EARLY X-RAY AND OPTICAL AFTERGLOW OF GRAVITATIONAL WAVE BURSTS FROM MERGERS OF BINARY NEUTRON STARS

Mergers of neutron star/neutron star (NS–NS) binaries are strong sources of gravitational waves (e.g., Kramer et al. 2006). The upcoming advanced gravitational wave detectors such as Advanced LIGO (Abbott et al. 2009) and Advanced VIRGO (Acernese et al. 2008) are expected to expand the detection horizon to a few hundred Mpc for NS–NS mergers as early as 2015. Theoretical motivation (Eichler et al. 1989; Narayan et al. 1992; Rosswog et al. 2012) and observational progress (e.g., Gehrels et al. 2005; Barthelmy et al. 2005; Berger et al. 2005) suggest that at least some short gamma-ray bursts (SGRBs) may be related to NS–NS mergers. This hypothesis can be proved when both an SGRB and a gravitational wave burst (GWB) are detected in coincidence with each other in trigger time and direction. On the other hand, observations of SGRBs suggest that at least some of them are collimated (e.g., Burrows et al. 2006; De Pasquale et al. 2010). Since the strength of the gravitational wave signals does not sensitively depend on the orientation of the NS–NS merger orbital plane with respect to the line of sight, most GWBs would not be associated with SGRBs even if the SGRB–GWB association is established. Searching for electromagnetic counterparts of SGRB-less GWBs is essential to confirm the astrophysical origin of the GWBs, and to advance our understanding of the compact star merger physics. In the literature, an optical "macronova" (Li & Paczyński 1998; Kulkarni 2005; Metzger et al. 2010) due to decay of the ejecta launched during the merger⁴ and a long-lasting radio afterglow due to interaction between the ejecta and the ambient medium (Nakar & Piran 2011; Metzger & Berger 2012; Piran et al. 2012) have been predicted. Both are challenging to detect (Metzger & Berger 2012). Here we suggest another possible electromagnetic counterpart of GWBs. We argue that if the post-merger product is a short-lived massive NS rather than a black hole, an SGRB-less GWB could be followed by an early X-ray and optical afterglow extending for thousands of seconds. We provide observational hints of such a possibility in Section 2. In Section 3, we estimate the duration and brightness of the X-ray and optical afterglows, and discuss their detectability. A brief summary is given in Section 4.

There are two lines of reasoning to suspect that NS–NS mergers can produce a massive NS rather than a black hole, which may survive for an extended period of time of the observational interest. The first is along the line of the observations of NSs and NS–NS binaries in the Galaxy (see, e.g., Lattimer 2012 for a review). A secure lower limit of the maximum NS mass is set by PSR J1614−2230 (in an NS–WD binary) to 1.97  ±  0.04 M_☉ through a precise measurement of the Shapiro delay (Demorest et al. 2010). NSs with possibly even higher masses, albeit with large uncertainties, are also suggested. For example, the NS candidate in the X-ray binary 4U 1700−377 has a mass 2.44 ± 0.27 M_☉ (Rawls et al. 2011), and the NS in the NS–WD binary PSR B1516+02B has a mass 2.08 ± 0.19 M_☉ (Freire et al. 2008). A stiff equation of state (EOS) of neutron matter is demanded by the data. Although current data do not allow us to differentiate among various stiff EOS models, most of these stiff-EOS NS models predict a maximum NS mass close to or higher than 2.5 M_☉ for a non-rotating NS (Lattimer 2012). For rapidly spinning NSs that are likely relevant for the post-merger products, the maximum mass can be even higher due to a centrifugal support. On the other hand, the observations of the Galactic NS–NS systems suggest that the NS mass in these systems peaks at 1.35 M_☉, and the sum of the two NS masses for a significant fraction of the population is around 2.6 M_☉ (Lattimer 2012). Numerical simulations suggest that NS–NS mergers typically eject several percent solar masses (Rosswog et al. 2012). As a result, the post-merger products of at least a fraction (e.g., f_NS ∼ 0.5) of NS–NS merger events should have a total mass below the maximum NS mass of a rapidly spinning NS. This NS would not collapse until losing a significant amount of angular momentum within the characteristic spin-down timescale. Such a possibility was suggested by Dai et al. (2006) and Gao & Fan (2006) to interpret X-ray flares and plateaus following SGRBs, and is now strengthened by additional data.

