Dual Jets from Binary Black Holes
Supermassive black holes are found at the centers of most galaxies and their inspiral is a natural outcome when galaxies merge. The inspiral of these systems is of utmost astrophysical importance as prodigious producers of gravitational waves and in their possible role in energetic electromagnetic events. We study such binary black hole coalescence under the influence of an external magnetic field produced by the expected circumbinary disk surrounding them. Solving the Einstein equations to describe the spacetime and using the force-free approach for the electromagnetic fields and the tenuous plasma, we present numerical evidence for possible jets driven by these systems. Extending the process described by Blandford and Znajek for a single spinning black hole, the picture that emerges suggests the electromagnetic field extracts energy from the orbiting black holes, which ultimately merge and settle into the standard Blandford-Znajek scenario. Emissions along dual and single jets would be expected that could be observable to large distances.
Introduction: Among the most spectacular of astrophysical events are observations of tremendous amounts of energy careening out along highly collimated jets from a localized central region. Within this central region is the engine behind the jets, generally believed to be a spinning black hole which helps to convert binding and rotational energy into kinetic and thermal energy of the surrounding plasma (see e.g. Blandford (2002)). This basic picture is widely accepted, but a detailed understanding of these systems remains elusive in part due to the inability of detecting clean electromagnetic signals from the depths of the central engine. Such understanding is particularly needed to understand phenomena such as gamma ray bursts and AGNs, which radiate a tremendous amount of energy and, in some cases, are thought to play a fundamental role in the formation and evolution of massive galaxies Bower et al. (2006).
In addition to intense efforts in various electromagnetic bands, observations in the gravitational wave band will soon be added. Because gravitational waves propagate essentially unscattered through the universe and are most strongly produced in highly dynamical regions of strong spacetime curvature, their observation promises to open up a new complementary window to the universe, allowing for multi-messenger astronomy Thorne (1997); Sathyaprakash and Schutz (2009). Astrophysical systems expected to be bright in both gravitational and electromagnetic spectrums are therefore attracting intense attention.
A particularly interesting scenario involves the merger of a supermassive binary black system which could be observable with LISA to redshifts up to and beyond Vecchio (2004). Such a system is expected as a natural consequence of galaxy mergers, whose individual black holes eventually settle into an orbit sufficiently tight that the binary’s subsequent dynamics is governed by the gravitational radiation timescale and disconnected from the properties of the disk Milosavljevic and Phinney (2005). As they orbit, they emit gravitational waves which carry off both energy and angular momentum, driving the black holes to merger producing bright gravitational waves. The expected gravitational wave signals from such a system, their impact on gravitational searches and their exploitation for physics mining through data analysis are now well understood thanks to concentrated efforts on the analytical and numerical fronts (see e.g. Aylott et al. (2009) and references cited therein). Such efforts have studied the dynamics of orbiting binary black holes in vacuum, which is a good approximation as the black hole’s inertia is orders of magnitude larger than any other one.
A logical next step is to comprehend possible electromagnetic counterparts which would allow for studying key systems via both bands. Such a possibility is quite strong in the context of supermassive binary black hole mergers, because in the merger process the black holes will interact with at least: (i) a circumbinary accretion disk Milosavljevic and Phinney (2005), (ii) remnant gas in between the black holes Armitage and Natarajan (2005); MacFadyen and Milosavljević (2008), (iii) a magnetosphere Blandford and Znajek (1977) and give rise to possible electromagnetic emissions (e.g. Lippai et al. (2008); Shields and Bonning (2008); O’Neill et al. (2008); Megevand et al. (2009); Corrales et al. (2009); Rossi et al. (2009); Zanotti et al. (2010); Chang et al. (2009); Bode et al. (2009); Krolik (2010); Palenzuela et al. (2009, 2010); Mosta et al. (2010)). As discussed in Milosavljevic and Phinney (2005), as the binary tightens, a common circumbinary disk will be formed within which the black holes will eventually merge. Such a disk will typically be magnetized, anchoring a magnetic field which will permeate the region inside the disk containing the black holes. Once the black holes merge, the generic outcome will be a spinning black hole within the magnetic field anchored by the disk. It is precisely this system studied in the seminal work of Blandford and Znajek Blandford and Znajek (1977) and a large body of subsequent works. In this model, the spinning black hole immersed in an external magnetic field accelerates stray electrons to energies sufficient to produce cascading pair-production which supplies the environment with a plasma Blandford (2002). Due to the negligible fluid inertia, the bulk of such plasma moves freely without experiencing any Lorentz force, and so the system can be cleanly studied with the so-called force-free approximation Goldreich and Julian (1969); Blandford and Znajek (1977). This approximation, together with the assumption of stationarity and axisymmetry, allows one to determine that a net outward electromagnetic flux is produced, which extracts rotational energy from the black hole. Furthermore, the electromagnetic energy flux is highly collimated and eventually will be transferred into kinetic energy of the plasma, accelerating charges and producing synchrotron radiation. Support for this basic picture has been provided in recent years through numerical models Komissarov (2004); Semenov et al. (2004); Komissarov and McKinney (2007); Tchekhovskoy et al. (2008); Krolik and Hawley (2010).
