TESTING THE MAGNETAR MODEL VIA LATE-TIME RADIO OBSERVATIONS OF TWO MACRONOVA CANDIDATES

The coalescence of two compact objects such as a neutron star (ns)-black hole merger or a ns² merger has been a leading candidate for the progenitor system for short-duration ($\lt 2$ s) gamma-ray bursts (sGRBs; Eichler et al. 1989; Narayan et al. 1992; see reviews by Nakar 2007; Berger 2014). Li & Paczyński (1998) suggested that mergers will be accompanied by the so-called "macronova" (or "kilonova"). They suggested that the radioactive decay of the neutron-rich matter ejected in a merger event would lead to a brief (∼1 day) optical signal that might be detectable. More recently, Barnes & Kasen (2013) and Tanaka & Hotokezaka (2013) have revised the original prediction of Li & Paczynski. Since the optical depth for r-process elements is high, the optical signal is expected to be mostly absorbed, and a longer (∼1 week) IR signal is expected instead.

A second prediction of the merger scenario is of late-time radio emission (Nakar & Piran 2011). The same ejecta that produce the macronova is expected to interact with the interstellar medium (ISM). The resulting shockwave, plowing through the ISM will accelerate electrons and produce magnetic fields. In turn, this will lead to synchrotron radio emission, similar to the process responsible for radio emission from supernovae (e.g., Chevalier 1982; Chevalier & Fransson 2006) or GRB afterglows (Sari 1997; Sari et al. 1998). The rise time and the peak flux of this radio flare, depend mainly on the ejecta mass, its velocity, and on the density of the ISM. For a macronova ejecta mass of ${M}_{\mathrm{ej}}\sim 0.01\;{M}_{\odot }$ and velocity range of ${v}_{\mathrm{ej}}\quad \sim$ 0.1–0.3 c, as predicted by recent numerical simulations (Bauswein et al. 2013; Hotokezaka et al. 2013; Rosswog et al. 2013), the radio emission is expected to rise over a timescale of months to years.

A variant of the simple merger scenario, motivated by a strong amplification of magnetic fields at the merger shown in numerical simulations (Price & Rosswog 2006; Rezzolla 2012; Giacomazzo & Perna 2013; Giacomazzo et al. 2015; Kiuchi et al. 2015), is the magnetar scenario, in which the remnant of the merger is a highly magnetized ns with a period of ∼1 ms and a large magnetic field of $B\gt {10}^{13}$ G (Usov 1992; Rosswog & Davies 2002; Bucciantini et al. 2012; Fan et al. 2013, Giacomazzo & Perna 2013; Metzger & Piro 2014; Siegel & Ciolfi 2015). The magnetar has been suggested (e.g., Duncan & Thompson 1992; Usov 1992; Zhang & Mészáros 2001; Metzger 2010) as the central engine that powers GRBs. In this scenario, the magnetar deposits most of its rotational energy, as it spins down, into the macronova ejecta, accelerating it to high relativistic velocities, thus significantly enhancing the expected radio flare signal. A magnetar with a ∼1 ms period deposits a kinetic energy of $\approx 3\times {10}^{52}$ erg. The timescale and the peak flux of the expected radio emission in this case can be calculated in a simplistic way (see Section 3), according to the formalism of Nakar & Piran (2011), but with a high relativistic velocity ($\beta \equiv {v}_{\mathrm{ej}}/c\approx 1$). The magnetar radio emission, that will also rise over a long timescale, is expected to be brighter by a few orders of magnitude than the non-magnetar merger scenario (as first discussed by Metzger & Bower 2014; see Section 5). In addition to the bright radio emission from the forward shock, there may be additional radio emission from the pulsar wind nebula, which is expected to peak over much shorter timescales (see Piro & Kulkarni 2013; Metzger & Piro 2014).

