The Journey of a Gravitational Wave II: GWs Get Bent

What happens to a gravitational wave between when it is produced and when LIGO can detect it?  It turns out not much, which makes it a key new medium in which to observe the Universe!

Last week, I began discussing what happens to a gravitational wave as it makes its way from its source to Earth; specifically that gravitational wave can travel through matter and come out the other side unchanged!  Today's post talks about how the gravitational effects of other masses in the Universe can deflect the gravitational wave from its otherwise straight path.


GRAVITATIONAL LENSING

Let's think again about what happens to light on its way to Earth.  We know from the last post that any matter light comes into contact with will reflect or absorb at least part of the light.  There is also another effect called gravitational lensing that causes light to bend around massive objects due to the massive object's gravitational influence.  This is caused by light following its natural path on curved spacetime (or light being bent by a gravitational field since we've previously established that the curvature of spacetime is a representation of the strength of the gravitational field there).  The first thing that pops into my mind that illustrates something following its natural path on a curved surface is miniature golf:

This is hole 13 at Safari Mini Golf in Vero Beach, FL.  This image is taken from a review of this course and can be read here.

Consider the example hole in the above image.  After you get your ball past the three bumps, there is a wonderful bowl-like curved portion behind the target hole (if you look very closely, you can see the hole directly after the last bump and in the center).  If you hit your ball into this area, the ball's trajectory will change from a straight path to a curved one.  If your ball begins its path on the left side of the bowl, it will curve right; if your ball enters the bowl from the right, it will curve left.  The same thing happens for light and gravitational waves that pass by a massive enough object to cause a significant depression in spacetime (i.e. a strong gravitational field):

The bending of light from a star that is really behind the Sun but appears to be to the side of the Sun.
[Credit: Ethan Siegel of Lewis & Clark College, OR]

The the light from a star, galaxy, or other source travels through the depression in spacetime made by a nearby massive object (in the image above it is the Sun).  The path that light takes is curved just like the golf ball in the miniature golf example above.  But our brains are wired to assume that any light that enters our eyes has come to us in a straight line (which is how light usually travels) so we perceive the location of the source to be directly behind where it appears to be.  Therefore, while the star is really behind the Sun (at point A in the image above), it appears to us to be to the side of the Sun (at point B).  This bending effect is called gravitational lensing and it applies to gravitational waves just like it does to light.


KINDS OF GRAVITATIONAL LENSING

The example of gravitational lensing given above was one of the first observational proofs that Einstein's general relativity was correct.  Before relativity, there was already a prediction of the bending of light due to Newtonian gravity (what we use in our everyday life) but Einstein predicted the bending effect should be twice that predicted without relativity.  In 1919, there was a total eclipse of the Sun which would allow those stars that are near the Sun to become visible.  Images of the eclipse were taken and it was seen that the shift in the position of stars near the Sun was indeed twice that of the shift predicted by Newtonian gravity.

There are also kinds of lensing that produce much more dramatic effects than shifting the position of stars!  Things like large galaxies and clusters of galaxies can cause the light from objects behind them to be split up to form multiple, separate, and complete images. 

[Image from NASA]

The image above shows gravitational lensing of a quasar and a galaxy by a distant galaxy cluster SDSS J1004+4112 (SDSS indicates that it was discovered by the Sloan Digital Sky Survey).  Each image of the quasar is of the same single object; the same is true of the galaxy! 

You may notice that each of the images are a little different from each other.  This is due to the distortion that a gravitational lens can cause.  This effect is illustrated well in the simulation below of a black hole creating a gravitational lens as it passes in front of a galaxy:

[Image from Wikipedia]

Note the circular distortion of the light from the galaxy as the black hole passes by.  When the black hole is directly in front of the galaxy, there is a circular halo of lensed light around it.  This halo called an Einstein Ring can can be caused by any extremely massive object (black hole, galaxy, galaxy cluster, etc.).

[Image credited within the image and retrieved from Wikipedia.]

