. It lasted for about sec, had an integrated fluence in 10 keV to 1 MeV band of erg cm  ( erg cm in 75 keV to 2 MeV band ), a photon count rate of photon sec cm for 64 msec binning, and its peak energy was keV . In comparison with other short GRBs these characteristics correspond to properties of a mildly faint short GRB, see Fig. 1-a,b. The follow up of this event by a plethora of ground and space based telescopes  allowed to find the optical/IR/radio counterparts AT 2017 gfo, its host galaxy NGC 4993, and thereby its redshift and its distance of Mpc111In this work we use vanilla CDM cosmology with km sec Mpc, and ., making GRB 170817A the closest GRB with known distance so far. See e.g.  for review of properties of short GRBs and their host. Using the distance to the host galaxy, GRB 170817A had an isotropic luminosity erg in 10 keV to 1 MeV band - the most intrinsically faint short burst ever observed, see Fig. 1-c,d. Moreover, the peak energy of the burst is close to lowest peak energy of short bursts observed by Fermi-GBM (see Fig. 31 in ).
Unfortunately at the time of prompt emission GRB 170817A was not in the field of view of Swift-BAT and no early follow-up observation is available, except for a sigma limit on any excess from background in the time interval in 10 keV to 10 MeV band from Konus-Wind satellite .
2.1 X-ray counterpart
The earliest observation of GW/GRB 170817A in X-ray was at about days sec . Nonetheless, from preliminary observations by the Swift-XRT in the sky area calculated from gravitational wave observation by the Advanced LIGO-Virgo, a flux limit of erg sec cm in 0.3-10 keV band can be put on the X-ray afterglow of GRB 170817A around days. Although the X-ray afterglow of some short GRBs have been brighter than this limit, others, e.g. GRB 160821B [81, 39], GRB 070724A [99, 4, 44], GRB 111020A , GRB 130912A [21, 98] had smaller fluxes at days after trigger. GRB 111020A is an interesting case because its host galaxy is most probably at redshift 0.02 , and its progenitor stars might share some properties with the progenitors of GRB 170817A. It had a total gamma-ray flux about 50% less than GRB 170817A and an average flux about 3 time larger than the latter. It was observed by Swift-XRT from sec up to sec, but failed both upper limits put on GRB 170817A flux by Swift and NuStar teams. Therefore, in absence of any early observation of this burst, it is not certain that GRB 170817A was an X-ray dark event. Moreover, the Swift-UVOT observations in the same period found a bright UV afterglow. Giving the faintness and softness of the prompt -ray emission, one expects that the afterglow of this GRB had to be equally soft and faint. This is consistent with the observation of a relatively bright early UV afterglow, which classifies this event as a blue kilonova [83, 14, 15] at early times, see also Sec. 7 for more details.
Evidence of a X-ray counterpart was ultimately observed by Chandra observatory [31, 93] at days - only a lower limit flux of erg sec cm in 0.3-8 keV - and a measurement of slightly brighter flux of erg sec cm at days. Similar late time brightening in X-ray and optical is observed in some short [25, 66] and long [16, 18] GRBs. They can be due to: MHD instabilities leading to increase in magnetic energy dissipation [47, 10]; external shock generated by the collision of a mildly relativistic thermal cocoon - ejected along with a relativistic GRB making jet - with the ISM or circumburst material [64, 17]; or late outflows from an accretion disk .
For comparison, at days and days the X-ray flux of GRB 111020A in 0.3-10 keV band was erg sec cm and erg sec cm, respectively. Considering the lower prompt gamma-ray flux of GRB 170817A, the above fluxes are proportionally similar to the Chandra observations of the late afterglow of GRB 170817A. However, there is also an upper flux limit of erg sec cm at days for any X-ray afterglow of GRB 170817A , which is very different from the flux of GRB 111020A at the same epoch, but consistent with much steeper decay slope observed in other GRBs, notably for GRB/kilonova 130603B. In conclusion, most probably the X-ray afterglow of GRB 170817A did not seem too unusual, if it had been observed a few hundreds of seconds after the Fermi-GBM trigger.
3 Plausibility of an off-axis observation
Here we argue that based on statistical arguments, there is a small probability that the faintness of GRB 170817A can be fully explained by the hypothesis of off-axis view of an otherwise ordinary short GRB.
A far observer receives radiation of a relativistic emitter only from an azimuthal angle with half-opening of for , where is Lorentz factor of emitter in the rest frame of observer . Lorentz factor of GRB jets are estimated to be , see e.g. [96, 97, 22]. Even in GRB models in which the prompt emission is assumed to be produced by a magnetically dominated Poynting flow , the Lorentz factor must be . Therefore, as long as the opening angle of the jet , which means for , the viewing can be considered as on-axis, unless the jet is structured and Lorentz factor at high latitudes is much smaller than on the jet axis.
