Intrinsic properties of the engine and jet that powered the short gamma-ray burst associated with GW170817

GRB 170817A was a subluminous short gamma-ray burst detected about 1.74 s after the gravitational wave signal GW170817 from a binary neutron star (BNS) merger. It is now understood as an off-axis event powered by the cocoon of a relativistic jet pointing 15 to 30 degrees away from the direction of observation. The cocoon was energized by the interaction of the incipient jet with the non-relativistic baryon wind from the merger remnant, resulting in a structured outflow with a narrow core and broad wings. In this paper, we couple the observational constraints on the structured outflow with a model for the jet-wind interaction to constrain the intrinsic properties with which the jet was launched by the central engine, including its time delay from the merger event. Using wind prescriptions inspired by magnetized BNS merger simulations, we find that the jet was launched within about 0.4 s from the merger, implying that the 1.74 s observed delay was dominated by the fireball propagation up to the photospheric radius. We also constrain, for the first time for any gamma-ray burst, the jet opening angle at injection and set a lower limit to its asymptotic Lorentz factor. These findings suggest an initially Poynting-flux dominated jet, launched via electromagnetic processes. If the jet was powered by an accreting black hole, they also provide a significant constraint on the survival time of the metastable neutron star remnant.


INTRODUCTION
The discovery of the gravitational wave source GW170817 (Abbott et al. 2017b) marked the first detection of gravitational waves (GWs) from a binary neutron star (BNS) merger. The observation of the same source in the electromagnetic spectrum, from the almost simultaneous γ-rays (Abbott et al. 2017a;Goldstein et al. 2017;Savchenko et al. 2017) to the later X-ray and UV, optical, IR, and radio signals (Abbott et al. 2017c), allowed, among other astrophysical implications, to firmly establish the connection between short gamma-ray bursts (SGRBs) and BNS mergers (e.g., Abbott et al. 2017a;Goldstein et al. 2017;Savchenko et al. 2017;Troja et al. 2017;Hallinan et al. 2017;Kasliwal et al. 2017;Lazzati et al. 2018;Ghirlanda et al. 2019;Mooley et al. 2018).
The early UV, optical, and IR radiation, detected within about a day from the GW/γ-ray detection, were shown to be consistent, both spectrally and temporally, with the expectations of a kilonova (e.g., Arcavi et al. 2017;Soares-Santos et al. 2017;Pian et al. 2017), i.e. a transient powered by the radioactive decay of heavy r-process elements synthesized within the matter ejected during and after merger. The later X-ray (Troja et al. 2017) and radio emission (Hallinan et al. 2017), first detected 10 days after the trigger, followed a single power-law spectrum over more than eight orders of magnitude in energy. This suggested an origin in a blastwave, and the spectral-temporal characteristics of the observed radiation were used to constrain the properties of the emission region. An isotropic fireball, as well as a top-hat jet (i.e. a jet with sharp edges) were ruled out early on (Kasliwal et al. 2017). However, it was only with VLA observations that the presence of a relativistic collimated jet -suggested by early modeling (Lazzati et al. 2018) -was confirmed beyond doubt (Ghirlanda et al. 2019;Mooley et al. 2018), hence establish-ing the consistency with a standard, cosmological SGRB observed off-axis.
The production of jets by astrophysical sources, which is an essential ingredient for both long and short GRBs, is an area of much interest in astrophysics. In order to understand the mechanisms by which jets are produced and launched, the first step is the characterization of their intrinsic properties, i.e. the jets properties as released by their central engines, before any interaction with the surrounding material. However, what we observe are the properties of the outflow when it becomes transparent to radiation, molded by the environment in which it has propagated. In the case of long GRBs this environment is the envelope of a massive star (MacFadyen et al. 2001), while in the case of SGRBs it is the material expelled in a compact binary merger (e.g., Rosswog et al. 1999;Fernández & Metzger 2013;Ciolfi et al. 2017;Radice et al. 2018;Ciolfi et al. 2019).
A model able to compute the SGRB outflow properties resulting from the jet interaction with the surrounding material was recently developed by Lazzati & Perna (2019), employing a semi-analytical method calibrated via numerical simulations (see also Salafia et al. 2019). Such model takes as input the properties of the surrounding material (most importantly its mass and velocity), those of the jet (namely its asymptotic Lorentz factor, injection angle, and time delay between the merger and the jet launching), and the viewing angle, i.e. the angle between the jet axis and the line of sight. Here, we apply this model to constrain the injection parameters of the jet from GW170817. For the properties of the surrounding material, we refer to the results of general relativistic magnetohydrodynamics (GRMHD) simulations of BNS mergers performed by Ciolfi et al. (2017). We also consider a more general parametric description as an alternative. For the jet intrinsic properties, we explore a conservative range for all the relevant parameters.
