ELECTROMAGNETIC COUNTERPARTS TO BLACK HOLE MERGERS DETECTED BY LIGO

The detection of the gravitational wave (GW) source GW150914 by the Laser Interferometer Gravitational Wave Observatory (LIGO) was interpreted as the merger of a black hole (BH) binary whose members have masses of ${M}_{1}={36}_{-4}^{+5}{M}_{\odot }$ and ${M}_{2}={29}_{-4}^{+4}{M}_{\odot }$ (Abbott et al. 2016). The GW signal exceeded the background noise level of LIGO for the last ∼0.2 s of the merger when the BH binary separation was shorter than $\sim 10{GM}/{c}^{2}$, where $M=({M}_{1}+{M}_{2})$. A merger of two BHs in vacuum is expected to have no electromagnetic counterpart. But nature is sometimes more imaginative than we are.

The Gamma-ray Burst Monitor (GBM) on board the Fermi satellite reported the detection of a transient signal at photon energies $\gt 50$ keV that lasted 1 s and appeared 0.4 s after the GW signal (Connaughton et al. 2016). The GBM signal encompasses 75% of the probability map associated with the LIGO event localization on the sky.

Below we explore the possibility that the GW and Gamma-Ray Burst (GRB) signals originated from a common origin, namely a single, rapidly rotating, massive star.¹ As the core of the star collapsed, it broke into two clumps in a dumbbell configuration. The two clumps collapsed separately into two BHs which eventually merged due to GW emission. The GRB was produced from an outflow generated by the merging BHs or from a jet emanating out of the accretion disk of residual debris around the BH remnant, similarly to the collapsar model of long-duration GRBs (Woosley 1993; MacFadyen & Woosley 1999). The mass accreted during the inspiral must have been a small fraction of M given the good match between the observed LIGO signal and the theoretical GW template for a BH binary in vacuum. The low accretion rate during the inspiral is naturally explained by the clearing of a central cavity that is expected for a circumbinary disk around a binary BH system (Hayasaki et al. 2008; Cuadra et al. 2009; Colpi & Dotti 2009; Hayasaki 2011; Kocsis et al. 2012; Farris et al. 2015).

The Fermi-GBM detection was not reproduced by the INTEGRAL satellite (Savchenko et al. 2016). The a posteriori nature of the GW150914-GBM detection raises additional concerns about its reality. With many more LIGO events expected in the future, it would be straightforward to test whether GRBs are a common by-product of BH-BH mergers. The mechanism considered in this letter offers motivation for conducting a systematic search for GRB counterparts to all LIGO sources.

The prevailing collapsar paradigm for long-duration GRBs involves the collapse of the core of a massive star to a single BH (Woosley 1993). In order to produce a GRB outflow, the infalling matter must have a sufficiently high specific angular momentum, $j\gtrsim 3\times {10}^{16}\;{\mathrm{cm}}^{2}\;{{\rm{s}}}^{-1}$ (MacFadyen & Woosley 1999), so that its centrifugal barrier lies outside the innermost stable circular orbit (ISCO) around the BH.

To explain the coincidence between a GRB and GW150914 as well as the full temporal window during which LIGO detected a GW signal, we hypothesize that a BH binary formed during the collapse of a rapidly rotating star with an initial orbital radius of ${R}_{b}\gtrsim 10{GM}/{c}^{2}\sim {10}^{8}\;{\rm{cm}}$ (corresponding to a binary separation of 2R_b for ${M}_{1}\sim {M}_{2}$). The centrifugal barrier of the infalling matter is outside this radius as long as,

$$\begin{eqnarray}&&j={({{GMR}}_{b})}^{1/2}\gtrsim \sqrt{10}\displaystyle \frac{{GM}}{c}\sim {10}^{18}\;{\mathrm{cm}}^{2}\;{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 1 }$$

Given that the core of the star needs to be more massive than $M={65}_{-8}^{+9}{M}_{\odot }$, the progenitor must be a massive star with a total mass that exceeds $100{M}_{\odot }$. A natural path to making such a star would be the merger of two less massive stars that are born in a tight binary. Each of the parent stars could have had a helium core with a mass below $35{M}_{\odot }$, avoiding the pulsational pair instability that is capable of dispersing the core (Heger & Woosley 2002; Woosley et al. 2007; Woosley & Heger 2015). Once the two stars merge, the merger product will be endowed with rapid rotation.