HOW LENSING AFFECTS THE SEARCH FOR GRAVITATIONAL WAVES

Gravitational lensing affects both light and gravitational waves.  This produces spectacular images of objects using light, but LIGO will not produce images and the sources that produce gravitational waves are more point-like (a black hole, a star exploding, etc.) than large scale objects (like galaxies which are thousands of light-years across).  The effect that will most likely be seen in gravitational waves is their focusing; the bending of gravitational waves can produce more intense gravitational waves from the lensed source (similar to a magnifying glass focusing light to a smaller point).  This paper suggests that the galactic center of the Milky Way could increase the intensity of a source in our galaxy (bur behind the galactic center) up to 4000x.  Also, if a gravitational wave is emitted from a galaxy that has multiple images from lensing, then that gravitational wave will come from each image!

However, most sources will not have appreciable lensing.  While this is something we will always need to consider while conducting gravitational-wave astronomy, it isn't something that is likely to change the information contained on the gravitational wave noticeably (and that's a good thing)!

The Journey of a Gravitational Wave I: GWs Cast No Shadows!

What happens to a gravitational wave between when it is produced and when LIGO can detect it?  It turns out not much, which makes it a key new medium in which to observe the Universe!

In order to make this information more digestible, I will address one aspect of a gravitational wave's journey through space.  Today's topic discusses how the Universe is essentially transparent to a gravitational wave.  Future editions will discuss how matter can bend gravitational waves (gravitational lensing) and how the expanding Universe can stretch out (redshift) gravitational waves.


GRAVITATIONAL WAVES CAST NO SHADOWS:

First, let's think about what happens to light.  As light travels through the Universe, any time that it encounters other matter, some of the light is absorbed by the matter or reflected away from its original path.  The opposite happens for a gravitational wave; it can pass through matter and come out the other side unchanged (although there are some negligible effects)!  That means that there is no such thing as a gravitational-wave shadow and nothing can obscure our detection of a gravitational wave!


The Spacetime Explanation:

But why is this?  In a previous post, I described a gravitational wave as a change in the gravitational field moving out into the Universe.  This change in gravitational field is often illustrated as a ripple, or wave, on spacetime (where the steepness of the curvature of spacetime represents the strength of the gravitational field, or the gravitational force a mass would feel, there).  Let's look at what the Earth sitting on space-time looks like:

This picture isn't a perfect representation since the size of the Earth will affect the shape of the depression and this has no effect on real spacetime.  Also, this is a simplified 2-dimenional representation of 3-dimensional (or a snapshot of the 4-dimensional spacetime) space.  But if you were to imagine giving a corner of this flexible grid (spacetime) a swift shake, the Earth in the middle would be affected by it but it would not impede the wave.  So, this is an example of how matter doesn't interact with gravitational waves, but I am still somewhat unsatisfied with this since you may think that the Earth will bounce after a wave passes creating more waves of its own (here is another aspect where this representation of spacetime is not perfect).

FYI: A better 3-dimensional representation of spacetime is shown in this clip from the American Museum of Natural History's short documentary called Gravity: Making Waves (which can be seen in its entirety on my Viewing Fun! page).  This animation shows a grid-like scaffolding filling space in which there is a depression caused by mass.  While it still isn't a perfect representation of spacetime, it is much better than the trampoline approximation above.

The Lunar Eclipse Explanation:

Recently, I thought of another more intimate example that most of us can identify with: a total lunar eclipse (which I have also blogged about).  This is a situation where the Sun, Earth, and Moon line up in that order so that the Moon is completely in the Earth's shadow:

Image from Wikipedia

When the Moon is completely in the Earth's shadow (or the umbra in the diagram above), a viewer on the Moon would not be able to see any part of the Sun.  If the gravitational field from the Sun were blocked by the Earth, then the Moon's orbit would appear to change.  Since there is no change in the Moon's orbit during a total lunar eclipse, then the Earth does not block the Sun's gravitational field.  By extension, the Earth also would not be able to block any changes in the gravitational field (which are gravitational waves).  If you are familiar with physics, this is an application of the principle of superposition.


Great!  But Why do We care?