According to numerical simulations of BNS merger [74, 34, 42, 41, 75, 20] the ejecta leading to a relativistic jet is poleward and has a half-opening angle of . Thus, it is much larger than minimum discussed above. However, it is expected that the ultra-relativistic component of ejecta have smaller opening angle [92, 45]. On the other hand, neutron star, black hole, and merger precession, which is in large extent independent of jet properties, increases the probability that the line of sight of a random far observer pass through the small opening angle of the relativistic jet [67, 53, 24, 26]. In presence of a precession with maximum angle , the sky surface covered by the jet is rather than for a non-precessing jet. In addition, precession of the progenitors of GRBs may explain some of substructures in their light curves [101, 24]. Precession frequencies as fast as HZ are expected during BNS merger . In the case of long GRBs produced by collapsars, observation of millisecond pulsars and close to extremal Kerr black holes is the evidence that angular momentum of accreted material induces a fast precession in the collapsed core. Moreover, GRMHD simulations of jet formation [92, 45] show that the maximum Lorentz factor is attained in the middle or close to the outer part of jet funnel rather than on its rotation axis. Therefore, even in absence of precession in the central object, its rotation alone in enough for inducing a precession in the relativistic jet. Another consequence of jet precession is the intermittency of GRB emission for a far observer, which may be responsible for some of observed substructures in GRB flux.
In conclusion, there is a large probability that during sec of a short burst, the line of sight of a far observer pass through a narrow jet. Without precession the probability of an off-axis line of sight is for . Thus, if GW/GRB 170817 were an off-axis event with our line of sight passing through low Lorentz factor external part of a structured jet or a cocoon with half-opening angle, statistically speaking LIGO had to have observed similar events - marginalized on the distance - without a GRB counterpart. Evidently, based on this statistical argument alone and observation of just one event it is not possible to rule out an off-axis prompt emission from GRB 170817A. Nonetheless, this statistical argument encourages us to consider the possibility that orders of magnitude faintness of this burst have an intrinsic origin.
4 Prompt emission model
To understand properties of a relativistic jet or a cocoon, which might have generated such an unusual GRB, we use the phenomenological model and corresponding simulation code described in [100, 101]. In this model the GRB prompt emission is produced by synchrotron/self-Compton processes in a dynamically active region at head front of shocks between density shells inside a relativistic cylindrical jet. In addition to the magnetic field generated by Fermi processes in the active region, the model and corresponding simulation code can include an external magnetic field precessing with respect to the jet axis. The origin of such a field is irrelevant for the model. It can be a precessing Poynting flow or the magnetic field of a precessing central object, which after releasing the ejecta precesses with respect to the latter. An essential aspect of this model, which distinguishes it from other phenomenological GRB formulations, is the evolution of parameters with time. In addition, simulation of each burst consists of a few time intervals during which evolution indices are kept constant. Division of simulated burst to these intervals allows to change parameters which are kept constant during one time interval. Continuity conditions implemented in the simulation code guarantees the continuity of most physical quantities between intervals, and adjustment of ensemble of parameters and intervals leads to light curves and spectra which well reproduce properties of real GRBs. Table 1 summarizes parameters of this model. Despite their long list, simulations performed for typical long and short GRBs show that the range of values which lead to realistic bursts are fairly restricted, see  for some examples.
In this section we use this model to simulate the prompt emission of GRB 170817A and compare its properties with those of other short bursts, in particular GRB 130603B, which thanks to its brightness is extensively observed  and classified as a kilonova [5, 91].
|Model (mod.)||Model for evolution of active region with time/distance from central engine; See eqs. (3.26 to 3.30) of .|
|(cm)||Initial distance of shock front from central engine.|
|Initial (or final, depending on the model) thickness of active region.|
|Slope of power-law spectrum for accelerated electrons; See eq. (3.8) of .|
|Slopes of double power-law spectrum for accelerated electrons; See eq. (3.14) of .|
|Cut-off Lorentz factor in power-law with exponential cutoff spectrum for accelerated electrons; See eq. (3.11) of .|
|Initial Lorentz factor of fast shell with respect to slow shell.|
|Index in the model defined in eq. (3.28) of .|
|Index in the model defined in eq. (3.29) of .|
|Fraction of the kinetic energy of falling baryons of fast shell transferred to leptons in the slow shell (defined in the slow shell frame).|
|Power index of as a function of .|
|Fraction of baryons kinetic energy transferred to induced magnetic field in the active region.|
|Power index of as a function of .|
|Baryon number density of slow shell.|
|Power-law index for N’ dependence on .|
|Column density of fast shell at .|
|Lorentz factor of slow shell with respect to far observer.|
|Magnetic flux at .|
|Precession frequency of external field with respect to the jet.|
|Power-law index of external magnetic field as a function of .|
|Initial phase of precession, see  for full description.|
Quantities with prime are defined with respect to rest frame of slow shell, and without prime with respect to central object, which is assumed to be at rest with respect to a far observer. Power indices do not follow this rule.
The phenomenological model of  neglects variation of physical properties along the jet or active region. They only depend on the average distance from center , that is .
Because of large number of parameters in the phenomenological model, in order to find best fits to the data we restricted our search in the parameter space to most important characteristics, namely: , , , , , , , , and . Other parameters are fixed to values suitable for simulation of short GRBs with more typical characteristics, see  for some examples. Beginning with a choice for , which determines kinematic of the ejecta: on-axis ultra-relativistic jet, off-axis structured relativistic jet, or mildly relativistic cocoon, we changed the value of other parameters such that an acceptable fit to the data be found. We should emphasize that as the exploration of parameter space was not systematic, the value of parameters in the selected models with best fits should be considered as typical rather than exact. Another important issue, specially when considering the best models, is the fact that parameters of the model are not completely independent. For instance, fraction of kinetic energy transferred to induced electric and magnetic fields depends on the strength of the shock, which is determined by the density difference of colliding shells and their relative Lorentz factor. We leave further discussion of this issue to the next section, where we assess plausibility of selected simulations.
