# Will it Merge? Investigating How Gas Disks Can Determine the Future of a Binary Black Hole System

Authors: Magdalena Siwek, Rainer Weinberger, Lars Hernquist

First Author’s Institution: Center for Astrophysics, Harvard University, Cambridge, MA 02138, USA

Status: Submitted to MNRAS, available on arXiv

When galaxies merge, their respective black holes fall to the new galaxy center to form a binary black hole system. It is expected that the black holes in the binary will orbit around each other and inspiral towards each other over time, eventually coalescing into a single new black hole. One driver of inspiral is gravitational waves being emitted by the binary, however, gravitational waves by themselves cannot drive the inspiral fast enough to cause a merger within the age of the universe. If only gravitational waves drove binary inspirals, we would expect to see binary black holes at the centers of galaxies, but we typically only see a single black hole. For a while, this was a problem known as the Final Parsec Problem. We now know that the binary can interact with other bodies such as the circumbinary gas disk (CBD), a disk of gas and dust that forms around the binary.

Today’s paper investigates how the CBD affects the separation between the black holes in the binary as well as their orbital eccentricity. Analytical and numerical models suggest that gravitational interactions between the black holes and the CBD, as well as accretion of the CBD onto the black holes, are mechanisms that can accelerate binary inspiral because they remove angular momentum from the binary. However, recently, some research with hydrodynamical simulations suggests that the CBD-binary interactions cause the separation between the black holes to increase in some cases! To understand this, the authors of today’s paper investigated in which circumstances the CBD contributes to decreasing the binary separation and driving the inspiral, and in which circumstances the CBD prevents the binary from eventually merging.

The authors created a set of hydrodynamical simulations of a black hole binary with a CBD surrounding it. The orbit of the black holes in the binary is Keplerian, therefore it depends on the mass ratio $q_b$ between the two black holes, the semi-major axis of the orbit $a_b$ (i.e. the separation between the two black holes), and the eccentricity of the orbit $e_b$ (a circular orbit has $e_b=0$, while an elliptical orbit has an eccentricity between 0 and 1). Their simulations modelled how gravitational interactions between the black holes and the CBD, and how accretion of gas from the CBD onto the black holes, cause the eccentricity and semi-major axis of the binary’s orbit to change over time.

Figure 1 shows the rate of change of the semi-major axis of the binary orbit as a function of binary mass ratio and orbital eccentricity. For circular orbits ($e_b=0$) with mass ratios greater than 0.2, and for low mass ratio systems in eccentric orbits, the CBD does in fact cause the separation of the orbit of the binary to increase! These are the red cells. However, for most other cases, the CBD causes the binary to lose angular momentum and therefore cause them to inspiral into each other, shown by the blue cells. Therefore, if the binary is not in a circular orbit or has a small mass ratio, we expect the binary to inspiral.

Figure 2 shows the rate of change of orbital eccentricity as a function of orbital eccentricity and binary mass ratio. The red cells show eccentricity increasing, and blue cells show eccentricity decreasing. As you can see from the figure, there is a diagonal of white cells which suggest that the eccentricity of the orbit is neither increasing or decreasing at these parameter values. At these points, the binary has reached a steady state value, and the eccentricity will not change very much over time.

These figures provide us with a very useful guide to predict how a binary system will evolve because of a CBD. For example, imagine an eccentric binary system with mass ratio $q_b=0.1$. Figure 2 suggests that this system will have a steady-state eccentricity of about 0.2 (because it has the smallest rate of change for this mass ratio). Searching for a mass ratio of 0.1 and eccentricity of 0.2 in Figure 1 gives a red cell, suggesting that this system’s orbit will expand over time. If we increase the mass ratio of the binary, the steady-state eccentricity will fall into the regions of Figure 1 where the binary inspirals. Therefore, the authors hypothesise that the orbital separations of binaries with mass ratios less than about 0.2 will typically increase, while binaries with greater mass ratios are driven towards coalescence.

This is the most detailed investigation of how a CBD affects the orbits of black hole binaries yet. The CBD’s effect on the binary could in future be observed by pulsar timing arrays and LISA, therefore this work is important to understand what we may soon observe.

Astrobite edited by Lili Alderson

Featured image credit: NASA, ESA, and G. Bacon (STScI), adapted by William Lamb