[chris (OP)]

The recent announcement of the detection of gravitational waves by the LIGO team included the pronouncement that the origin of the waves was the merger of two black holes a billion or so light years away.

How could they tell where and when the gravitational waves originated?

[Space Flow]

Because there are two L shaped detectors separated by a known distance, it affords a certain not quite triangulation but directionality ability.
Each detector has some directional information just from detecting which of the two arms detected it before the other. Combine this information from each of the two detectors with the timing between the two detectors themselves and you can narrow the direction somewhat.
It isn't enough to give an exact direction in the sky, but it does give a generally much narrowed area.
If we had 3 detectors equally spaced around the planet we could do some real triangulation and get a definite direction line. Probably not a wide enough base line for parallax to help with distance, but definitely an accurate direction.
eLISA due to launch in the mid thirties will stretch our baseline for some real accuracy.

How they came by distance and therefore mass figures is totally beyond me.
Look forward to someone answering that part.

[evan_au]

Skimming the paper again:
The only real mention of distance in the body of the document is in Section VI, Table I. It really only states the answer that is in the abstract.

The source lies at a luminosity distance of 410(+160, −180)  Mpc corresponding to a redshift z=0.09(+0.03,−0.04).

I am guessing that the researchers would know:

• the approximate sensitivity of their detectors, since they are continuously injecting calibration signals
  
• the approximate size of the incoming black holes, from computer modeling of the chirp signal
  
• the strength of the gravitational waves that would be produced from such a merger, based on Einsteins General Relativity.
  
• the polarization of the gravitational waves, from the different signals picked up by the two detectors
  
• From this "luminosity", you could estimate the distance (410 MegaParsecs)
  
• It may also be possible to estimate the red shift (z=0.09) from the oscillation frequency measured on Earth compared to the oscillation frequency you would expect if you were located in the same frame of reference as the black holes.
• Cosmological red shift then allows you to estimate a distance.
  

It is not clear to me how much the chirp signal dictated the answers, and how much of it was throwing possible scenarios into a supercomputer, and seeing which one produced results closest to what was observed. At least they have tried to place confidence intervals on the results.

[Space Flow]

I must say that mentioning redshift when talking a bout a gravitational wave is both interesting and confusing. Even talking about a Luminosity distance feel strange. 
I would like to know more..

[evan_au]

the origin of the waves

This week's show asked about how the direction of the source was determined.

The unfortunate answer is that it was not determined very accurately at all. It is constrained to within a total area of about 600 square degrees, which is a fair swathe of the sky (the Moon occupies about a quarter of a square degree).
 [ Invalid Attachment ]

Calculation
The time of arrival at the two detectors differed by about 6.7 ms over a distance of around 5000 km.

• The source could not have been on a straight line between the two detectors, as that would mean that it exceeded the speed of light, which physicists think is impossible.
  
• Assuming that the gravitational wave traveled at the speed of light (as predicted by Einstein), you can deduce that the wave originated at a point in the sky which is at a certain angle to the line joining the detectors. This would inscribe a circle in the sky. Due to uncertainties in the measurements, this circle is about 10 times the width of the Moon in the sky.
  
• There was additional (phase?) information which they drew on to further limit it to less than a quarter of this candidate circle around the sky
  

Finding the Source
It was suggested that astronomers could point their telescopes at the source and see a black hole. They certainly tried.
Unfortunately, 600 deg² is not a small enough region to know where to point a big optical telescope, which typically cover a very small area of the sky, much smaller than the Moon. This event was so distant that it would need long exposures on a large telescope. Radio and gamma ray telescopes have less resolution, so they can cover larger areas of the sky.

Black holes are particularly hard to see - astronomers now have a good idea of the location and mass of the black hole in the center of our galaxy - but only because they have spent the past 15 years observing the paths of about a dozen stars that are in close orbit around it. The black hole itself is practically invisible -  and this one is only 25,000 light years away, not 1,000,000,000 as estimated for this gravitational wave source.

Fortunately, by the time they have 3 or 4 operational gravity wave detectors (in 4 or 5 years), they will be able to narrow down the source to an area in the sky that is perhaps no larger than the Moon. That is still a large area to search, but if the source were the merger of two neutron stars within our own galaxy, that may produce a burst of visible, radio and X-Rays radiation that is easily visible on Earth.

Unfortunately, the merger of two otherwise isolated black holes is unlikely to produce much visible radiation.

This paper shows more details on the analysis: http://arxiv.org/pdf/1602.03840v1.pdf
This paper is expected to appear soon (for now it is just the diagram above): https://dcc.ligo.org/public/0122/P1500227/006/placeholder.pdf

[evan_au]

This pre-print suggests that a faint gamma-ray burst detected from the Fermi satellite may be linked to the gravitational wave event.
It arrived within 2 seconds of the gravitational wave detection.
http://gammaray.nsstc.nasa.gov/gbm/publications/preprints/gbm_ligo_preprint.pdf

This gamma ray satellite tries to cover most of the sky (apart from the sizeable part obscured by the Earth). It is not very directional, so it can't narrow down the source to a particular point in space, but if it was the same event, it may reduce the search area by a factor of 3.

[chris (OP)]

This week's naked scientists podcast is an in-depth analysis of the story of gravitational waves and their origins; it features Astronomer Royal Martin Rees and cosmology Andrew Pontzen; it's a good listen and fills in some of the gaps:

http://www.thenakedscientists.com/HTML/podcasts/naked-scientists/show/20160301-1/