Fig. 2 shows the light curves of the 4 best simulated bursts according to their chi-square fit in 10 keV-1 MeV band along with the Fermi-GBM data. The two peaks in the observed light curve are simulated separately and adjusted in time such that the sum of two peaks minimize of fit to the data. Fig.3 shows the light curves in narrower bands for each peak. Table 2 shows the value of parameters for these simulations. Table 3 shows the value of a few parameters that we have explored to find best fits to the data for failed simulations and describes their deficiencies. We use these results to assess how the variation of parameters affects properties of simulated GRBs, and to which extent parameters are degenerate.
Similarity of light curves of these simulations, despite large differences in some of their parameters, shows the degeneracy of the latters. Nonetheless, fitting the spectrum of the first peak to data provides further selection criteria. We did not fit the simulated model to the spectrum of the second peak because the data in  includes only 2 measured data points at lowest energies for this peak and other data points are observational limits. Fig. 4 shows spectra of 4 simulations which their light curves are shown in Fig. 2. From this figure it is evident that the 4 model (4-d) is a weaker fit to data with cumulative probability of random coincidence222Here the cumulative probability is defined as , where is a random variable with chi-square distribution and degrees of freedom; is the number of data points; and is the value of chi-square fit of data to model. of for 10 degrees of freedom. The other 3 models have . Despite differences in goodness of fit, all these simulation are very similar to each others an to the data, and it is not possible to choose one of them as the best fit to the GBM data. However, the comparison of spectra 4-a and 4-b, which their only difference is an external magnetic field in the former, may be interpreted as the necessity of a mild magnetic field in addition to the field induced by Fermi processes in the shock front.
4.1 Comparison with GRB 130603B
For the purpose of comparison the 4 model in Table 2 presents parameters of a simulation reproducing properties of the bright short burst GRB 130603B, classified as a kilonova [5, 91]. The simulated light curves and spectrum of this model are shown in Fig. 5. The differences between characteristics of this model and simulations of GRB 170817A are significant: jet extent is folds (in comparison with model No. 1) or folds (in comparison with model No. 2) larger; fraction of kinetic energy transferred to electrons weighed by electron yield, that is is 2 folds larger than in model No. 1; bulk Lorentz factor of ejecta is larger by a factor of 5 (in comparison with model No. 1) and by a factor of (in comparison model No. 2); external magnetic field is times stronger than models No. 1 and 2.
To see whether degeneracy in the value of Lorentz factor, which we found in simulations of GRB 170817A, are also present in harder and brighter bursts, we attempted to simulate GRB 130603B with a Lorentz factor of . We could not find any model with a flux as high as what was observed for this burst, a peak energy of keV in the rest-frame of the burst, and , which is motivated by Particle-In-Cell (PIC) simulations . For the peak energy is not too far from observed value. However, with an electron yield expected in kilonova ejecta, the fraction of kinetic energy transferred to electron must be , too large to be inconsistent with prediction of PIC simulations. Therefore, it seems that in what concerns the apparent degeneracy of models with and , GRB 170817 is an exception.
|1||GW/GRB 170817: first peak, rel.jet||1||2.5||-||10||0||1.5||-||1||-1|
|2||GW/GRB 170817: first peak, off-axis||1||2.5||-||10||0||1.5||-||1||-1|
|3||GW/GRB 170817: second peak||1||2.5||-||10||0||1.5||-||1||-1|
|1||GW/GRB 170817: first peak, rel.jet||0.01||-1||100||0.8||500||-||-|
|2||GW/GRB 170817: first peak, off-axis||0.03||-1||10||0.5||500||1||-|
|3||GW/GRB 170817: second peak||0.01||-1||30||0||-||-||-|
Each line corresponds to one simulated regime, during which quantities listed here remain constant or evolve dynamically. A dash as value for a parameter presents one of the following cases: it is irrelevant for the model; it is evolved from its initial value according to an evolution equations described in [100, 101]; or it is kept constant during all regimes. Horizontal lines separate independent simulations.
|Relativistic jet models|
|1||1.5||200||1.5||400||0.02||1||429.9||1.49||Too hard; Too bright|
|2||1.5||200||1.5||100||0.02||1||311.9||0.58||Too bright; Positive spectral index at high energies|
|3||1.5||200||1.5||200||0.02||0||284.6||1.07||Too hard; Too bright|
|4||2.2||10||1.5||100||0.01||1||464.4||0.8||Too soft; Too bright|
|6||2.5||10||1.5||100||0.01||1||7.335||0.525||Slightly too hard; Too bright|
|8||2.5||10||1.5||100||0.01||1||1.382||0.568||Slightly too soft; Too faint|
|9||2.5||10||1.5||100||0.01||1||0.642||0.439||Slightly too hard|
|10||2.5||10||1.5||100||0.01||1 ( HZ)||0.644||0.524||Slightly too hard|
|11||2.5||10||1.5||100||0.01||1||1.903||1.68||Peak too soft; Too bright in soft -ray energies|
|12||3||10||1.5||100||0.02||0||1.094||2.81||Too hard; Too faint|
|15||2.5||10||1.5||10||0.1||0||-||Too bright; Too long|
|18||2.5||10||1.5||3||0.03||26||Too bright; Too soft; Too long|
|18||2.5||10||1.5||3||0.03||26||Too soft; Too long|
|18||2.5||10||1.5||3||0.03||2.6||Too soft; Too long|
|18||2.5||10||1.5||3||0.01||2.6||-||-||Too bright; Too soft; Too long|
|18||2.5||10||1.5||3||0.01||26||-||-||Too bright; Too soft; Too long|
|18||2.5||10||1.5||3||0.01||2.6||-||-||Too soft; Too long|
Values in this table correspond to initial value (first regime) of each parameter. Other parameters and alternation in other regimes are similar to models given in Table 2.
