Black hole mergers: the first light

Abstract

The coalescence of supermassive black hole binaries occurs via the emission of gravitational waves, that can impart a substantial recoil to the merged black hole. We consider the energy dissipation, that results if the recoiling black hole is surrounded by a thin circumbinary disc. Our results differ significantly from those of previous investigations. We show analytically that the dominant source of energy is often potential energy, released as gas in the outer disc attempts to circularize at smaller radii. Thus, dimensional estimates, that include only the kinetic energy gained by the disc gas, underestimate the real energy loss. This underestimate can exceed an order of magnitude, if the recoil is directed close to the disc plane. We use three dimensional Smooth Particle Hydrodynamics (SPH) simulations and two dimensional finite difference simulations to verify our analytic estimates. We also compute the bolometric light curve, which is found to vary strongly depending upon the kick angle. A prompt emission signature due to this mechanism may be observable for low mass (10^6 Solar mass) black holes whose recoil velocities exceed about 1000 km/s. Emission at earlier times can mainly result from the response of the disc to the loss of mass, as the black holes merge. We derive analytically the condition for this to happen.Comment: 16 pages, accepted by MNRAS. Animations of the simulations are available at http://jilawww.colorado.edu/~pja/recoil.htm

Electromagnetic counterparts of recoiling black holes: general relativistic simulations of non-Keplerian discs

“…Very interesting results have also been obtained by Rossi et al (2010), who estimated the maximum discto-hole mass ratio that would be stable against fragmentation due to self-gravity to be M d /M ∼ 6 × 10 −4 for a supermassive black hole with mass M = 10 6 M . In addition, by performing threedimensional but Newtonian SPH simulations of geometrically thin discs, they found that the emitted luminosity corresponding to such small disc-to-hole mass ratios is unlikely to make the EM counterpart visible via wide-area sky surveys.…”

“…In particular, Lippai et al (2008); O'Neill et al (2009); Megevand et al (2009), all just looked at density and/or pressure gradients to infer the propagation of a spiral caustic and, therefore, of a possible shock (we note that in the collisionless particles treatment of Lippai et al (2008), the existence of a shock is purely indicative as no shocks can be produced in this approximation). On the other hand, Rossi et al (2010) used the introduction of an artificial viscosity, which is itself related to local density increases, to identify the location of shocks. Finally, Corrales et al (2010) used a shock detector present in the FLASH code, which marks a given region as a shocked one if ∇ · u < 0 and if the pressure difference between the monitored zone and at least one of its neighbors exceeds the difference expected from the Rankine-Hugoniot jump condition for a shock of a pre-specified minimum Mach number.…”

“…8). The formation of such a cavity is noticeable also in the simulations of Rossi et al (2010), where however it is not discussed. The cavity leads to quasi-periodic variation of the accretion rate as clumps of matter in the downstream of the flow enter the cavity and streams onto the black hole (cf.…”

Estimating the Prompt Electromagnetic Luminosity of a Black Hole Merger

“…Three mechanisms can cause heating at these larger distances, one resulting from the sudden loss of mass from the merged black hole due to its emission of gravitational waves (Bode & Phinney 2007), another due to its sudden loss of angular momentum, and a third the result of the merged black hole's recoil as a result of asymmetric gravitational wave radiation (Lippai et al 2008). We stress, however, that the radial scales whose radiation is under consideration here are not those responsible for the longer-term afterglow that has been the focus of prior work (Milosavljević & Phinney 2005;Lippai et al 2008;Shields & Bonning 2008;Schnittman & Krolik 2008;Rossi et al 2009;Corrales et al 2009); the afterglow is due to heating of mass in the circumbinary disk proper, at the relatively large radii (at least ∼100r g : Milosavljević & Phinney 2005) where conventional accretion dynamics were able to bring it during the time when gravitational wave evolution of the binary was faster than the typical inflow rate. Although the relevant heating mechanisms in the radial range considered here are very similar to those acting at larger radii, the focus of this work is on matter interior to the disk proper, where any gas present arrived as the result of angular momentum loss faster than that acting on the bulk of the circumbinary disk.…”

“…It has been argued, for example, that there should be little gas closer to the merging pair than ∼100-1000r g (r g ≡ GM/c 2 , where M is the total mass of the system) because eventually the timescale for shrinkage of the binary orbit by gravitational wave radiation becomes shorter than the timescale for mass inflow due to internally generated fluid stresses (Milosavljević & Phinney 2005). On the other hand, the mass of such a circumbinary disk might be as large as ∼100 M or more (Milosavljević & Phinney 2005;Armitage & Natarajan 2002;Rossi et al 2009;Corrales et al 2009); if even 1 M were close enough to the merging black holes to be given heat equal to 1% of its rest mass, the total energy-∼10 50 erg -might well be large enough to produce observable radiation. It is therefore a worthwhile exercise to estimate what sort of light might be generated if even a small fraction of the surrounding gas were able to make its way in close to the merging black holes.…”