# Why would the merger of spinning black holes within the accretion disk of a supermassive black hole cause them to “shoot straight up” out of the disk?

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I just tried to read the new New York Times article Two Black Holes Colliding Not Enough? Make It Three which links to the new 25-June-2020 Physical Review Letter Graham et al. Candidate Electromagnetic Counterpart to the Binary Black Hole Merger Gravitational-Wave Event S190521g

The event described is the merger of two black holes that were embedded in the accretion disk of a supermassive black hole in the center of a galaxy; i.e. in a quasar (loosely speaking).

The NYTimes article describes the following

In the story that Dr. Graham and his team patched together, the black holes were spinning, which caused a recoil that shot the merged result almost straight up and eventually out of the accretion disk at 120 miles per second, at which point the flare stopped. If the explanation is accurate, the black hole should fall back into the accretion disk at the same speed in a few months or a year, generating another flare. “We'll be looking for that,” Dr. Graham said.

Question: Why would the merger of spinning black holes within the accretion disk of a supermassive black hole cause them to "shoot straight up" out of the disk? How was momentum conserved, i.e. did something else recoil and "shoot straight down"?

Gravitational waves carry away the momentum

From wikipedia

Black-hole merger recoil An unexpected result can occur with binary black holes that merge, in that the gravitational waves carry momentum and the merging black-hole pair accelerates seemingly violating Newton's third law. The center of gravity can add over 1000 km/s of kick velocity.[30] The greatest kick velocities (approaching 5000 km/s) occur for equal-mass and equal-spin-magnitude black-hole binaries, when the spins directions are optimally oriented to be counter-aligned, parallel to the orbital plane or nearly aligned with the orbital angular momentum.[31] This is enough to escape large galaxies. With more likely orientations a smaller effect takes place, perhaps only a few hundred kilometers per second. This sort of speed will eject merging binary black holes from globular clusters, thus preventing the formation of massive black holes in globular cluster cores. In turn this reduces the chances of subsequent mergers, and thus the chance of detecting gravitational waves. For non spinning black holes a maximum recoil velocity of 175 km/s occurs for masses in the ratio of five to one. When spins are aligned in the orbital plane a recoil of 5000 km/s is possible with two identical black holes.[32]

The citations are to

[30] Pietilä, Harri; Heinämäki, Pekka; Mikkola, Seppo; Valtonen, Mauri J. (10 January 1996). Anisotropic Gravitational Radiation In The Merger Of Black Holes. Relativistic Astrophysics Conference. CiteSeerX 10.1.1.51.2616.

[31] Campanelli, Manuela; Lousto, Carlos; Zlochower, Yosef; Merritt, David (7 June 2007). "Maximum Gravitational Recoil". Physical Review Letters. 98 (23): 231102. arXiv:gr-qc/0702133. Bibcode:2007PhRvL… 98w1102C. doi:10.1103/PhysRevLett.98.231102. PMID 17677894.

[32] Lousto, Carlos; Zlochower, Yosef (2011). "Hangup Kicks: Still Larger Recoils by Partial Spin-Orbit Alignment of Black-Hole Binaries". Physical Review Letters. 107 (23): 231102. arXiv:1108.2009. Bibcode:2011PhRvL.107w1102L. doi:10.1103/PhysRevLett.107.231102. PMID 22182078.

Let me see if I can try answering both parts of your question. The key is a combination of two things: 1) Most of the binary BHs in an accretion disk will have their binary orbits in the same plane as the accretion disk, so that "perpendicular to the binary plane" = "perpendicular to the accretion disk"; 2) The most effective form of binary recoil -- in which, as Steve Linton noted, excess linear momentum is carried away by gravitational waves (GWs) -- causes the merged remnant to be kicked in a direction perpendicular to the binary orbital plane.

For the first part, the combination of a gaseous accretion disk and compact, massive objects orbiting within the disk (stars, white dwarfs, neutron stars, black holes) is thought to accelerate the formation of binary objects (including binary black holes) -- but only for objects that are orbiting in the plane of the accretion disk. Since such objects are orbiting about the central SMBH in the same plane, when two such objects form a binary, they will generally end up orbiting each other in the same plane. So you should imagine a population of binaries within this disk, mostly with their own orbital planes aligned with the plane of the accretion disk. (Note that there is no reason to expect the spins of the individual BHs to be aligned with each other, which will be important later.)

Now we consider the gravitational recoil effect. The simplest scenario -- one that's not actually relevant here! -- for binary-BH merger involves two non-spinning BHs. If they are equal in mass, then everything is symmetric and you get no "kick". If they are unequal in mass, then the lower-mass BH has a higher orbital velocity, and will (due to relativistic beaming) give off momentum in the form of GWs in its orbital direction more effectively than is the case for the more massive BH. So the whole system gives off an excess of (linear) momentum in one direction, and the binary recoils to conserve momentum. There would be no net effect if the orbits were circular and unchanging (because then the "jet" of excess momentum in the GWs would just sweep through $$360^{circ}$$ as the BHs orbited each other); but because the orbits are decaying due to the emission of GWs, you end up with a net asymmetric emission of momentum in the GWs, matched by a recoil of the merging binary. But this is in the plane of the binary, so it wouldn't produced the perpendicular kick we're interested in. (See this Astrobites article for a nice picture, taken from this article.)

Although the recoil in the case of non-spinning BHs had been studied theoretically for some time, recent simulations (starting around 2007) showed that if the BHs were spinning (as almost all black holes almost certainly are), and had their spins mis-aligned, then there was an additional, much stronger recoil effect -- a "superkick". The key is that this recoil effect causes the merging binary to be kicked in a direction perpendicular to the binary's orbital plane (see this Astrobites article for a discussion, although it doesn't really offer an nice, simple explanation of the underlying cause). Since, as noted above, the orbital plane of the binary is generally aligned with the plane of the accretion disk, the end result is the merger remnant being kicked approximately perpendicular to the accretion disk.