There is strong evidence that single massive stars often originate from the merger of two lower-mass stars (de Mink et al. 2014; de Mink 2015). The stellar evolution of the merger product is significantly different from the standard evolution of an isolated star due to the chemical mixing and rapid rotation that result from the merger (de Mink et al. 2014; Hwang et al. 2015; Mandel & de Mink 2015). The channel envisioned here for the birth of BH binaries within the core of a single massive star could be realized in only a small fraction of all massive stars and still be within the wide range of BH-BH merger rates that are consistent with the detection of GW150914 (LIGO & Virgo 2016b).

Very massive stars of mass ${M}_{\star }\gtrsim 100{M}_{\odot }$ are dominated by radiation pressure and hence their luminosity is close to the Eddington limit (Bond et al. 1984; Bromm et al. 2001; Loeb & Furlanetto 2013),

$$\begin{eqnarray}&&{L}_{E}=1.3\times {10}^{40}\times \left(\displaystyle \frac{{M}_{\star }}{100{M}_{\odot }}\right)\;\;\mathrm{erg}\;{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 2 }$$

Since their effective surface temperature, ${T}_{s}\sim {10}^{5}\;{\rm{K}}$, has only a weak dependence on mass (Bromm et al. 2001), their radii are approximately given by (Loeb & Furlanetto 2013),

$$\begin{eqnarray}&&{R}_{\star }={\left(\displaystyle \frac{{L}_{E}}{4\pi \sigma {T}_{s}^{4}}\right)}^{1/2}\approx 4.3\times {10}^{11}{\left(\displaystyle \frac{{M}_{\star }}{100{M}_{\odot }}\right)}^{1/2}\;{\rm{cm}},\end{eqnarray} \tag{ 3 }$$

where σ is the Stepfan–Boltzmann constant. To remain gravitationally bound, the stars must have a specific angular momentum that is significantly lower than

$$\begin{eqnarray}&&{j}_{{\rm{max}}}\;=\;{({{GM}}_{\star }{R}_{\star })}^{1/2}=7.6\times {10}^{19}{\left(\displaystyle \frac{{M}_{\star }}{100{M}_{\odot }}\right)}^{3/4}\;{\mathrm{cm}}^{2}\;{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 4 }$$

Assuming hydrostatic equilibrium and electron scattering opacity, one can show that very massive stars are convectively unstable (see Appendix of Loeb & Rasio 1994). With elastic isotropic scattering of the convective blobs, the star would admit solid body rotation (although differential rotation is expected for more realistic cases; see Kumar et al. 1995). For a fixed rotation frequency Ω, the specific angular momentum would have the profile $j={\rm{\Omega }}{r}^{2}$, with r being the cylindrical radius from the rotation axis. The constraint in Equation (1) can therefore be rewritten as

$$\begin{eqnarray}&&\displaystyle \frac{{j}_{s}}{{j}_{{\rm{max}}}}\gtrsim 1.3\times {10}^{-2}{\left(\displaystyle \frac{{R}_{c}}{{R}_{\star }}\right)}^{-2}{\left(\displaystyle \frac{{M}_{\star }}{100{M}_{\odot }}\right)}^{-3/4},\end{eqnarray} \tag{ 5 }$$

where ${j}_{s}\equiv {\rm{\Omega }}{R}_{\star }^{2}$ and ${R}_{c}\gtrsim 0.1{R}_{\star }\gg {R}_{b}\sim {10}^{8}\;{\rm{cm}}$ is the radius of the core that collapses to make the BH binary. We therefore conclude that the progenitor star must have been rapidly rotating, not much below its break-up frequency.

