GRB 170817A Associated with GW170817: Multi-frequency Observations and Modeling of Prompt Gamma-Ray Emission

The description of GRB 170817A INTEGRAL observations and detailed analysis of the burst based on INTEGRAL data are presented in Savchenko et al. (2017a). We performed a basic analysis of the SPI AntiCoincidence Shield (SPI-ACS) data with a slightly different method to classify the burst and to estimate its energetics, and then compare our results with those of GBM/Fermi in order to calibrate SPI-ACS consequently. We found the burst to be from a short (or Type I) population with no precursor and extended emission components. Derived values of fluxes in energetic units are consistent with both our GBM/Fermi and Savchenko et al.'s (2017a) results. The time delay between the burst onset and GW trigger was found to be ≃2 s. The background-subtracted light curve of the burst in SPI-ACS data with a time resolution of 0.2 s is shown in Figure 1(e). The details of the analysis are presented in Appendix C.

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We used the publicly accessible FTP archive⁹ as the source of the GBM/Fermi data.

GRB 170817A was detected in GBM/Fermi (Nai: 1, 2, 5) at the 8.7σ significance level in the (8, 300) keV energy range. The background-subtracted dynamic count spectrum in the (8, 400) keV range and light curves of the burst with time resolution of 0.2 s are presented in three energy channels in Figures 1(a)–(d). The burst onset in GBM/Fermi data is delayed by ≃2 s compared to the GW trigger. The third-order polynomial model was used to fit background in time intervals (−40, −5) and (20, 70) s for all presented GBM/Fermi light curves.

As seen in Figure 1, light curve of the burst consists of two different components (pulses): the first one is short hard and the second one is visible only in soft energy range (8, 50) keV. The two-component structure of the burst is also confirmed by T₉₀ duration parameter values: in the (8, 70) keV energy range ${T}_{90}^{8-70\,\mathrm{keV}}=2.9\pm 0.3\,{\rm{s}}$, which is six times longer than the duration in the (70, 300) keV energy range, ${T}_{90}^{70-300\,\mathrm{keV}}\,=0.5\pm 0.1\,{\rm{s}}$. (That behavior cannot be explained by the well-known dependence of GRB duration on energy range, T₉₀ ∝ E^−0.4; see, e.g., Fenimore et al. 1995; Minaev et al. 2010b).

To construct and fit the energy spectra, we used the RMfit v4.3.2 software package¹⁰ developed to analyze the GBM data of the Fermi observatory. The method of spectral analysis is similar to that proposed by Gruber et al. (2014), who also used the RMfit software package. To fit the energy spectra and to choose an optimal spectral model, we used modified Cash statistics (C-Stat; see Cash 1979).

Results of spectral analysis performed for GRB 170817A using data of GBM/Fermi (Nai: 1, 2, 5, BGO: 0) are summarized in Table 1. We analyzed three time intervals covering the whole burst—(−0.3, 2.0) s since GBM trigger, the first hard pulse (−0.3, 0.3) s, and the second soft pulse (0.8, 2.0) s—with three spectral models—power law (PL), power law with exponential cutoff (CPL), and thermal model (BB). To choose the optimal spectral model, we used the ΔC-Stat > ΔC-Stat_crit criterion, where ΔC-Stat is the difference between C-Stat values obtained for various models (the last column in Table 1) and ΔC-Stat_crit ≃ 8.5 was obtained via simulations in Gruber et al. (2014) for PL versus CPL model comparison.

Table 1.  Results of Spectral Analysis of GRB 170817A Based on GBM/Fermi Data

Time Intervala	Modelb	α	Epeakc	Fluenced	Hardness Ratioe	C-Stat/dof
(s)			(keV)	(10−7 erg cm−2)
(−0.3, 0.3)	PL	−1.50 ± 0.08	...	2.8 ± 0.4	0.72 ± 0.13	425/367
first	BB	...	31.6 ± 3.2	1.4 ± 0.2	2.8 ± 0.6	437/367
pulse	CPLf	−0.9 ± 0.4	${230}_{-80}^{+310}$	2.2 ± 0.5	1.0 ± 0.2	416/366
(0.8, 2.0)	PL	−2.0 ± 0.3	...	1.0 ± 0.4	0.37 ± 0.15	439/367
second	BBf	...	11.2 ± 1.5	0.68 ± 0.11	0.24 ± 0.09	422/367
pulse	CPL	${2.3}_{-1.9}^{+4.5}$	${43}_{-7}^{+9}$	0.67 ± 0.12	0.23 ± 0.10	422/366
(−0.3, 2.0)	PL	−1.8 ± 0.1	...	3.7 ± 0.7	0.49 ± 0.09	450/367
whole	BB	...	13.3 ± 1.3	1.7 ± 0.2	0.39 ± 0.08	447/367
burst	CPLf	$-{0.5}_{-0.7}^{+0.9}$	${65}_{-14}^{+35}$	2.1 ± 0.3	0.46 ± 0.09	440/366

Notes.

^aTime interval relative to GBM trigger (UTC 2017 August 17 12:41:06.475). ^bPL is for power law, CPL is for power law with an exponential cutoff, and BB is for a thermal model. ^cFor the BB spectral model, the E_peak column gives the parameter kT. ^dFluence in the (10, 1000) keV energy range. ^ehardness ratio calculated as a ratio of photon fluxes in (50, 300) keV and (15, 50) keV energy bands. ^foptimal spectral model.

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The energetic spectrum of the whole burst (time interval (−0.3, 2.0) s) is best fitted by the CPL model with $\alpha =-{0.5}_{-0.7}^{+0.9}$ and ${E}_{\mathrm{peak}}={65}_{-14}^{+35}\,\mathrm{keV}$ (the improvement over PL model is ΔC-Stat = 10). The fluence in the (10, 1000) keV range is F = (2.1 ± 0.3) × 10⁻⁷ erg cm⁻². Using the CPL spectral model, we calculated the hardness ratio of photon fluxes between (50, 300) keV and (15, 50) keV energy bands, HR = 0.46 ± 0.09, which, along with duration ${T}_{90}^{70-300\,\mathrm{keV}}=0.5\pm 0.1\,{\rm{s}}$, characterizes the burst to be a typical short but soft one (e.g., see Figure 6 in von Kienlin et al. 2014). The probability that GRB 170817A is from the short population was estimated using duration and hardness values in Goldstein et al. (2017a) and found to be P ≃ 73%.

The optimal spectral model for the first pulse (time interval (−0.3, 0.3) s) of the GRB 170817A is the CPL model (Table 1) with α = −0.9 ± 0.4 and ${E}_{\mathrm{peak}}={230}_{-80}^{+310}\,\mathrm{keV}$ (the improvement over the PL model is ΔC-Stat = 9). Using the CPL spectral model, we calculated a hardness ratio between (50, 300) keV and (15, 50) keV energy bands, HR = 1.0 ± 0.2, which describes the first pulse as a hard one (see Figure 6 in von Kienlin et al. 2014).

The optimal spectral model for the second pulse (time interval (0.8, 3.0) s) of the GRB 170817A is a thermal model with kT = 11.2 ± 1.5 keV and the fluence is in the (10, 1000) keV energy range of F = (6.8 ± 1.1) × 10⁻⁸ erg cm⁻² (Table 1). The CPL model gives the same goodness of fit, but with a positive value of $\alpha ={2.3}_{-1.9}^{+4.5}$, bringing this model maximally close to Wien's law N_E ∼ E² exp(−E/kT)—the spectral shape that the radiation originating in an optically thick hot medium whose opacity is dominated by Compton scattering off electrons acquires (Kompaneets 1957), which also confirms the thermal nature of the second pulse. The ${E}_{\mathrm{peak}}$ parameter was found to be ${E}_{\mathrm{peak}}={43}_{-7}^{+9}\,\mathrm{keV}$ within the CPL model. The improvement of C-Stat for CPL and BB models comparing to the PL one is ΔC-Stat = 17, which is two times larger than ΔC-Stat_crit ≃ 8.5 found in Gruber et al. (2014) and used as model selection criterion. Within the CPL model, the hardness ratio between (50, 300) keV and (15, 50) keV energy bands, HR = 0.23 ± 0.10, which describes the second pulse to be a very soft one (see Figure 6 in von Kienlin et al. 2014).

