LIGO detected gravitational waves created from the collision between two black holes. The detection was awesome, but let’s look at the name of the detector for a second: Laser Interferometer Gravitational wave Observatory (maybe I should call it LIGWO). LIGO is first and foremost an observatory. It’s a type of telescope that uses gravitational waves instead of electromagnetic waves. I’ve already gone over the methods LIGO uses to determine the distance to the black hole collision, but how do they determine the direction of the event?

It’s important to remember that if you detect a gravitational wave and know the source of the wave, you might be able to observe the event with an electromagnetic (x-ray, radio wave, visible) telescope. That would really be impressive.

Two Detectors and Two Times

There are two LIGO detectors. One is in Louisiana (only 30 minutes from where I live) and the other is in Washington. Other gravitational wave detectors exist on Earth, but they were not operational at the time LIGO measured a signal. There are two huge reasons to have more than one detector:

  • With two detectors you can check to make sure they both have a signal. This can eliminate the possibility that something local caused a vibration that looks like a gravitational wave.
  • Using the difference in times for the two detectors, you can get an idea of what direction the gravitational wave came from.

But how does the time difference work? Let’s start with a diagram. This shows the location of the Livingston, LA and Hanford, WA detectors (approximately).

Spring 2016 Sketches key

Looking at this diagram, there are two important things. First, there is the yellow line that passes through both detectors. Second, the white lines represent the path of the wavefront of a gravitational wave. Since gravitational waves travel at the speed of light, this particular wave hits the Livingston detector and then the Hanford detector. I added a dotted line to show the extra distance one of the waves has to travel to get to Hanford.

Here’s what we know about these waves. If a gravitational wave traveled along the yellow line and went through Livingston and then on to Hanford, the difference in time would be 10 ms due to the distance between these two location. The measured time difference for the detected gravitational wave was about 7 ms. Since light travels at a constant speed, there is a direct relationship between time and distance (that’s also why we can measure distances in light years).

Based on these two times (the wave time difference and the time difference between the two detectors), I can find the incident angle of the incoming gravitational wave. Let me focus just on the triangle created in the above diagram.

Spring 2016 Sketches key

Since this forms a right-triangle and I know two of the sides, I can find the angle θ as:

La te xi t 1

And that’s it. I know the angle of incidence for this gravitational wave—or do I? Actually, I just found one possible location. If the gravitational wave came in from the bottom of the diagram, I would have a flipped triangle but the exact same solution. Really, if you consider that space is three-dimensional, there are an infinite number of points that would give this time difference—however, those points are confined to a ring where the angle to this ring is the same θ. Maybe that’s difficult to picture in your head so I will make a 3-D model of this ring.

If you right-click and drag, you can rotate this model around and scrolling will zoom in and out. Actually, this ring goes out to an infinite size, but then you wouldn’t be able to see it.

Narrowing Down Further

Just know that the gravitational wave came from some ring isn’t that useful. There would be little chance that a telescope could find the event by scanning over such a large area. Perhaps the best way to decrease the search area would be to use a third (or even fourth) gravitational wave detector. If I added another detector, I would actually get two more rings like the one above. The intersection of these rings would then show the location of the source.

With just two detectors, you need to use some other tricks. Honestly, I don’t fully understand the analysis that LIGO uses (official details here) but that won’t stop me from attempting an explanation.

Spring 2016 Sketches key

For any particular detector, it is most sensitive to gravitational waves that come in perpendicular to the two interferometer arms. Since these detectors are on Earth, that means the best source (easiest to detect) would be straight overhead. Of course straight overhead would be different for the Livingston and Hanford detectors because of this thing called “a spherical Earth”.

Furthermore, the two detectors have slightly different orientations. Here you can see their orientation (with respect to local North) for each detector.

    Gw Localization l jpg 800×800 Image Credit: LIGO/Axel Mellinger

    Since they are on slightly different axes (and reversed), they also have different sensitivities to the polarization of the gravitational wave. So, in the end we can compare the relative strengths of signals at the two detectors and based on these values find a location on the ring (from above) that could give these signals. Of course there is a significant problem—you can’t use the gravitational wave polarization to determine direction without guessing the polarization. This means that we get a probability distribution for the locations on the ring. But still, that’s better than nothing. Here is the official LIGO map of possible locations of the black hole collisions.

    Notice the ring shape of these locations—that is due to the time difference between the two detectors. It’s pretty cool, but still it just emphasizes the need for more gravitational wave detectors (or should we call them gravitational wave telescopes)?

    See original article here: 

    LIGO Ain’t a Gravitational Wave Detector—It’s an Observatory