Berger et al. (2013) and Tanvir et al. (2013) have identified a macronova candidate associated with GRB 130603B. The macronova signal was detected, as predicted, in the IR band and it lasted less than 30 days.⁶ Berger et al. (2013) find that an ejecta with a mass of ${M}_{\mathrm{ej}}\quad =$ 0.05–0.08 ${M}_{\odot }$ and velocities of ${v}_{\mathrm{ej}}\quad \approx$ 0.1–0.3 c is needed⁷ to produce the observed signal. A second macronova candidate associated with the earlier event GRB 060614, has been recently discovered by Yang et al. (2015) who re-examined the data obtained with the Hubble Space Telescope (Gal-Yam et al. 2006) and found excess emission at the F814W band (see also Jin et al. 2015). Yang et al. find that it can be explained by a macronova with a significantly more massive ejecta, ${M}_{\mathrm{ej}}\quad =$ 0.03–0.1 ${M}_{\odot }$, with velocities of ${v}_{\mathrm{ej}}\quad \approx$ 0.1–0.2 c.

In search of a late-time radio emission originating from a forward shock in the ISM, as predicted by Nakar & Piran (2011), we obtained late-time radio observations of both GRB 130603B and GRB 060614. In the next section, we briefly describe the radio observations. In Section 3, we provide details of how the predictions of the radio signal are calculated. We compare our predictions with the results of our observations in Section 4, and briefly summarize in Section 5.

2.1. VLA Observations of GRB 130603B

2.2. ATCA Observations of GRB 060614

The interaction of the ejected mass with the ISM leads to a late-time (months to years) radio signal. The luminosity of the signal and the peak time depend both on the properties of the ejecta and of the ISM. At high frequencies, the signal is expected to peak once the ejecta starts to decelerate. This will occur when the ejecta plowed through sufficient ISM mass to slow it down, i.e., comparable to the ejecta mass. The deceleration radius and time, and the peak radio flux, are then simply defined by Nakar & Piran (2011).

In the magnetar scenario, the stable ns remnant formed in a binary ns merger is expected to have a typical rotational period of P ∼1 ms. The rotational energy of the ns is

$$\begin{eqnarray}&&{E}_{{\rm{rot}}}=\displaystyle \frac{I{(2\pi )}^{2}}{2{P}^{2}}\end{eqnarray} \tag{ 1 }$$

where I is the moment of inertia. For the above period, the rotational energy is $\approx 3\times {10}^{52}$ erg. Depositing this additional energy into an ejecta mass of ${10}^{-2}{M}_{\odot }$ will result in a relativistic outflow, leading to a stronger radio signal at late times. It is important to stress that our estimates are sensitive just to the magnetar period and not to its magnetic field. The total rotational energy of the magnetar is released and deposited in the ejecta on a timescale much shorter than the timescales that we consider here.

Adopting the above typical magnetar energy and assuming the ejecta mass and ISM density, the predicted radio light curves can be calculated using the Nakar & Piran (2011) formalism (see also Piran et al. 2013). However, there are two additional points that need to be treated more carefully. First, the peak flux is given assuming that the observed frequency is above the self-absorbed frequency. Second, Nakar & Piran address the case of non-relativistic ejecta and thus neglected relativistic effects.

The major relativistic effects on the observed flux are (1) relativistic time effects, (2) the Doppler shift, and (3) relativistic beaming¹⁰  (see, e.g., Piran 2004 for a review). These effects play important roles depending on the initial Lorentz factor. Roughly speaking, an observer will measure a brighter flux than those expected from Newtonian motion until the blast wave has sufficiently decelerated. The deceleration timescale, in the relativistic case, is shorter than the Newtonian one by a factor of ${{\rm{\Gamma }}}^{-8/3}$. The synchrotron frequency ${\nu }_{m}$ corresponding to ${\gamma }_{m}$ ¹¹ decreases with time. For an observed frequency ν that was initially below ${\nu }_{m}$ the flux peaks when $\nu ={\nu }_{m}$ at