Optimal spectral models are presented in Figures 2 and 3, while confidence regions of the parameters of CPL models for both pulses are presented in Figure 4. As can be seen from Figure 4, the spectrum describing these two pulses is not evolving, but rather is a manifestation of the different nature of the emission. The results of our spectral analysis are comparable with ones presented in Goldstein et al. (2017a).

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We did not find any precursor or extended emission components in GBM/Fermi data at timescales from 0.1 up to 20 s in the time interval (−10, 30) s since GBM triggers in the energy range of (8, 300) keV. To estimate upper limits on their intensity in energetic units, we derived a conversion factor in the (8, 300) keV range using count fluence of the burst and energetic fluence within CPL spectral model (Table 1). We found that 1 count in GBM/Fermi corresponds to ∼3.2 × 10⁻¹⁰ erg cm⁻² in an energy range of (8, 300) keV. At a timescale of 0.1 s, the upper limit on precursor activity is S_prec ≃ 1.6 × 10⁻⁸ erg cm⁻² at the 3σ significance level. At a timescale of 20 s, the upper limit on extended emission activity is S_EE ≃ 2.3 × 10⁻⁷ erg cm⁻² at a 3σ significance level. The upper limits are two times deeper than ones obtained with SPI-ACS (see Appendix C).

A spectral lag analysis based on the CCF method (see, e.g., Minaev et al. 2014) was performed for GRB 170817A using the light curves detected by GBM/Fermi (Nai: 1, 2, 5) in the energy bands (8, 50) keV, (50, 100) keV, and (100, 300) keV with a time resolution of 0.04 s. The spectral lag between (8, 50) keV and (50, 100) keV bands is negligible, lag = 0.01 ± 0.08 s, but between (8, 50) keV and (100, 300) keV lag is significant, lag = 0.27 ± 0.05 s. It might represent the hard-to-soft spectral evolution of the first pulse (see Figure 1(a)).

One of the interesting phenomenological relations for GRBs is the Amati diagram, i.e., the dependence of the equivalent isotropic energy E_iso emitted in gamma-rays between (1, 10,000) keV on parameter ${E}_{\mathrm{peak}}(1+z)$ in the source frame (Amati 2010), which can also be used for the classification of GRBs (e.g., Qin & Chen 2013).

Using the experimental data given in Svinkin et al. (2016), Qin & Chen (2013), and Minaev & Pozanenko (2017), we constructed the Amati diagram for 20 short bursts and fitted the relation with a power-law-like logarithmic model: $\mathrm{log}\left(\tfrac{{E}_{\mathrm{peak}}(1+z)}{1\,\mathrm{keV}}\right)=(0.50\pm 0.04)\mathrm{log}\left(\tfrac{{E}_{\mathrm{iso}}}{1\,\mathrm{erg}}\right)+(-22.4\pm 1.8)$. Details on the investigation of the Amati relation for short GRBs can be found elsewhere (P. Minaev 2018, in preparation).

Using optimal spectral models derived in the previous subsection for GRB 170817A (Table 1) and assuming a redshift of z = 0.00968 and a luminosity distance of D_L = 42.0 Mpc for the source (Jones et al. 2009), we estimated E_iso and L_iso parameters in the (1, 10,000) keV range (Table 2). All burst components (first, second pulses, and the whole burst) lie far above the 2σ correlation region (Figure 5).

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Table 2.  GRB 170817A Energetics

Time Intervala	Spectral	Fluxc	Fluenced	${E}_{\mathrm{iso}}$	Liso
(s)	modelb	10−7 erg/(cm2 s)	10−7 erg cm−2	1046 erg	1046 erg s−1
(−0.3, 0.3)	CPL	3.8 ± 0.9	2.3 ± 0.9	4.9 ± 1.2	8.1 ± 1.9
(0.8, 2.0)	BB	0.59 ± 0.10	0.71 ± 0.12	1.5 ± 0.3	1.3 ± 0.2
(0.8, 2.0)	CPL	0.56 ± 0.10	0.67 ± 0.13	1.4 ± 0.3	1.2 ± 0.2
(−0.3, 2.0)	CPL	0.96 ± 0.14	2.2 ± 0.32	4.7 ± 0.7	2.1 ± 0.3

Notes.

^aRelative to the GBM trigger (UTC 2017 August 17 12:41:06.475). ^bCPL is for power law with an exponential cutoff, BB for a thermal model. ^cEnergy flux in the (1, 10,000) keV energy range. ^dEnergy fluence in the (1, 10,000) keV energy range.

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If we assume that the burst GRB 170817A should obey the Amati relation, we can draw a trajectory of the burst parameters as ${E}_{p}\sim {E}_{\mathrm{iso}}^{1/3}$ if it is a cone relativistic jet emission, and ${E}_{p}\sim {E}_{\mathrm{iso}}^{1/4}$ if it is a spherical relativistic emission (see, e.g., Eichler & Levinson 2004; Levinson & Eichler 2005). One can see that neither of the trajectories cross the Amati relation at a reasonable E_iso, especially for the first pulse. This strongly supports an alternative explanation for the nature of the first pulse as well as the whole burst in comparison with the usual short GRBs presented in the Amati relation (Figure 5).

The BZ mechanism of jet launching requires clean plasma—there should be little mass loading and magnetic dissipation close to the source. This is indeed expected if the flow originates on field lines that penetrate the BH. It is expected that a jet launched by the BH is highly magnetized, σ ≫ 1. Importantly, the confined jet with σ ≫ 1 that propagates with non-relativistic velocity must necessarily be dissipative (Lyutikov 2006). Briefly, the magnetic flux and energy are supplied to the inflating bubble by a rate that cannot be accommodated within the bubble (this problem is also known as the σ-problem in pulsar winds; Rees & Gunn 1974; Kennel & Coroniti 1984). If dissipation becomes important, it will destroy a significant fraction of the magnetic energy and most importantly the toroidal flux will be eliminated. Latest 3D numerical simulations of pulsar wind nebulae indeed demonstrate that magnetic flux (and some magnetic energy) are dissipated within non-relativistically expanding cavities, thus resolving the σ-problem (Porth et al. 2013, 2014). A considerable fraction of the magnetic energy that has been produced before the jet breakout is dissipated.

At the time of the jet breakout its magnetization is not very high. At the breakout, the highly over-pressured jet loses both radial and lateral confinement. At this point, the jet dynamics changes in two important ways. First, the leading part of the jet expands nearly spherically, within a solid angle ∼2 π, with large Lorentz factors (see Lyutikov 2010 and Lyutikov & Hadden 2012 for discussions of breakout dynamics in relativistic magnetized outflows; also, in Appendix D, we construct a simple model of a breakout of a magnetically dominated jet—the "force-free magnetic bomb"); the dynamics of non-magnetized relativistic breakout flows was considered by Johnson & McKee (1971) and Nakar & Sari (2012); for discussions of breakout dynamics in core collapse supernovae, see, e.g., Weaver (1976), Tan et al. (2001), and Ensman & Burrows (1992). At this point, the dynamics of pair-loaded magnetized outflows will resemble the conventional picture of magnetized GRB outflows (see, e.g., the early discussion by Lyutikov & Usov 2000 and Beloborodov 2017).

