ALMA and GMRT Constraints on the Off-axis Gamma-Ray Burst 170817A from the Binary Neutron Star Merger GW170817

Our initial ALMA campaign started on 2017 August 18 at 22:50:40 UTC (1.4 days after GW170817) and lasted for eight days (Schulze et al. 2017). In addition, we secured a final epoch ∼44 days after GW170817. In total, we obtained six epochs at 338.5 GHz (Table 1). The integration time of each observation was set to reach a nominal rms of ∼40 μJy/beam. The initial ALMA observations were performed in the C40-7 configuration, with a field of view of $18\buildrel{\prime\prime}\over{.} 34$ in diameter and an average synthesized beam of $\approx 0\buildrel{\prime\prime}\over{.} 13\times 0\buildrel{\prime\prime}\over{.} 07$. The observation at 44 days after GW170817 was performed in the most extended ALMA configuration, C40-8/9, yielding a synthesized beam of $0\buildrel{\prime\prime}\over{.} 026\times 0\buildrel{\prime\prime}\over{.} 016$.

Table 1.  Log of Sub-mm/mm and Radio Observations of AT2017gfo

${T}_{\mathrm{start}}$	Epoch	Frequency	Integration	Fν
(UT)	(day)	(GHz)	time (s)	(μJy)
ALMA
2017 Aug 18 22:50:40	1.4	338.5	2238	$\lt 126$
2017 Aug 20 18:19:35	3.2	338.5	2238	$\lt 90$ a
2017 Aug 20 22:40:16	3.4	338.5	2238
2017 Aug 25 22:35:17	8.4	338.5	2238	$\lt 150$
2017 Aug 26 22:58:41	9.4	338.5	1724	$\lt 102$
2017 Sep 30 15:22:00	44.1	338.5	1832	$\lt 93$
GMRT
2017 Aug 25 09:30:00	7.9	1.39	5400	$\lt 69$
2017 Sep 09 11:30:00	23.0	1.39	5400	$\lt 108$
2017 Sep 16 07:30:00	29.8	1.39	5400	$\lt 126$

Note. The epoch is with respect to the time of GW170817.

^aThe rms was measured after combining both epochs from 2017 August 20.

Download table as:  ASCIITypeset image

The ALMA data were reduced with scripts provided by ALMA and with the software package Common Astronomy Software Applications (CASA) version 4.7.2 (McMullin et al. 2007).²⁴ For each epoch, we created images using tclean, with a pixel size of $0\buildrel{\prime\prime}\over{.} 01$/px. We interactively selected cleaning regions around detected sources (none corresponding to the AT2017gfo counterpart). The cleaning process was repeated until no clear emission was left. The rms was measured in a $10^{\prime\prime}$-width box around the central position in the images without primary beam correction.

No significant signal is detected at the position of AT2017gfo. Table 1 summarizes the $3\sigma$ detection limits. The galaxy nucleus is well detected and marginally resolved in our data ($\alpha ,\delta \,({\rm{J}}2000)\,={13}^{{\rm{h}}}{09}^{{\rm{m}}}47\buildrel{\rm{s}}\over{.} 69,-23^\circ 23^{\prime} 02\buildrel{\prime\prime}\over{.} 37$). We measure 1.07 ± 0.21 mJy at 338.5 GHz. In addition, we detect a marginally resolved sub-mm galaxy with ${F}_{338.5\mathrm{GHz}}=1.15\pm 0.21$ mJy at $\alpha ,\delta \,({\rm{J}}2000)\,={13}^{{\rm{h}}}{09}^{{\rm{m}}}48\buildrel{\rm{s}}\over{.} 39,-23^\circ 22^{\prime} 48\buildrel{\prime\prime}\over{.} 29$. The quasars J1337−1257 and J1427−4206 were used for band and flux calibration, and J1256−2547, J1937−3958, and J1258−2219 for phase calibration.