Peak of light curves out of observation time.
Finally, because no observation in low energies from trigger time up to few tens thousands of seconds is available, we did not try to simulate afterglows of GRB 170817. Later afterglows are expected to be superimposed with emission from slow components such as wind and ejecta from a disk, and do not directly present properties of emission generated by external shock during passage jet through circumburst environment. In absence of any early data, it would be meaningless and confusing to make conclusions about an unobserved emission only based on theoretical assumptions.
5 Interpretation of prompt emission simulations
As discussed earlier, we can divide candidate models and corresponding simulations of GRB 170817A into 3 categories: mildly relativistic cocoon, structured / off-axis jet, and ultra-relativistic jet. This classification is motivated by short GRB models and suggestions in the literature for the origin of this unusually soft and faint burst [49, 23, 70, 38]. In this section we consider and discuss the plausibility of each of these cases.
5.1 Mildly relativistic cocoon
From results presented in Table 3 and discussions in Sec. 4, it is clear that mildly relativistic cocoons with characteristics similar to what is suggested in  cannot reproduce observed properties of GRB 170817A prompt emission. All the simulations with and prompt shock at a distance of cm - are too soft and have a duration sec, too long to be inconsistent with observations of Fermi-GBM and Konus-Wind.
5.2 Off-axis jet
Table 2 shows that if , other parameters, in particular , can be adjusted to obtain a burst with properties of GRB 170817A prompt emission. Assuming that the low Lorentz factor obtained in the simulations is due to off-axis view of an ultra-relativistic jet, the relation between emitted and received power is :
where is angle between a far observer and jet axis. From this relation it is clear that an off-axis view of the jet alone is not enough to explain the faintness of GRB 170817A. On the other hand, a structured jet by definition has lower Lorentz factor at high latitudes and may explain a softer and a few orders of magnitude lower emission of this burst. However, in this case one expects significant brightening of the afterglow when the dissipation of energy through collision of the jet with circumburst material reduces beaming and makes the central region of the jet visible to a far off-axis observer . Such a brightening is not observed for GRB 170817A, and as we discussed in Sec. 2.1 the slight late brightening in X-ray is not unique to this burst and has been seen in bright, presumably on-axis, bursts. For instance, in the case of GRB 130603B the brightening of the X-ray afterglow was observed at days after prompt emission , which is roughly the same epoch as that of GRB 170817A. Therefore, we conclude that the Chandra’s detection cannot be uniquely associated to interaction of the relativistic jet with circumburst material and its brightening due to the opening of an off-axis jet, as predicted by  formulation.
Furthermore, the UV/optical/IR counterpart AT 2017 gfo indicates a dominantly thermal ejecta of mass [2, 83, 70]. A relativistic jet of mass [38, 23] and its synchrotron/self Compton emission cannot explain neither the observed flux nor the features seen in the low energy spectrum. Thus, additional ejecta components must be involved in the production of these emissions. Indeed, evidence for additional ejecta, such as an expanding thermal cocoon, expanding envelop, and/or evaporating disk are found in other GRBs too [71, 89].
Alternatively, the GRB forming jet could have intrinsically a low Lorentz factor of order , rather than estimated for most short GRBs. As we discussed in Sec. 4, this explanation is consistent with our simulations. However, Table 2 shows that to compensate for low Lorentz factor, the efficiency of energy transfer to electrons (more generally charged leptons) must be times larger than the case of . But fulfilling such a requirement is more difficult when densities of colliding shells and total extent of the jet are few folds smaller than in case of bright bursts. In a diluted jet there is less turbulence and weaker induced electromagnetic field in the shock front. Moreover, low electron yield of neutron rich BNS ejecta reduces the total transferred energy to electrons. Estimations of electron yield for various components of the ejecta of GW/GRB 170817A based on the observation of r-process products [35, 82] are: for dynamical component, for wind, and in another wind component . Considering these yields, the simulation No. 2 in Table 2 gives a value of , which is inconsistent with PIC simulations estimation of .
We remind that simulations of relativistic shocks are still very far from being realistic and PIC simulations are performed either for a plasma , or with smaller mass ratio between opposite charges than in electron-proton plasma . Nonetheless, giving the fact that electromagnetic interaction is independent of mass, one expects that in a baryon dominated shock the transferred energy to charged leptons make up a smaller fraction of total available energy, despite the possibility that its amount may be larger. Thus, the value of in the GRB jets may be even less than the finding of PIC simulations.
5.3 Ultra-relativistic jet
Finally, after disfavoring other models, we conclude that the most physically plausible origin of GRB 170817A is synchrotron/self-Compton emission from internal shocks in an ultra-relativistic jet, which its Lorentz factor and density was few folds less than more typical short GRBs. According to our simulations such a jet needs , which is 3 times smaller than what is needed for a jet with . Considering estimated values for of various ejecta of GW 170817 event, we obtain , which is comfortably in the range of values observed in PIC simulations.
If further analysis and future observation of more NS-NS merger events confirm our conclusion about GRB making jet of GW/GRB 170817A, intrinsic properties of progenitor neutron stars and dynamics of their merger must be responsible for the faintness of GRB 170817A. In the next section we use results from observation of neutron stars, GRMHD simulations of BNS merger, and simulations of jet acceleration to assess what might have been different in this event.
