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by topquark 3783 days ago
It sounds like you've already read about how we estimate the false-alarm rate for signals, so I'll just add that the estimated rate of BBH mergers was highly uncertain before this observation; the error bars spanned three orders of magnitude. See, for example, Fig 5 of http://arxiv.org/abs/1111.7314, which compares the previous LIGO-Virgo upper limits on similar events to the expected rate from population synthesis models and observations of high-mass X-ray binaries, known BNS systems, etc.

The rate inferred from GW150914 is on the high end of the rate estimates from astronomers, but it's completely consistent with prior observations. Certainly, if we had seen ten events in the first 16 days of data, it would not have made sense! But one event is well within expectations.
2 comments
nonbel 3783 days ago
A lot of this information seems to be available, for example figure 4 here[1]. According to that, the horizon distance for "a binary black hole system with the same observed spin and mass parameters as GW150914 for optimal sky location and source orientation and detected with an SNR of 8" was 1.5-2 Gpc. Now we only need an estimate of the rate at which events with these properties occur, not using the data from GW150914. I presume this is somewhat (a few orders of magnitude) less than the rate at which the mergers occur in general.

[1] http://arxiv.org/abs/1602.03844

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nonbel 3783 days ago
Thanks, I'll have to look more closely at that paper since I only see discussion of the upper bounds. The reason for my concern is that I noted elsewhere that the prior lower bounds on the merger rates got pretty low: ~0.1 Gpc^-3 yr^-1. For only 16 days of observing the expected number of events drops to 4.38e-3 Gpc^-3.

Then if the horizon distance is somewhat less than than 1 Gpc we need to scale this further. Say it was 0.5 Gpc, we scale by 0.5^3 to get ~5.475e-4 expected events. For 0.2 Gpc horizon we get ~3.5e-5! These values are getting dangerously close to the estimated background rate, at least using this crude calculation at the lower ends of the prior estimates.

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