Accretion flows around coalescing SBHs

Properties of accretion flows around coalescing supermassive black holes

Tamara Bogdanović111Einstein Postdoctoral Fellow, Tanja Bode, Roland Haas, Pablo Laguna and Deirdre Shoemaker Department of Astronomy, University of Maryland, College Park, MD 20742-2421 Center for Relativistic Astrophysics, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 tamarab@astro.umd.edu
Abstract

What are the properties of accretion flows in the vicinity of coalescing supermassive black holes (SBHs)? The answer to this question has direct implications for the feasibility of coincident detections of electromagnetic (EM) and gravitational wave (GW) signals from coalescences. Such detections are considered to be the next observational grand challenge that will enable testing general relativity in the strong, nonlinear regime and improve our understanding of evolution and growth of these massive compact objects. In this paper we review the properties of the environment of coalescing binaries in the context of the circumbinary disk and hot, radiatively inefficient accretion flow models and use them to mark the extent of the parameter space spanned by this problem. We report the results from an ongoing, general relativistic, hydrodynamical study of the inspiral and merger of black holes, motivated by the latter scenario. We find that correlated EM+GW oscillations can arise during the inspiral phase followed by the gradual rise and subsequent drop-off in the light curve at the time of coalescence. While there are indications that the latter EM signature is a more robust one, a detection of either signal coincidentally with GWs would be a convincing evidence for an impending SBH binary coalescence. The observability of an EM counterpart in the hot accretion flow scenario depends on the details of a model. In the case of the most massive binaries observable by the Laser Interferometer Space Antenna, upper limits on luminosity imply that they may be identified by EM searches out to . However, given the radiatively inefficient nature of the gas flow, we speculate that a majority of massive binaries may appear as low luminosity AGN in the local universe.

pacs:
4.30.Tv, 04.70.-s, 95.30.Lz, 95.30.Sf, 98.62.Js, 98.62.Mw, 98.65.Fz

1 Introduction

Supermassive black hole binaries (SBHBs) are one of the prime targets for the future gravitational wave observatory, Laser Interferometer Space Antenna (LISA). In anticipation of future gravitational wave detections, a lot of effort has been directed towards the study and characterization of these objects. Some of the most important open questions pertain to the formation and cosmological evolution of the supermassive black holes (SBHs), the rate of their coalescences and associated observational signatures. All are intricately connected to the properties of the environment in which the SBHs find themselves during the cosmic time. An outstanding astrophysical question with direct importance for the feasibility of coincident EM and GW detections of coalescing SBHs is regarding the physical properties of the gaseous environment surrounding a binary before and during coalescence. Most of the information about these systems so far had to be derived from theoretical studies and computational simulations since finding them in EM searches proved to be a difficult task. Over the past several years non-relativistic hydrodynamical simulations have significantly contributed to our understanding of the evolution of BH pairs and their host galaxies, both during and after the galactic mergers (Kazantzidis et al., 2005; Armitage and Natarajan, 2002; Escala et al., 2004, 2005; Dotti et al., 2007; Mayer et al., 2007; Colpi et al., 2007; MacFadyen and Milosavljević, 2008; Hayasaki et al., 2008; Cuadra et al., 2009). However, simulations spanning the entire dynamical range, from galactic merger scales () to binary coalescences (), are still prohibitively computationally expensive. As a consequence, non-relativistic simulations stop at binary separations of while fully general relativistic simulations are possible only at separations of . Hence, the properties and structure of accretion flows around coalescing binaries remain uncertain.

In this paper, we discuss physically motivated scenarios for the SBHB environments in centers of galaxies. We outline the properties of the circumbinary disk and a hot and radiatively inefficient accretion flow enveloping a binary and their implications for observations. Guided by the radiatively inefficient accretion flow scenario we carried out fully general relativistic, hydrodynamical study of the inspiral and merger of equal-mass, spinning SBHBs. We describe the results from this ongoing study which is a step towards understanding the how properties of a SBHB environment correlate with observational signatures.