6 Progenitors and merger dynamics
The main question here is: which properties of the progenitor neutron stars of GW 170817 event and their merger may have been responsible for lower than usual Lorentz factor of the relativistic jet and its lower density ?
To answer this question we need a full theoretical and numerical formulation of neutron star physics and NS-NS merger. It should include: Quantum state and interactions of neutron rich material in the framework of general relativity; Gravitational interactions; magnetic field of progenitor stars, which depends on their mass and age; Dynamics of merging, specially its latest stages before formation of a Hyper Massive Neutron Star (HMNS) or a black hole; Accretion disk and its dynamics; Interaction of pressurized neutron rich ejecta and its Magneto-Hydro-Dynamics (MHD) and interactions with radiation and neutrinos fields. Acceleration of particles in the ejecta to ultra-relativistic velocities and formation of a relativistic jet.
Such a task highly exceeds both our analytical and numerical calculation capabilities, and at present no complete simulation of all of these processes together and in a consistent manner is available. Thus, to understand properties of a merging event such as GW/GRB 170817A, we have to rely on partial and far from ideal simulations, which in most cases are performed as proof of concept rather than exploration of parameter and configuration space. In addition, NS-NS and NS-BH mergers occur at distances of order of few tens of kilometers, whereas particle acceleration occurs in a magnetically loaded outflow along a distance of at least few orders of magnitude longer [92, 45]. These two scales cannot be numerically treated with same precision in a same code. Therefore, for the time being only a qualitative assessment of reasons behind apparent abnormality of GRB 170817A is possible.
Despite complexity of NS-NS and NS-BH merger, a few properties stand out as the most influential for formation of a GRB. In the following subsections we discuss their possible contribution in the observed properties of GRB 170817A. For this purpose, we use mostly, but not exclusively, the results of simulations reported in  for NS-NS merger and results of  for simulation of jet acceleration.
6.1 Equation of state
It is by far the most important characteristic of neutron stars and defines the relation between their mass and radius. It also determines other properties such as core and crust densities, tidal deformability, which affects ejecta mass, density, and buoyancy during merger, differential rotation, maximum mass, magnetic field, and formation of a HMNS and its lifetime . Simulations of NS-NS merger by authors of  are performed for two equation of states: IF-q333Nomenclature used in . consisting of a single polytropic fluid with polytropic index and polytropic constant ; and Hyperon-rich H4 model . According to comparisons performed in  IF-q and H4 are prototypes of soft and stiff equations of states, respectively. LIGO-Virgo analysis of GW 170817 event disfavors stiff equations of states such as H4 . Specifically, the latter falls just on 90% exclusion probability curve for both fast and slow rotating progenitor BNS.
In what concerns state dependent properties, which may affect electromagnetic emission from merger, for close mass NS progenitors the density of inner part of the accretion disk and poloidal magnetic field of the merger are lower in IF-q case than H4 . Although currently no systematic study of the impact of the equation of state on the properties of polar outflow is available, it is known that the latter is closely related to: magnetic field, mass, density, extent of accretion disk , and accretion rate . As all these quantities are reduced for IF-q equation of state, which better represents the state of GW 170817, we expect less outflow than if the state was similar to H4. Thus, BNS progenitors of intrinsically brighter short bursts at higher redshifts may have stiffer equation of state and higher magnetic field, and generate denser, faster, and more outflow.
6.2 Magnetic field strength
Simulations of  show that for equal mass BNS, after the collapse of HMNS to black hole if the initial magnetic fields of progenitors are aligned with each other and anti-aligned with the rotation axis of the BNS (case DD in nomenclature of ), the average poloidal magnetic field is about 5 times weaker than if both initial fields are aligned with rotation axis (case UU). If the initial fields are anti-aligned with each other (cases UD), the average poloidal field is even smaller by a few folds. Moreover, in DD and UD cases, the average field at , where is the angle with the rotation axis of the merger, is a few times weaker than UU case. A reduced magnetic field proportionally reduces attainable Lorentz factor for material ejected close to polar directions .
If the progenitor neutron stars of GRB 170817A had dipole magnetic fields which extended out of their surface, they were surrounded by strongly magnetized atmospheres before their merger. In this case, the magnetic interaction during close encounter of the stars might have disaligned their fields well before the last stages of inspiral and at the time of merging they were in a state close to UD in the simulations of . Moreover, considering the old population of the host galaxy NGC 4993, which have an estimated minimum age of Gyr [9, 36, 3], magnetic fields of progenitors could be as low as G, if they had been recycled millisecond pulsars, or even smaller if they had evolved in isolation [33, 46] (review). Such field strength is much smaller than G used in simulations of BNS merger. Therefore, the magnetic field of HMNS also could be a few orders of magnitude less than G seen in the simulations [74, 42, 41, 75].
6.3 Disk/torus, jet, and accretion rate
As discussed earlier, density and initial Lorentz factor of magnetically collimated outflow, in other words the polar ejecta when it is still close to the disk, is correlated with the Poynting energy carried by the flow. Simulations performed with high initial magnetic field of G and equal mass progenitors  lead to a large magnetic field of G for the merger and a relatively large initial Lorentz factor of for the outflow. Simulations with smaller initial magnetic field of G attain a magnetic field of G on the disk having an axial velocity component of , where is the speed of light . Thus, we expect that if the initial masses of progenitors of GW/GRB 170817 were close to each other and their initial magnetic field similar to millisecond pulsars, the magnetic field of the merger were G, which is few orders of magnitude less than what is expected for younger progenitors. Although the velocity of blue ejecta in GW 179817 event is estimated to have been [70, 83, 65], which is similar to what is obtained in simulations with a merger magnetic field of G, a larger disk mass and/or density might have partially energized the outflow. Moreover, it seems that the smaller magnetic field had left its impact on the acceleration of particles at high altitude and generated a much weak relativistic jet and GRB.