The GMRT is one of the most sensitive low-frequency radio telescopes in operation currently. It operates at low radio frequencies from 150 MHz to 1.4 GHz (Swarup et al. 1991). We secured three epochs in the L band, centered at 1.39 GHz, between 2017 August 25 and 2017 September 16 (i.e., between 7.9 and 29.8 days since GW170817; Table 1; Resmi et al. 2017). The observing time was ∼1.5 hr for each observation. The first epoch was performed with the new 200 MHz correlator that divides the bandpass into 2048 channels, of which $\sim 70 \%$ were usable due to radio frequency interference. The second and the third epoch were performed with the 32 MHz correlator. The synthesized beam sizes were typically $4^{\prime\prime} \times 2^{\prime\prime}$. The quasar 3C286 was used as flux and bandpass calibrator, and J1248−199 was used for phase and additional bandpass calibration. Data reduction was carried out with the NRAO Astronomical Image Processing Software²⁵ (AIPS; Wells 1985) using standard procedures.

While the marginally resolved nucleus of the host galaxy of AT2017gfo, NGC 4993, was detected with ∼570 μJy in 1.39 GHz, no significant signal is detected at the position of AT2017gfo itself. Table 1 summarizes the $3\sigma$ detection limits, where the rms level is estimated from source-free regions using the task TVSTAT.

To augment our data set, we incorporated radio measurements from Corsi & Kasliwal (2017a, 2017b, 2017c), Corsi et al. (2017a, 2017b), Hallinan et al. (2017a), Kaplan et al. (2017), Mooley & Hallinan (2017), Mooley et al. (2017; see also Hallinan et al. 2017b), obtained with the Australia Telescope Compact Array (ATCA) and the Very Large Array (VLA). We used the VLA exposure time calculator²⁶ to convert the relative measurements of Corsi et al. (2017b) and Mooley et al. (2017) into radio flux densities, adopting rms values 50% higher than nominal to mitigate possible losses due to antennae problems and adverse observing conditions. We also included the X-ray constraints of Evans et al. (2017b), Haggard et al. (2017a), and Troja et al. (2017a) from the Swift satellite and Chandra X-ray Observatory, as reported in Abbott et al. (2017a), as well as optical photometry obtained with the Hubble Space Telescope and ESO's 8.2 m Very Large Telescope (VLT) by Tanvir et al. (2017b).

The interaction of the GRB blastwave with the circumburst medium produces an afterglow from X-ray to radio frequencies. The peak of the synchrotron afterglow spectrum is, however, expected to be in the sub-mm/mm band and it rapidly crosses the band toward lower frequencies (${\nu }_{{\rm{m}}}\propto {t}^{-3/2};$ Sari et al. 1998). Our initial ALMA 3σ limit of ${F}_{338.5\mathrm{GHz}}\,\lt$ 126 μJy at 1.4 days after GW170817 corresponds to a luminosity of $3\times {10}^{26}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1}$ at the redshift of AT2017gfo. Comparing this estimate for the peak flux of GRB 170817A to estimates of other GRBs from de Ugarte Postigo et al. (2012; see Figure 1, top panel), our sub-mm afterglow limits are ∼3–4 orders of magnitude fainter than those associated with any long-duration GRBs (LGRBs) or SGRBs.²⁷

Zoom In Zoom Out Reset image size

However, the maximum frequency is also correlated with the energy within the jet and the energy release in γ-rays, e.g., ${\nu }_{m}\propto {E}^{1/2}$ for a constant density circumburst medium (Piran 2004). Abbott et al. (2017c) reported an exceptionally low isotropic-equivalent energy of only ${E}_{\gamma ,\mathrm{iso}}=(3.08\pm 0.72)\times {10}^{46}$ erg. Hence, it is conceivable that the peak of the afterglow spectrum was already in the radio band during our first ALMA observation. To get an additional estimate of the peak luminosity, we use results in Corsi et al. (2017a). Their measurement of ${F}_{6\mathrm{GHz}}\sim 28.5\,\mu$ Jy at 28.5 days after GW170817 translates to a luminosity of $\sim 7\times {10}^{25}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1}$. Compared to radio measurements of LGRBs and SGRBs in Fong et al. (2015) and Chandra & Frail (2012), respectively (Figure 1, bottom panel), the radio afterglow is 2 orders of magnitude fainter than those of LGRBs and SGRBs.