Since mass does not absorb or reflect gravitational fields, the Universe is transparent to a gravitational wave.  This is a huge advantage when using gravitational waves to make astronomical observations since nothing can block our view of a gravitational wave!  If you have ever seen the our own Milky Way galaxy in the sky on a clear, dark night, you've seen the billions and billions of stars that live in our "backyard": 

Fish-eye mosaic of the Milky Way galaxy as seen from Chile.  [Image from Wikipedia]

While this is beautiful, it also it almost impossible to see past all the stars and dust there to observe what is behind our "backyard".  We will be able to see right through the Milky Way with gravitational waves! 

P.S.  We can also detect gravitational waves from the other side of the Earth with LIGO since gravitational waves can travel through matter.  Read more about this in this previous post (under the subheading of "Why are there 2 LIGOs?")!

What Is a Higgs Boson?, What Did CERN See?, and Why It's a Big Deal!

This is my disclaimer - I AM NOT A PARTICLE PHYSICIST!  Therefore, this subject does not fall into my realm of expertise.  However, I do have a very basic training in the physics behind all of this so I would like to share with you a little bit about why all of us physicists have been so excited of late...


WHAT IS A HIGGS BOSON?

The Higgs boson (regular Wikipedia entry, Simple English Wikipedia entry) is the elementary particle that gives matter mass.  Many of us have probably heard about Einstein's famous equation:

This image is taken from Wikipedia.

While this equation is famous, the true meaning behind what it means is often not fully appreciated (I used to see it and simply think "Einstein!").  It means that mass can be converted to energy and energy can be converted to mass, also known as the mass-energy equivalence.  The energy, E, from an amount of mass, m, is equal to the mass multiplied by the speed of light, c, squared (c² = c*c, c is about 670,616,629 miles/hour).  If you were to convert 1 oz of matter into energy, you would have about 2,500,000,000,000,000 Joules of energy and this would keep a 100 W light bulb lit for over 807,389 years!  So, a little bit of matter can be converted into an immense amount of energy!  It is this conversion of mass to energy that makes nuclear weapons so destructive.

But, if we convert energy into mass, where does this mass come from?  The Standard Model, which is the working description of how the fundamental particles interact (I talked about this in my post discussing gravitons), says it comes from the Higgs field.  This is a field similar to the electric field and the magnetic field (more on fields in general here).  At the instant after the Big Bang, all particles moved at the speed of light (c from above) since none of them had mass because there was no Higgs field.  In the next instant (about a trillionth of a second later), the Higgs field came into existence and produced a resistance to particles based on what they were made of.  This resistance manifests itself as mass: the slower a particle moves through the Higgs field, the more massive it is.  The Standard Model also allows fields to manifest themselves as particles (the photon is the particle associated with the electric and magnetic fields).  Therefore, this Higgs field should also manifest itself as a particle and we call it the Higgs boson.

The only particle from the Standard Model that has not been detected is this Higgs boson.  (Note that gravity is not described by the Standard Model.)  This is because the Higgs boson is very massive for a fundamental particle at about 133 times the mass of a proton.  The amount of energy conversion needed to produce this mass is much larger than we have been able to create in the past.  That is, until CERN built the Large Hadron Collider (LHC)...


WHAT DID CERN SEE?

View of the CMS experiment [note the person near the center] (© CERN)

CERN is the home to several experiments including CMS and ATLAS.  Both of these experiments smash together protons with very large energies.  The protons and their energy can change into a Higgs boson (if there is enough energy).  The Higgs boson decays (changes into something else) almost immediately, so the LHC experiments look for the Higgs boson's signature in the resulting particles.  There are 5 pairs of particles that result from the decay of a Higgs boson, including 2 photons.

Both CMS and ATLAS saw the Higgs signature in 2 of the 5 different resulting decay pairs.  Only CMS had sufficient data to look for all 5 kinds of decay pairs and saw with high certainty signatures in 4 of the pairs.  More research is needed for the signature CMS didn't see.

Diagram of the ATLAS experiment [note the people on the bottom left] (© CERN)

WHY IT'S A BIG DEAL!

The official conclusion is that CERN has indeed observed a Higgs-like particle.  "Higgs-like" does not mean that they are unsure if they found what they were looking for.  Instead, it appears that the Higgs boson they observed has more properties to it than the Standard Model predicted.  The LHC has found what it is looking for as well as hints that there is new physics to be discovered.