We suggest that this nearly spherical, highly relativistic outflow produces the prompt GRB spike. As the optically thick jet breaks out from the confining disk wind, the pair density falls out of equilibrium. Comptonization with the mildly optically thick region produces the observed GRB emission, similar to the photospheric emission in conventional GRB outflow (Beloborodov 2010; Beloborodov & Mészáros 2017). The emission is expected to peak at energies ∼ Γ _ph ≥ 400 keV, where _ph ∼ 20 keV is the photospheric temperature in relativistic outflows (Paczynski 1986) and Γ ≥ 25 is the bulk Lorentz factor, see Equation (1). Relativistic hydrodynamical simulations and calculation of jet brightness from a viewing angle can be found in Lazzati et al. (2017).

Second, the bulk of the jet accelerates along the jet axis—there is no more wind material to plow through. As the bulk of the jet accelerates to Γ ≫ 1 (see (1)), its propagation becomes nearly ballistic.

For the hard prompt emission, using the total fluence of 2.3 × 10⁻⁷ erg cm⁻², the total energetics estimates to ∼4.9 × 10⁴⁶ erg, with peak power ∼10⁴⁷ erg s⁻¹. The corresponding compactness parameter is large

$\begin{eqnarray}&&{l}_{c}=\displaystyle \frac{{L}_{\gamma }{\sigma }_{T}\xi }{{m}_{e}{c}^{4}t}=3\times {10}^{8}\xi {t}_{-0.3}^{-1},\end{eqnarray} \tag{ 1 }$

here ξ is the fraction of photons above the pair production threshold. Since the optical depth to pair production is $\propto {l}_{c}/{{\rm{\Gamma }}}^{6}$ (e.g., Goodman 1986; Lithwick & Sari 2001), it is required that the flow producing the prompt burst accelerates to

$\begin{eqnarray}&&{{\rm{\Gamma }}}_{{\rm{j}},\min }={\left(\displaystyle \frac{{\sigma }_{{\rm{T}}}{L}_{\mathrm{ht}}\xi }{{m}_{{\rm{e}}}{c}^{4}t}\right)}^{1/6}\approx 25{\xi }^{1/6},\end{eqnarray} \tag{ 2 }$

unfortunately, we have no information about the number of high-energy photons and our estimation Equation (2) can be significantly reduced. This in turn requires the emitting jet to be sufficiently clean (lacks baryons). This is an important constraint since the neutron-rich environment is expected to pollute the jet (Derishev et al. 1999; Beloborodov 2003).

Properties of the soft thermal emission can be used to infer the geometrical properties of the outflow. In our model, the soft gamma-ray component originates from the wind material shocked by the jet and thus should have a physical size of the order of the jet radius at the moment of breakout. The total (thermal) luminosity of the second soft component is L_ee = 1.3 × 10⁴⁶ erg s⁻¹. Thus, the emitting area is

$\begin{eqnarray}&&S=\displaystyle \frac{{L}_{\mathrm{ee}}}{{\sigma }_{\mathrm{SB}}{T}_{\mathrm{ee}}^{4}}=1.1\times {10}^{18}\,{{\rm{cm}}}^{2}\end{eqnarray} \tag{ 3 }$

and the radius of emitting region r_S is

$\begin{eqnarray}&&{r}_{{\rm{S}}}=\sqrt{\displaystyle \frac{S}{\pi }}=6\times {10}^{8}\,{\rm{cm}}.\end{eqnarray} \tag{ 4 }$

If the wind from the torus propagates with velocity v_w ≈ 0.1c (see Barkov & Baushev 2011), then in 2.4 s it would expand to r_w ≈ 7 × 10⁹ cm. Thus, the jet opening angle is

$\begin{eqnarray}&&{\theta }_{{\rm{j}}}=\displaystyle \frac{{r}_{{\rm{S}}}}{{r}_{{\rm{w}}}}\approx 0.08.\end{eqnarray} \tag{ 5 }$

This value agrees well with results of GRMHD simulations (see Barkov 2008; Barkov & Baushev 2011; Kathirgamaraju et al. 2017).

As the jet breaks out from the wind, the quasispherical expansion of the jet material will form a fireball that resembles the pair-loaded fireball discussed earlier in the literature (Paczynski 1990; Rees & Mészáros 2005). A fraction $1/{\eta }_{\mathrm{em}}\ll 1$ of the energy stored in the wind prior to the jet-break will be radiated (η_em depends on parameters of outflow like the energy injection rate, magnetization, and baryonic loading (e.g., Lyutikov & Usov 2000).

We can relate the observed flux in the first/hard peak to the jet head energy density as

$\begin{eqnarray}&&{u}_{\mathrm{em}}={\eta }_{\mathrm{em}}\displaystyle \frac{4{L}_{\mathrm{peak}}}{{Sc}}.\end{eqnarray} \tag{ 6 }$

This can be used to estimate the equipartition magnetic field B_eq in the jet:

$\begin{eqnarray}&&{B}_{\mathrm{eq}}=\displaystyle \frac{\sqrt{8\pi {u}_{\mathrm{em}}}}{\sqrt{3}}\approx 3\times {10}^{10}{\eta }_{\mathrm{em},1}^{1/2}\,{\rm{G}}.\end{eqnarray} \tag{ 7 }$

If originating from a BH with the surface field B_BH, the magnetic field at the emission site is

$\begin{eqnarray}&&{B}_{\mathrm{eq}}={B}_{\mathrm{BH}}{\left(\displaystyle \frac{{r}_{{\rm{g}}}}{{R}_{\mathrm{LC}}}\right)}^{2}\displaystyle \frac{{R}_{\mathrm{LC}}}{{r}_{{\rm{S}}}},\end{eqnarray} \tag{ 8 }$

where r_g is BH Kerr radius, R_LC ∼ 4r_g/a_BH is the light cylinder radius, and a_BH is the Kerr parameter. (Scaling is different from the NS case, here it is ${R}_{\mathrm{LC}}^{2}$ not ${R}_{\mathrm{LC}}^{4}$.)

Thus, the magnetic field on the surface of the BH can be estimated as

$\begin{eqnarray}&&{B}_{\mathrm{BH}}\sim \displaystyle \frac{4}{{a}_{\mathrm{BH}}}\displaystyle \frac{{r}_{{\rm{S}}}}{{r}_{{\rm{g}}}}{B}_{\mathrm{eq}}\sim 2\times {10}^{14}{\eta }_{\mathrm{em},1}^{1/2}{a}_{\mathrm{BH},-0.2}^{-1}{\rm{G}},\end{eqnarray} \tag{ 9 }$

where we scaled the Kerr parameter to 0.7. These fields are higher, by about one or two orders of magnitude than is expected from surface magnetic fields of merging neutron stars, indicating that a dynamo process was operational during or after the merger (either on the collapsing neutron star or in the surrounding torus).

Substituting magnetic field from Equation (9) to the equation of jet power

$\begin{eqnarray}&&{L}_{\mathrm{BZ}}\approx \displaystyle \frac{{B}_{\mathrm{BH}}^{2}{r}_{{\rm{g}}}^{2}c}{24}{f}_{\mathrm{BH}}({a}_{\mathrm{BH}}),\end{eqnarray} \tag{ 10 }$

here 0 ≤ f_BH(a_BH) < 1 is a factor that depends on the BH spin parameter (see more details in Blandford & Znajek 1977; Barkov & Komissarov 2008b), we obtain expected power as

$\begin{eqnarray}&&{L}_{j}\sim 7{\eta }_{\mathrm{em}}{L}_{\mathrm{peak}}\sim {10}^{49}{\eta }_{\mathrm{em},1}\,{\text{erg s}}^{-1}.\end{eqnarray} \tag{ 11 }$

To reiterate, Equation (11) related the power L_ee of the hard gamma-ray emission to the power of the BZ jet L_j. The estimate (11) compares favorably to the estimate of the jet power derived from modeling the evolution of the accretion torus, Equation (17), conversion parameter η_em ≈ 10, which corresponds to a jet power on of 10⁴⁹ erg s⁻¹ (see Paczynski 1990).