$$\begin{eqnarray}&&{t}_{{\rm{peak}}}=\;120\;{\rm{days}}{\left(\displaystyle \frac{E}{3\cdot {10}^{52}\mathrm{erg}}\right)}^{1/3}{\left(\displaystyle \frac{{\epsilon }_{e}}{0.1}\right)}^{4/3}{\left(\displaystyle \frac{{\epsilon }_{B}}{0.1}\right)}^{1/3}\\ &&\qquad \quad {\times \left(\displaystyle \frac{\nu }{3{\rm{GHz}}}\right)}^{-2/3}.\end{eqnarray} \tag{ 2 }$$

where, E is the energy deposited in the ejecta, and ${\epsilon }_{B}$ and ${\epsilon }_{e}$ are the shock equipartition parameters of the magnetic field and electron energy, respectively. The peak flux at this time is

$$\begin{eqnarray}&&{F}_{\nu ,{\rm{peak}}}=\;8\;{\rm{mJy}}\left(\displaystyle \frac{E}{3\cdot {10}^{52}\mathrm{erg}}\right){\left(\displaystyle \frac{{\epsilon }_{B}}{0.1}\right)}^{1/2}{\left(\displaystyle \frac{n}{0.1{\mathrm{cm}}^{-3}}\right)}^{1/2}\\ &&\quad {\times \left(\displaystyle \frac{D}{{10}^{28}{\rm{cm}}}\right)}^{-2},\end{eqnarray} \tag{ 3 }$$

where D is the distance to the source, and n is the ISM density. The above estimates are valid when synchrotron self-absorption is negligible. The radio frequencies are often below the self-absorption frequency ${\nu }_{a}$. For ${\nu }_{m}\lt \nu \lt {\nu }_{a}$, the peak time (after the deceleration) is when $\nu ={\nu }_{a}$:

$$\begin{eqnarray}&&{t}_{{\rm{peak}}}=\;170\;{\rm{days}}{\left(\displaystyle \frac{E}{3\cdot {10}^{52}\mathrm{erg}}\right)}^{\frac{p+2}{3p+2}}{\left(\displaystyle \frac{{\epsilon }_{e}}{0.1}\right)}^{\frac{4(p-1)}{3p+2}}\\ &&\quad {\times \left(\displaystyle \frac{n}{0.1{\mathrm{cm}}^{-3}}\right)}^{\frac{4}{3p+2}}{\left(\displaystyle \frac{{\epsilon }_{B}}{0.1}\right)}^{\frac{p+2}{3p+2}}{\left(\displaystyle \frac{\nu }{3{\rm{GHz}}}\right)}^{\frac{-2(p+4)}{3p+2}},\end{eqnarray} \tag{ 4 }$$

and the peak flux is estimated as

$$\begin{eqnarray}&&{F}_{\nu ,{\rm{peak}}}=\;5\;{\rm{mJy}}{\left(\displaystyle \frac{E}{3\cdot {10}^{52}\mathrm{erg}}\right)}^{\frac{2p+3}{3p+2}}{\left(\displaystyle \frac{{\epsilon }_{e}}{0.1}\right)}^{\frac{5(p-1)}{3p+2}}\\ &&\qquad \quad {\times \left(\displaystyle \frac{n}{0.1{\mathrm{cm}}^{-3}}\right)}^{\frac{8-3p}{6p+4}}{\left(\displaystyle \frac{{\epsilon }_{B}}{0.1}\right)}^{\frac{p+4}{6p+4}}{\left(\displaystyle \frac{\nu }{3{\rm{GHz}}}\right)}^{\frac{5p-5}{3p+2}}\\ &&\qquad \quad {\times \left(\displaystyle \frac{D}{{10}^{28}{\rm{cm}}}\right)}^{-2}.\end{eqnarray} \tag{ 5 }$$