The second line of reasoning is based on the observations of the SGRB X-ray afterglows. The most direct evidence of a spinning-down object at the SGRB central engine is in GRB 090515 detected by Swift (Rowlinson et al. 2010). After a short prompt emission phase lasting for T₉₀ = 0.036 ± 0.016 s, the burst showed an X-ray plateau that lasted for ∼240 s, after which the flux declines rapidly, and became undetectable by X-ray Telescope (XRT) at ∼500 s after the trigger (Rowlinson et al. 2010). Such a steady plateau with rapid decline would be a signature of a magnetar at the central engine (Zhang & Mészáros 2001; Troja et al. 2007). Even though no redshift measurement was made for this burst, an analysis suggests that the presumed heavy NS has parameters consistent with a magnetar for a reasonable redshift range (Rowlinson et al. 2010). A later systematic analysis of Swift SGRB X-ray light curves suggests that a significant fraction of SGRBs have evidence of an X-ray plateau followed by a steep drop in flux, which is consistent with a magnetar central engine (Rowlinson & O'Brien 2012). If SGRBs are associated with NS–NS mergers, it is likely that a millisecond magnetar survived in these SGRBs.

Another indirect piece of evidence is X-ray flares following some SGRBs (Barthelmy et al. 2005). A possible interpretation is the magnetic activity of a differentially rotating massive NS after an NS–NS merger (Dai et al. 2006). If the magnetic field strength of this post-merger massive NS is not too high (similar to that of normal pulsars), the magnetic activity of the NS has the right timescale and luminosity to account for X-ray flares.

At least some SGRBs are collimated (Burrows et al. 2006; De Pasquale et al. 2010). For the standard X-ray afterglow component (that originates from the external shock of the SGRB jet), the afterglow jet opening angle is believed to be comparable to the prompt emission jet opening angle, so that a GWB without an SGRB association would have a very faint "orphan" afterglow peaking at a time when the jet is decelerated enough so that the 1/Γ cone enters line of sight. The prospects of detecting such an SGRB orphan afterglow are poor. Here we suggest that the afterglow powered by a rapidly spinning massive NS has a much wider solid angle than the solid angle of the SGRB jet, so that SGRB-less GWBs can also have a bright afterglow from a dissipating proto-magnetar wind with a large solid angle. At the base of the central engine (light cylinder), the wind launched from the millisecond magnetar is essentially isotropic. Numerical simulations suggest that this proto-magnetar wind from an NS–NS merger progenitor would be collimated by the ejecta launched during the merger process, but with a much larger angle, 30°–40°, than the case of a massive-star core-collapse progenitor (Bucciantini et al. 2012). This is much larger than the jet opening angle inferred from the afterglow modeling of some SGRBs (Burrows et al. 2006; De Pasquale et al. 2010). A wider solid angle of proto-magnetar wind than the GRB jet angle was also inferred from an analysis of the magnetar engine candidates for long GRBs (Lyons et al. 2010).

In the following, we adopt the ansatz that some NS–NS mergers produce a massive magnetar. The proto-magnetar wind is essentially isotropic at the base, with a wide solid angle θ_{w, 1} ∼ 40° for a free wind (with a beaming factor f_{b, w, 1} = ΔΩ_{w, 1}/4π ∼ 0.2) and an even larger solid angle ΔΩ_{w, 2} in the equatorial direction for a confined wind that pushes the heavy ejecta launched during the merger phase (with a beaming factor f_{b, w, 2} = ΔΩ_{w, 2}/4π ∼ 0.8, so that the total beaming factor is f_{b, w} = f_{b, w, 1} + f_{b, w, 2} ∼ 1). This hypothesis applies regardless of whether the GWB is associated with an SGRB. If there is a GWB/SGRB association, we expect that SGRB jets have a much smaller solid angle. For example, if the typical SGRB jet opening angle is θ_j ∼ 10°, one has the jet beaming factor f_{b, j} = ΔΩ_j/4π ∼ 0.015, so that ΔΩ_j ≪ ΔΩ_{w, 1} < ΔΩ_{w, 2}.