We should however remind that no systematic study of the effect of initial magnetic on the final innate and surface field of HMNS or accretion disk of black hole has been so far performed by numerical simulations. Therefore, we cannot quantify the plausibility of the above interpretation. Properties of the polar outflow and other ejecta are even less quantified. The density of outflow is expected to be orders of magnitude less than that of the accretion disk/torus [20, 74, 41, 75]. This makes detection and follow up of this component in simulations very difficult . According to  equal mass NS-NS mergers generate less massive and more diluted disks - by a factor of in their inner part - than mergers with a mass ratio of . In GW/GRB 170817A event progenitor masses were not equal but were close to each other: and , leading to . The upper limit of this mass ratio is close to 1. Thus, the merger might have ejected much less material than NS binaries with larger mass difference or NS-BH mergers, which based on observation of BH-BH merger can have much larger mass difference. Moreover, relativistic MHD simulations of magnetized jet in  show that the reduction of initial total kinetic and Poynting energy by a factor of 2 reduces the density of outflow with highest Lorentz factor by a factor of 5 or so. Both of these observations are consistent with reduced shell densities and Lorentz factor found in our simulations of GRB 170817A.
Simulations reported in [20, 41] show that a poloidal coherent magnetic field and an outflow funnel begin to form after the collapse of HMNS to a black hole. Moreover, the outflow rate is correlated to accretion rate from the disk/torus [8, 86]. Giving the fact that the outflow will be accelerated gradually at high latitudes, a delay between the end of merger and generation of a relativistic jet is expected. It would be inversely proportional to the strength of poloidal magnetic field and the injection velocity. To this acceleration delay one has to add time delay necessary for the evolution of significant anisotropy in the ejecta and collision between density shells . Furthermore, if the accretion disk formed after the collapse of the HMNS to BH is low density and diluted, the accretion rate, and thereby the growth of anisotropies will be slower than in cases with higher magnetic field and faster accretion. These delays may explain the observed delay between GW 170817 maximum and trigger time of GRB 170817A. The origin of the delay is also consistent with arguments we raised to explain low jet density and relatively long GRB, which followed GW 170817. In summary, observed properties of GW and electromagnetic emissions are consistent with each others.
6.4 Effect of initial spin
Initial spins of progenitor neutron stars have a crucial role in the dynamics of merging process, in particular in the amount of ejecta, density and extent of accretion disk/torus, spin of HMNS and black hole. Moreover, they provide information about formation and history of the BNS. Gravitational waves from a merger contain information about spins of progenitors and their alignment with orbital rotation axis, see e.g. simulations in [7, 19, 55]. However, due to numerical complexity GRMHD simulations such as [20, 74, 41, 75] have not studied the effect of BNS spins on these quantities and processes. For the same reason, simulations of spinning BNS merger do not include a full GRMHD. Nonetheless, even separate simulations of dynamical and MHD processes help construct a better understanding of merger properties. Unfortunately in the case of GW 170817 the weakness of the signal and a glitch in LIGO-Livingston data prevented quantitative estimation of progenitors spins. Therefore, we can only perform a qualitative analysis to see which spin-orbit relation is more consistent with observations.
Simulations in  show that spin orientation of progenitors affects mass ejection through tidal deformation, specially for non-equal mass mergers, and thereby leave its signature on both gravitational waves and electromagnetic emissions. Notably, the binding energy of NS-NS merger is stronger(weaker) for anti-aligned(aligned) initial spins with respect to orbital axis, and leads to shorter(longer) inspiral regime and smaller(larger) ejecta. Thus, the direction of differences are similar to those of magnetic field discussed in Sec. 6.2. Similar to GRMHD effects, the amount of ejected material due to purely gravitational effects significantly depends on the mass ratio of progenitors and is smaller for equal masses. The effect of spin orientation on the mass ejection is however subdominant with respect to mass and magnetic contributions and modifies it by a few percents.
On the other hand, spin of BNS affects the precision of mass determination from gravitational wave observations [11, 52]. In the case of GW 170817, variation of in the range resulted to mass ranges and for NS progenitors . However, an error of on the masses of progenitors and thereby the ejecta alone cannot explain orders of magnitude faintness of GRB 170817A, unless the equation of state changes drastically with mass. Despite relatively small effect of spins, their anti-alignment with orbital directions is more consistent with weak polar outflow.
7 Implication for afterglow of GW/GRB 170817 and other short gamma-ray bursts
Formation of a GRB is manifestation of just one component of complicated events, which occur during merger of binary neutron stars. Therefore, any argument for unusual properties of GRB 170817A must be also consistent with low energy afterglows and emissions from other components of the merger remnant. Here we verify whether properties of the progenitor neutron stars and their merger discussed in the previous section, which may explain the faintness of GRB 170817A prompt gamma-ray, are compatible with low energy observations.
