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For LIGO's first gravitational wave detection, GW150914, the signal first reached Livingston, LA and then about 7 ms later reached Hanford, WA. Based on the sequence it was stated that black-hole collision occurred in southern sky. For the second detection, GW151226, the time difference between the signal arrival at the two sites was 1.1 ms.

Does this mean the black-hole collision occurred in southern sky, in this case also?

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LIGO's paper on Advanced LIGO Observing Run 1 summarizes the whole 3 month analysis including the two detections and one "trigger".

This panel from figure 5 shows the probable sky localization for all three events. figure 5 from paper

The sky location is mostly determined by triangulation of the time of arrival. Additional localization comes from the antenna pattern. The detectors are more sensitive to some directions (directly overhead and below) than others (along the arms). So comparing the amplitude of a signal in multiple detectors can help as well.

With two detectors a signal can be triangulated to a ring on the sky. Of course there is uncertainty in the time of arrival, so the ring is a bit wider than line. Amplitude comparison can reduce the ring. GW150914 was high amplitude. This makes the comparison easier, so it can be better localized.

GW151226 was low amplitude, so it is hard to do the amplitude comparison. That's why its probable origin is still smeared out across the sky. The projection of the spherical globe to the flat map makes the ring look a bit odd, but hopefully you can see how the two parts fit together to make the ring (missing small patches that the amplitude comparison rule out).

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