2 Physical conditions in the accretion flow

Figure 1: Illustration of the two accretion flow scenarios discussed in this paper. Left: Circumbinary disk scenario in which binary torques create a low density region in the center of the disk. The accretion onto the binary members is mediated by their individual circumblackhole disks as long as a balanced accretion rate can be maintained from the circumbinary disk. Right: In radiatively inefficient accretion flow scenario the SBHs remain immersed in the hot gas until coalescence. At larger radii, the geometrically thick flow transitions into a geometrically thin accretion disk or a lower temperature ambient medium. The illustrations are not drawn to scale.

2.1 Circumbinary disk model

It has been shown that the presence of gas on larger scales in the aftermath of a gas rich galactic merger may not guarantee an abundant supply of gas for accretion once a gravitationally bound binary is formed. This is because the binary torques can evacuate most of the surrounding gas, preventing in such a way any significant accretion on either member of the binary (Armitage and Natarajan, 2002; Milosavljević and Phinney, 2005; Hayasaki et al., 2007, 2008; MacFadyen and Milosavljević, 2008; Cuadra et al., 2009). The scenario in which binary torques clear a central low density region is commonly described in the literature as the circumbinary disk (Fig. 1). In this scenario the orbital evolution of a gravitationally bound SBHB initially occurs on the viscous timescale of the surrounding disk, until the binary reaches the gravitational wave regime. At that point, the rapid loss of orbital energy and angular momentum through gravitational radiation cause the binary to detach from the circumbinary disk and to accelerate towards coalescence. After decoupling, the accretion rate onto the black holes is expected to diminish and, consequently, the EM signatures associated with the binary may cease. How early in the inspiral phase this happens depends on the properties of the disk. Here we outline the conditions in the circumbinary disk at the decoupling. We follow Armitage and Natarajan (2002), who note that the viscous rate at which the inner edge of a Shakura-Sunyaev disk (Shakura and Sunyaev, 1973) moves inwards is

(1)

where is the viscosity coefficient, , the Keplerian circular velocity at a semimajor axis , and is the half-thickness of the disk at a given radius, . The rate at which the semimajor axis of a circular binary shrinks is

(2)

Here, and are the mass and mass ratio of the SBHB. Setting the two rates equal, while adopting a thin disk aspect ratio and a commonly used value for gives

(3)

We use geometrized units with , and so and . For an equal mass binary . In reality, the inner edge will be farther away, because for comparable-mass black holes the disk is truncated at about double the binary semimajor axis (Artymowicz and Lubow, 1994). This implies the inner edge of the disk is at . We estimate the luminosity and temperature of such a disk using the Shakura-Sunyaev disk solution. The luminosity of the disk is , where we adopt , the maximum efficiency with which the accretion disk around a Schwarzschild black hole converts the potential energy into radiative energy at a given radius, r, and is the accretion rate. Note that at , is much less than the radiative efficiency of the disk that extends all the way to the innermost stable orbit (ISCO), where . To estimate the maximum mass accretion rate we use Shakura-Sunyaev expression for half-thickness of the disk in the gas pressure-dominated region

(4)

where and  erg cm s is the Eddington luminosity. Using and we calculate the accretion rate as and consequently, . Using the same model we evaluate the temperature of the disk

(5)

or, . These values imply that geometrically thin circumbinary disks around comparable mass binaries are expected to be moderately luminous with spectral energy distribution peaking in the UV band, as long as the inner region of the disk remains largely depleted of gas. If gas flow across the “hole” region is present (as illustrated in Fig. 1), it could feed the circumblackhole disks and give rise to shocks in which case the coalescing system may appear more luminous and emit harder radiation. It is worth noting that in order to maintain accretion disks around individual SBHs for a longer period leading to the coalescence, the accretion rate between the circumbinary disk and smaller circumblackhole disks would need to be carefully balanced. It is not obvious that such a steady state can be naturally achieved, especially for comparable mass binaries, because the gas in the vicinity of the binary is subject to strong, non-axisymmetric binary torques and is not in dynamic equilibrium. However, the accretion process need not be a steady state to be luminous, since a relatively small amount of gas in this region is sufficient to produce a luminous event (Krolik, 2010).