As matter is accreted from the torus onto the BH, magnetic flux is accumulated on the BH. This triggers the BZ mechanism. It is expected that the value of the magnetic field that can be accumulated on the BH, and thus the jet power, depend on the accretion rate. Let us next estimate the maximal luminosity of a magnetically driven jet.

The accretion rate from the disk is ${\dot{M}}_{{\rm{d}}}=1.6\,{M}_{{\rm{d}}}/{t}_{\mathrm{vis}}$ (Shakura & Sunyaev 1973; Metzger et al. 2008a). Wind from the disk surface can significantly reduce the accretion rate at the inner parts of the disk. Using the model of Blandford & Begelman (1999) and following Metzger et al. (2008a), the accretion rate onto the BH can be calculated as

$\begin{eqnarray}&&\displaystyle \frac{{{dM}}_{\mathrm{BH}}}{{dt}}=\displaystyle \frac{1.6{M}_{{\rm{d}}}}{{t}_{\mathrm{vis}}}{\left(\displaystyle \frac{{r}_{\mathrm{ISCO}}}{{r}_{{\rm{d}}}}\right)}^{p}{\left(\displaystyle \frac{(2p+1){t}_{\mathrm{vis}}}{(2p+1){t}_{\mathrm{vis}}+4.8t}\right)}^{\tfrac{4(p+1)}{3}},\end{eqnarray} \tag{ 12 }$

here 0 < p < 1 is a non-dimensional parameter that describes wind intensity,

$\begin{eqnarray}&&{r}_{{\rm{d}}}={({\alpha }_{\mathrm{ss}}^{2}{h}_{{\rm{d}}}^{4}{{GM}}_{\mathrm{BH}}{t}^{2})}^{1/3},\end{eqnarray} \tag{ 13 }$

here h_d = H/R is the relative thickness of the disk and α_ss is the non-dimensional viscous parameter. The radius of the innermost stable circular orbit (ISCO) is

$\begin{eqnarray}&&{r}_{\mathrm{ISCO}}=\displaystyle \frac{{{GM}}_{\mathrm{BH}}f({a}_{\mathrm{BH}})}{{c}^{2}},\end{eqnarray} \tag{ 14 }$

here 1 < f(a_BH) < 6 is the non-dimensional radius of the last marginally stable orbit (Bardeen et al. 1972), which is a function of the BH spin parameter "a_BH."

The accretion rate onto BH is

$\begin{eqnarray}&&\displaystyle \frac{{{dM}}_{\mathrm{BH}}}{{dt}}\\ &&\,=\,\displaystyle \frac{0.16{(2p+1)}^{\tfrac{4(p+1)}{3}}f{({a}_{\mathrm{BH}})}^{p}{M}_{{\rm{d}},-2}{M}_{\mathrm{BH},0.5}^{\tfrac{2p}{3}}{t}_{\mathrm{vis},-1}^{\tfrac{(2p+1)}{3}}}{{60}^{p}{h}_{{\rm{d}},-0.5}^{\tfrac{4p}{3}}{\alpha }_{\mathrm{ss},-1}^{\tfrac{2p}{3}}{((2p+1){t}_{\mathrm{vis},-1}+48t)}^{\tfrac{4(p+1)}{3}}}\,\quad {M}_{\odot }{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 15 }$

For the typical parameters of the NS+NS mergers (see Section 4), if we assume a conservative value of p = 1/2, the Equation (15) takes the form of

$\begin{eqnarray}&&\displaystyle \frac{{{dM}}_{\mathrm{BH}}}{{dt}}=0.02\displaystyle \frac{f{({a}_{\mathrm{BH}})}^{1/2}{M}_{{\rm{d}},-2}{M}_{\mathrm{BH},0.5}^{1/3}{t}_{\mathrm{vis},-1}^{2/3}}{{h}_{{\rm{d}},-0.5}^{2/3}{\alpha }_{\mathrm{ss},-1}^{1/3}{({t}_{\mathrm{vis},-1}+24t)}^{2}}\quad {M}_{\odot }\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 16 }$

The maximal jet power can be ${L}_{\mathrm{BZ}}=C({a}_{\mathrm{BH}}){\dot{M}}_{\mathrm{BH}}{c}^{2}$, here C(a_BH) is the efficiency of the accretion coefficient, 0 < C(a_BH) < few (see, e.g., Komissarov & Barkov 2010; McKinney et al. 2012), which can be combined with factor f(a_BH) and, for a wide range of the BH spin parameter (a_BH > 0.3), we obtain a simple approximation formula $C{({a}_{\mathrm{BH}})f({a}_{\mathrm{BH}})}^{1/2}\approx {a}_{\mathrm{BH}}^{2.4}$. If we adopt a_BH ≈ 0.7, we can estimate jet power as

$\begin{eqnarray}&&{L}_{\mathrm{BZ}}\sim {10}^{49}{M}_{{\rm{d}},-2}{M}_{\mathrm{BH},0.5}^{1/3}{t}_{\mathrm{vis},-1}^{2/3}{t}_{0.3}^{-2}\quad {{\rm{erg}}{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 17 }$

This equation is valid in the case t ≫ 0.4 t_vis. So this electromagnetic luminosity corresponds to the strength of the magnetic field near the horizon of order (Blandford & Znajek 1977; Barkov & Komissarov 2008b)

$\begin{eqnarray}&&{B}_{\mathrm{BH}}\approx {\left(\displaystyle \frac{24{L}_{\mathrm{BZ}}}{{r}_{{\rm{g}}}^{2}c}\right)}^{1/2}\sim 2\times {10}^{14}\quad {\rm{G}}.\end{eqnarray} \tag{ 18 }$

This value, inferred from modeling the accretion torus, compares well with the one inferred from the soft X-ray component (Equation (9)).

The wind originates in a very optically thick and hot disk with T ∼ 1 MeV. The optical thickness of the disk itself near the BH can be estimated from Equation (16) τ_d ∼ 3 × 10¹¹t⁻². The wind is very optically thick, even without pair creation the expected optical depth to Thomson scattering is τ_T ≫ 1,

$\begin{eqnarray}&&{\tau }_{T}\approx \displaystyle \frac{{\sigma }_{T}{M}_{{\rm{d}}}}{4{m}_{{\rm{p}}}{v}_{{\rm{w}}}^{2}{t}^{2}}\sim 5\times {10}^{10}{M}_{{\rm{d}},-2}{v}_{\mathrm{ex},-1}^{-2}{t}_{0.3}^{-2},\end{eqnarray} \tag{ 19 }$

here we assume uniform density of the disk wind ${\rho }_{{\rm{w}}}={M}_{{\rm{d}}}/4{r}_{{\rm{w}}}^{3}$. This result depends on the wind parameter p, which is neglected here. A large number of electron–positron pairs will be created near the disk. However, the e^± pairs do not affect wind dynamics since baryon density exceeds the pair density by many orders of magnitude,

$\begin{eqnarray}\displaystyle \frac{{\rho }_{{\rm{w}}}}{{m}_{e}{n}_{\pm }} & = & \displaystyle \frac{\sqrt{\pi /2}}{4}\displaystyle \frac{{e}^{r/({r}_{0}{\theta }_{T,0})}}{{m}_{e}{v}_{{\rm{w}}}{r}^{1/2}{r}_{0}^{3/2}{\theta }_{T,0}^{3/2}}\gg 1\\ {n}_{\pm }{\lambda }_{C}^{3} & = & \displaystyle \frac{\sqrt{2}}{{\pi }^{3/2}}{e}^{-\tfrac{1}{{\theta }_{T}}}{\theta }_{T}^{3/2},\end{eqnarray} \tag{ 20 }$

where ${\lambda }_{C}={\hslash }/({m}_{e}c)$ is the electron Compton length and we assumed the wind temperature is T = T₀ (r₀/r), normalized θ_T = T/m_ec² (and similar for T₀) and used the equilibrium thermal pair density n_± (Lightman 1982; Svensson 1982).