The Blandford-Znajek model outlined above is not directly applicable to the very dynamical
merger of two black holes, thus the interaction of electromagnetic fields and plasma and their
possible emissions in a such system has remained a mystery.
Our studies indicate that the dynamical behavior of the system: induces a collimation around
each intervening black hole –generating a toroidal magnetic field—;
amplifies the electromagnetic field strength (when comparing to the single black hole case),
and emits a strong electromagnetic burst associated with the merger.
The collimated area can thus become a channel for accelerated particles which, in turn,
can emit observable electromagnetic radiation, in particular of synchrotron type.
Furthermore the behavior of the EM fields, tightly tied to the binary’s dynamics,
make them strong tracers of the spacetime and the collimation tubes can be seen as a cover
for the familiar “pair of pants” description of the black holes’ event horizons Matzner et al. (1995).
Implementation details: We study the black hole binary via numerical simulations which implement the (coupled) Einstein-Maxwell system of equations. Also coupled to the system is a low density plasma for which the inertia is negligible compared with the electromagnetic stresses. The plasma essentially experiences no Lorentz force and so the electromagnetic fields are well described by the force free condition (with , the charge and current densities). The role of the plasma is then to provide charge and current densities. The complete system is implemented using finite difference approximations within a computational infrastructure that provides distributed adaptive mesh refinement had () with seven levels of refinement. Our computational domain is defined by with a finest resolution of , where is the total mass of the system in terms of the solar mass and . We adopt fourth order accurate spatial discretizations and third order Runge-Kutta integration in time, while the singularity inside each black hole is excised from the computational domain. Since the region inside the black hole is causally disconnected from the outside, this procedure does not affect the physics obtained there. More details of our techniques for implementing Einstein equations can be found in e.g. Calabrese et al. (2004); Lehner et al. (2006); Palenzuela et al. (2007, 2009) and for our adoption of the force free condition we follow closely the approach presented in Komissarov (2004).
The circumbinary disk is assumed to lie outside the computational domain and so its details are unimportant. Such an assumption is strongly justified by the fact that the viscosity in the disk is such that the disk cannot keep pace with the shrinking orbit of the black holes, and as a result the disk “freezes-in” at a radius typically considerably larger than our computational domain Milosavljevic and Phinney (2005).
The disk’s role is therefore to anchor the magnetic field which is
incorporated as boundary and initial conditions describing a dipolar magnetic field
with strength in the region around the black holes.
We adopt black holes in a quasi-circular orbit (which is
a reasonable approximation as gravitational wave emission circularizes the orbit).
We study late orbiting stages and merger, and so we concentrate on an initial separation
that gives rise to over one orbit before the merger takes place. This scenario
allows us to study
the transition of the binary from orbit to merger into a final black hole. Furthermore, we
adopt equal-mass (, with a radius ) non-spinning black holes to disentangle
orbitally-driven effects from those that would be induced by any individual spins (i.e. individual
BZ effects that would be present around each spinning black hole).
