The Formation of Two Supermassive Black Holes from A Single Collapsing Supermassive Star

From left to right: (top row) Christian Reisswig, Christian D. Ott, Ernazar Abdikamalov; (bottom row) Roland Haas, Philipp Mösta, Erik Schnetter

Authors: Christian Reisswig^1,*, Christian D. Ott^1,2,+, Ernazar Abdikamalov¹, Roland Haas¹, Philipp Moesta¹, Erik Schnetter^3,4,5

Affiliation:
¹TAPIR, California Institute of Technology, Pasadena, CA, USA
²Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo, Kashiwa, Japan
³Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada
⁴Department of Physics, University of Guelph, Guelph, ON, Canada
⁵Center for Computation & Technology, Louisiana State University, Baton Rouge, LA, USA

^*NASA Einstein Fellow
⁺Alfred P. Sloan Research Fellow

The existence of supermassive black holes with masses a billion times the mass of our sun at high redshifts z>7 [1] is one of the mysteries in our understanding of the early history of the universe. At redshift z=7, the universe was less then one billion years old. This leads to a serious problem: how is it possible for black holes to acquire this tremendous amount of mass over a short timescale of just one billion years? A common theory of black hole growth assumes as a starting point the collapse of the very first stars, so called Population III stars. Population III stars may have had masses around 100 times the mass of our sun. The collapse of such a star can leave behind a black hole of similar mass that then grows via subsequent accretion of material from its surroundings. This process can yield quite massive black holes, but in order to reach supermassive scales within only one billion years, the accretion process must be rather extremely rapid to enable fast black hole growth. These high required accretion rates, however, seem to be difficult to be maintained due to, e.g. strong outgoing radiation that can blow away the surrounding gas that otherwise would be accreted onto the black hole [2]. The model, therefore, has difficulties of explaining the existence of very massive black holes in the early universe.

Another model which has recently regained attention is supermassive star collapse. Supermassive stars have originally been proposed by Hoyle & Fowler in the 1960s as a model for strong distant radio sources [3]. Such stars have masses up to a million times the mass of our sun and potentially formed in the monolithic collapse of primordial gas clouds that existed in the early universe [4, 5]. Unlike ordinary stars, which are mainly powered by nuclear burning, supermassive stars are mainly stabilized against gravity by their own photon radiation field that originates from the very high interior temperatures generated by gravitational contraction. During their short lives, they slowly cool due to the emitted photon radiation that keeps the stars in hydrostatic equilibrium. The colder stellar gas can be more easily compressed by the inward gravitational pull, and as a consequence, the stars slowly contract and become more compact. This process continues for a few million years until the stars reach sufficient compactness for gravitationally instability to set in. This general relativistic instability inevitably leads to gravitational collapse. One possible outcome of the collapse is a massive black hole containing most of the original mass of the star. Since the 'seed' mass of the nascent black hole is already pretty large, subsequent growth via accretion from the surroundings can easily push the black hole to supermassive scales within the available time without the need of extreme accretion rates and thus without any strong photon radiation that may blow away the surrounding accreting gas.

In our recent article published in Physical Review Letters [6], we study non-axisymmetric effects in the collapse of supermassive stars. The starting point of our models are supermassive stars which are at the onset of gravitational collapse. We use general relativistic hydrodynamic supercomputer simulations with fully dynamical non-linear space-time evolution to investigate the behavior and dynamics of collapsing supermassive stars. Such computer models have been considered in previous studies [7,8,9,10], however, mostly in axisymmetry.

 In an axisymmetric configuration, a supermassive star maintains a spherical shape during its collapse, which is possibly flattened due to rotation. In these previous studies, it has been shown that the possible outcome is either a single massive rotating black hole, or, alternatively, a powerful supernova explosion which completely disrupts the star. In our case, we select an initial stellar model which is rapidly rotating and leads to black hole formation. In fact, it is so rapidly rotating that the shape of our star is no longer spheroidal, but rather resembles the shape of a 'quasi'-torus where the maximum density is off-center and thus forming a central high-density ring (see upper left panel of Figure 1).

Figure 1: (To view higher resolution click on the image) The various stages encountered during the collapse of a supermassive star with an initial m=2 standing density wave perturbation. Each panel shows the density distribution in the equatorial plane.