The wind will not produce any appreciable EM signatures due to steep adiabatic cooling. It is expected that the decay of radioactive elements contributes to wind heating, which together with far-flung tidal tails produce the kilonova emission (Li & Paczyński 1998; Metzger et al. 2010).

Next, we consider the propagation of the BZ jet through the disk-generated wind. Since it takes time to accumulate the magnetic flux on the BH and to trigger the BZ mechanism, the jet will propagate through the pre-existing wind. Let the wind have constant properties (we neglect the fact that at early times the wind has higher $\dot{M};$ we might expect that this will be partially compensated by the initially higher v_w). Consider a jet of power L_j that is confined within a solid angle ΔΩ ≈ πθ². The head of the jet located at r_h propagates with speed v_jh and according to (in the Kompaneets approximation, Kompaneets 1960)

$\begin{eqnarray}&&{P}_{\mathrm{jh}}=\displaystyle \frac{{L}_{j}}{\pi {\theta }^{2}{r}_{h}^{2}c}={\rho }_{{\rm{w}}}{({v}_{\mathrm{jh}}-{v}_{{\rm{w}}})}^{2},\end{eqnarray} \tag{ 21 }$

where P_jh is the pressure created by the jet. Let us assume that the disk provides an outflow

$\begin{eqnarray}&&{\dot{M}}_{{\rm{w}},\mathrm{disk}}=4\pi {v}_{{\rm{w}}}{\rho }_{{\rm{w}}}{r}^{2}.\end{eqnarray} \tag{ 22 }$

Using wind density from (22), the jet head propagates according to (see Bromberg et al. 2011)

$\begin{eqnarray}&&{v}_{\mathrm{jh}}={v}_{{\rm{w}}}+\sqrt{\displaystyle \frac{4{L}_{j}{v}_{{\rm{w}}}}{{\theta }^{2}{\dot{M}}_{{\rm{w}},\mathrm{disk}}c}}\end{eqnarray} \tag{ 23 }$

or

$\begin{eqnarray}&&{v}_{\mathrm{jh}}={v}_{{\rm{w}}}+5\times {10}^{9}{L}_{j,49}^{1/2}{v}_{{\rm{w}},-1}^{1/2}{\dot{M}}_{{\rm{w}},\mathrm{disk},-2}^{-1/2}\,\mathrm{cm}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 24 }$

Thus, if the jet propagates with nearly constant velocity, then the jet propagation time is

$\begin{eqnarray}&&{t}_{\mathrm{jb}}=\displaystyle \frac{{v}_{{\rm{w}}}t}{{v}_{\mathrm{jh}}}\sim \displaystyle \frac{{t}_{\mathrm{delay}}}{3},\end{eqnarray} \tag{ 25 }$

at the second half of this equation, we assume v_w = 0.1c =3 × 10⁹ cm s⁻¹ and v_jh = 5 × 10⁹ cm s⁻¹ ≈ 2 v_w. Moreover, if we again assume v_w = 0.1c, this delay time is in good agreement with results of the statistical analysis of short GRBs (Moharana & Piran 2017). Importantly, the head propagates within the wind with non-relativistic velocity.

If the speed of the jet's head shock in the wind rest frame v_s = v_jh − v_w ≥ v_w is less than the wind speed, then the jet cocoon would have an approximately spherical shape in the expanding disk wind. And, in this case, after the shock breakout the head shock is not intense and could not form relativistic outflow and form a sufficiently large impact region at the boundary of the wind with the radius of r_s ∼ r_w. So, comparing v_s and v_w from Equations (5) and (23), we can derive a restriction on the jet power as

$\begin{eqnarray}&&{L}_{{\rm{j}}}\geqslant \displaystyle \frac{S{\dot{M}}_{{\rm{w}},\mathrm{disk}}c}{4\pi {v}_{{\rm{w}}}{t}_{\mathrm{delay}}^{2}}\sim 3\times {10}^{48}{\dot{M}}_{{\rm{w}},\mathrm{disk},-2}{v}_{{\rm{w}},-1}^{-1}\,{{\rm{erg}}{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 26 }$

Let us estimate the Lorentz factor of the magnetically driven jet before the breakout from the wind. Magnetically driven jets can be accelerated up to very high Lorentz factors in the linear regime (Beskin & Nokhrina 2006; Barkov & Komissarov 2008a; Komissarov et al. 2009). In the case of the parabolic shape of the jet, we can estimate the jet Lorentz factor on the border expanding envelop as Γ_j = (r_S/r_lc)^1/2, here the cylindrical radius of the jet ${r}_{{\rm{S}}}=6\times {10}^{8}\,\mathrm{cm}$ and light cylinder radius r_lc. In a case of fast spinning BH, ${r}_{\mathrm{lc}}=4{r}_{{\rm{g}}}/{a}_{\mathrm{BH}}\approx 2\times {10}^{6}\,\mathrm{cm}$, for model parameters adopted in Section 4 this corresponds to Γ_j ≈ 17. We can treat this value as the minimal Lorentz factor of the jet. After the breakout, the jet can have additional boosting due to the formation of a strong rarefaction wave on its outer border (see Komissarov et al. 2010; Tchekhovskoy et al. 2010; Lyutikov 2011a; Kathirgamaraju et al. 2017). The additional opening angle, which is formed by sideways jet expansion, can be estimated as Δθ ≈ 1/Γ_j ≈ 0.06 (Lyutikov et al. 2003). So, the total opening angle of the jet can be estimated as θ_tot = θ + Δθ ≈ 0.15.

We can estimate the properties of the shock-heated wind flow at the point of breakout. Before the breakout, the BZ jet drives a shock in the wind. This shock is strongly radiation-dominated, as we demonstrate next (see Katz et al. 2010; Ito et al. 2018, for a discussion of radiation-dominated shocks). Equating post-shock plasma energy density to that of radiation, a shock becomes radiation-dominated for the post-shock (ion) temperatures T_r that satisfies

$\begin{eqnarray}&&{T}_{r}\gt {\left(\displaystyle \frac{15n}{{\pi }^{2}}\right)}^{1/3}\displaystyle \frac{c{\hslash }}{k},\end{eqnarray} \tag{ 27 }$

where n is the pre-shock number density, and k is the Boltzmann constant. From the condition ${kT}={m}_{{\rm{p}}}{v}_{r}^{2}$, the required shock velocity is then

$\begin{eqnarray}&&{v}_{r}\geqslant \sqrt{\displaystyle \frac{{\hslash }c}{{m}_{{\rm{p}}}}}{\left(\displaystyle \frac{15n}{{\pi }^{2}}\right)}^{1/6}.\end{eqnarray} \tag{ 28 }$

Comparing this with the relative velocity of the jet head with respect to the wind, (23),

$\begin{eqnarray}&&\displaystyle \frac{{v}_{\mathrm{jh}}-{v}_{{\rm{w}}}}{{v}_{r}}=\displaystyle \frac{{2}^{4/3}{\pi }^{1/2}}{{15}^{1/6}}\displaystyle \frac{{m}_{{\rm{p}}}^{2/3}}{c{{\hslash }}^{1/2}}\displaystyle \frac{{L}_{j}^{1/2}{v}_{{\rm{w}}}{t}^{1/3}}{\theta {\dot{M}}_{{\rm{d}},\mathrm{wind}}^{2/3}}\end{eqnarray} \tag{ 29 }$

or

$\begin{eqnarray}&&\displaystyle \frac{{v}_{\mathrm{jh}}-{v}_{{\rm{w}}}}{{v}_{r}}=70\displaystyle \frac{{L}_{j,49}^{1/2}{v}_{{\rm{w}},-1}{t}_{0.3}^{1/3}}{\theta {\dot{M}}_{{\rm{d}},\mathrm{wind},-2}^{2/3}}.\end{eqnarray} \tag{ 30 }$

The speed of the shock wave significantly exceeds the critical one, so we conclude that the jet-driven shock is radiatively dominated close to the breakout point.