Constraints for the time interval between merger and jet launching have been discussed before in the literature, with somewhat controversial results. Studies based on the need to eject enough material to support a kilonova (Gill et al. 2019) and structure in the jet (Granot et al. 2017) favor a long merger-jet delay of the order of one second. Such delay, however, requires a coincidence with the propagation time of the jet to yield a total observed delay of ∼ 1.74 s. This, and the fact that the pulse duration of GRB170817A coincides with the total observed delay favors instead a much shorter mergerjet delay (Lin et al. 2018;Zhang et al. 2018;Zhang 2019).
Our paper is organized as follows: Section 2 describes the employed methods, based on the model developed by Lazzati & Perna (2019), as well as the range of values allowed for the input parameters (for the jet and the surrounding material) and the observational constraints from GW170817/GRB 170817A that we enforce. The results of our study are presented in Section 3. Then, we summarize and discuss our results in Section 4.

METHODS
Our reference scenario is a BNS merger forming a (meta)stable massive NS remnant which might eventually collapse to a black hole (BH). We assume that a SGRB jet is launched at a time ∆t m−j after merger, either by the massive NS or right after BH formation (see, e.g., Ciolfi 2018). In both cases, a nearly isotropic baryon-loaded wind from the NS remnant continuously pollutes the surrounding environment for a time ∆t m−j before the jet is launched. Our model describes the propagation of the incipient jet across such an environment and the resulting properties and structure of the final escaping outflow. 1 Throughout the manuscript, we will refer to the incipient collimated outflow from the central engine with high-entropy (and eventually high Lorentz factor) as "jet", to the wide-angle non-relativistic matter released by the massive NS remnant prior to jet launching as "wind", and to the ultimate structured outflow at large distances resulting from the jet-wind interaction as "outflow".
The analysis that we present is based on the jet-wind interaction model developed by Lazzati & Perna (2019). By imposing energy conservation and pressure balance at the jet, cocoon and wind interfaces (Begelman & Cioffi 1989;Matzner 2003;Lazzati & Begelman 2005;Morsony et al. 2007;Bromberg et al. 2011), they were able to develop a set of semi-analytic equations to compute the properties of the outflow for any given jet and wind setup. The underlying assumptions are the following: (i) the jet has initially a top-hat structure, with uniform properties within a half-opening angle θ j ; (ii) the engine turns on at time ∆t m−j after merger, releasing a constant luminosity L j for a time T eng and then turning off; (iii) the jet is characterized by a constant dimensionless entropy η, which corresponds to the maximum asymptotic Lorentz factor that the jet material would attain if the acceleration were complete and dissipationless.
For the wind, we consider two different prescriptions. In the first, we model the wind following the results of GRMHD simulations of BNS mergers by Ciolfi et al. (2017). In partic- It is found that a scaling factor of 1.75 between the jet opening angles is necessary for a good match of the angular the profiles. ular, we refer to the outcome of their simulations for two possible equations of state (EOS), APR4 (Akmal et al. 1998) and H4 (Glendenning & Moszkowski 1991), and for two values of the mass ratio, q = 1 and q = 0.9, 2 labelled as q10 and q09, respectively. For these different cases, we impose an isotropic wind with constant mass flow rate matching the value given in Fig. 23 of Ciolfi et al. (2017) and constant velocity equal to the reported escape velocity, namely v w =0.11 c, 0.12 c, 0.13 c, and 0.11 c for the APR4q09, APR4q10, H4q09, and H4q10 models, respectively. In our second prescription, the wind is instead parametrized and we consider constant mass flow rate and velocity spanning a wide range of values, namely 0.001 ≤ṁ w /(M s −1 ) ≤ 1 and 0.05 ≤ v w /c ≤ 0.25. In all cases, the wind starts at the time of merger and persists until the jet launching time.