While sub-mm and radio observations are direct tracers of the peak of the afterglow spectrum, only $\sim 7 \%$ of all Swift GRBs were bright enough to attempt sub-mm and radio observations. This observational bias is likely to skew the known population toward the bright end of any luminosity function. On the other hand, almost all of the Swift GRBs are detected at X-rays. The mapping between X-ray brightness and the peak of the afterglow spectrum is more complex. It depends on the location of the cooling break, which is usually between the optical and the X-rays, and the density profile of the circumburst medium. Nonetheless, de Ugarte Postigo et al. (2012) showed that X-ray brightness is a useful diagnostic for comparing afterglow luminosities.

To generate an X-ray diagnostic plot, we retrieved the X-ray light curves of 402 LGRBs and 31 SGRBs with detected X-ray afterglows (at least at two epochs) and known redshift from the Swift Burst Analyzer (Evans et al. 2010). Identical to Schulze et al. (2014), we computed the rest-frame light curves and resampled the light curves of the LGRB sample on a grid (gray shaded region in Figure 2). The individual light curves of the SGRB sample are shown in light blue. Already the Swift non-detections presented in Evans et al. (2017b; downward pointing triangles in Figure 2) revealed that the afterglow is $\gt 1.5$ dex fainter than the faintest SGRB with detected afterglow (downward pointing triangles in Figure 2). The deep Chandra observation by Troja et al. (2017b) at 2.3 days after GW170817 excluded any afterglow brighter than $\gt {10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, i.e., a factor of 10 below the Swift upper limits.

Zoom In Zoom Out Reset image size

To put these limits in context, Evans et al. (2017a) placed 10,000 fake GRBs, generated from the flux-limited SGRB sample in D'Avanzo et al. (2014), at the distance of GW170817. These authors estimated that the Swift X-ray telescope would have detected $\sim 65 \%$ of all simulations. The deeper Chandra observations probed a larger portion of the parameter space. However, Rowlinson et al. (2010) showed that a number of SGRBs have extremely rapidly fading X-ray afterglows, which would have evaded detection at the time of the Swift and Chandra observations.

The new quality of the X-ray emission of AT2017gfo is not only its faintness, but actually its emergence more than a week after GW170817. This behavior is inconsistent with known X-ray afterglows. When the X-ray afterglow was detected with Chandra (Haggard et al. 2017b; Margutti et al. 2017; Troja et al. 2017b), the luminosity of ${L}_{(0.3-10)\mathrm{keV}}\sim 8\,\times \,{10}^{38}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ was still 2.6 dex fainter than that of any GRB with detected X-ray afterglow.

This faintness of the afterglow is also reflected in the very low energy release at γ-rays, ${E}_{\gamma ,\mathrm{iso}}$. The observed ${E}_{\gamma ,\mathrm{iso}}$ distribution of SGRBs and LGRBs is shown in the inset of Figure 2. The vertical blue line and the shaded region display the median $[\mathrm{log}({E}_{\mathrm{iso}}/\mathrm{erg})=50.88\pm 0.18]$ and the sample dispersion $[\sigma \{\mathrm{log}({E}_{\mathrm{iso}}/\mathrm{erg})\}={0.99}_{-0.12}^{+0.14}]$ of the SGRB sample, computed with (Py)MultiNest (Feroz et al. 2013; Buchner et al. 2014). With a prompt energy release of $3.08\times {10}^{46}$ erg (green vertical line the inset of Figure 2), GRB 170817A was ∼1.5 dex less energetic than the least energetic SGRB known so far and its deviation from the distribution median is $\sim 4.4\sigma$.

In conclusion, observations of the afterglow revealed an exceptionally under-luminous afterglow at all wavelengths at the position of AT2017gfo. This extremeness is also reflected in the γ-ray properties.