In radiation-dominated shocks the post-shock temperature T_s is determined by the condition

$\begin{eqnarray}\displaystyle \frac{4{\sigma }_{\mathrm{SB}}}{c}{T}_{{\rm{s}}}^{4} & \sim & {\rho }_{{\rm{w}}}{({v}_{\mathrm{jh}}-{v}_{{\rm{w}}})}^{2}=\displaystyle \frac{{L}_{{\rm{j}}}}{\pi {({v}_{{\rm{w}}}t\theta )}^{2}c}\\ {T}_{{\rm{s}}} & = & \displaystyle \frac{{L}_{j}^{1/4}}{{(4\pi {\sigma }_{\mathrm{SB}})}^{1/4}\sqrt{{v}_{{\rm{w}}}t\theta }}.\end{eqnarray} \tag{ 31 }$

(Note that this estimate has a weak dependence on the properties of the jet (power and opening angle), is independent of the assumed mass loss rate of the disk, and only mildly dependent on wind velocity.)

Substituting jet power from Equation (17), we get

$\begin{eqnarray}&&{T}_{{\rm{s}}}=40\displaystyle \frac{{M}_{{\rm{d}},-2}^{1/4}}{{\theta }_{-1}^{1/2}{v}_{{\rm{w}},-1}^{1/2}{t}_{0.3}}\,{\rm{keV}},\end{eqnarray} \tag{ 32 }$

where time t is time of shock breakout. Eestimate T_s is the upper limit since part of the energy incoming into the shock will be converted into bulk motion and into the production of pairs—these effects will reduce somewhat the post-shock temperature. At t ∼ few seconds, and given our order-of-magnitude approach, this estimate is very close to the observed temperature of the second prompt peak.

In the present model, after the breakout, the collimated jet accelerates to highly relativistic velocities, and thus becomes highly debeamed and not observable. Let us estimate the constraints on the viewing angle.

The expected observed jet power of a relativistically boosted jet can be estimated as (see more details in Sikora et al. 1997)

$\begin{eqnarray}&&{L}_{\mathrm{obs}}=\displaystyle \frac{{\delta }^{3}}{{{\rm{\Gamma }}}_{\mathrm{jet}}}{L}_{\mathrm{jet}},\end{eqnarray} \tag{ 33 }$

here Γ_jet is the Lorentz factor of the jet, $\delta \,=1/[{{\rm{\Gamma }}}_{\mathrm{jet}}(1-v\cos \theta /c)]$ is the Doppler factor of the jet, v is the velocity of the jet, θ is the angle between observer and jet axis, and L_jet = χL_BZ is the electromagnetic jet luminosity with efficiency χ. In the case of small angles ($| 1-\cos \theta | \ll 1$, but θ can be ≫1/Γ_jet), we can write Γ_jet/δ = (α² + 1)/2 (Giannios et al. 2010; Aharonian et al. 2017), here α = θ Γ_jet and Equation (33) take the form

$\begin{eqnarray}&&\alpha ={\left[{\left(\displaystyle \frac{8{{\rm{\Gamma }}}_{\mathrm{jet}}^{2}\chi {L}_{\mathrm{BZ}}}{{L}_{\mathrm{obs}}}\right)}^{1/3}-1\right]}^{1/2}.\end{eqnarray} \tag{ 34 }$

In the case of large viewing angles (α ≫ 1), the Equation (34) can be writen as

$\begin{eqnarray}&&{\theta }_{\mathrm{side}}={\left(\displaystyle \frac{8\chi {L}_{\mathrm{BZ}}}{{{\rm{\Gamma }}}_{\mathrm{jet}}^{4}{L}_{\mathrm{obs}}}\right)}^{1/6}.\end{eqnarray} \tag{ 35 }$

So, taking the jet opening angle from Section 6.4, the minimal viewing angle can be estimated as

$\begin{eqnarray}&&{\theta }_{\mathrm{obs}}\gt {\theta }_{\mathrm{tot}}+{\left(\displaystyle \frac{8\chi {L}_{\mathrm{BZ}}}{{{\rm{\Gamma }}}_{\mathrm{jet}}^{4}{L}_{\mathrm{obs}}}\right)}^{1/6}.\end{eqnarray} \tag{ 36 }$

Substituting parameters of the GRB 170817A to Equation (36), we can estimate the minimal viewing angle as

$\begin{eqnarray}&&{\theta }_{\mathrm{obs}}\gt 0.15+0.3{\left(\displaystyle \frac{\chi {M}_{{\rm{d}}0,-2}{M}_{\mathrm{BH},0.5}^{1/3}{t}_{\mathrm{vis},-1}^{2/3}}{{{\rm{\Gamma }}}_{\mathrm{jet},15}^{4}{L}_{\mathrm{obs},47.2}{\alpha }_{\mathrm{ss},-1}{h}_{{\rm{d}},-0.5}{t}_{0.3}^{2}}\right)}^{1/6}.\end{eqnarray} \tag{ 37 }$

The probability to not observe such a burst is $\mathrm{Prob}\,\approx 1-{\theta }_{\mathrm{obs}}^{2}/2\approx 1\mbox{--}0.1\approx 0.9$. We should note that our limitation of observational angle is close to the value θ_GW = 0.54 obtained from BNS coalescence (LIGO Scientific Collaboration et al. 2017).

Combining Equations (15) and (34), we derive a minimal observational angle and probability to observe the transient and present them in Figure 8.

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The CHILESCOPE¹² is a remote controlled commercial observatory located in the Chilean Andes (W 70.75 S 30.27) equipped with a 1 m Ritchey Chretien telescope (RC-1000) and two identical 50 cm fast Newton astrographs (Newtonian 1 ASA-500 and Newtonian 2).

Both Newtonians with f/3.8 are on "Z" equatorial mounts, both are equipped with 4 K × 4 K FLI PROLINE 16803 CCD cameras with Astrodon Generation 2 E-Series Luminance filter,¹³ which is approximately equivalent to a clear light. The field of view is 67 × 67 arcminutes.

The 1-meter RC-1000 telescope is mounted on an alt-azimuth mount with direct drives on both axes and has a focal ratio f/6.8 with a reducer. The telescope is also equipped with a 4 K × 4 K FLI PROLINE 16803 CCD camera with Astrodon Generation 2 E-Series Luminance filter. It effectively cuts off the wavelengths <4000 Å and >7100 Å, thus its transmission curve corresponds to clear light. In the paper, we refer to this filter as Clear. The resulting field of view is 18.6 ×18.6 arcminutes. It also has a good thermal stabilization with the working temperature of −30°C.

RC-1000 telescope covered the central part of the LIGO/Virgo trigger G298048 error box (LIGO Scientific Collaboration & Virgo Collaboration 2017) with a typical limiting magnitude of 20^m at 60 s exposure in each frame. A total of 48 images were obtained. The coverage of the 1σ error box of G298048 is 14.4%. The start time (UT) and the center coordinates of each frame are collected in Table 3. The optical counterpart candidate SSS17a was independently discovered by six teams (Allam et al. 2017; Arcavi et al. 2017; Coulter et al. 2017; Lipunov et al. 2017; Tanvir & Levan 2017; Yang et al. 2017) with the first announcement at 01:05 UT August 18 (12.4 hr since GW trigger and 25.6 minutes after the end of RC-1000 telescope observations). The localization of SSS17a is out of the coverage in the first epoch of our observations. The covering map can be found in Figure 9, left panel.