So this is the big deal: the population of the Standard Model is complete but the model itself doesn't appear to describe everything.  That is something we knew before, but now we are seeing it with the apparent complication in what was and wasn't observed in the discovery of the Higgs boson.

I am a physicist because every time you discover something new, not only do you understand the Universe better, but you have even more exciting questions to answer!  Soon enough, it is going to be gravitational waves stirring up excitement like this and I am going to be in the midst of it all!


Side Note:
IT'S NOT THE 'GOD PARTICLE'

The Higgs boson is sometimes referred to as the "God particle," especially by the media.  However, it has nothing more to do with God than any other particle in the Universe.  The origin of this misnomer is a book by Nobel Laureate Leon Lederman titled The God Particle: If the Universe Is the Answer, What Is the Question?.  Likening the Higgs boson as a God particle refers to it being the origin of all matter's mass.  Physicists (like me as well as Lederman himself) generally dislike this nickname since it places much more import on this particle than it deserves.  But above that, it is offensive to people of faith and makes us look like we are trying to replace God.  We aren't. 


Want More? ...
Watch the announcement seminar
Read the official CERN press release

Q: What Do Gravitational Waves "Sound" Like?

Okay, this isn't a question that I usually get asked but the answer to this question is the basis of my answer to questions about how we can determine information about what produced a gravitational wave from the signals we detect.  So, how do we do that?

One convenient feature of LIGO is that it is most sensitive in the frequencies that the human ear could hear if gravitational waves made sound - but they don't.  I can't stress this enough: gravitational waves do NOT make sounds since a sound waves are fundamentally different from gravitational waves.  But, if we take the data we gather from LIGO of a gravitational wave, we can put that signal through speakers and convert them into sound.  In this way, LIGO is very much like a gravitational-wave radio...


LIGO AS A GRAVITATIONAL-WAVE RADIO

Radio stations broadcast radio waves at a specific frequency (this is the number that you tune your radio to) and music is encoded onto this wave.  Whereever you are right now, you are most likely surrounded by radio waves from numerous stations but you can't hear radio waves or the music that is encoded onto them.  To hear this music, you need to have an instrument that can detect the radio waves, decode the music from them, and turn this signal into sound using a speaker.  Now, you can hear the music.

LIGO is a completely passive detector (meaning we just wait for something to happen, we cause nothing that we can detect other than noise) just like your radio is passive (it can't create music).  We wait for a gravitational wave to pass by Earth, and if it is strong enough and in the frequency range that we are sensitive to, then LIGO will detect a signal.  From that signal, we can extract information about what made the gravitational wave, like a radio decodes the music from the broadcast radio waves.  Once we have detected the signal, we can put that signal through speakers to convert it into sound.  Just like a radio, it is the speakers that make the sound and not the detector.  Since LIGO is sensitive to frequencies that are in the same ranges of sounds we can hear, we can hear the gravitational-wave signals when put through a speaker.  Now we can extract information about what made the gravitational wave just like we can hear the different instruments and voices in music.


LIGO'S SENSITIVE FREQUENCIES = AUDIBLE FREQUENCIES

Initial LIGO's most sensitive range (as we were before we started our current upgrades) was between about 60 Hz to 800 Hz.  This corresponds to the lowest note on a cello (click here to hear what 65.41 Hz sounds like) to the lower notes on a piccolo (click here to hear what 523.25 Hz sounds like), respectively (according to Wikipedia).  Once Advanced LIGO is complete and operating at sensitivity, it will be more than 10x as sensitive as Initial LIGO and its most sensitive region will be between about 20 Hz to 2000 Hz (this is the range that produces at least 10x the sensitivity of the sensitive range noted for Initial LIGO).  This corresponds to the lowest frequencies humans can hear (like the lowest note on a tuba) which is usually felt more than heard to a little below the highest note on a flute (click hear to hear what 2093 Hz sounds like).  LIGO's sensitivity to different frequencies are shown graphically below:

LIGO sensitivity vs. frequency (see this post for a description of how to interpret this plot).
Click on the graph to see a larger image.