The previous considerations placed the GRB in the context of LGRBs and SGRBs detected by Swift. The discussion neglected the peculiar evolution of the afterglow: non-detection of the afterglow during the first week and its emergence at later epochs. These properties are highly atypical for GRBs, assuming that the GRB jet axis is aligned with our line of sight. In the following, we model the observed evolution from X-rays to radio with templates from two-dimensional relativistic hydrodynamical jet simulations using boxfit version 2 with the methods described in van Eerten et al. (2012). The templates are generated from a wide range of physical parameters. Here, we use a nine-parameter model:

$$\begin{eqnarray*}&&{F}_{\nu }=L({E}_{\mathrm{AG},\mathrm{iso}},n,{\theta }_{1/2,\mathrm{jet}},{\theta }_{\mathrm{obs}},p,{\epsilon }_{e},{\epsilon }_{B},{\xi }_{N},z)\end{eqnarray*}$$

where ${E}_{\mathrm{AG},\mathrm{iso}}$ is the isotropic-equivalent energy of the blastwave (afterglow),²⁸ n is the circumburst density at a distance of 10¹⁷ cm, p is the power-law index of the electron energy distribution, ${\theta }_{1/2,\mathrm{jet}}$ is the jet half-opening angle, ${\theta }_{\mathrm{obs}}$ is the observer/viewing angle, ${\epsilon }_{e}$ and ${\epsilon }_{B}$ are the fractions of the internal energy in the shock-generated magnetic field and electrons, respectively, and ${\xi }_{N}$ is the fraction of electrons that are accelerated and z is the redshift.

We fix the fractions of ${\epsilon }_{e}$ and ${\xi }_{N}$ at 0.1 and 1, respectively, and p to 2.43 and the redshift to 0.009854. The other parameters are varied within the following ranges: ${\theta }_{1/2,\mathrm{jet}}=5^\circ -45^\circ ,{{\rm{E}}}_{\mathrm{AG},\mathrm{iso}}\,={10}^{47}$–10⁵³ erg, ${\epsilon }_{B}={10}^{-5}\mbox{--}{10}^{-2},n={10}^{-4}$–10⁻¹ cm⁻³ and ${\theta }_{\mathrm{obs}}=0^\circ -45^\circ$. The afterglow was modeled in a homogeneous ISM environment and we apply this model to eight representative frequencies: 1.4, 3, 6, 21, 338.5 GHz as well as the optical filters $F606W$ and $F475W$ and X-rays at 3 keV.

A critical aspect of the off-axis afterglow modeling is the resolution in azimuthal direction, in particular for models with large ${\theta }_{\mathrm{obs}}$ to ${\theta }_{1/2,\mathrm{jet}}$ ratios. We chose a numerical resolution of 20 and 30, for ${\theta }_{1/2,\mathrm{jet}}\gt 9^\circ$ and ${\theta }_{1/2,\mathrm{jet}}\lt 9^\circ$, respectively. Comparisons to simulations with a numerical resolution in azimuthal direction of 70 show that the lower-resolution templates accurately capture the temporal evolution of the afterglow, and they are also able to recover the absolute flux scale at maximum to within 20%. The maximum flux of models with very narrow jet are recovered less accurately in off-axis afterglow models. As we show below, these models are not adequate to describe the observed afterglow evolution independent of the issue of the absolute flux scale. The numerical resolution in azimuthal direction was set to unity if the viewing angle is negligible, as suggested by the boxfit manual.

The gray curves in Figure 3 display a set of strict on-axis afterglow models (i.e., ${\theta }_{\mathrm{obs}}=0$) with a half-opening angle of $5^\circ ,{\epsilon }_{B}=0.01,n={10}^{-2}\,{\mathrm{cm}}^{-3}$, and for ${E}_{\mathrm{AG},\mathrm{iso}}$ between 10⁴⁸ and 10⁵³ erg. Common to on-axis afterglow models (${\theta }_{\mathrm{obs}}\lt {\theta }_{1/2,\mathrm{jet}}$) is the strict monotonic decline in X-rays and the optical, whereas the radio can exhibit a plateau or an initial rise. This evolution is in stark contrast to observations of AT2017gfo. The best-matching templates (colored curves in Figure 3) strongly argue for a GRB seen off-axis (i.e., ${\theta }_{\mathrm{obs}}\gt {\theta }_{1/2,\mathrm{jet}};$ possible off-axis LGRB candidates were discussed in Fynbo et al. 2004; Guidorzi et al. 2009; Krühler et al. 2009).