Such a configuration is unstable to tiny density perturbations that may be present at the onset of collapse [10]. This instability is particularly strong for perturbations in the form of standing poloidal density waves with one (m=1) or two (m=2) maxima. Due to this instability, these perturbations grow exponentially during the collapse, and can lead to significant deformations away from axisymmetry. The nature of the instability typically leads to the formation of orbiting high-density clumps of matter inside the collapsing star (see upper right panel of Figure 1). Since the m=1 and m=2 perturbations grow fastest, either one or two high-density clumps will form, depending on the initial perturbation of the stellar density. These high density fragments continue to grow rapidly during the collapse, thus becoming denser and hotter. 

Once temperatures of more than one billion Kelvins are reached, a process sets, which is called electron-positron pair creation. The creation of particle pairs is possible because there is enough energy available in the surrounding gas to spontaneously create a particle and its anti-particle, in this case electrons and positrons. The pair creation process has the effect of taking out energy from the gas fragments, thus dramatically reducing their local pressure. The reduction in pressure support leads to a rapid increase in the central density within each fragment up to the point at which the fragments become so dense that event horizons appear around each of them (center left panel of Figure 1). In the case of an initial m=2 density perturbation, two black holes form that orbit each other. Since two black holes in close orbit emit very powerful gravitational radiation - ripples of space-time that travel at the speed of light - , the associated loss of energy causes the black hole orbits to shrink, leading to an inspiralling motion (red lines in the center left panel of Figure 1). The leading order mode of the corresponding emitted gravitational wave signal is shown in the lower panel Figure 2.

Figure 2: (To view higher resolution click on the image) The upper panel shows the time evolution of the density maximum until black hole formation. The center panel shows the mass and spin evolution of the black holes. The lower panel shows the emitted leading order gravitational wave signal.

It resembles the typical quasi-sinusoidal oscillatory signal expected from binary black hole mergers: as the orbit shrinks, the emitted radiation becomes higher in frequency. The inspiral continues until a common event horizon appears, marking the merger of the two black holes (lower left panel of Figure 1). The black hole merger remnant is initially deformed into a peanut shape, which quickly relaxes into a spherical shape by emitting exponentially decaying gravitational ring-down radiation. This is shown in the lower panel of Figure 2. The peak amplitude of the waveform corresponds to the black hole merger. From there, the signal quickly decays due to black hole ring-down. By the end of our simulation, the remnant black hole is rapidly rotating and is surrounded by a massive accretion disk (lower right panel of Figure 1).

The formation of two merging black holes requires a particular choice of initial stellar model parameters at the onset of collapse: (i) we require rapid rotation and (ii) a poloidal m=2 standing density wave perturbation must be present. This naturally leads to the question of the likelihood of our model. Recent cosmological simulations of collapsing primordial gas clouds - the potential birth sites for supermassive stars - indicate that rapid rotation is very likely [4]. Curiously, the same simulations also show that an m=2 deformation arises at the center of the clouds where the supermassive star will eventually form. Unfortunately, these simulations currently do not offer sufficient spatial resolution to investigate the formation of supermassive stars in the collapse of primordial gas clouds in detail. Further research will be necessary to self-consistently model the formation of supermassive stars that may inform us about the stellar conditions at the onset of collapse.


The new and exciting prediction that two black holes can form in the collapse of a single star gives rise to very efficient gravitational wave emission compared to models where only one black hole forms. The emitted gravitational radiation in our model configuration is so powerful that future space-borne gravitational wave observatories might see the signal from the edge of our universe. This has important implications for cosmology. If detected, the signal will inform us about the formation processes of supermassive stars and supermassive black holes in the early universe and will allow us to test the validity of the supermassive star collapse pathway to supermassive black hole formation.

Acknowledgements: This research is partially supported by NSF grant nos. PHY-1151197, AST-1212170, PHY-1212460, and OCI-0905046, by the Alfred P. Sloan Foundation, and by the Sherman Fairchild Foundation. CR acknowledges support by NASA through Einstein Postdoctoral Fellowship grant number PF2-130099 awarded by the Chandra X-ray center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. RH acknowledges support by the Natural Sciences and Engineering Council of Canada. The simulations were performed on the Caltech compute cluster Zwicky (NSF MRI award No. PHY-0960291), on supercomputers of the NSF XSEDE network under computer time allocation TG-PHY100033, on machines of the Louisiana Optical Network Initiative under grant loni_numrel08, and at the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the US Department of Energy under contract DE-AC02-05CH11231.

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