In order to account for the blast-wave dynamics in both relativistic and non-relativistic regimes, we follow the numerical procedures of Hotokezaka & Piran (2015). Note, that we do not directly use the approximate equations above, but perform a full numerical calculation. In short (see the following references for more details), the blast-wave expansion is determined by conservation of energy of the ejecta and swept-up material as $M{(R)({\rm{\Gamma }}\beta c)}^{2}=E$, in a similar way to Piran et al. (2013). Here M(R) is the sum of the ejecta mass and the mass of the swept-up ISM at a radius R. For a given blast-wave dynamics, we calculate the synchrotron radiation, using the fluid velocities and energy density just behind the shock. Then, at each observer time, we sum up the emission from each fluid element following Equation (4) of Granot et al. (1999a). This includes all relativistic propagation effects consistently and reproduces the light curves of Sari et al. (1998) in the ultra-relativistic limit and of Nakar & Piran (2011) in the non-relativistic limit. To account for synchrotron self absorption, we calculated the absorption coefficients based on Granot et al. (1999b). In addition, throughout our calculations, we adopt the following parameter values: ${\epsilon }_{e}=0.1$ and $p=2.5$.

Next, we calculate (following Hotokezaka & Piran 2015) the expected radio flare signature, using a range of values for E and n. We repeat the calculations using two distinct values for the microphysical parameter, ${\epsilon }_{B}$, i.e., ${\epsilon }_{B}=0.1$ and ${\epsilon }_{B}=0.01$. The expected radio signal was separately calculated for each of the macronova candidates at the frequencies in which they were observed. Our predictions of the radio signals are presented in Figure 1.

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Figure 2 shows examples of radio light curves specifically for the fiducial magnetar model with an energy of $E=3\times {10}^{52}$ erg and ejecta mass of ${M}_{{\rm{ej}}}=0.01,0.1\;{M}_{\odot }$ for various ISM density values. The relativistic effects alone shorten the peak time, compared to the Newtonian case, by a factor of ∼20 (for Γ = 3). Adding the effect of synchrotron self absorption, however, prolongs the peak time. Thus, the combined effect of synchrotron self absorption and relativistic motion on the peak time is only a factor of a few, compared to the Newtonian case. The peak flux can also vary by an order of magnitude. If we take the case of n = 0.1 as an example, the peak luminosity and time in the naive Newtonian case would have been $\approx 2\times {10}^{40}$ erg s⁻¹, and ≈930 days, compared to $\approx 4\times {10}^{41}$ erg s⁻¹, and ≈200 days, in the full relativistic calculation.

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As seen in Figure 1, we can rule out a large fraction of the E-n phase space for both GRB 130603B and GRB 060614. A main uncertainty in the determination of radio flare signals involves the external density of the ISM. The surrounding circumburst density is typically determined from the analysis of the GRB's afterglow. However, this determination typically suffers from numerous uncertainties and degeneracies between this density and other afterglow parameters (in particular, with ${\epsilon }_{B}$). For example, Fong et al. (2014) analyzed X-ray, optical, and radio observations of the afterglow of GRB 130603B. They find that the possible circumburst density ranges from 0.005 to $30\;{{\rm{cm}}}^{-3}$. This large range of uncertainty demonstrates the difficulty in estimating the density even when afterglow information is available in three bands. Xu et al. (2009) have analyzed the afterglow of GRB 060614. They find that a density of $0.04\;{{\rm{cm}}}^{-3}$ is consistent with the data, but they do not try to bracket it. The range of values of the ISM densities for both GRB 130603B and GRB 060614 are within the range that we have discussed here and are both sufficiently large to rule out the canonical magnetar model.

In light of the uncertainty in the ISM density and the microphysical parameters, we present in Figure 3 different areas in the ${M}_{{\rm{ej}}}-E$ phase space that can be ruled out for various ISM density and ${\epsilon }_{B}$ values. This large phase space, as in Figure 1, accounts not only for the magnetar scenario (discussed below) but also for the cases where there is no additional energy injection such as the "standard" non-relativistic macronova scenario presented in Nakar & Piran (2011).

