# Frequency of gravitational wave detection

You may have heard in the news that the LIGO experiment recently detected a gravitational wave.

Though I'm not an astronomer, the paper is a good read and mostly accessible. The detection of the gravitational wave is one thing, but the black hole merger is quite new to me. From the data I could collect in the paper and this site, the source is estimated at 1.3 billion years, and the chirp lasted only a few milliseconds.

My question: what is the frequency of events of this size order? Is there any estimate of the density of such events in the universe?

Harry (2009) cited several different sources stated that, as far we know, the rate of detectable events will be

• 40 neutron star mergers per year
• 30 10 M$_\odot$ black hole mergers per year
• 10 neutron star/black hole mergers per year

This is within a radius of about 200 Mpc. This cannot, however, be used to extrapolate the total rate of such events, because of detection bias - the more massive the objects, the more easy they are to detect. The same thing happens with exoplanets, but for different reasons (e.g. planets that are more massive or closer to their stars are easier to detect via transit or by radial velocity methods).

• The numbers in your reference are for the full sensitivity of aLIGO, not what it is currently. The sensitivity is about a factor of 2-3 worse at present, which means the volume of space probed is 10 times less, as would be the numbers of detections for a uniform source population. – Rob Jeffries Feb 17 '16 at 22:58
• @RobJeffries I'm aware of that; AFAIK, it won't be fully upgraded to that sensitivity for some time. – HDE 226868 Feb 17 '16 at 23:01
• Yes, it is for that reason that it is not perhaps a surprise that the first detection is a very massive black hole at a large distance. – Rob Jeffries Feb 17 '16 at 23:02
• @RobJeffries Yeah, I was initially surprised that the black holes were much more massive than other stellar black holes we have evidence for, but it makes sense that any detections in the near future will also be of massive objects, and rising sensitivity will increase the number of lass-massive systems detected. – HDE 226868 Feb 17 '16 at 23:05

The rate of detected gravitational waves of this amplitude or detections of gravitational waves due to the merger of black hole binaries are both unknown quantities for the moment. Measuring these is partly the purpose of the experiment.

The rates of detection can be converted into a rate of mergers per unit volume in space and these can be compared with models and predictions. The aLIGO collaboration have released their first post-detection paper on that very topic - Abbott et al. (2016).

The high mass of the discovered black holes implies that they either formed in a metal-poor environment from the core-collapse of massive stars or that they formed from the merger of smaller black holes in dense clusters. The range of rates previously predicted for the mergers of such objects covered a huge range because of the massive uncertainties in the production rate and mechanisms for binary formation of these objects, and lay in the range from 0 to about 1000 per year per cubic Gigaparsec.

The rate actually implied by the single detection of a BH binary merger (from only 16 days of data) at $z=0.09$ is somewhere between 2 and 400 per year per cubic Gigaparsec. So at present, this doesn't really rule out a lot, but it is expected that with a few further detections in the coming months the uncertainty on this number will come down rapidly.

• Kip Thorne said on the press conference that we should see a few more in the coming year. He does refer to a statistical study, but maybe he would be more careful unless he perhaps knows that aLIGO already has some candidates since September. With the lowest expectation of 2/Gpc³, they should. – LocalFluff Feb 21 '16 at 10:48
• @LocalFluff I really hope so. It would silence some extremely cynical people. – Rob Jeffries Feb 21 '16 at 18:37

As you may have guessed, this question is of great interest to the LIGO team. Simultaneously with the publication of the paper you mentioned announcing the discovery, the LIGO team submitted a number of companion papers with further details about the discovery, and predictions. One of these addresses your question:

The Rate of Binary Black Hole Mergers Inferred from Advanced LIGO Observations Surrounding GW150914

Their event rate estimation method considers both GW150914, and another significantly weaker (and less statistically significant) event. They consider a number of models for how the event rate might depend on system properties, and ask what the observations of GW150914 and the other candidate event imply for the overall rate. The results vary from model to model, but they chose models they felt could roughly bracket astrophysically plausible behavior. As summarized in their abstract:

Considering only GW150914, assuming that all BBHs in the universe have the same masses and spins as this event, imposing a false alarm threshold of 1 per 100 years, and assuming that the BBH merger rate is constant in the comoving frame, we infer a 90% credible range of $2-53 \, \mathrm{Gpc}^{-3} \, \mathrm{yr}^{-1}$ (comoving frame). Incorporating all triggers that pass the search threshold while accounting for the uncertainty in the astrophysical origin of each trigger, we estimate a higher rate, ranging from $6-400 \, \mathrm{Gpc}^{-3} \, \mathrm{yr}^{-1}$ depending on assumptions about the BBH mass distribution. All together, our various rate estimates fall in the conservative range $2-400 \, \mathrm{Gpc}^{-3} \, \mathrm{yr}^{-1}$.

Note that the paper is submitted, not published, i.e., still under peer review. Speaking as someone with expertise in such calculations, some aspects of the method look fishy to me, so I think it's worth checking back on the article in a few weeks for revisions. It doesn't take fancy methodology to see that the order of magnitude here (a few to ~100 per cubic gigaparsec per year) is in the right ballpark. But the paper presents a methodology that could make more detailed and more precise estimates and predictions as data accumulate, so it's important to make sure the methodology is sound.

• What are your suspicions? – Rob Jeffries Mar 4 '16 at 18:09
• If they aren't addressed once the paper is accepted for publication, I'll consider weighing in then. I'd rather not discuss it publicly while it's under review. I don't think any of my concerns would substantively change the estimates in the present large-uncertainty regime. – Tom Loredo Mar 5 '16 at 20:17