# Eccentric binary black holes

Comparable-mass binary black hole inspirals and mergers are expected to be an important source of gravitational wave signals for current and future ground-based detectors.

It is generally expected that such mergers occur as the end product of the evolutions of certain supergiant stellar binaries. In that case, since gravitational radiation strongly damps eccentricity, the inpiral should be "quasicircular" (circular over the orbital timescale, which is much shorter than the inspiral timescale).

This is unfortunate because the interesting relativity effects typically manifest only at substantial eccentricities. Therefore my question, which represents a certain amount of wishful thinking: are there any astrophysically-plausible mechanisms that might yield an inspiral with substantial eccentricity?

## 2 Answers

Short answer: No. There are numerous effects which can enhance the eccentricity of BH binaries. This is a very active area of study (and thus fairly uncertain), but the leading mechanisms are tangential-deceleration preferentially at apocenter (by, e.g. dynamical friction or [perhaps] stellar scattering in massive BH systems) or excitation from a perturber (almost exclusively a stellar-mass BH-binary, with a massive tertiary). The problem is that these effects act slowly, on secular timescales, while the Gravitational-Wave (GW) damping of eccentricity is extremely effective as the system nears inspiral --- and acts rapidly, on a dynamical timescale.

To observe the effects of eccentricity during merger, you would basically need to excite a near-unity eccentricity in only the final orbit --- which is extremely difficult to do (cough, effectively impossible, cough).

Slight Aside:
Just to be an especial-downer, let me point out that this doesn't really matter because high-eccentricity effects are practically unobservable. This is because LIGO detections are based on templated searches which rely on observing hundreds to thousands of oscillations to make a statistical detection. To observe high-eccentricity effects at the time of inspiral would require really high signal to noise. We can make a quick estimate by noting that the Signal-to-Noise Ratio (SNR) is proportional to $1/r$ where $r$ is the distance to the binary (note this is not $1/r^2$). A binary blackhole can be detected at an SNR of about 8 in each of 3 detectors, at about 1 Gpc. Lets say that a factor of 10 higher SNR would yield observable eccentric effects (I think it's probably a lot worse than this...), which would require a 10x closer system, sampling a $10^3$ smaller volume of space, and thus a $10^3$ lower detection rate. Let's say the first binary BH detection occurs after a month of operation (and we haven't heard yet...), this would suggest it would take another 100 yrs before a sufficiently nearby system were observed. If we're lucky, LISA might be up within roughly that time --- which would have much better chances!

• I happen to be involved with a group that is creating eccentric-waveform templates, so the latter point is perhaps less of a problem for me than you might think :) – AGML Dec 10 '15 at 16:55
• @AGML oh cool! Do you think it's less of a problem overall than I'm assuming? – DilithiumMatrix Dec 10 '15 at 18:42
• @DilithiumMatix I don't know so much about the population modelling (hence the question), but your reasoning sounds convincing. But the aside isn't, I think, so bad as you say. For one thing quite a lot of the SNR comes not from the early inspiral, but from the plunge/merger, which are very loud. Also, a highly eccentric binary would not be caught by the template bank at all: LIGO also employs non-templated "burst modelling" to find generic loud pulses of SNR. A highly eccentric periastron passage would qualify. – AGML Dec 15 '15 at 17:29
• LISA is sensitive to extreme-high-mass-ratio mergers, which may more feasibly be eccentric. There's a different problem here coming from orbital resonance. If the orbital frequencies of the inspiral are in certain rational ratios, the GW emission can be beamed in a particular direction, 'kicking' the system like a rocket. The exact kick is phase-dependent. It is therefore not possible to template such systems, since their behaviour is a function of the orbital phase, not just the mass ratio, spins, etc. – AGML Dec 15 '15 at 17:33

I actually wrote a paper on this. The prime motivation was to propose a unmodeled search as matched-filtering search aiming circular binaries will miss eccentric binaries. The argument regarding LIGO seeing an event in one month will change as the sensitivity improves. By the time LIGO gets to advanced sensitivity we will probably see around 10-40(roughly as there are large statistical errors right now) events per month.

On a side note I have yet to see some work which shows that eccentricity can bring out strong field effects.

• Welcome on Physics SE :) I think it might be interesting to have the paper referenced so that people can look it up :) – Sanya Oct 17 '16 at 13:12
• Well, zoom-whirl orbits for example are necessarily eccentric – AGML Oct 17 '16 at 23:44
• Here you go: PhysRevD.93.043007 – user2555272 Oct 18 '16 at 10:13