Zoom In Zoom Out Reset image size

Model 1 (which we call the wide-jet model, thin curves in Figure 3) represents an afterglow with an energy reservoir of $\sim {10}^{50}\,\mathrm{erg}$, an energy fraction stored in magnetic fields of ${\epsilon }_{B}\sim {10}^{-2}$, and a moderately collimated outflow with a half-opening angle of ${\theta }_{1/2,\mathrm{jet}}\sim 20^\circ$, traversing a circumburst medium with a density of ${10}^{-2}\,{\mathrm{cm}}^{-3}$. The jet axis and the line of sight are misaligned by 41°. Model 2 (which we call the narrow-jet model, thick curves in Figure 3) represents a more collimated jet with ${\theta }_{1/2,\mathrm{jet}}\sim 5^\circ ,{E}_{\mathrm{AG},\mathrm{iso}}\sim {10}^{51}\,\mathrm{erg}$ and ${\epsilon }_{B}\sim 2\times {10}^{-3}$, traversing a more tenuous circumburst medium $(n\sim 5\times {10}^{-4}\,{\mathrm{cm}}^{-3})$. In this scenario, the line of sight and the GRB jet axis are misaligned by 17°.

The inferred afterglow properties are in both cases very close to the average values of SGRBs in Fong et al. (2015), corroborating that this GRB is not different from the population of known SGRBs. The properties of the wide-jet model are consistent with Alexander et al. (2017b), Granot et al. (2017), Margutti et al. (2017), and Troja et al. (2017b). However, the two distinct models, discussed in this Letter, show that there is significant degeneracy between the afterglow parameters (for a more detailed study of the afterglow parameter space, see Granot et al. 2017). More detections are required to better constrain the parameter space. We note that the derived viewing angles for both models are consistent with the conservative limit of $\lt 56^\circ$ from the LIGO signal. Moreover, the narrow-jet template (Model 2) is consistent with the even stricter LIGO limit of $\lt 28^\circ$ (Abbott et al. 2017b).

With the best-match templates in hand, we quantify the contamination of the kilonova by the afterglow. The upper panels in Figure 3 display the light curve in $F475W$ ($6.2\times {10}^{12}$ Hz) and $r^{\prime}$/$F606W$ ($4.9\times {10}^{12}$ Hz) by Tanvir et al. (2017b). The contamination by the afterglow in the optical is negligible ($\lt 1 \%$) during the week after GW170817 for both models. Hence the inferred KN properties in Tanvir et al. (2017b) do not require any afterglow correction.

The observed energy release of a GRB, ${E}_{\gamma ,\mathrm{iso},\mathrm{off}}$, measured by an observer at a viewing angle ${\theta }_{\mathrm{obs}}$, depends on ${\theta }_{\mathrm{obs}},{\theta }_{1/2,\mathrm{jet}}$, the jet geometry, and the initial bulk Lorentz factor of the jet, ${{\rm{\Gamma }}}_{0}$. Similarly, the observed ${E}_{\mathrm{peak},\mathrm{off}}$ is a function of the same quantities. The simplest jet model assumes a uniform jet with a negligible surface and predicts that the ratios between ${E}_{\gamma ,\mathrm{iso},\mathrm{off}}$ and on-axis ${E}_{\gamma ,\mathrm{iso}}$, as well as ${E}_{\mathrm{peak},\mathrm{off}}$ and on-axis ${E}_{\mathrm{peak}}$, are simple powers of the Doppler factor of the jet (Abbott et al. 2017c; Troja et al. 2017b). However, results already start to change considerably if the finite size of the jet is taken into account (Yamazaki et al. 2003a, 2003b).