A rapidly rotating progenitor would be the natural outcome of the merger between two stars in a tight binary system with a common envelope. As discussed above, the merger of a binary star system is a common channel for producing a progenitor star of the needed mass to explain GW150914 (de Mink et al. 2014; de Mink 2015). Ejection of the hydrogen envelope during the merger would be needed, since a red supergiant envelope would choke the BH jet and suppress the appearance of a short GRB. In addition, the restriction on a weak mass loss through a stellar wind (to maintain a high progenitor mass) during nuclear burning would favor a progenitor of low metallicity. The evolution of this progenitor star would be non-standard due to its rapid rotation and anomalous chemical composition and stratification after its evolutionary clock was reset by the merger, similarly to blue stragglers (Sills et al. 2001). The star would evolve by burning hydrogen into heavier elements up to iron, and eventually develop a layered core structure that loses pressure support and collapses. During the burning stages, the central region of the star would contract, spin more rapidly, and develop strong differential rotation.

In our model, the BH binary forms out of the collapse of a rapidly rotating helium core of more than $\sim 65{M}_{\odot }$ (but less than twice this value to avoid pair instability), which surrounds an iron core of more than $\sim 5{M}_{\odot }$ in hydrostatic equilibrium before the collapse. Furthermore, rapid rotation is needed to stabilize the core against an explosion. The specific angular momentum of the iron core needs to exceed a few times ${10}^{17}\;{\mathrm{cm}}^{2}\;{{\rm{s}}}^{-1}$ in order for it to fission into two clumps. After its collapse, the iron core would form a flattened, rapidly rotating configuration that cools through neutrino emission. The resulting disk-like structure is unstable to the formation of a bar that breaks into two clumps. Each clump collapses to a BH and the BHs grow in mass by accreting most of the surrounding carbon and oxygen core within a free fall time of about a minute after their formation. If the two BHs achieve their final masses of $\sim 30\;{M}_{\odot }$ at a separation a, their subsequent merger time due to the emission of GWs would be ${t}_{{\rm{GW}}}\sim 4\;{\rm{minute}}\quad \times {(a/5\times {10}^{8}{\rm{cm}})}^{4}$. Additional accretion of core material onto the remnant BH would lead to the formation of the GRB jet. The strong dependence of the GW merging time on clump separation implies that only a subset of all rapidly rotating massive stars might have the conditions that lead to the birth of a $\sim (30{M}_{\odot }+30{M}_{\odot })$ BH binary followed by a GRB jet, as in GW150914-GBM. Many more cases may lead to a GRB without a GW signal or to a GW signal with a choked GRB. The deposition of jet energy in the envelope of the star will likely lead to a supernova explosion.

The appearance of a dumbbell configuration in a collapsing, rapidly rotating system was considered in the literature as a path toward the formation of common envelope massive star binaries through fission (New & Tohline 1997; Tohline 2002) as well as binaries of supermassive BHs from the collapse of supermassive stars (Reisswig et al. 2013). In particular, the general relativistic simulation of Reisswig et al. (2013) demonstrated that a rapidly differentially rotating star without nuclear burning could produce a bar that breaks into two clumps of comparable masses, consistently with the similarity between M₁ and M₂ in GW150914. Efficient neutrino cooling or magnetohydrodynamic processes are required to enable rapid collapse of each clump to a BH (Di Matteo et al. 2002; Liu et al. 2015). The formation of a disk (Fryer et al. 2001) may represent an intermediate step before the bar instability and clump formation identified by the simulations of Reisswig et al. (2013).

An alternative path to forming a BH binary inside the envelope of a massive star would involve maintaining the identity of the two helium cores of the merging progenitor stars as they orbit each other and collapse separately into two BHs surrounded by a common envelope. As the orbit of the resulting binary BH shrinks due to GW emission, residual matetial may accrete to make the GRB jet. However, it is unclear whether the highly super-Eddington accretion rate required by a GRB can be achieved in this case.

The LIGO limits on the spin amplitude of the two BHs are rather weak (${a}_{1}\lt 0.69\pm 0.05$ and ${a}_{2}\lt 0.88\pm 0.10$). The final spin of the remnant BH inferred by LIGO is ${0.67}_{-0.07}^{+0.05}$, but the subsequent accretion of matter could endow it with additional spin and promote the production of a GRB outflow.

