LIGO -- Direction of sensing

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Summary:

LIGO operation, for gravity waves
As I understand, the gravity wave detection system is possible due to the change in length of the two arms, as a wave passes, thus changing the distance the light beams travel. As this distance changes, the time of flight will change in relationship to each other. This difference is then measured, after combining, and monitored, for the changing phase angle, caused by a passing gravity wave.

My question: If the source of the wave is located directly above or below LIGO, will the gravity wave be detected?

Thank You,
 
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Ibix
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Point of language: LIGO detects gravitational waves. Gravity waves are a type of surface wave on water.

The directional sensitivity of a LIGO detector is quite complex. The "stretch and squish" effect is perpendicular to the direction of travel of the waves. So a single LIGO instrument is actually most sensitive to waves coming from directly above or below with polarisation parallel to its arms, since one arm is stretched and the other one is squished. It is blind to waves coming in the same direction with polarisation at 45° to its arms because they don't stretch either arm. It is less sensitive to waves coming in at other angles even if the polarisation is optimal. The velocity of the source also matters since this can make some component of the stretch and squish parallel to the detector's timelike direction, to which it is also blind.

All of this is why it started with two detectors in different orientations, and why they have added and plan to add more.
 
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Ibix
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There's a nice diagram at Wikipedia showing how a ring of free floating masses react to a gravitational wave passing through perpendicular to the plane of the image. You can see the stretch-and-squish in action.

LIGO doesn't have a ring of free floating masses. It has just the topmost and rightmost dots and another one in the centre, which would be unmoving. If you ignore everything except those two dots and the middle of the ring, you can see that one arm lengthens as the other shortens. But that's if the wave is polarised conveniently. If the wave happens to come in polarised so that LIGO is at 45° (so its arms point north east and south east on the diagram) then you can see that those dots don't move at all.
 

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