In the following, we assume a top-hat jet, similar to Troja et al. (2017b) and Abbott et al. (2017c), but we take into account the finite size of the jet. Donaghy (2006) and Graziani et al. (2005) provided analytical expressions for ${E}_{\gamma ,\mathrm{iso},\mathrm{off}}$ and ${E}_{\mathrm{peak},\mathrm{off}}$ for such a geometry that also match well the numerical calculations in Yamazaki et al. (2003a, 2003b). In this model, ${E}_{\gamma ,\mathrm{iso},\mathrm{off}}$ and ${E}_{\mathrm{peak},\mathrm{off}}$ are given by

$$\begin{eqnarray*}&&{E}_{\gamma ,\mathrm{iso},\mathrm{off}}\\ &&\quad =\,\displaystyle \frac{{E}_{\gamma ,\mathrm{iso}}}{2\beta {{\rm{\Gamma }}}_{0}^{4}}[f(\beta -\cos {\theta }_{\mathrm{obs}})-f(\beta \cos {\theta }_{1/2,\mathrm{jet}}-\cos {\theta }_{\mathrm{obs}})],\\ &&\quad {E}_{\mathrm{peak},\mathrm{off}}=\displaystyle \frac{\langle D({\theta }_{\mathrm{obs}})\rangle }{\langle D({\theta }_{\mathrm{obs}}=0)\rangle }{E}_{\mathrm{peak}},\end{eqnarray*}$$

where β the velocity normalized to the speed of light, Γ is the Lorentz factor, the function f(y) is defined as

$$\begin{eqnarray*}&&f(y)=\displaystyle \frac{{{\rm{\Gamma }}}_{0}^{2}(2{{\rm{\Gamma }}}_{0}^{2}-1){y}^{3}+(3{{\rm{\Gamma }}}_{0}^{2}{\sin }^{2}{\theta }_{\mathrm{obs}})y+2\cos {\theta }_{\mathrm{obs}}{\sin }^{2}{\theta }_{\mathrm{obs}}}{{({y}^{2}+{{\rm{\Gamma }}}_{0}^{-2}{\sin }^{2}{\theta }_{\mathrm{obs}})}^{3/2}},\end{eqnarray*}$$

and the average Doppler shift is given by

$$\begin{eqnarray*}&&\langle D\rangle ={{\rm{\Gamma }}}_{0}^{-1}\displaystyle \frac{f(\beta -\cos {\theta }_{\mathrm{obs}})-f(\beta \cos {\theta }_{1/2,\mathrm{jet}}-\cos {\theta }_{\mathrm{obs}})}{g(\beta -\cos {\theta }_{\mathrm{obs}})-g(\beta \cos {\theta }_{1/2,\mathrm{jet}}-\cos {\theta }_{\mathrm{obs}})},\end{eqnarray*}$$

with

$$\begin{eqnarray*}&&g(y)=\displaystyle \frac{2{{\rm{\Gamma }}}^{2}y+2\cos {\theta }_{\mathrm{obs}}}{{({y}^{2}+{{\rm{\Gamma }}}^{-2}{\sin }^{2}{\theta }_{\mathrm{obs}})}^{1/2}}.\end{eqnarray*}$$