Results: As mentioned, gravitational waves from this system, in which the plasma and electromagnetic inertia are orders of magnitude smaller than that of the black holes, are well understood by now (see Aylott et al. (2009) and references cited there in) and our results reproduce the expected behavior. The electromagnetic field behavior on the other hand, is completely new and we concentrate on it here. The global dynamical behavior is illustrated in Fig 1. The two black holes orbit and merge within about an orbital period ( hours), after which the black final hole region radiates its excess structure, settling into a Kerr black hole with spin . To study the system in more detail, we monitor different quantities: The Newman-Penrose scalars and (the square of the former and the integral of the latter describe the electromagnetic and gravitational energy fluxes respectively); the Poynting flux; the function (which in axisymmetric, stationary scenarios describes the angular velocity of magnetic field lines Blandford and Znajek (1977)) and the electric and magnetic field topologies. To describe the behavior of the system, it is easier to concentrate on the different stages identified in the binary black hole dynamics:
In the first stage, before the merger takes place, the black holes act as stirrers for the surrounding plasma. Their orbital dynamics and strong curvature affect the electromagnetic field in the close neighborhood of each black hole, inducing both a poloidal electric field and a toroidal magnetic field –both scaling as – (as in models for magnetospheric interactions of binary pulsars Vietri (1996); Rafikov and Goldreich (2005)). Fig. 2 illustrates field lines corresponding to and as well as the . The induced time-dependent topology gives rise to a net Poynting flux aligned/antialigned with the orbital momentum vector around each black hole, with an EM frequency given by . As a result, despite the fact that the black holes are not spinning, there is a strongly collimated electromagnetic flux of energy dominated by an multipolar structure with a time-dependence determined by the orbital motion.
During the merger, which lasts about hours –from late orbiting, through the plunge phase to the formation of a highly distorted black hole– the highly non-linear dynamics translates into a significant increase in both electromagnetic and gravitational energy radiated. As expected, a common collimated tube arises and a natural transition from is observed. In addition to the collimated flux of energy, a rather isotropic flux is also emitted whose energy is much smaller than the collimated one during the inspiral but of the same order at the merger, where both these energy fluxes reach a peak and the collimated part doubles in magnitude.
Afterwards, the late stage is described by a single black hole which, after a relatively short time, is well approximated by a Kerr black hole. The remnant black hole radiates gravitational radiation described by quasinormal modes which decay to zero exponentially as the black hole settles into a Kerr configuration. Thus, the post-merger behavior of the electromagnetic field behavior is increasingly better represented by the Blandford-Znajek process for a spinning black hole with . As a result, the collimated electromagnetic energy flux does not decay to zero, rather it approaches the value predicted by the Blandford-Znajek model. For a single spinning black hole, this energy flux evaluated at the horizon goes like , where is the rotation frequency of the black hole (which is similar to the orbital velocity at the merger). In this case, we numerically find that the EM rotation frequency for a single black hole relaxes to .
Energetically, the system radiates gravitational waves primarily through modes. These waves display a chirping behavior as the orbit tightens, followed by exponential decay after the merger (see e.g. Aylott et al. (2009)). Overall, the system radiates and of the rest mass energy and angular momentum (at the initial separation) respectively. In the electromagnetic band the radiation profile displays a more complex structure. Throughout the orbiting stages, the electromagnetic radiation exhibits a strongly collimated character along the magnetic field lines in the region around the individual black holes, together with a weaker isotropic emission. These features are illustrated in Fig. 1 in which the flux of electromagnetic energy is shown at four different times during the evolution. In the early stages the black holes stir the surrounding plasma, leading to a clear collimation of electromagnetic flux induced by the orbiting black holes pulling the EM field lines. These collimated tubes twist about each other as the black holes proceed. When the merger takes place, the collimated tubes merge into one and acquire a rather smooth structure around the final black hole’s ergosphere. In addition to the collimated energy flux, a strong burst of isotropic electromagnetic radiation is produced at the merger.
Figure 3 illustrates the behavior of the electromagnetic energy flux over a sphere located at . A clear collimation is observed which is evident in the “bright-spots”. These spots are symmetric with respect to the orbital plane and revolve around each other as a result of the orbiting until that they merge into a single one along the poles. In addition to these collimated flows, the figure also illustrates the energy flux through different latitudes and the transition from the structure to .
Figure 4 provides the total energy flux in both the electromagnetic and gravitational wavebands for a particular astrophysically relevant case with and (i.e. not exceeding the Eddington magnetic field strength Dermer et al. (2008)).
A clear sweep upwards is apparent in both channels as the merger takes place. Afterwards, both decrease rapidly. However it is interesting to note that while the gravitational flux essentially shuts off in a short time (as the system relaxes to a stationary black hole), the electromagnetic flux rises up to the level predicted by the Blandford-Znajek mechanism.
Overall, the total (Poynting flux) radiated electromagnetic energy behaves like (with . This is about an order of magnitude larger than the same system studied in the electrovacuum case (i.e. not including the plasma) Palenzuela et al. (2009, 2010), indicating that the plasma taps the orbital/rotational energy from the system more efficiently. As studied in Moesta et al. (2010), the isotropic radiation transport of magnetic field perturbations can be transmitted to the disk in the form of magnetosonic waves when the ratio between the viscous time scales of the disk and the transport magnetic timescale is above . Thus, in Moesta et al. (2010) it was indicated that an electromagnetic counterpart to a gravitational wave event could be determined by a variability induced in a possible accretion mechanism taking place.