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Table 3.  Observations of the RC-1000 Telescope

UT Date	Time Since GW Trigger (days)	Center (R.A.)	Center (Decl.)
2017 Aug 17 23:44:31	0.46108	12h 48m 28414	−14° 25' 07037
2017 Aug 17 23:45:53	0.46203	12h 47m 05895	−14° 25' 04261
2017 Aug 17 23:47:16	0.46299	12h 45m 43416	−14° 25' 01827
2017 Aug 17 23:48:38	0.46394	12h 48m 28594	−14° 45' 01452
2017 Aug 17 23:50:00	0.46488	12h 47m 05988	−14° 44' 59153
2017 Aug 17 23:51:23	0.46584	12h 45m 43329	−14° 44' 57545
2017 Aug 17 23:52:45	0.46679	12h 48m 28701	−15° 04' 58286
2017 Aug 17 23:54:07	0.46774	12h 47m 05854	−15° 04' 58530
2017 Aug 17 23:55:30	0.46870	12h 45m 43005	−15° 04' 59031
2017 Aug 17 23:58:01	0.47045	12h 51m 28799	−15° 25' 03691
2017 Aug 17 23:59:23	0.47140	12h 50m 05874	−15° 25' 02099
2017 Aug 18 00:00:46	0.47236	12h 48m 42901	−15° 25' 00518
2017 Aug 18 00:02:17	0.47341	12h 51m 28942	−15° 45' 00766
2017 Aug 18 00:03:49	0.47448	12h 50m 05842	−15° 44' 59895
2017 Aug 18 00:05:22	0.47556	12h 48m 42695	−15° 44' 56860
2017 Aug 18 00:06:53	0.47661	12h 51m 28907	−16° 04' 59101
2017 Aug 18 00:08:15	0.47756	12h 50m 05657	−16° 04' 57618
2017 Aug 18 00:09:38	0.47852	12h 48m 42360	−16° 04' 57688
2017 Aug 18 00:13:16	0.48104	12h 51m 28630	−15° 25' 05288
2017 Aug 18 00:14:38	0.48199	12h 50m 05706	−15° 25' 02368
2017 Aug 18 00:17:15	0.48381	12h 54m 29036	−16° 25' 02125
2017 Aug 18 00:18:50	0.48491	12h54m 29003	−16° 25' 03603
2017 Aug 18 00:20:21	0.48596	12h 53m 05630	−16° 25' 02356
2017 Aug 18 00:21:52	0.48701	12h 51m 42259	−16° 25' 00875
2017 Aug 18 00:23:22	0.48806	12h 54m 29055	−16° 45' 00484
2017 Aug 18 00:24:53	0.48911	12h 53m 05560	−16° 44' 58705
2017 Aug 18 00:26:26	0.49019	12h 51m 41997	−16° 44' 57424
2017 Aug 18 00:27:57	0.49124	12h 54m 29024	−17° 04' 59058
2017 Aug 18 00:29:20	0.49220	12h 53m 05393	−17° 04' 59049
2017 Aug 18 00:30:42	0.49315	12h 51m 41709	−17° 04' 58549
2017 Aug 18 00:34:03	0.49547	12h 57m 29158	−17° 25' 03586
2017 Aug 18 00:35:33	0.49652	12h 56m 05408	−17° 25' 02790
2017 Aug 18 00:37:04	0.49757	12h 54m 41653	−17° 24' 59856
2017 Aug 18 00:38:26	0.49852	12h 57m 29218	−17° 45' 01451
2017 Aug 18 00:39:49	0.49948	12h 56m 05305	−17° 44' 59001
2017 Aug 18 00:41:19	0.50052	12h 54m 41310	−17° 44' 57055
2017 Aug 18 00:42:50	0.50157	12h 57m 29230	−18° 04' 59511
2017 Aug 18 00:44:13	0.50253	12h 56m 05075	−18° 04' 58201
2017 Aug 18 00:45:35	0.50348	12h 54m 40882	−18° 04' 57991
2017 Aug 18 00:48:13	0.50531	13h 00m 29457	−18° 25' 01845
2017 Aug 18 00:49:43	0.50635	12h 59m 05148	−18° 25' 01236
2017 Aug 18 00:51:06	0.50731	12h 57m 40809	−18° 24' 59051
2017 Aug 18 00:52:28	0.50826	13h 00m 29458	−18° 44' 59417
2017 Aug 18 00:53:50	0.50921	12h 59m 04993	−18° 44' 57667
2017 Aug 18 00:55:23	0.51029	12h 57m 40424	−18° 44' 56776
2017 Aug 18 00:56:54	0.51134	13h 00m 29415	−19° 04' 57375
2017 Aug 18 00:58:25	0.51240	12h 59m 04778	−19° 04' 57208
2017 Aug 18 00:59:57	0.51346	12h 57m 40097	−19° 04' 55261

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We also covered the northern part of the GBM/Fermi localization 1σ containment (statistical only, Connaughton et al. 2017) with several frames taken by the ASA-500 telescope in the Clear filter. The total coverage of the GBM 1σ localization area is about 16% and contains 76 frames. The typical limiting magnitude of a single frame is 175 at 60 s exposure. Date, start time of observations (UT), and center coordinates of each frame are collected in Table 4. The covering map can be found in Figure 9, right panel.

