# How did the scientists know two black holes collided 1.3 billion years ago?

I saw a TEDx talk the previous day about the LIGO experiment and in that video he said they are waiting for the day Jan 1st 2017 for the Ripple in Gravity caused by two black holes colliding each other to reach us. But how could they make such an estimation? How the scientist knew about some incident happened 1.3 billion years ago?

• Please give the exact tine in the video where this erroneous claim is made. – Rob Jeffries Feb 13 '16 at 9:45
• The waveform detected by LIGO depends on the masses of the black holes, which determines the total energy release in form of gravitational waves. When they compare that with the strength of the signal that was received they can estimate how far the event had to be away... assuming that the theory is correct. The claim about future signals is completely nonsensical, though. – CuriousOne Feb 13 '16 at 9:45
• @RobJeffries around 14:20 – Varun Feb 13 '16 at 9:49

Right so what you have misunderstood is that this was a statistical prediction about when the first detection might be made, based on assumptions about the number of possible sources in the universe and their distance from us.

It is mildly surprising that (advanced) LIGO found such a big signal so soon after it began operations.

Detecting a few more will start to tell us a lot about how many large black holes there are in the universe as a function of cosmic time. Because the signal strength scales as 1/distance and binary mass to the power of 5, whilst the number of massive stars scales as $M^{-2.3}$ I think one expects most detections to be from distant very massive objects if their density is uniform in time.

The latter can be inferred because the signal strength and frequency from binary mergers tells you how far away they are, and GWs travel at the speed of light.

• LIGO was commissioned in 2002, so the "first light" was quite some time ago. They had something like four runs in the original configuration, then runs as "enhanced LIGO" and this, I believe, is the second major upgrade "Advanced LIGO". Since the new design is going to be ten times more sensitive than the original LIGO, the detection volume has increased 1000 fold. One can wonder, though, if this was a "pure luck" mega-event that could have been detected by the original design or if the non-detection in previous runs indicates a problem with the earlier experiment. – CuriousOne Feb 13 '16 at 10:37
• I think the prediction refers to advanced LIGO. If I've got it right the signal was at 35-250 Hz with a peak strain of $10^{-21}$ and a "characteristic strain" of about half that. I can't find a zoomed-in plot to make sure but it looks like LIGO would certainly not have detected this. – Rob Jeffries Feb 13 '16 at 11:18
• I don't think so, either, but the less sensitive detector may have detected smaller events that were closer. I don't know what power law the distribution follows (or if there is even such a distribution, since the black hole masses are limited from below), so maybe there aren't more smaller events closer to us... in which case the non-detection would have been consistent with this event. – CuriousOne Feb 13 '16 at 11:24
• @CuriousOne If the mass function is say $N(m) \propto m^{-2.5}$ and assuming a uniform density and production rate in time and ignoring cosmological complications, then I think the number of detectable events as a function of distance $r$ and mass $m$ should scale as $m^{+2.5} r$, so you expect fewer detectable events at small distances and far fewer from lower mass objects even though they are more common (we know that much less massive black holes and neutron stars exist). – Rob Jeffries Feb 13 '16 at 11:30
• I know all about the spectrum problem (from neutrinos and cosmic rays), what I don't know is what the predicted spectrum looks like. Is the exponent -2.5? Is there even a spectrum? There are, for sure, no 0.5 solar mass black holes if we trust general relativity. – CuriousOne Feb 13 '16 at 11:34