Clearly, the absence of gas in the central region would represent a fundamental obstacle for the EM searches of coalescing binaries. If so, even if the circumbinary disk itself is sufficiently luminous to be observed, the absence of characteristic EM variability would make it difficult to discern a binary from a “regular” active galactic nucleus (AGN). Nevertheless, several binary candidates discovered so far have been interpreted in the context of a thin (or moderately thick) circumbinary accretion disk scenario. One is a well known binary candidate, the blazar OJ 287, that exhibits outburst activity in its optical light curve with a period close to 12 years, interpreted as a signature of the orbital motion (Valtonen et al., 2008). It is, however, hard to make inferences about a population of SBHBs based on one object. While indications of a long-term periodicity may also exist in a handful of other objects, they are generally less pronounced than in case of OJ 287. An additional observational technique for selection of the SBHB candidates anchors on the existence of the circumbinary accretion disk and individual circumblackhole accretion disks. This method utilizes the emission-lines associated with multiple velocity systems in the spectrum of a candidate object. It relies on a detection of the Doppler-shift that arises from the orbital motion of a binary. So far a handful of SBHB candidates have been selected in this way: J092712.65+294344.0 (Bogdanović et al., 2009; Dotti et al., 2009), J153636.22+044127.0 (Boroson and Lauer, 2009), J105041.35+345631.3 (Shields et al., 2009), 4C+22.25 (Decarli et al., 2010), and J093201.60+031858.7 (Barrows et al., 2010). A common property shared by all objects is that their emission line systems exhibit large shifts in the range . If such velocity shifts are interpreted in the context of a binary model, and if the emission-line systems are associated with circumblackhole accretion disks around one or both of the black holes, the expectation is that the orbital motion of the binary should give rise to a measurable velocity change of the emission lines on a time-scale of several years. For the first four objects this basic test was carried out by taking spectra of the object at different epochs and measuring the change in the position of the emission line peaks. In all four the measured rate of velocity shift is very low () and consistent with zero within the measurement error bars. This strongly challenges the hypotheses that these candidate objects are binaries, but the uncertainties in emission geometry and radiative processes of accretion flows around binaries currently preclude elimination of the binary model. The lack of definite observational signatures associated with the gravitationally bound binaries, as expected in the context of the circumbinary disk model, leaves open a possibility that accretion flows in vicinity of the SBHBs may have a different structure.

2.2 Radiatively inefficient hot gas flow

It is plausible that if the surrounding gas is sufficiently hot and tenuous, the binary may find itself engulfed in a radiatively inefficient, turbulent flow all the way through coalescence. Such conditions are expected to exist in nuclear regions of some low luminosity AGN (LLAGNs; Quataert, 1999; Ptak et al., 2004; Nemmen et al., 2006; Elitzur and Ho, 2009, for example). If binaries indeed do exist in radiatively inefficient accretion flows (RIAFs), then the circumbinary disk and hot gas flow scenarios effectively bracket the range of physical situations in which pre-coalescence binaries may be found in centers of galaxies. Which scenario prevails depends on the balance of heating and cooling mechanisms in the accretion flow. In the circumbinary disk scenario, relatively efficient cooling processes result in the gas settling into a rotationally-supported, geometrically thin accretion disk around the binary. The main property of radiatively inefficient flows is that very little energy generated by accretion and turbulent stresses is radiated away. Instead, it is stored as thermal energy in the gas at the level comparable to its gravitational potential energy, giving rise to a very hot flow (Ichimaru, 1977; Rees et al., 1982; Narayan and Yi, 1994). It follows that , where is the binary mass and is the separation from its center of mass. Since thermal pressure forces within the gas are significant, the hot accretion flows are expected to be geometrically thick. Also, given high thermal velocities, the inflow speeds are comparable to the speed of sound and to the orbital velocity that a test particle would have at a given radius. This implies that in the hot gas flow, unlike the circumbinary disk scenario, binary torques are incapable of creating the central low density region, because the gas ejected by the binary is replenished on the dynamical time scale. Consequently, the binary may remain immersed in the gas until coalescence. This may bode well for the EM searches for coalescing binaries should such hot gas flows remain sufficiently luminous through the coalescence. We now discuss the properties of such a plasma and estimate its characteristic luminosity.