7.1 Evidence from UV/optical/IR/radio counterparts
From UV/optical/IR/radio observations various conclusions are made in the literature about properties of the progenitors and their merger, which are not always consistent with each other and with numerical simulations. Here is a summary of conclusions and some of inconsistencies:
- The merger made a HMNS which after msec or so collapsed to black hole. This is a common conclusion in the literature [37, 70]. The strongest evidence is the fact that much larger ejecta is necessary for explaining observed luminosity of the optical counterpart AT 2017 gfo than tidally stripped tail of the merger can provide [7, 19, 55, 88, 80, 90].
- Comparing with theoretical models, AT 2017 gfo was a red kilonova, meaning that heavy r-processes occurred in a dense optically thick material ejected from an accretion disk/torus .
- The early, that is days, bright blue/UV emission  is from a Lanthanide-free low density post-merger squeezed polar wind consisting of light elements and having a relatively large electron yield of [35, 90, 37, 70]. Observation of this component may imply that the viewing angle of observer must have been close to polar to be able to detect it. As in NS-NS merger the toroidal field is always much stronger than poloidal one , photons would have photons polarization would be mainly parallel to the jet axis [jetpolar]. The absence of linear polarization even at early times  is an evidence for scattering of photons in a turbulent funnel rather than direct sideways view of the ejecta on the surface of sky.
- There is not a general consensus about the amount of ejected mass and contribution of different components: dynamical tidal tail; poleward outflow, cocoon, and wind; and post-merger close to spherical ejecta due to the heating of the accretion disk/torus. Only a one-component thermally evolving ejecta can be ruled out [2, 70].
- Based on analysis of optical/IR/radio observations of AT 2017 gfo the ejecta mass responsible for the observed r-process rich spectra is estimated to be as high as and a velocity as mentioned above [70, 2, 83]. However, this is much larger than predicted by simulations for the fast outflow. It is also times larger than tidal ejecta mass estimated for the bright short GRB 130603B, which is also classified as a kilonova event [5, 91].
- At about days X-ray, optical and radio afterglow do not show any signature of a relativistic jet [61, 57]. These observations are consistent with a slow evolving ejecta component and with a weak ultra-relativistic jet, which at this late times should be most probably dissipated by interacting with circumburst material.
The tidally stripped dynamical ejecta is expected to be cold and to have high and light-element composition due to interaction with released neutrinos . These predictions are consistent with observations. However, GRMHD simulations of BNS merger estimate a mass of for dynamical ejecta irrespective of progenitors mass ratio and equations of state [7, 19, 55, 37]. Therefore, a contribution from post-merger ejected material from an accretion disk/torus is necessary to explain the data. Moreover, this additional early ejecta should become optically thin and observable in UV and visible bands as early as days [2, 70]. However, simulations predict that post-merger wind would have a low velocity of and high opacity [19, 55, 35, 80, 90].
It is shown  that the optical/IR spectrum during days to days can be reproduced by a 3-component model constructed according to simulations in [80, 90]: a component representing dynamical tidal tail ejecta with a velocity of ; and two components with and and a low velocity of representing post-merger ejecta. A scaling of the simulated spectra, which was performed for , is necessary to obtain a correct amplitude for the spectrum. However, thermal evolution of this model does not reproduce later spectra . Moreover, even in the earliest time interval, the contribution of slow components - presumably from disk - is subdominant and does not solve the problem of too large ejecta mass mentioned above. Therefore, despite overall agreement, current models based on simulations poorly fit the AT 2017 gfo data [70, 2, 83, 12, 95].
We should also remind that in  a velocity of for post-merger magnetically loaded polar outflow is reported only for H4 equation of state. For a softer state the velocity is expected to be less. Moreover, as we discussed earlier, weaker magnetic field reduces both the amount and velocity of the outflow at ejection time . And although it continues to be somehow collimated, it should have a larger opening angle. Because polar wind is accelerated by dissipation of Poynting energy after its ejection , the effect of low ejection velocity may be smeared out by acceleration at high latitudes. At present simulations of BNS merger does not include these late processes. In addition, acceleration of charged particles segregates them from neutron rich component and increase the effective in the fast outflow. Energy dissipation of neutrinos may also be involved in increasing the velocity of initially slow ejecta from accretion disk . Most GRMHD simulations do not include a full treatment of neutrinos.
Another solution for resolving inconsistencies, as we discussed in Sec. 2.1 and also suggested in , is a contribution from the afterglow of GRB 170817A in the observed blue peak during days to days. In this case, less early ejecta would be necessary to explain observations. Indeed, analysis of bolometric light curve in  shows that if the bluest data points of the spectrum at days are not included in the fit and a thermalization efficiency is added to the model, a smaller ejecta mass of and a larger opacity - a signature of higher atomic mass elements, presumably from accretion disk - fit the data better. Thus, the blue part of the early optical spectrum needs another component of the ejecta. This analysis is another evidence that the early non-thermal blue emission was at least partially due to the afterglow of the relativistic jet, which at days was significantly slowed-down by shocks and internal dissipation. Unfortunately, in absence of an early observation of X-ray afterglow, it is not possible to estimate the contribution of synchrotron emission from the afterglow in the observed blue peak.
According to the analysis of [54, 57] late observations are consistent with a structured jet. However, the models used in their analysis are not consistent with the early epoch data. On the other hand, heating and evaporation of outer part of the accretion disk explains the gradually increasing luminosity across the spectrum due to the reduction of opacity. In both structured jet and slow evaporation of disk/torus, the luminosity will eventually decrease. Indeed, according to structured jet models with an opening angle studied in  the flux decline should have been already begun. A better way of discriminating between these models is observation of lines and features in the spectrum and their evolution. But the faintness of afterglow and host galaxy emission are serious obstacle for observations.