The equations for ${E}_{\gamma ,\mathrm{iso},\mathrm{off}}$ and ${E}_{\mathrm{peak},\mathrm{off}}$ depend on the unknown ${E}_{\gamma ,\mathrm{iso}},{E}_{\mathrm{peak}}$ and the initial bulk Lorentz factor ${{\rm{\Gamma }}}_{0}$. Considering the complexity of the expressions, we perform a parameter study. We can limit the possible parameter space by using results from other SGRBs and our afterglow modeling. Cenko et al. (2011) reported that the ratio between ${E}_{\gamma ,\mathrm{iso}}$ and ${E}_{\mathrm{AG},\mathrm{iso}}$ varies between 0.05 and 40 (mean value being ∼4). An ${E}_{\gamma ,\mathrm{iso}}$-${E}_{\mathrm{AG},\mathrm{iso}}$ ratio of a few has also been observed for SGRBs (Fong et al. 2015). The broadband modeling (Section 3.2) suggests that ${E}_{\mathrm{AG},\mathrm{iso}}$ is between 10⁵⁰ erg and 10⁵¹ erg, corresponding to ${E}_{\gamma ,\mathrm{iso}}=5\times {10}^{48}-40\times {10}^{51}$ erg. The ${E}_{\mathrm{peak}}$ distribution of our SGRB comparison sample extends from ∼40 to ∼8400 keV (mean peak energy being ∼490 keV). Goldstein et al. (2017a) reported a peak energy of 185 ± 62 keV for the main emission of GRB 170817A. Hence, we vary ${E}_{\mathrm{peak}}$ between 123 keV and 8400 keV.

In the left and right panels of Figure 4, we display the ${E}_{\gamma ,\mathrm{iso},\mathrm{off}}$ and ${E}_{\mathrm{peak},\mathrm{off}}$ as a function of ${{\rm{\Gamma }}}_{0}$. The expected parameter spaces for the two afterglow models are shown in blue (wide-jet) and red (narrow-jet). Overlaid in yellow are the observed ${E}_{\gamma ,\mathrm{iso},\mathrm{off}}/{E}_{\mathrm{peak},\mathrm{iso},\mathrm{off}}$ values reported by Goldstein et al. (2017a). The overlapping regions show the allowed parameter space for the GRB, if seen on-axis, for each afterglow model.

Zoom In Zoom Out Reset image size

The observed span in the ${E}_{\gamma ,\mathrm{iso}}$ and ${E}_{\mathrm{AG},\mathrm{iso}}$ allows an initial bulk Lorentz factor between 6 and 40, and 20 and 125 for the wide-jet (Model 1) and narrow-jet (Model 2), respectively (left panel in Figure 4). However, the highest Lorentz factor would always require ${E}_{\gamma ,\mathrm{iso}}/{E}_{\mathrm{AG},\mathrm{iso}}\gtrsim 10$. While such values are not atypical, they are at the upper end of the observed distribution in Fong et al. (2015). The observed distribution of peak energies of short GRBs narrows the possible parameter space further: ${{\rm{\Gamma }}}_{0}\lt 15$ and ${{\rm{\Gamma }}}_{0}\lt 43$ for Model 1 and Model 2, respectively (right panel in Figure 4), while the required peak energies need to exceed at least several hundred keV. The Lorentz factors are similar to the values in Zou et al. (2017), who assumed a top-jet with negligible surface and used the ${E}_{\mathrm{peak}}$-${E}_{\gamma ,\mathrm{iso}}$ (derived from SGRBs) and ${{\rm{\Gamma }}}_{0}$–${E}_{\gamma ,\mathrm{iso}}$ (derived from LGRBs) correlations.

To understand these results, we reflect upon the assumptions of this calculation. This parameter study of the jet parameters depends upon the jet half-opening angle, the viewing angle, and the jet geometry. The model in Donaghy (2006) and Graziani et al. (2005) assumes that the γ-ray emission is produced via internal shocks in the GRB jet. According to Graziani et al. (2005), systematic uncertainties may exist between the ${E}_{\mathrm{peak},\mathrm{off}}$ calculated by the above expression and the observed peak of the effective GRB spectrum. Therefore, it may not always be a very accurate representation of the observed ${E}_{\mathrm{peak}}$. Furthermore, the parameter space is limited to the observed ${E}_{\mathrm{peak}}$ distribution of short GRBs and the known ratios between ${E}_{\gamma ,\mathrm{iso}}$ and ${E}_{\mathrm{AG},\mathrm{iso}}$, and the parameters of GRB170817 as measured by Fermi.