Radiatively inefficient hot gas flows are characterized by lower gas densities than their radiatively efficient counterparts (such as accretion disks described in § 2.1) and here we use density as an effective discriminator between the two scenarios. Below some critical gas density, in RIAF-type flows, the time scale for the Coulomb collisions between electrons and ions () becomes longer than the inflow time of the gas (). This may result in the formation of a two-temperature flow in which the ion plasma remains at and the electron plasma cools to temperatures in the range (Ichimaru, 1977; Rees et al., 1982; Narayan and Yi, 1994). Above this density limit, the collisional plasma flow of electrons and ions is fully thermally coupled and can cool efficiently via electron-emitted radiation, yielding an evolution more similar to the accretion disk scenario. We calculate this critical plasma density by setting , assuming and , and find it to be . The characteristic timescales evaluated at the critical density and in vicinity of the binary are:

(6)
(7)

The size of the region under consideration, , is the Bondi radius of gravitational influence of the coalescing binary. is the number density of the gas, and is the cross-section for Coulomb scattering of an electron with kinetic energy on a more massive ion. is the speed of sound evaluated assuming the equation of state of an ideal gas and , for monoatomic gas. Other symbols have their usual meaning.

The two orbiting SBHs will accrete from a hot, turbulent flow in a Bondi-like fashion

(8)

where we assumed that the relative velocity between the gas and each black hole (BH) is comparable to . The luminosities due to bremsstrahlung, synchrotron, and inverse Compton radiation (Rybicki and Lightman, 1986) from such flow can be estimated as

(9)
(10)
(11)

where bremsstrahlung luminosity was calculated assuming a thermal distribution of electrons and the subscript “5.4” indicates that the numerical factor in the square brackets is normalized to 5.4. The synchrotron luminosity is evaluated for relativistic electrons with . In (11), represents a supply of low energy photons transported from the edge of the RIAF, a distance of away. Note that the luminosity of the synchrotron emission remains below that of the bremsstrahlung radiation unless the magnetic field strength is close to the equipartition value, which in our case is . It is plausible that the spinning BHs can amplify the magnetic fields in their vicinity to nearly the equipartition value (Palenzuela et al., 2010b). Given the properties of the gas flow in our model and assuming , the estimated luminosity of synchrotron radiation becomes significant, . Similarly, in order for the inverse Compton luminosity to be significant, a supply of soft, lower energy photons is required. In estimating , we assumed that this soft photon component is produced at large radii, where radiative cooling is efficient and the geometrically thick flow described here transitions into a geometrically thin accretion disk or a lower temperature ambient medium (see the schematic representation in Fig. 1). In the case of Sgr  for example, observations indicate that a radiatively inefficient accretion flow extends into the ambient medium out to away from the center (Quataert, 2003). The estimate for obtained with this value of the transition radius implies that inverse Compton scattering is a very inefficient process even if a generous supply of low energy photons is available from the distant ambient medium, parametrized here in terms of the luminosity . Note however that if synchrotron radiation is boosted by strong magnetic fields, it could feed the inverse Compton luminosity of comparable magnitude by providing an immediate source of soft photons. For comparison, the Eddington luminosity of the system is .

The corresponding cooling timescale of the plasma at the critical density due to bremsstrahlung radiation (while keeping in mind the potential importance of the other two mechanisms) is

(12)

Note that implies that the hot gas plunges into the BHs before it had a chance to radiatively cool and settle into an accretion disk, as expected in the case of radiatively inefficient flow.