The NS–NS merger event rate is very uncertain. The rate inferred from the Galactic NS–NS systems has a wide range 2–2 × 10⁴ Gpc⁻³ yr⁻¹ (Phinney 1991; Kalogera et al. 2004; Abadie et al. 2010). This is consistent with the upper limit 2 × 10⁵ Gpc⁻³ yr⁻¹ set by the current non-detection with the last LIGO and VIRGO run (Abbott et al. 2009). Within the advanced LIGO horizon ∼300 Mpc, the NS–NS merger rate (and therefore GWB rate) would be R_GWB ∼ (0.2–2000) yr⁻¹. Among these, R_GWB-ag ∼ (0.1–1000)(f_NS/0.5)(f_{b, w}) yr⁻¹ would have strong afterglow emission associated with the proto-magnetar wind, most of which would not have an SGRB association, since the line of sight is outside the SGRB cone even if there is an SGRB/GWB association.

After the merger, the proto-NS is initially very hot and cools via neutrino emission. After about 10 s, the NS is cooled enough so that a Poynting-flux-dominated outflow can be launched (Usov 1992; Metzger et al. 2011). It will be spun down by magnetic dipole radiation and by the torque of a strong electron–positron pair wind flowing out from the magnetosphere. Since before the merger the two NSs are in the Keplerian orbits, the post-merger product should be near the breakup limit. We take P₀ = 1 ms P_{0, −3} as a typical value of the initial spin period of the proto-magnetar. An uncertain parameter is the polar-cap magnetic field of the dipole magnetic field component, B_p, which depends on whether the α − Ω dynamo is efficiently operating, and on the magnetic field strength of the parent NSs if the dynamo mechanism is not efficient. Given nearly the same amount of the total rotation energy E_rot = (1/2)IΩ²₀ ∼ 2 × 10⁵² erg I₄₅ (Ω₀ = 2π/P), the luminosity and hence the afterglow flux critically depend on B_p. As a rough estimate, we apply the dipole spin-down formula. Correcting for the beaming factor f_w and the efficiency factor η_x to convert the spin-down luminosity to the observed X-ray luminosity in the detector band, one gets

$$\begin{eqnarray} F_x & = & \frac{\eta _x L_{{\rm sd}}}{4 \pi f_{b,w} D_L^2} \simeq 2\times 10^{-8}\, {\rm erg\, s^{-1}\, cm^{-2}} \nonumber \\ && \times \eta _{x,-2} f_{b,w}^{-1} \left(\frac{D_L}{300\, {\rm Mpc}} \right)^{-2}\, I_{45}\, P_{0,3}^{-2}\, T_{{\rm sd},3}^{-1}, \end{eqnarray} \tag{ 1 }$$

where L_sd = IΩ²₀/(2T_sd) is the characteristic spin-down luminosity, and

$$\begin{equation} T_{{\rm sd}} \simeq 2\times 10^3\, {\rm s}\, I_{45}\, B_{p,15}^{-2}\, P_{0,-3}^2\, R_6^{-6} \end{equation} \tag{ 2 }$$

is the characteristic spin-down timescale. Here I = 10⁴⁵I₄₅ is the moment of inertia (typical value I₄₅ = 1.5 for a massive NS), R = 10⁶R₆ is the radius of the NS, and the convention Q_x = Q/10^x has been adopted. Here we have assumed that a good fraction (η_x ∼ 0.01) of spin-down energy is released in the X-ray band. This is based on the following two considerations: first, some SGRBs indeed have a bright X-ray plateau that is likely due to the magnetar spin-down origin (Rowlinson et al. 2010; Rowlinson & O'Brien 2012), which suggests that the main energy channel of releasing the magnetic dissipation energy is in the X-ray band; second, a rough theoretical estimate shows that the typical energy band of a dissipating magnetized wind could be in X-rays.