Recall from a previous post that it is because LIGO is most sensitive to the audible frequency range that we cannot detect gravitational waves from the Moon, Sun, and planets; they produce gravitational waves at much lower frequencies.


THE "SOUNDS" OF DIFFERENT KINDS OF GRAVITATIONAL WAVES

We can tell just from what a gravitational wave "sounds" like what category it is classified as; there are 4 major categories:

1. Inspiral gravitational waves: two massive objects orbiting each other faster and faster as they get closer together and eventually merge into one.  Pairs of neutron stars, black holes, or the combination of the two are prime candidates for detection.
     ⇒These waves are expected to sound like a "chirp" (click here to hear the example in the plot below):





2. Continuous gravitational waves: a distorted object rotating about its axis with a constant frequency (the Earth rotates with a very constant frequency of once per day).  A neutron star rotating rapidly with a "mountain" on it are prime candidates.  ("Mountain" is in quotation marks because it is a deformation as little as a few inches high on the nearly perfectly spherical neutron star.)
     ⇒These waves are expected to sound like a single tone (click here to hear the example in the plot below):





3. Stochastic gravitational waves: many weak signals from different sources combining into one "jumble" of a signal.  Relic gravitational waves from the Big Bang are expected to be candidates for detection.
      ⇒These waves are expected to sound like static noise (click here to hear the example in the plot below):





4. Burst gravitational waves: these waves are short duration and from unanticipated sources or from known sources where we can't be sure what the gravitational waves will "sound" like.  I like to call these the gravitational waves that go 'bump' in the night.
      ⇒These waves are expected to sound like 'snaps', 'crackles', and 'pops' (click here to hear the example in the plot below):

While is is great to see and hear the differences between the different kinds of gravitational waves, it is harder to see how we can glean more specific information about the thing(s) that made the gravitational wave.  The answer is that we can use general relativity to predict what kinds of signals ("sounds") a certain situation will create.  Below is a movie by Steve Drasco (Caltech/CalPoly) showing the sped up evolution of a body 270 times the mass of our Sun orbiting and finally merging with a supermassive black hole 3 million times the mass of our Sun.  The movie starts one year before the two objects merge and the bottom of the frame shows a graph of the gravitational waves while the majority of the frame shows the orbit of the system.  As you listen, you can hear how the tone changes into the chirp that is characteristic of this kind of system (the movie is ~13 MB so it may take a minute or two to load):

 

By studying the predictions of what different gravitational waves will "sound" like, we can translate a detected gravitational wave into information on the system that made it.


DO WE ACTUALLY LISTEN FOR GRAVITATIONAL WAVES?

Yes and no...  The option to listen to the data as it is collected is available to scientists working in the LIGO control room.  I've done it but I don't make a habit out of it since almost all of what LIGO detects is small vibrations from our environment.  You can listen to real LIGO noise by clicking here (if you carefully listen all the way to the end, you can hear a fake inspiral chirp that has been added to the data - you may miss it).  Since what you predominantly hear sounds like static, it can lull you to sleep which isn't advisable when you are the responsible scientist on duty!  Also, almost all gravitational waves will be too weak to hear with our ears which is why we mainly analyze data using sophisticated data analysis techniques that have been specially designed to search for each of the four categories of gravitational waves.  (This is what I do for a living!)

I also wrote in March 2011 about a fake signal that was placed (injected) into the LIGO data to test if our data analysis techniques could really detect a gravitational wave if there was one.  This was a blind test (called the "Big Dog" due to its apparent location in the constellation Canis Major) meaning that only a few individuals knew about this fake signal and the rest of us were left to find it and interpret its results.  While we did not detect this signal by listening to it, it can be heard in both the LIGO detectors (about 17 seconds into the recording linked below).  This is real LIGO data and the sound may be VERY LOUD - so turn your volume down before you play it and then adjust it!
     ⇒Click here to hear the data around the blind injection for LIGO Hanford, WA.
     ⇒Click here to hear the data around the blind injection for LIGO Livingston, LA.*
          *Note that there is a audible instrumental "glitch" in the Livingston data about 8 seconds into the recording; this is unrelated to the injection.