The results highlighted in the current work indicate that a more important observational prospect is achieved by the jets induced by the binary’s dynamics. These jets have a (Poynting flux) luminosity during the last hours before the merger of (with the Eddington luminosity). This electromagnetic energy can be transferred to kinetic energy of the plasma, which will radiate through synchrotron processes in frequencies around the GHz region. Such a flux of energy implies it would be possible to observe these systems to , with missions such as IXO and EXIST, depending on the efficiency of the photon emission process. As Fig 4. illustrates, the system will be sufficiently bright for hours before the merger and remain so through merger. This radiated power has a time dependence given by and the flux exhibits a clear transition at the time of the merger. Thus, prospects for detecting pre-merger and prompt electromagnetic counterparts are certainly interesting. Furthermore, joint detections in both electric and gravitational wave bands (the power of the latter scales as ) are therefore quite probable as LISA will be capable of observing supermassive binary black hole systems for weeks to months before merger and considerable time afterwards.
Conclusions: Observational prospects of detecting gravitational waves with LISA from supermassive black hole mergers will be excellent Holz and Hughes (2005). Indeed, LISA’s superb noise spectra will allow for clean determination of gravitational waves and extraction of key physical parameters of the system such as certain combinations of the their masses and spins, orientation, position in the sky and luminosity distance. Gravitational waves from supermassive binary systems could be detected as far as redshifts of Vecchio (2004). However, LISA’s localization in the sky–an ellipse with a few arcminutes to a few degrees in size- will not be sufficient to unequivocally determine the source’s position Holz and Hughes (2005); Lang and Hughes (2009), and it is here where an electromagnetic counterpart would aid tremendously in determining the location. Precise localization and confrontation of the observed signals will allow for tremendous physics pay off: general relativity, cosmology, astrophysics and even efforts towards a quantum theory of gravity will likely enjoy a revolution in their understanding Holz and Hughes (2005); Bloom et al. (2009); Haiman et al. (2008).
As we have shown here, binary black hole mergers could give rise to strong electromagnetic output with (Poynting flux) luminosities as high as a few ergs/s. This would correspond to an isotropic bolometric flux of erg/( s). Such a flux could be detected to a redshift of and possibly larger if accounting for anisotropies on the one hand, but on the other hand depending on the photon emission process efficiency on the other. Interestingly, our work indicates that a marked transition in the electromagnetic flux from will take place around the merger time which will leave its imprint in possible observable signals. Furthermore, we have shown that even non-spinning black holes could give rise to interesting levels of output, which becomes even stronger as the merger takes place. Certainly, higher power would be expected if any of the individual black holes is spinning and/or the magnetic field strength is larger in the region of the black holes either as sourced by the disk or further enhanced by the merger process. In the latter case, a tantalizing option would be for such enhancement to be driven by an analog of the BZ effect; i.e. by significantly tapping orbital rotational energy before the merger takes place as in the single black hole case where rotational energy from the black hole is extracted. A requirement for this scenario would be that the black holes orbit within an ergo-region and before the plunge so that there is sufficient time to efficiently tap into this source of energy. As argued in Palenzuela et al. (2010), this scenario appears unlikely unless the black holes are significantly spinning and aligned with the orbital angular momentum; otherwise, the black holes would be in the plunging phase when crossing (an estimate of) the ergosphere. While the magnitude of spins in supermassive black holes is still largely unknown –gravitational wave detections will be the ultimate tool to understand this issue– alignment of spins with the orbital angular momentum is expected in a large class of systems Kesden et al. (2010).
Acknowledgments: It is a pleasure to thank J. Aarons, N. Afshordi, A. Broderick, P. Chang, T. Garrett, B. MacNamara, E. Poisson, A. Spitkovsky and C. Thompson as well as our long time collaborators M. Anderson, E. Hirschmann, P. Motl, M. Megevand and D. Neilsen for useful discussions and comments. We acknowledge support comes NSF grant PHY-0803629 to Louisiana State University and PHY-0803624 to Long Island University as well as NSERC through a Discovery Grant. Research at Perimeter Institute is supported through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation. Computations were performed Teragrid and Scinet. CP and LL thank the Princeton Center for Theoretical Physics for hospitality where parts of this work were completed.
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