We consider two mechanisms to dissipate the magnetar wind energy to radiation. (1) In the free wind zone with solid angle ΔΩ_{w, 1}, one may consider a magnetized wind with a luminosity L_w and magnetization parameter σ(R) dissipated at a radius R from the central engine. Assuming that the magnetic energy is abruptly converted to the internal energy of power-law distributed electrons (such as in the scenario of the ICMART model), one can generally estimate the typical synchrotron energy as (Zhang & Yan 2011) E_p ≃ 320 keV L^1/2_{w, 48} R⁻¹₁₅ η_{x, −2}^3/2 σ²₄. A cooled-down proto-magnetar typically has σ₀ ∼ 10⁹ at the central engine (Metzger et al. 2011). A magnetized flow can be quickly accelerated to Γ ∼ σ^1/3₀ ∼ 10³ at R₀ ∼ 10⁷ cm, where σ ∼ σ^2/3₀ ∼ 10⁶ (Komissarov et al. 2009). After this phase, the flow may still accelerate as Γ∝R^1/3, with σ falling as ∝R^−1/3 (Drenkhahn & Spruit 2002). At R ∼ 10¹⁵ cm, one has σ ∼ 2 × 10³, so that E_p ∼ 15 keV, which is in the X-ray band. (2) One can also consider the confined magnetar wind zone with solid angle ΔΩ_{w, 2} where the magnetar wind is expanding into a heavy ejecta launched during the merger process.⁵ The magnetic energy may be rapidly discharged upon interaction between the wind and the ejecta, which occurs at a radius R ∼ vt_delay = 3 × 10¹⁰ cm(v/0.1c)t_{delay, 1}, where v ∼ 0.1c is the speed of ejecta, and t_delay ∼ 10 s is the delay time between the merger and the launch of a high-σ magnetar wind. The Thomson optical depth for a photon to pass through the ejecta shell is τ_th ∼ σ_TM_ej/(4πR²m_p) ∼ 7 × 10⁸(M_ej/(0.01 M_☉)) ≫ 1. Thus the spectrum of the dissipated wind is thermal-like. One can estimate the typical energy ∼k(L_w/4πR²σ)^1/4 ∼ 5 keV L^1/4_{w, 49}(R/(3 × 10¹⁰ cm))^−1/2, which is also in the X-ray band.

One can see that the X-ray band flux of the early afterglow (Equation (1)) is very high, well above the sensitivity threshold of Swift XRT (Moretti et al. 2007):

$$\begin{equation} F_{x,{\rm th}} = 6 \times 10^{-12}\, {\rm erg\, s^{-1}\, cm^{-2}} T_{\rm obs,2}^{-1}, \end{equation} \tag{ 3 }$$

where T_obs is the observation time. The light curve is expected to be flat (a plateau) lasting for a duration T_sd followed by a t⁻² decay. However, since the NS spins down quickly in the t⁻² regime, it is likely that it would lose centrifugal support and collapse to a black hole shortly after the end of the plateau. In this case, essentially all the materials collapse into the black hole, without substantial accretion afterward. The light curve then shows a very sharp drop in flux at the end of the plateau, similar to what is seen in GRB 090515 (Rowlinson et al. 2010).

The challenge to detect such a bright X-ray afterglow following a GWB is its short duration (Equation (2)) and the large error box of a GWB trigger. This requires a Swift-like space detector for quick slew, but the error box of the GWB trigger, typically a few tens to a hundred square degrees (Abadie et al. 2012), is much larger than the XRT field of view (0.16 deg²). How to efficiently search for the bright X-ray source within T_sd in such a large sky area is challenging. Even though some strategies using Swift have been proposed (Kanner et al. 2012), the current searches for the GWB afterglow typically happen about half-day after the GWB trigger (Evans et al. 2012). The problem can be alleviated if B_p of the proto-NS is weaker. For example, even for a typical pulsar field B_p ∼ 10¹² G (Dai & Lu 1998; Dai et al. 2006), the X-ray luminosity can be still as high as 5 × 10⁻¹¹ erg s⁻¹ cm⁻² for detection, while the duration of the plateau extends to T_sd ∼ 2 × 10⁷ s. This would give enough time to search for the X-ray afterglow. However, strong magnetic fields are likely generated during the merger events (Price & Rosswog 2006). One very likely has to face the large-error-box, short-duration problem. An ideal strategy to observe this early afterglow is to design a large field-of-view imaging X-ray telescope, preferably with fast-slewing capability. Such a telescope, even with a moderate sensitivity, can catch the bright early X-ray afterglows of SGRB-less GWBs. The new mission concept ISS-Lobster (Gehrels et al. 2012) invokes an X-ray wide-field imager with a 0.5 sr field of view that covers ∼50% of the sky every 3 hr, which is ideal to detect this bright X-ray afterglow.