We evaluated the properties of the hot gas flow at the critical density, however note that by construction radiatively inefficient flows reside at densities and so the derived luminosities should be regarded as upper limits. Because , and are sensitive functions of density and SBHB mass, it follows that a large fraction of AGNs associated with this type of accretion flow will likely have low luminosities. More specifically, the properties of these sources appear consistent with the group of the LLAGNs observed in the nearby universe that have been proposed to host radiatively inefficient accretion flows. Elitzur and Ho (2009) find that below a bolometric luminosity of AGNs characterized by the broad emission lines (i.e., type 1 AGN) cease to exist while narrow line (type 2) sources can exist both below and above this limit in the luminosity range for a central BH mass of . According to the unification model of AGN the absence of the broad emission lines in type 2 sources can be explained by the observer’s orientation with respect to the toroidal obscuration of the broad line region (BLR) and central AGN. However, despite the considerable success of the unification scheme, there is growing evidence that the BLR is actually missing, and not just hidden, in many LLAGN (Ho, 2008). These sources are commonly referred to as “true” type 2 AGNs. The current paradigm suggests that the BLR naturally arises from a clumpy wind coming off an accretion disk rotating around the BH (Emmering et al., 1992). In the context of this paradigm, the disappearance of the BLR at lower luminosities in type 1 sources and absence of it in true type 2 AGNs signals a change in the properties of the accretion flow associated with the inner  pc and can be explained by the transition from the radiatively efficient to radiatively inefficient accretion flows. If radiatively inefficient flows around SBHBs indeed have properties similar to LLAGNs, they would appear as low to moderate luminosity narrow line AGN. Note that in this case the method for selection of binary candidates based on the detection of the velocity shift or an unusual shape of the broad emission lines may not be useful. It is also plausible that some fraction of radiatively inefficient EM counterparts could be as faint as the accretion flow in the center of our Galaxy (Narayan et al., 1995, 1998; Quataert, 2003) in which case the EM detection of a binary would be unlikely even in the local universe.

If indeed relevant to SBHB systems, the properties of the radiatively inefficient flows could naturally explain the paucity of SBHBs in EM searches, which have so far been predominantly organized around the assumption of radiatively efficient accretion flows. Furthermore, radiatively inefficient accretion flows are characterized by a hard spectral energy distribution, peaking at . It is worth noting that the Swift-BAT survey of the hard X-ray sources (for description of the most recent catalogs see Cusumano et al., 2010; Baumgartner et al., 2010) is uniquely suited for detection of nearby (z¡0.05), moderate-luminosity AGN with such properties, because it is conducted in the 14195 keV energy band. In this sample Koss et al. (2010) find a higher incidence of galaxies with signs of disruption and higher incidence of AGN and galaxy pairs within 30 kpc separation compared to a matched control sample of galaxies. This may have interesting implications for gravitationally bound and coalescing binaries at much smaller separations, if it can be shown that they reside in similar environments.

3 Simulations of black hole coalescence in radiatively inefficient accretion flow

Figure 2: Snapshots of the rest mass density of the gas, in the orbital plane of the binary. The color scale is logarithmic and lighter shades mark higher density.

Guided by the analytic expectations described in the previous section we set out to numerically investigate how properties of the binary environment correlate with observational signatures associated with the SBHB coalescence. This is a work in progress that encompasses a larger suite of simulations and some of its initial results have been described in Bode et al. (2010a). For the purpose of this proceeding we describe one of the subsequently modeled scenarios in order to illustrate the EM signatures characteristic for the hot accretion flow scenario. This investigation should be considered in the context of the relativistic calculations that investigate the dynamics of test particles (van Meter et al., 2010) and the evolution of EM fields (Palenzuela et al., 2009, 2010a, 2010b; Mösta et al., 2010) and gas (Bode et al., 2010a; Farris et al., 2010) in the gravitational potential of a coalescing binary.

We use fully relativistic numerical hydrodynamics simulation to follow the interaction of an equal-mass SBH binary with a gaseous environment through the last five orbits and merger. The simulation described here has been carried out with the new version of the Maya code of the numerical relativity group at Georgia Tech (Bode et al., 2010b).222Maya is a modified version of the publicly available code Whisky developed by the European Union Network on Sources of Gravitational Radiation (http://www.whiskycode.org; Baiotti et al., 2005). The data consist of a SBHB immersed in a uniform gaseous medium with the initial temperature  K. The binary separation at the beginning of the simulation is and SBHs have spins that are equal, parallel, and aligned with the orbital angular momentum. The dimensionless spin parameters are and is the mass of each black hole. We consider the scenario in which the total rest mass of the gas in the SBHB vicinity is much smaller than the BH masses and therefore the dynamics of the binary is effectively the same as in vacuum. After the initial phase of relaxation, the gas in the vicinity of the binary orbit settles to a temperature  K, and its thermal velocity is comparable to the binary orbital speed. The gas is evolved assuming the equation of state of ideal gas and . The only mechanisms for heating and cooling of gas in our simulation are adiabatic compression and expansion in the potential of the binary and we do not account for heating of the gas by the AGNs nor for cooling by emission of radiation. In order to avoid any spurious transients that may stem from the imperfections in the initial conditions the binary and gas dynamics have been relaxed during the initial of the simulation. We removed this initial phase and do not show it as a part of the results reported here.333Description of the numerical setup utilized in our runs can be found in Bode et al. (2010a).