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Assuming that a magnetar output energy is $3\times {10}^{52}$ erg, then even for a very low ISM density $n=0.001\;{{\rm{cm}}}^{-3}$ and for a relatively low energy conversion of shockwave energy to magnetic fields, ${\epsilon }_{B}\sim 0.01$, the expected radio signals at the time of our radio observations for both events are above our detection limits. Given that we did not detect any radio emission, this rules out the fiducial magnetar model for macronova events associated with GRBs.

It is worth mentioning that the above conclusion is based on the assumption of spherical symmetry. Deviations from spherical symmetry, that are expected, would somewhat reduce the signal and delay the peak time (Margalit & Piran 2015). However, this amounts only to about 10% difference in peak luminosity and a factor of ∼2 in peak time. We cannot rule out a magnetar with a large mass ejection ($\gt 0.1\;{M}_{\odot }$) in a low density environment by the absence of radio emission. The velocity of this large ejecta mass will be non-relativistic and is expected to produce weak emission below our detection limits (Figure 2). Other cases where the radio emission can be highly suppressed is an even more extreme case, where a minute amount of energy is converted in the shock to magnetic fields, i.e., ${\epsilon }_{B}\ll 0.001$. Atypical high ISM density will also lead to suppression of the radio signal because the optical depth will increase.

Compact binary mergers are expected to be followed by a macronova emission and long-lasting radio emission. In this paper, we have searched for this radio signal including the one that is predicted specifically by the magnetar scenario. In this latter case, a merger results in highly magnetized ns that deposits energy into a small amount of ejecta mass that becomes relativistic. If this relativistic ejecta interacts with an ISM that is not too dilute, it is expected to produce a bright radio emission that will peak over timescales of months to years.

Our search was focused on the two GRBs (GRB 130603B & GRB 060614) that were the first to exhibit macronova-like emission, thus indicating the ejection of a small amount of mass, a condition needed for the late production of a radio flare. Therefore, we have observed these GRB positions at late times with the VLA and the ATCA telescopes. Our radio observations resulted in null-detections. Comparing the predicted radio emission with our upper limits, we can rule out a wide range of kinetic energies, ejecta masses, ISM densities, and microphysical parameters. As shown in Figures 1–3, the range of parameters we rule out includes the canonical magnetar model.

A previous search for magnetar radio emission from sGRBs has been performed by Metzger & Bower (2014). They observed seven sGRBs within one to three years after the discovery using the VLA, but did not detect any emission. They used their non-detections to constrain the merger magnetar scenario as well. However, their work is different from ours in several ways. First, they have used the Newtonian calculations following Nakar & Piran (2011), but with $\beta =0.8$ and kinetic energy of $3\times {10}^{52}$ erg. Thus, they have not accounted for relativistic effects and did not explore a wide range of ejecta masses. Given these limitations and the lower observational sensitivities (due to the old capabilities of the VLA), Metzger & Bower (2014) only ruled out magnetar scenarios with densities above $n=0.03\;{\mathrm{cm}}^{-3}$. Our observed sample is also different since the sGRBs that we observed have been associated with macronova emission previously not observed in other sGRBs.

As discussed above, our conclusion is limited by several factors. While, we use a wide range of values for the model parameters, there are still extreme parameters under which the magnetar model is consistent with our observations. This includes extremely high (or low) ISM density, extremely low values ($\lt 0.001$) of ${\epsilon }_{B}$, and extremely small ejecta mass. These limitations, and the fact that we studied only two macronova events, provide further motivation to undertake a large campaign of carefully designed late-time radio observations of sGRBs.

We thank the ATCA and the VLA staff for promptly scheduling the observation of these targets of opportunity. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Research leading to these results has received funding from the EU/FP7 via ERC grant 307260; ISF, Minerva, and Weizmann-UK grants; as well as the I-Core Program of the Planning and Budgeting Committee and the Israel Science Foundation, and the Israel Space Agency. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020.