The optical flux of the proto-magnetar wind is subject to uncertainties. In the free wind zone (solid angle ΔΩ_{w, 1}), the emission spectral shape is synchrotron. If one has the standard F_ν∝ν^1/3 synchrotron spectrum below E_p, the specific X-ray flux at 1 keV F_ν(X) ∼ 4 mJy would correspond to an R-band magnitude 17. This would be an optimistic estimate of the optical brightness. For the confined wind zone (solid angle ΔΩ_{w, 2}), the spectrum of a dissipating wind is quasi-thermal, and the optical flux is greatly suppressed. Indeed, no bright optical emission was detected during the plateau phase of GRB 090515 (Rowlinson et al. 2010), suggesting that the optical emission of a dissipative proto-magnetar wind is suppressed. Nonetheless, the interaction between the magnetar wind and the ejecta in the confined wind zone can give very interesting radiation signatures in the optical band (Gao et al. 2013). Wide-field optical telescopes are essential to search for such optical GWB afterglows in the large GWB error box.

The gravitational wave signals from these GWBs have an interesting signature: after the standard chirp signal during the in-spiral and merger phases (Flanagan & Hughes 1998; Kobayashi & Mészáros 2003), there should be an extended GW emission episode afterward due to a secular bar-mode instability of the newly formed proto-magnetar (Corsi & Mészáros 2009). The signature is in the advanced LIGO frequency band and in principle can be detected. Jointly detecting such a GW signal along with the X-ray afterglow would give an unambiguous identification of the proto-magnetar nature of the central engine.

Some SGRBs are followed by an extended emission, which sometimes can be very bright (e.g., Gehrels et al. 2006). It is unclear whether the extended emission shares the same solid angle with the short hard spikes. If it has a wider solid angle than the short hard spike emission, as expected in the magnetar engine scenario (e.g., Metzger et al. 2008), then such a bright extended emission (lasting ∼100 s) can be also associated with SGRB-less GWBs. This emission is brighter than the X-ray afterglow emission discussed above, and can be readily detected by wide-field imagers such as ISS-Lobster.

We have proposed another electromagnetic counterpart of GWBs from NS–NS mergers. It applies to the cases when the two NSs are not very massive (as observed in Galactic double NS systems), so that the post-merger product has a mass below the maximum mass of a rapidly spinning NS. We show that such a scenario is plausible in view of the observations of Galactic NSs, NS–NS systems, and SGRB afterglows. The proto-magnetar would eject a wide-beam wind, whose dissipation would power an X-ray afterglow as bright as ∼(10⁻⁸–10⁻⁷) erg s⁻¹ cm⁻². The duration is typically 10³–10⁴ s, depending on the strength of the dipolar magnetic fields. It is challenging to detect the X-ray afterglow with the current facilities such as Swift, but a wide-field X-ray imager (such as ISS-Lobster) would be ideal to catch this bright X-ray signal. The optical afterglow flux is subject to large uncertainties, but could be as bright as 17th magnitude in R band. Prompt, deep optical follow-up observations of GWBs are desirable. The detection of these signals would confirm the astrophysical origin of GWBs, and shed light into the physics of NS–NS mergers and the NS EOS.

I thank a Cheung Kong Scholar fellowship in China, the hospitality of the KIAA and Department of Astronomy of Peking University, and the sabbatical committee of the UNLV faculty senate for providing me an ideal working environment to conduct research efficiently. I thank Xue-Feng Wu, He Gao, Zi-Gao Dai, and Yi-Zhong Fan for stimulative discussions, and Kunihito Ioka, Elenora Troja, and an anonymous referee for helpful comments. This work is partially supported by NSF AST-0908362.