Fig. 2 shows the snapshots of the rest mass density of the gas. The distinct features that arise in the gas during binary evolution are the density wakes that develop behind the inspiraling BHs and a high density region enclosed in the binary orbit. Early in the inspiral, the shocks are confined to the wakes expanding outside of the binary orbit. Later on, the dynamically unstable region between the two BHs gives rise to another shock region which is swallowed by the remnant hole at the time of the coalescence. We find that shock heating of the gas by the binary and subsequent dynamics can give rise to a characteristic variability of the EM emission signatures which, if observable, could be uniquely associated with merging binaries in hot accretion flows.

To assess this we evaluate the bremsstrahlung luminosity, , arising from the gas near the binary by integrating the emissivity of the gas over the volume with radius but excluding the volumes inside the apparent horizons of the two BHs. Top panel of Fig. 3 shows the light curve calculated for this run where marks the time of the merger. The luminosity in Fig 3 was normalized to the luminosity of the gas around a single BH with the mass equal to that of the binary. The luminosity of a single BH system can be parametrized in terms of the BH mass and the gas properties and its upper limit is set by the value shown in (9). Fig 3 illustrates that the shocks driven by the orbiting binary provide an extra source of heating to the gas, causing it to be more luminous than in the single BH scenario. At about before the merger, when the binary enters the final plunge, the luminosity curve exhibits a broad flare. The flare reaches before a sudden drop that occurs soon after the BHs have merged. A sudden decrease can be attributed to the disappearance of the dynamic region of high emissivity between the two BHs, which is rapidly swallowed by the BHs in the process of coalescence. Given a large magnitude of the luminosity drop, it is possible that a source that was initially visible on the sky may disappear shortly after coalescence, making this its characteristic signature.

Figure 3: Top: Bremsstrahlung luminosity as a function of time normalized by the luminosity of the system in which the binary SBH was replaced by a single black hole of the same mass. Bottom: Comparison of bremsstrahlung and GW variability. Real part of the gravitational waveform (dotted line) is arbitrarily scaled and superimposed on the top of the oscillations in the bremsstrahlung light curve (solid). The latter are obtained by division of the curve in the top panel by the unbeamed light curve. Merger occurs at .

The bottom panel of Fig. 3 shows the quasi-periodic oscillations in the bremsstrahlung light curve (solid line) that arise due to the relativistic beaming and Doppler boosting of the light emitted by the high density wakes that develop behind the inspiraling BHs. To emphasize the oscillations we divided the light curve in the top panel by the shape of the unbeamed light curve.444In calculation of the luminosity of the beamed light we neglected relativistic bending of photon trajectories and gravitational redshift of photons in the potential well of the binary. The amplitude of the variations in luminosity is approximately between subsequent peaks and troughs, as seen by a fiducial observer placed in the plane of the binary at infinity. In this way, the observer is placed directly in the path of the sweeping emission beams associated with the two BHs and can sample both the minimum and maximum luminosity of the system, depending on its orbital phase. The amplitude of the variability sensitively depends on the distribution gas around the SBHB and we find it to be smaller in this run compared to the previously reported scenario where the SBHB was immersed into a finite size “cloud” (the amplitude in that case was ; Bode et al., 2010a).