Our analysis proceeds as follows. A random set of parameter values is first generated for the system. These are the jet entropy η, total emitted energy E j , half-opening angle θ j , duration of the engine activity T eng , delay time of the jet launching ∆t m−j , and viewing angle with respect to the jet axis θ l.o.s. (see Table 1). For the parametrized wind case, the list includes also the mass flow rateṁ w and the wind velocity v w . All these parameters are randomly drawn from flat prior distributions within a range that is either theoretically reasonable or constrained by observations. We assumed the following priors for the injection properties: • The jet is launched with an asymptotic Lorentz factor 10 ≤ η = L j /ṁc 2 ≤ 3000. The conservative lower limit is set by observational constraints (e.g., Ghirlanda et al. 2019), while the upper limit is simply set to a rather large value.
• The initial half-opening angle of the jet is limited to 1 • ≤ θ j ≤ 45 • . In this case we strove to consider a range 1.5 − 10 − The Lorentz factor of the outflow along the line of sight θcore 1.5 − 4 degrees The half-opening angle of the core of the outflow ∆t obs 1.5 − 1.75 s The observed delay between merger time and prompt gamma-ray pulse as large as possible. The lower limit of 1 degree is set to avoid a divergence at 0, while the upper limit of 45 • is conservatively larger than any successful jet that has been numerically studied (Murguia-Berthier et al. 2014Nagakura et al. 2014;Lazzati et al. 2017b;Xie et al. 2018;Hamidani et al. 2020; Lyutikov 2020).
• The delay time between the BNS merger and the jet launching is limited to 0 ≤ ∆t m−j ≤ 1.75 s. The upper limit in this case is set by the observed time delay (Abbott et al. 2017a).
• The viewing angle is limited to 1 • ≤ θ l.o.s. ≤ 45 • . As for the injection angle, the lower limit is set to avoid a divergence at 0, while the upper limit is larger than the one obtained from both gravitational waves and electromagnetic observations (Abbott et al. 2017a;Mooley et al. 2018;Ghirlanda et al. 2019).
• The duration of the engine activity is limited to 0.1 s ≤ T eng ≤ 2 s. In this case the lower limit is set to avoid a divergence at 0, while the upper limit is chosen to be at the traditional separation between long and short gamma-ray bursts (Kouveliotou et al. 1993).
Once the jet and wind parameters have been drawn, the code computes the properties of the outflow. 3 The procedure is repeated for over 100 million random samples. The resulting outflow properties are then checked against further observational constraints and only consistent models are retained. The additional constraints that we enforce are the following (see also Table 2): • The isotropic equivalent energy of the outflow in the direction of the line of sight has to be within the range 3 × 10 47 ≤ E iso,l.o.s. /erg ≤ 2 × 10 50 . The lower limit is set by assuming an efficiency of 10% for the prompt gamma-ray emission (Abbott et al. 2017a). The upper limit is obtained by analyzing various best fit models 3 The jet is launched from a nozzle at r 0 = 10 7 cm with an initial Lorentz factor of Γ = 1. • The half-opening angle of the core of the outflow (or final escaping jet) is limited to 1.3 • ≤ θ core ≤ 4 • . This constraint comes exclusively from the modeling of proper motion and spatial extent of the radio counterpart (Mooley et al. 2018;Ghirlanda et al. 2019). Note that both Mooley et al. (2018) and Ghirlanda et al. (2019) use power-law outflow models, while here we use a double exponential profile. To compensate for such difference, we re-scaled by a factor of 1.75 the opening angle values suggested by their analyses. As shown in Fig. 1, this compensation provides a rather good match between our angular profiles and theirs.
• The observed time delay between the merger (or the peak of the GW signal) and the gamma-ray detection is constrained to be 1.5 s ≤ ∆t obs ≤ 1.75 s and is given by the sum of three terms (Zhang 2019): where R bo is the radius at which the jet breaks out of the wind, β jh is the speed of the head of the jet inside the wind in units of c, R ph, l.o.s. is the photospheric radius of the outflow, and β l.o.s. is its velocity in units of c, both measured along the line of sight of the observation.
Here we have considered a fairly wide interval, down to 1.5 s, to take into account the fact that the beginning of the gamma-ray emission may have been misidentified if initially below the the background. 2.1. Calculation of the photospheric radius A critical piece of information for constraining the observed time delay is the calculation of the location of the photosphere (see Eq. 1). Calculations of the photospheric radius in gamma-ray burst outflows have been commonly performed either in the approximation of a thin shell or of an infinite wind (e.g., Mészáros & Rees 2000;Daigne & Mochkovitch 2002). A large Lorentz factor for which (1 − β) 1/2Γ 2 has also been assumed. In the case of off-axis outflows, all approximations should be relaxed, since relatively slow outflows in thick -but not infinite -shells are relevant. In addition, it has been customary to assume a neutron free fireball in past GRB literature, for which Y e ≡ np np+nn = 1. Here, n p and n n are the proton and neutron densities, respectively, and we generalize the equations for the photospheric radius to the case of an outflow with Y e ≤ 1. We assume our fiducial electron fraction to be Y e = 0.5 or lower, as expected for most GRB engines (Beloborodov 2003), but quote also results for Y e = 1.