7.2 A qualitative picture of GW/GRB/kilonova 170817
Finally, our interpretation of data and simulations of GW/GRB/kilonova 170817 can be summarized in the following qualitative picture:
- Progenitors were old and cool neutron stars with close masses, i.e. ;
- They had soft equations of state and small initial magnetic fields of G. Their fields were anti-aligned with respect to orbital rotation axis and each other.
- For dynamical or historical reasons, such as encounter with similar mass objects, their spins before final inspiral were anti-aligned..
- The merger produced a HMNS with a moderate magnetic field of G. This value is in the lowest limit of what is obtained in GRMHD simulations.
- The HMNS eventually collapsed to a black hole and created a moderately magnetized disk/torus and a low density, low magnetized and mildly collimated polar outflow.
- A total amount of material, including of tidally stripped pre-merger and a post-merger wind were ejected to high latitudes. They were subsequently collimated and accelerated by transfer of Poynting to kinetic energy. The same process increased electron yield by segregation of charged particles.
- A small mass fraction of the polar ejecta was accelerated to ultra-relativistic velocities and made a weak GRB. The reason for low Lorentz factor and density of this component was the weakness of the magnetic field.
- Either due to the weakness of the relativistic jet, which soon after internal shocks had a break and lost its collimation, or due to the lack of sufficient circumburst material, the afterglows of the GRB in X-ray and lower energy bands were very faint at days, and only detectable as a non-thermal addition in UV/blue emission of cocoon/wind.
- The late X-ray brightening was most probably independent of unusual weakness of GRB 170817 and was generated by interaction of a slower component of ejecta with the ISM or other surrounding material.
At present faint GRBs similar to GRB 170817A are detectable by high energy satellites only if they occur in the local Universe. Therefore, the small accessible volume significantly suppresses the rate of such events. Indeed, since the launch of the Swift satellite until present only 7 confirmed short bursts without an X-ray counterpart were observed444According to our search in the on-line Swift-BAT database https://swift.gsfc.nasa.gov/archive/grb_table/.. In addition, association of these transients to BNS merger is not certain and some of them may be giant flares from SGRs in nearby galaxies. Only long duration follow-up of future X-ray faint or dark GRBs with or without associated GW can prove or refute hypotheses raised here to explain the unusual characteristics of GRB 170817A.
7.3 Progenitors of short GRBs with X-ray afterglow
Due to observational bias most of GRBs with known redshift or their host galaxy are bright. If our explanation of reasons behind the weakness of GRB 170817A are correct, BNS mergers at higher redshift must be on average intrinsically brighter, because younger neutron stars have stronger magnetic fields. Their spin-orbit orientation is apriori independent of redshift. But, it also depends somehow on age, formation history and environment of the BNS. Older ones on average had more opportunity to interact with other celestial bodies. For instance, neutron stars in the dense environment of globular clusters have a large chance for forming BNS, but the probability of their gravitational disruption, which may change their spin-orbit orientation is also larger.
Despite small number of short GRBs with known redshift, the effect of BNS aging on the outcome of the merger gradually become discernible in the data. Indeed, in Fig. 1-c,d there is a clear trend of increasing total and average fluence with redshift. Although the absence of faint bursts at higher redshifts can be interpreted as an observational bias, the lack of bright bursts at lower redshifts is not explainable. Their rarity does not seem sufficient to explain clear stratification of fluence with redshift.
Although no BH-NS merger is so far detected, they remain a plausible origin for energetic short bursts. The larger mass difference may produce larger ejecta and magnetic field [69, 40, 43, 26]. Only with detection of more gravitational wave events with electromagnetic counterparts it would be possible to verify this hypothesis.
GW/GRB 170817A event gave us the opportunity to discover the nature of wimpy short GRBs, which for decades their origin was a subject of speculation and no direct evidence or proof of hypotheses about their sources was in hand.
In this work through simulation of prompt emission of GRB 170817A and GRB 130603B, we showed that despite its outlier characteristics, GRB 170817A was generated by the same physical processes involved in the production of more standard short GRBs. Based on the results of 3D GRMHD from the literature and published analysis of multi-wavelength observations of this event we argued that the faintness of GRB 170817A was caused by old age, coolness, and reduced magnetization of its progenitor neutron stars. These intrinsic factors were probably helped by environment and history of gravitational disturbances, which had induced an anti-aligned spin-orbit orientation.
Current observation facilities, specially gravitational wave detectors, are sensitive to events similar to GW/GRB 170817 only if they occur at redshifts . Moreover, despite the ability of the Swift satellite to detect the counterpart of GRBs in X-ray and UV and white bands from on average sec onward, since its launch in November 2004 only a very small fraction of short GRBs have had a long duration follow up. Nonetheless, there is hope that the huge scientific outcome achieved from intense observation of GW/GRB 170817A/AT 2017 gfo, which was a first in its kind, would encourage more intense and long duration follow up of short GRBs, even without any associated GW. Such observations would help verify some of hypotheses suggested in this work about the progenitors of short GRB/kilonova events. For instance, whether the late brightening of their X-ray is a common behaviour, and whether there is any systematic correlation between age and star formation history of their host galaxy and properties of NS-NS and NS-BH mergers.
The author thanks Phil Evans for providing her with Swift-XRT data before their publication.
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