The dashed line in the bottom panel of Fig 3 shows the GW variability in form of the arbitrarily scaled and shifted real part of the waveform. In this model the frequency of oscillations observed from the bremsstrahlung’s relativistically beamed light is directly tied to the orbital dynamics of the binary and thus is also correlated with the frequency of the GWs in this run. As mentioned before, detection of correlated EM+GW oscillations from the same object would be a smoking gun for a SBHB system on the way to coalescence and would directly link a detected GW source to its EM counterpart. It is important to point out that the quasi-periodic EM variability is only expected to arise in systems where the two BHs can form a stable set of symmetric wakes in the gas. However, as most SBHB systems in the universe are expected to be unequal-mass binaries, and thus have some inherent asymmetry, the likelihood of observing such correlated oscillations therefore depends on the extent to which asymmetries can modify the variability. It is also worth noting that the discussed EM variability stands a chance of being seen by a distant observer if the amplitude of the quasi-periodic variability stands above the intrinsic variability of an AGN. At the level the amplitude of the quasi-periodic oscillations is comparable to the natural variability of the AGNs and unless quasi-periodic oscillations can be more pronounced, they will remain hidden by the AGN flickering. An additional requirement is that the photons emitted in the vicinity of the BHs are not absorbed by the surrounding medium or reprocessed in such a way that the variability signature is lost. If the cloud is optically thick to emitted radiation, the characteristic variability will most likely be “erased” and dephased during the reprocessing of photons by the intervening medium. In this case a gradual rise and drop-off in bremsstrahlung luminosity may be more robust signatures of binary coalescence as they are still expected to arise even in the case of the opaque ambient medium.

4 Summary and future prospects

In this paper we summarized the key properties of accretion flows around coalescing supermassive black holes in the context of the two different models: circumbinary accretion disk and a hot, radiatively inefficient accretion flow. The models effectively explore two opposite ends of the parameter space, in terms of the thermodynamic properties of the binary environment, and bracket a range of physical scenarios in which coalescing SBHBs can be found. Both classes of models predict luminous (detectable) or underluminous (undetectable) outcomes, depending on the details of a particular model. Tauntingly, astrophysical models currently cannot offer a definitive answer about the EM signatures associated with coalescences but do offer a variety of outcomes for consideration.

Guided by the hot, radiatively inefficient accretion flow model, we carried out a suite of exploratory simulations of the final stages of binary evolution, where we initially consider only equal mass, spinning SBHBs. Here we highlighted the key results from one such run, which shows that correlated EM-GW variability can arise in merging binary systems immersed in hot gas flows due to the effects of relativistic beaming and Doppler boosting modulated by the binary orbital motion. While some degree of quasi-periodic variability is present in all cases we explored so far, where SBHs form a stable set of wakes from inspiral through the plunge, there is an indication that this signature may not be preserved and observable in general. In this case, additional signatures may be sought for in searches for EM counterparts. We also find that our modeled light curves exhibit a gradual rise, arriving at a peak at the time of coalescence, followed by a sudden drop-off. If present, these two features are sufficiently robust to allow identification of an EM counterpart to a GW source. The remaining question is whether EM signatures of coalescences in RIAF type flows will be sufficiently luminous to be detected. Optimistically, the most luminous solutions physically allowed in the context of this model imply that most massive binaries detectable in the LISA band may be identified in X-ray searches out to (assuming an IXO or EXIST-like X-ray mission). Pessimistically, if the properties of the SBHB environments are similar to the hot and underluminous accretion flow in the center of our Galaxy, detection of EM counterparts will be unlikely. More moderately, if their emission properties are similar to the observed LLAGN hypothesized to host RIAFs, then EM counterparts may be observable in the local universe.

Given the extent of the parameter space involved in coalescing SBHBs interacting with gas, more follow-up work is needed. As noted before, most of the SBH binaries in the universe are expected to involve unequal masses and general spin orientations, and it is thus important to further explore the parameter space. Similarly, because the thermodynamic properties of the surrounding gas can significantly influence the properties of EM signals, in the future we will also consider the circumbinary accretion disk scenario. An improvement of current numerical models can be achieved by further inclusion of relevant physics, such as magnetic fields and radiative transfer, which will allow more robust predictions about EM counterparts to be made. Indeed, given recent and complementary work by several different groups, numerical relativity has decisively stepped into the “astrophysical regime”, bringing new levels of complexity to numerical relativistic models but also the opportunity for new insights into the so far secret life of SBH binaries in the final stages of their evolution.

Support for Bogdanović provided by NASA through Einstein Postdoctoral Fellowship Award PF9-00061 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the NASA under contract NAS8-03060. This work was supported in part by the NSF grants 0653443, 0855892, 0914553, 0941417, 0903973, 0955825. Computations described in this paper were carried out under Teragrid allocation TG-MCA08X009.

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