Let us consider a photon that is at the back of the outflow. If its location corresponds to the photospheric radius, then the photon has probability 1/2 of undergoing a scattering before leaving the flow at the front. We can therefore write a condition on the opacity such that where R ph + ∆ is the outer radius of the outflow at the time at which the photon leaves the outflow, n e is the fireball's electron number density in the observer frame, and θ γe is the angle between the photon's and the outflow's velocity vectors. Assuming θ γe ∼ 1/Γ, we have where σ T is the Thomson cross section, and we have used We have also assumed that the fireball is fully accelerated by the time it reaches the photospheric radius, which is reasonable for a low Lorentz factor outflow. Performing a trivial integration we obtain which is solved to yield Note that the latter equation is valid for any shell thickness, and that it has the correct asymptotic behavior for a high-Lorentz factor wind case, for which (1 − β) = 1/2η 2 : 10 1 10 0 10 1 10 2 10 3 T eng (s) In the opposite extreme of a thin fireball, we obtain 4 lim Teng→0; η→∞ Figure 2 shows, for an outflow with properties similar to those revealed by GRB 170817A along the line of sight, how the result of Eq. (6) depends on the engine duration T eng . Also shown are the two limiting cases of wind and shell approximations, correctly recovered. In all the calculations of this paper, we use the more general Eq. (6).

RESULTS
The results of the analysis are best shown through corner plots, where each of the model parameters is plotted versus the other ones. In the corner plot figures, the colored panels show the density map of models that satisfy the observational constraints, while the solid lines mark the areas of 1σ, 2σ, and 3σ statistical significance level. Histograms on the diagonal show the posterior probability distribution for each parameter marginalized over the others. Finally, histograms in the upper right part of the figures show the posterior probability distribution for the observational quantities of interest.
In Figure 3, we report the outcome for the wind properties inspired by the GRMHD simulations of Ciolfi et al. (2017). Here, we are combining together the four different cases APR4q09, APR4q10, H4q09, and H4q10, and we show the outcome of the simulations for our baseline case with Y e = 0.5. We found that some of the parameters are well constrained. To begin with, the viewing angle, which was not directly constrained in our procedure, is constrained to θ l.o.s. = 23.5 +5.5 −4.5 degrees (all quoted uncertainties are at the 1σ statistical significance level, unless stated otherwise), a value that is in good agreement with the estimates based on highresolution radio imaging (Mooley et al. 2018;Ghirlanda et al. 2019).
Parameters for which we cannot obtain direct limits from observations and which are also well constrained are θ j , η, and ∆t m−j . The injection half-opening angle, never measured for long or short GRBs, is found to be θ j = 17.9 +12.6 −3.2 degrees. Additionally, we obtained a lower limit for the dimensionless jet entropy (i.e. the maximum attainable Lorentz factor) as η > 240 at the 3σ level. Finally, we found that the delay time between the merger and the injection of the jet is bound to be rather small: ∆t m−j < 0.36 s. These values are also reported in Table 3, which further shows how such constraints change by considering different electron fractions (Y e = 1.0 and 0.2) and stricter constraints on Γ l.o.s. and/or the total wind mass m w .
For the remaining parameters, our results favor jet energies at the lower edge of the simulated values (E j ∼ 5 × 10 48 erg), engine activity duration T eng ∼ 2 s, line-of-sight Lorentz factor Γ l.o.s. 6, isotropic equivalent outflow energy along the line of sight E iso, l.o.s. ∼ 2 × 10 49 erg, and a total mass of the wind in the range m wind ∼ 10 −3 − 10 −2 M . We note that the finding on the outflow energy is in general agreement with previous constraints from the afterglow modeling.
To check whether our results are sensitive to the different EOS and/or mass ratios under consideration, we show in Figure 4 the two panels ∆t m−j vs. η and θ l.o.s. vs. θ j , corresponding to the most constrained parameters from Figure 3, now separating the four cases. We find that the method is not able to distinguish among the four, with only a marginal difference in the θ l.o.s. vs. θ j panel for the H4q10 case (rightmost lower panel). This degeneracy reflects the fact that the mass flow rates and velocities are rather similar despite the different q and EOS.