Our broadband modeling is based on a small number of detections and we showed that there is substantial degeneracy in the model parameters. This degeneracy is also visible in the ${{\rm{\Gamma }}}_{0}$–${E}_{\gamma ,\mathrm{iso},\mathrm{off}}$ and the ${{\rm{\Gamma }}}_{0}$–${E}_{\mathrm{peak},\mathrm{off}}$ parameter spaces (Figure 4). A more sophisticated afterglow modeling and the inclusion of more afterglow observations can reduce the degeneracy. The conclusions of this analysis also depend significantly on the observed γ-ray properties of GRB 170817A. Goldstein et al. (2017b) reported an error of 33% on the peak energy. A substantially lower peak energy would allow higher ${{\rm{\Gamma }}}_{0}$ for lower peak energies (for an independent analysis of the Fermi-GBM data, see Zhang et al. 2017).

Non-relativistic shocks from the merger ejecta are thought to emit at radio frequencies (Nakar & Piran 2011). This model predicts that the emission peaks in the MHz regime and at the epoch of deceleration of the non-relativistic shock, which is expected to be on the order of months to years after the merger.

To examine whether this mechanism could produce a bright transient months after GW170817, we use the observed properties of the kilonova and the afterglow. The expected brightness at optically thin GHz frequencies would be

$$\begin{eqnarray*}&&{f}_{\nu }(t)=655\mathrm{mJy}\ {{n}_{0}}^{1.8}{\displaystyle \frac{R(t)}{{10}^{17}}}^{3}\beta {(t)}^{3.75}{\epsilon }_{B}^{0.78}{\epsilon }_{e}{\left(\displaystyle \frac{\nu }{\mathrm{GHz}}\right)}^{-0.55},\end{eqnarray*}$$

for an electron index of 2.1, where R(t) is the radius of the shock front (normalized to 10¹⁷ cm), and $\beta (t)$ is the velocity normalized to the speed of light c. This expression is derived from the peak synchrotron flux and the characteristic synchrotron frequency ${\nu }_{m}$ of the power-law electron distribution, and is in agreement with expressions in Nakar & Piran (2011). The radius and the observed time t are related through $R(t)=\beta {ct}$. The epoch of deceleration, where the swept-up mass equals the ejected mass, is given by ${t}_{\mathrm{dec}}=7\,\mathrm{yr}{\left(\tfrac{{M}_{\mathrm{ej},\odot }}{{n}_{0}}\right)}^{1/3}{\beta }_{0}^{-1}$, where ${\beta }_{0}$ is the normalized initial velocity.

Tanvir et al. (2017b) concluded that the merger ejected $\sim 5\times {10}^{-4}\,{M}_{\odot }$ with a velocity of $0.1\,c$. Along with a circumburst medium density, $n=0.01\,{\mathrm{cm}}^{-3}$, we estimate the brightness at 1.4 GHz to be $\sim 60\,\mu \mathrm{Jy}$ for a deceleration timescale of 55 years. A smaller ambient density will further reduce the flux and increase the ${t}_{\mathrm{dec}}$.

Considering the results of Smartt et al. (2017), where a higher ejected mass of $0.01{M}_{\odot }$ was estimated to be released with a similar β, the deceleration time will be ∼70 years, and the observed flux will remain the same as it is insensitive to ${M}_{\mathrm{ej}}$. Therefore, the outlook, assuming this model is valid, is bleak.

The merger remnant, if a magnetar, can inject additional energy into the shock (Metzger & Bower 2014). This increased energy will also delay ${t}_{\mathrm{dec}}$. In this model, from the observed $\beta =0.1$ and best-fit ambient density ${n}_{0}=0.01\,{\mathrm{cm}}^{-3}$, ${t}_{\mathrm{dec}}=260\,{E}_{\mathrm{mag},52}$ years, where ${E}_{\mathrm{mag},52}$ is the energy input from the magnetar. The peak flux in 1.4 GHz at ${t}_{\mathrm{dec}}\sim 3$ mJy for our parameters, which, as in the previous case, scales down as a t³ power-law to the current epoch. Therefore, we do not expect any detectable emission at GMRT frequencies at present from the merger ejecta, consistent with our observations.