Questions About Spatial Orientation of Event w/ Respect to LIGO

[Raffer]

I didn't see these areas addressed, my apologies if I missed them.

If there was no delay in the detection of the signals at the two sites, would that mean that the location of the event was 'directly overhead' or 'directly below'?

Was the delay, compared to the speed of light and distance between the sites, indicative of the angle the the event was off center from a line connecting the two sites? Would a very small delay suggest a very wide angle over which the the event could have originated.

Also, what can be inferred about the orientation of the plane of the two BHs as they approached each other, with respect to the earth? Was it a static plane as shown in the simulations, or one that had other rotational components with respect to the earth? Is visualizing it as a plane even accurate?

If the rotation of the two BHs as they approached each other were in fact in a plane and we were looking at the rotational plane from 'directly above' rather than on edge, how would that affect the amplitude of the GW? Would we see it at all? Would either of the sites be able to detect an event from a plane 'parallel' to the plane of the site? or an event in the same plane as the mirror(s)?

One last question, how does the fact that the two sites are presumably not oriented in the same plane (curvature of the earth) impact the observations?

 

[Buzz Bloom]

Hi Raffer:

Here are some quotes from LIGO threads that I think answer some of your questions.

#144 in https://www.physicsforums.com/threads/advanced-ligo-detection.836670/page-8

The speed of gravity has to be less than the distance between Richland and Livingston, which is about 1850 miles, divided by the difference in time, which is less than 10 ms. So that gives as a ballpark estimate of within a factor of a few of 185,000 miles per second.​

https://www.physicsforums.com/threads/advanced-ligo-detection.836670/page-6#post-5374892

From http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.061102
With only two detectors the source position is primarily determined by the relative arrival Time and localized to an area of approximately 600 deg2 (90% credible region).
z = 0.09^+0.03_-0.04.
If my math is OK, this means that the source can be located with 90% confidence to a region of the sky with an angular diameter of about 14 deg. Combining that with the z value, how many galaxies are candidates for the source?[/SUP]​

https://www.physicsforums.com/threads/dispersion-of-gravitational-waves.856797/#post-5376832

@Buzz Bloom: that localization assumed light-speed propagation.​

Regards,
Buzz

​

 

[bcrowell]

If there was no delay in the detection of the signals at the two sites, would that mean that the location of the event was 'directly overhead' or 'directly below'?

Was the delay, compared to the speed of light and distance between the sites, indicative of the angle the the event was off center from a line connecting the two sites? Would a very small delay suggest a very wide angle over which the the event could have originated.

I think your question was answered to some extent in this thread: https://www.physicsforums.com/threads/ligo-and-speed-of-propagation-of-gravity.856953/

Also, what can be inferred about the orientation of the plane of the two BHs as they approached each other, with respect to the earth? Was it a static plane as shown in the simulations, or one that had other rotational components with respect to the earth? Is visualizing it as a plane even accurate?

In your second sentence, it's not clear to me why you use "static plane" in contradistinction to "had other rotational components with respect to the earth."

IIRC Kip Thorne discussed this briefly at the press conference while presenting one of the animations. The black holes each had their own angular momentum, and that angular momentum was interchanged with orbital angular momentum, causing wobbles in the motion that were visually obvious in the animation.

Gravitational waves are transverse, and they have a polarization that I believe these detectors were sensitive to. I think this polarization probably does tell us something about the orientation of the stars' orbits, but I haven't seen any details on that, and it didn't seem to be discussed at all in the paper, which was a short letter.

If the rotation of the two BHs as they approached each other were in fact in a plane and we were looking at the rotational plane from 'directly above' rather than on edge, how would that affect the amplitude of the GW? Would we see it at all? Would either of the sites be able to detect an event from a plane 'parallel' to the plane of the site? or an event in the same plane as the mirror(s)?

Gravitational waves are quadrupole in nature, so they should have a quadrupole radiation pattern, which I believe would have two polar lobes and one equatorial "doughnut" lobe. Zero intensity would occur at some angle ca. 45 degrees.

One last question, how does the fact that the two sites are presumably not oriented in the same plane (curvature of the earth) impact the observations?

I believe the arms of the two interferometers are also not oriented the same way. Each interferometer will have some sensitivity that depends on both the direction of propagation of the wave and its polarization.