In Figure 5, we select the same two panels from Figure 3, but in this case we show how the result changes by imposing only one of the four observational constraints at a time. The lower limit on η is always reproduced independently from  which constraint is imposed, while for the other parameters the outcome is significantly affected by the specific choice. Interestingly, all constraints are consistent with each other at the 1σ level, since the 1σ contours have a non-null intersection.
We now turn to consider the results obtained with a parametrized wind, i.e. allowing for any value of the mass flow rate and wind velocity within the plausible ranges 0.001 ≤ṁ w /(M s −1 ) ≤ 1 and 0.05 ≤ v w /c ≤ 0.25. The outcome, shown in Figure 6, is qualitatively similar to the previ-ous case (cf. Fig. 3), with the viewing angle and the initial jet half-opening angle well constrained, a lower limit on the jet dimensionless entropy, and an upper limit on the time interval between merger and jet launching.
At a quantitative level, however, some differences emerge. The viewing and jet angles are constrained to different values, namely θ l.o.s. = 30.3 +8.5 −8.0 degrees and θ j = 10.2 +8.8 −3.0 degrees, which remain nonetheless consistent within the 1σ range. The constraints on the dimensionless entropy and on the time delay are less stringent: η > 150 and ∆t m−j < 1.1 s. These vari- ations are brought about by winds which tend to have smaller velocities and smaller total masses compared to the values suggested by the GRMHD simulations of Ciolfi et al. (2017) (cfr. Figure 6 and Table 3).

DISCUSSION AND CONCLUSIONS
In this work, we have studied the key properties of the SGRB jet that was launched by the remnant of the BNS merger event GW170817 (Abbott et al. 2017b) and that eventually powered the gamma-ray signal GRB 170817A (Abbott et al. 2017a;Goldstein et al. 2017;Savchenko et al. 2017). We employed the semi-analytic model for the jet-wind interaction developed by Lazzati & Perna (2019) to obtain the properties of the escaping outflow depending on (i) the properties of the jet at the initial injection from the central engine and (ii) the properties of the massive baryon-loaded wind expelled beforehand by the NS remnant and acting as an obstacle for the propagation of the jet itself. By exploring the plausible parameter ranges with over 100 million random samples and then selecting only cases with an outcome consistent with four main observational constraints (see Section 2), we were able to obtain posterior distributions for the entire parameter set, and hence indications on their most favourable values.
For the wind properties, we assumed an isotropic flow expelled from the time of merger to the time of jet launching with constant mass flow rate and velocity. In our first analysis, the values of the latter were chosen in accordance to the results of GRMHD BNS merger simulations by Ciolfi et al. (2017), referring to BNSs with two different EOS and two different mass ratios. Then, we considered a more general parametrized wind and explored a wide range of mass flow rates and velocities.
For the analysis inspired by GRMHD simulations, we found an initial half-opening angle of the jet of θ j = 17.9 +12.6 −3.2 degrees (at 1σ level) and a robust 3σ lower limit on the di- Table 3 Results for the four most constrained parameters: the merger-jet delay, the asymptotic Lorentz factor of the jet, the viewing angle, and the injection angle.
Quoted uncertainties are at the 1σ level, while upper and lower limits are 3σ. We highlight in bold the results for our baseline model for both the simulation-inspired wind and the parametric wind cases. mensionless entropy η = L/ṁc 2 > 240. We remark that constraints on these intrinsic jet properties are of particular interest, as they cannot be directly obtained from the observations. The rather large lower limit for the injection entropy suggests a low baryon loading, as in the case of electromagnetically driven acceleration mechanisms (Mészáros & Rees 1997;Drenkhahn & Spruit 2002;Metzger et al. 2011). In addition, we obtained an upper limit on the time delay between the merger and the jet launching: ∆t m−j < 0.36 s at the 3σ level. 5 This limit would imply that most of the observed delay (≈ 1.74 s) is due to the outflow breaking out of the wind and its subsequent propagation until the photospheric radius is reached (along the line of sight), in agreement with the idea that the similarity between the gamma-ray pulse duration and the total observed delay is not a simple coincidence (Zhang et al. 2018;Lin et al. 2018). Such a result is likely influenced by the fairly large prompt emission energetics and, at the same time, by the fact that the Lorentz factor of the emerging outflow along the line of sight could not be too large to account for the late onset of the afterglow emission (Troja et al. 2017;Hallinan et al. 2017). These two features, when taken together, imply that the fireball carried a significant number of baryons, therefore pushing the photosphere to relatively large radii. Since the photosphere location is of such importance for estimating the propagation delay, we have derived in this paper a formula for the photospheric radius that relaxes the two commonly used approximations of either an infinite wind or a thin shell (see Equation 6).