A massive BH binary is expected to eventually clear a central cavity of twice its semimajor axis in the surrounding circumbinary disk (Hayasaki et al. 2008; Colpi & Dotti 2009; Cuadra et al. 2009; Hayasaki 2011; Kocsis et al. 2012; Farris et al. 2015). The delay in filling up this cavity after the BHs' final plunge inside the ISCO would be of order the ISCO dynamical time, which is much shorter than the 0.4 s delay between the GRB and GW150914. For a progenitor star in the mass range ${M}_{\star }={10}^{2}$–${10}^{3}{M}_{\odot }$, most of the observed 0.4 s delay can be accounted for by the neutrino cooling timescale or by the extra time it takes the GRB jet to cross the star relative to GWs for a jet Lorentz factor in the range $\gamma \sim 4$–7.

We described a novel mechanism for a prompt electromagnetic counterpart to the merger of stellar-mass BH binaries, such as GW150914. The proposal was motivated by the Fermi GBM detection of a γ-ray transient 0.4 s after GW150914 (Connaughton et al. 2016). Even if these two signals are unrelated, the possible existence of electromagnetic counterparts to BH mergers at cosmological distances argues in favor of sending LIGO alerts for follow-up observations by radio, infrared, optical, UV, X-ray and γ-ray telescopes.

The inferred GRB luminosity for GW150914-GBM (at photon energies between 1 keV and 10 MeV) of ${1.8}_{-1.0}^{+1.5}\times {10}^{49}\;\mathrm{erg}\;{{\rm{s}}}^{-1}$ and its measured duration of 1 s (Connaughton et al. 2016) are significantly lower than their typical values in long-duration GRBs (Meszaros & Rees 2014). The observed GRB may be just one spike in a longer and weaker transient below the GBM detection threshold. The weakness of the burst could be attributed to the extended envelope of the very massive progenitor star, from which the GRB outflow just barely managed to escape (Bromberg et al. 2012, 2013). For this to work, the BH activity must have persisted for roughly the light crossing time of the star, $\sim 14{({M}_{\star }/100{M}_{\odot })}^{1/2}$ s. In particular, the low GRB luminosity could have resulted from a broader than usual opening angle of the GRB outflow as it slowed down and widened just before exiting the stellar envelope. A broad GRB outflow brings the added benefit of removing the need for a rare alignment between the line of sight and the central axis of the outflow. The parameter fit of LIGO disfavored orientations where the orbital angular momentum of the BH binary is misaligned with the line of sight (see Figure 2 in LIGO & Virgo 2016a).

The main advantage of the single star origin for GW150914-GBM is that it naturally provides a high infall rate of gas around the merging BHs. The γ–ray luminosity of GW150914-GBM corresponds to a mass infall rate of $\sim 1/(\epsilon /{10}^{-5}){M}_{\odot }\;{{\rm{s}}}^{-1}$, where is the efficiency of converting accreted mass to the observed γ-rays. An accretion from a long-lived disk (e.g., originating from the tidal disruption of an ordinary star) around the BH binary would be typically limited to the Eddington luminosity (Kamble & Kaplan 2013), which for a binary mass of $M\sim 65{M}_{\odot }$ amounts to $\sim {10}^{40}\;\mathrm{erg}\;{{\rm{s}}}^{-1}$, a factor of $\sim {10}^{9}$ lower than the inferred γ-ray luminosity in GW150914-GBM.

A future detection of a GRB afterglow would allow to determine the redshift and precise localization of the GW source (but see the upper limits in Smartt et al. 2016; Soares-Santos et al. 2016). Since LIGO detected GW150914 only shortly after starting to collect data at its improved sensitivity, it will likely detect many similar events during its future operation. A population of standard GW sirens with GRB redshifts would provide a new path for measuring cosmological distances as a function of redshift to a high precision (Holz & Hughes 2005; Nissanke et al. 2013).

Numerical simulations are required to better characterize the detailed hydrodynamics and neutrino cooling associated with a binary BH formation through a dumbbell configuration during the collapse of the core of a massive star. Magnetic fields could also play an important role in transporting angular momentum and mediating the collapse of the two clumps.

I thank Peter Edmonds, Dani Maoz, Ramesh Narayan, Fred Rasio, Martin Rees, Amiel Sternberg and especially the referee Stan Woosley for insightful comments on the manuscript (with any remaining errors being all mine), and my family for giving me freedom to write this paper over a holiday weekend. This work was supported in part by the NSF grant AST-1312034.