Table 4.  Observations of the ASA-500 Telescope

UT Date	Time Since GW Trigger (days)	Center (R.A.)	Center (Decl.)
2017 Aug 17 23:17:16	0.44215	12h 30m 15598	−30° 12' 47661
2017 Aug 17 23:18:42	0.44315	12h 25m 37552	−30° 12' 46982
2017 Aug 17 23:20:08	0.44414	12h 20m 59825	−30° 12' 51272
2017 Aug 17 23:21:34	0.44514	12h 16m 22006	−30° 12' 54690
2017 Aug 17 23:23:00	0.44613	12h 11m 44220	−30° 12' 56952
2017 Aug 17 23:24:26	0.44713	12h 07m 06472	−30° 12' 59341
2017 Aug 17 23:25:51	0.44811	12h 02m 28537	−30° 13' 04766
2017 Aug 17 23:27:08	0.44900	11h 57m 50769	−30° 13' 06317
2017 Aug 17 23:28:26	0.44991	11h 53m 12785	−30° 13' 12156
2017 Aug 17 23:29:51	0.45089	11h 48m 34883	−30° 13' 16196
2017 Aug 17 23:31:09	0.45179	11h 43m 56993	−30° 13' 19841
2017 Aug 17 23:32:26	0.45269	11h 38m 46482	−31° 13' 44353
2017 Aug 17 23:33:51	0.45367	11h 34m 41269	−30° 13' 27977
2017 Aug 17 23:35:09	0.45457	11h 30m 03364	−30° 13' 34495
2017 Aug 17 23:36:26	0.45546	11h 25m 25436	−30° 13' 37753
2017 Aug 17 23:37:51	0.45645	11h 20m 47749	−30° 13' 41649
2017 Aug 17 23:39:16	0.45743	11h 16m 09869	−30° 13' 48310
2017 Aug 17 23:40:34	0.45833	11h 11m 31887	−30° 13' 52435
2017 Aug 17 23:41:51	0.45922	11h 06m 54122	−30° 13' 57672
2017 Aug 17 23:43:16	0.46021	11h 02m 16046	−30° 14' 03015
2017 Aug 17 23:44:34	0.46111	12h 30m 15005	−30° 13' 04766
2017 Aug 17 23:45:51	0.46200	12h25m 33996	−31° 13' 07322
2017 Aug 17 23:47:17	0.46300	12h 20m 53256	−31° 13' 10210
2017 Aug 17 23:48:43	0.46399	12h 16m 12320	−31° 13' 11223
2017 Aug 17 23:50:09	0.46499	12h 11m 31649	−31° 13' 15275
2017 Aug 17 23:51:36	0.46600	12h 06m 50885	−31° 13' 18115
2017 Aug 17 23:53:02	0.46699	12h 02m 10096	−31° 13' 24372
2017 Aug 17 23:54:28	0.46799	11h 57m 29387	−31° 13' 26510
2017 Aug 17 23:55:45	0.46888	11h 52m 48745	−31° 13' 31809
2017 Aug 17 23:57:02	0.46977	11h 48m 07899	−31° 13' 33279
2017 Aug 17 23:58:28	0.47076	11h 43m 27248	−31° 13' 38379
2017 Aug 17 23:59:53	0.47175	11h 38m 12086	−32° 14' 00137
2017 Aug 18 00:01:18	0.47273	11h 34m 05570	−31° 13' 47746
2017 Aug 18 00:02:35	0.47362	11h 29m 24922	−31° 13' 51547
2017 Aug 18 00:04:00	0.47461	11h 24m 44156	−31° 13' 57384
2017 Aug 18 00:05:18	0.47551	11h 20m 03402	−31° 14' 02252
2017 Aug 18 00:06:35	0.47640	11h 15m 22440	−31° 14' 06208
2017 Aug 18 00:08:00	0.47738	11h 10m 41821	−31° 14' 09616
2017 Aug 18 00:09:18	0.47829	11h 06m 01019	−31° 14' 16647
2017 Aug 18 00:10:35	0.47918	11h 01m 20029	−31° 14' 19995
2017 Aug 18 00:12:05	0.48022	12h 30m 13856	−32° 13' 21158
2017 Aug 18 00:13:23	0.48112	12h 25m 30032	−32° 13' 23827
2017 Aug 18 00:14:40	0.48201	12h 20m 46426	−32° 13' 25644
2017 Aug 18 00:16:06	0.48301	12h 16m 02484	−32° 13' 29700
2017 Aug 18 00:17:23	0.48390	12h 11m 18718	−32° 13' 32247
2017 Aug 18 00:18:40	0.48479	12h 06m 35049	−32° 13' 34391
2017 Aug 18 00:19:58	0.48569	12h 01m 51128	−32° 13' 39111
2017 Aug 18 00:21:15	0.48659	11h 57m 07348	−32° 13' 43128
2017 Aug 18 00:22:32	0.48748	11h 52m 23580	−32° 13' 47111
2017 Aug 18 00:23:57	0.48846	11h 47m 39710	−32° 13' 50407
2017 Aug 18 00:25:15	0.48936	11h 42m 56111	−32° 13' 54176
2017 Aug 18 00:27:57	0.49124	11h 33m 28248	−32° 14' 05578
2017 Aug 18 00:29:22	0.49222	11h 28m 44497	−32° 14' 08661
2017 Aug 18 00:30:39	0.49311	11h 24m 00649	−32° 14' 14154
2017 Aug 18 00:31:57	0.49402	11h 19m 16820	−32° 14' 20406
2017 Aug 18 00:33:14	0.49491	11h 14m 32974	−32° 14' 23645
2017 Aug 18 00:34:31	0.49580	11h 09m 49015	−32° 14' 27265
2017 Aug 18 00:35:58	0.49681	11h 05m 05077	−32° 14' 30945
2017 Aug 18 00:37:24	0.49780	11h 00m 21126	−32° 14' 35378
2017 Aug 18 00:38:54	0.49884	12h 30m 13123	−33° 13' 39301
2017 Aug 18 00:40:21	0.49985	12h 25m 26171	−33° 13' 37855
2017 Aug 18 00:41:38	0.50074	12h 20m 38975	−33° 13' 44215
2017 Aug 18 00:42:55	0.50163	12h 15m 52081	−33° 13' 45463
2017 Aug 18 00:44:12	0.50252	12h 11m 05080	−33° 13' 48273
2017 Aug 18 00:45:38	0.50352	12h 06m 18116	−33° 13' 51389
2017 Aug 18 00:47:04	0.50451	12h 01m 31219	−33° 13' 57070
2017 Aug 18 00:48:30	0.50551	11h 56m 44050	−33° 14' 00839
2017 Aug 18 00:49:56	0.50650	11h 51m 56967	−33° 14' 04169
2017 Aug 18 00:51:21	0.50749	11h 47m 10057	−33° 14' 07798
2017 Aug 18 00:52:47	0.50848	11h 39m 19229	−30° 13' 24617
2017 Aug 18 00:52:47	0.50848	11h 42m 22994	−33° 14' 11486
2017 Aug 18 00:54:13	0.50948	11h 37m 35838	−33° 14' 16286
2017 Aug 18 00:55:39	0.51047	11h 32m 49002	−33° 14' 20323
2017 Aug 18 00:57:05	0.51147	11h 28m 01904	−33° 14' 23832
2017 Aug 18 00:58:31	0.51247	11h 23m 14613	−33° 14' 28525
2017 Aug 18 00:59:48	0.51336	11h 18m 27436	−33° 14' 32516

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We started to observe the optical counterpart of the GW170817 (LIGO Scientific Collaboration & Virgo Collaboration 2017) labeled SSS17a (Coulter et al. 2017) on 2017 August 19 at 23:30:33 UT taking several 180 s exposures in the Clear filter with the RC-1000 telescope of the Chilescope observatory (Pozanenko et al. 2017c). We clearly detected the source strongly contaminated by the host galaxy NGC 4993 background. We continued our observations on 2017 August 20, 21, and 24, taking several 180 s exposures in each epoch (Pozanenko et al. 2017b, 2017d). The weather conditions were satisfactory with a median seeing of 2 arcsec. The seeing was not good for the Chilean sky because the source was observed in the end of twilight when the atmosphere was not stable. The source was clearly detected in the stacked frames on August 20 and 21 but faded on August 24 below the detection limit over a host galaxy background. The optical transient SSS17a is shown in Figure 10. The log of our observations is listed in Table 5.

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All primary reduction of CCD images (bias and dark subtraction, flat-fielding) was performed using the CCDPROC task of the IRAF software package.¹⁴ The flux of the source is strongly affected by the host galaxy contribution, so the strategy of direct image subtraction was decided. Since the source was not detected in the stacked frame of the last observational epoch (August 24), we chose this epoch as a template for the subtraction of the host galaxy. To align images of different observational epochs, we used the package ALIGN/IMAGE of ESO-MIDAS software¹⁵ and the geomap task of IRAF. The average image background was subtracted from all frames using median filter, and flux normalization for the image subtraction was performed using the MAGNITUDE/CIRCLE task of ESO-MIDAS.

The photometry of the source after the host subtraction was made with the PSF method using the DAOPHOT package from IRAF software. A rectangular area containing the host galaxy and the source SSS17a was replaced in the stacked background-subtracted frames with the host subtracted flux-normalized sub-images, made for each observational epoch. The reference PSF stars for each specific epoch were taken from the area outside of the host subtraction region.

The resulting instrumental photometrical magnitudes were calibrated with the USNO-B1.0 catalog R2 magnitudes. After the study of stellar non-saturated objects in the field, we chose four reference stars. The information about them is listed in the Table 6. The results of the photometry are presented in Table 5.

The light curve of the optical transient, including published so far photometry collected in Villar et al. (2017) and Tanvir et al. (2017) in R, r, and in J filters is presented the Figure 11. Bold black circles represent the data obtained by the RC-1000 telescope in the Clear filter. The data were shifted by 0.25 mag to compensate for the difference between the photometric bands. The shift was calculated using r or R data obtained simultaneously with ours. In the same figure, we plot the nIR afterglow of GRB 130603B (rescaled in both frequency and time) to the rest frame. We used parameters of the afterglow approximation (Flux ∼ t^−2.72) after jet-break at about 0.4 days (Tanvir et al. 2013). The absolute calibration in the rest frame was calculated from the broadband SED of GRB 130603B obtained at ∼0.6 days post-burst (in the observer frame) in filters grizJK (Table 2 in Tanvir et al. 2013). The plotted afterglow roughly corresponds to the J-filter in the rest frame. For the correct calculation of luminosity light curves of GRB 170817A and GRB 130603B, we used Galactic extinction in the direction of the bursts, E(B − V) = 0.109 and E(B − V) = 0.02, correspondingly (Schlafly & Finkbeiner 2011). A host galaxy extinction was not taken into account. It is evident from Figure 11 that the afterglow luminosity of GRB 170817A is more than 130 times fainter than that of GRB 130603B in the J-filter.

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