The above upper limit ∆t m−j 0.4 s has potentially important implications. In particular, under the assumption that the central engine launching the jet was a newly-formed BH, as currently favoured by GRMHD BNS merger simulations (Ruiz et al. 2016;Ciolfi 2020a; see Ciolfi 2020b for a recent review), this constraint would imply a NS remnant lifetime 0.4 s. In turn, this would help in further constraining the NS EOS, as well as physical models of the kilonova that accompanied the August 2017 event.
By looking at the other parameters, we note that the total 5 Here we are assuming a fiducial electron fraction of Ye = 0.5 within the fireball. For lower values, the photospheric radius would also be reduced, changing the constraint on the time delay ∆t m−j . Even allowing for a quite extreme Ye = 0.2, however, the upper limit remains rather small ∆t m−j 0.51 s (i.e. about a factor √ 2.5 larger, as expected).
jet energy and the engine duration are found in general agreement with the observations (see, e.g., Ghirlanda et al. 2019 andAbbott et al. 2017a, respectively), while the indication on the Lorentz factor along the line of sight, Γ l.o.s. 6, is at the higher end of (but still consistent with) the range of available estimates, for which Γ l.o.s. should not be larger than ≈ 7 (e.g., Beniamini et al. 2020). The viewing angle is constrained rather well and is also consistent (within the 1σ range) with the latest radio observations (Mooley et al. 2018;Ghirlanda et al. 2019). Finally, the favoured range for the total mass in the wind is m wind ∼ 10 −3 − 10 −2 M . We note that this is only marginally consistent with a scenario in which (i) the jet was launched after the collapse to a BH (Ciolfi 2020a) and (ii) the wind from the NS remnant is what mainly powered the early "blue" component of the associated kilonova (as assumed, e.g., in Gill et al. 2019); indeed, such a scenario would require a mass as high as ∼ 10 −2 M for the unbound portion of the wind material (e.g., Villar et al. 2017).
For completeness, we also checked how the constraints change by imposing Γ l.o.s. ≤ 7 (as in Beniamini et al. 2020) and/or m wind ≥ 10 −2 M (to better accomodate the hypothesis of the blue kilonova being powered by the NS remnant wind and the jet being launched after the collapse to a BH). The additional condition on Γ l.o.s. has the interesting effect of further reducing the upper limit on ∆t m−j by a factor around 2, while the other results are poorly affected. The additional condition on m wind does not show a significant effect on ∆t m−j , but makes the lower limit on η more stringent (although this effect disappears when both the additional conditions are applied).
The analysis based on a parametrized wind confirmed the above overall picture, although with some quantitative differences. Not surprisingly, we found that the derived constraints are relaxed once we allow for a broader range of mass flow rates and wind velocities, especially if we consider a very low electron fraction. The merger-jet time delay, in particular, is constrained to ∆t m−j < 1.1 s (at 3σ), which is less restrictive. We also note that in this case small wind velocities (lower than 0.1 c) appear to be favoured, as well as total wind masses no larger than few × 10 −3 M . Finally, this analysis favours a viewing angle of θ l.o.s. = 30.3 +8.5 −8.0 degrees that is somewhat larger than what estimated from high resolution radio imaging (Mooley et al. 2018;Ghirlanda et al. 2019), causing some strain with the observations. In this case, the additional condi-tions on Γ l.o.s. and m wind lower significantly the upper limit on ∆t m−j , substantially enlarge the lower limit on η, and also increase θ j up to values similar to the simulation-inspired wind case.
As a general note of caution, we remark that in this work we assumed constant mass flow rates and velocities for the baryon-loaded wind produced by the NS remnant. This simplifying assumption may have relevant effects on the outcome of our analysis. Relaxing this assumption and employing time-evolving wind properties (possibly motivated by BNS merger simulation results) will be the subject of future investigation.
While our approach can be further refined, the present study shows its potential. In particular, the possibility of inferring the intrinsic jet properties at the time the jet itself is launched by the central engine can provide a valuable input for the investigation of jet launching mechanisms via numerical simulations. We also stress that here we applied the model to the case of GW170817/GRB 170817A, but our method is general and can be readily applied to any other SGRB observed in the future.