While it is difficult to hear gravitational waves that will be buried in detector noise, there is no denying that the human brain is very effective at breaking sounds down into their individual components.  A recent Physics Today article titled "Shhhh.  Listen to the Data" discusses the advantages of humans listening to data and features a discussion of this application to LIGO.  Also, if you want to test your ear's talent at "hearing" gravitational waves, there is a fantastic website called Black Hole Hunter which places black hole gravitational wave "sounds" (like the system in the movie above) into simulated data and tests if you can discern the signal.  I've spent many an hour playing with this and even use some of the cell phone ringtones they've made (also available on the Black Hole Hunter site).

*** If you are interested in more gravity games, see my Gravity Games page (link here and under the blog banner)! ***


WANT TO HEAR MORE?

There are some great sites that feature the "sounds" of gravitational waves.  Here are a few of my favorites:

• Black Hole Hunter
• Scott Hughes' (MIT) page of gravitational wave sounds (and a more out of date one)
• black-holes.org page of gravitational wave sounds

Q: What Would a Gravitational Wave Feel Like?

Several people who have found this blog were led here after searching for this question:

What would a gravitational wave feel like?

This is an excellent question so I decided to answer it directly in today's post...


HOW DOES A GRAVITATIONAL WAVE INTERACT WITH MATTER?

First, let us review what a gravitational wave does to matter as it passes by.  Gravitational waves will expand space in one direction and compress it in the perpendicular direction.  This stretching and squishing happen in the plane that forms the cross-section of the wave; this is perpendicular to the direction the wave is traveling.  For a gravitational wave traveling into your computer screen, a circle of stuff will be affected like this:

Image from Wikipedia [gravitational waves]

HOW WOULD A GRAVITATIONAL WAVE FEEL FOR A SOURCE FAR AWAY?

Now let us consider what you are likely to feel here on Earth from what we here at LIGO consider to be "big" gravitational waves.  These waves are produced by some of the most violent, energetic things in the Universe like black holes colliding and stars exploding.  These sources are rare and there are none nearby us, say within a few light-years.  Since the strength of a gravitational wave decreases as the distance from its source increases, by the time these reach us here at Earth they are incredibly small.  A once every ten years gravitational wave will squish and stretch LIGO less than 1000x smaller than the diameter of a proton (< 1x10^-18m).

Therefore, a person will not feel anything from even the strongest gravitational waves we expect to detect with LIGO.  


HOW WOULD A GRAVITATIONAL WAVE FEEL FROM A STRONG, NEARBY SOURCE?

If we were near one of the huge, violent sources LIGO is sensitive to, the gravitational waves would be strong enough to rip us to pieces!  (So it is a very good thing that these sources are very far away!)  This is due to a phenomenon known as "spaghettification".  In a previous post, I described a gravitational wave as simply a change in the gravitational field moving out into the Universe like a ripple in a pond.  The gravitational field is a measure of how much a mass would feel at any given place.  So, if the gravitational wave is a changing gravitational field, then the force of gravity that a mass would feel as the gravitational wave passes should change too.  If the change is so large (due to a very large gravitational wave), then it is possible that your feet will feel a strong enough force, compared to your head, to rip your legs off your body!  And to make matters worse, the sides of your body would be compressed at the same time.

Below is a clip of Neil deGrasse Tyson giving a humorous description of spaghettification.  His description focuses on what would happen to you if you fell into a black hole, but the concept is the same for super-strong gravitational waves:

CONCLUSION

Given where the Earth is in the Universe and how far away sources of strong gravitational waves are, any passing gravitational waves will be so small that we will never be able to feel them.  But if we were close to a strong source of gravitational waves, they could tear us apart!

So it is both a blessing and a curse that the strong sources of gravitational waves are far away:  a blessing because we will never be harmed by them and a curse because they are so small, that we need huge, extraordinarily sensitive detectors like LIGO to detect them.

The Null Result: NOT Finding What You Were Looking For

I've written many times on this blog about why we are looking for gravitational waves and what we hope to learn from them.  I also get to tell real people about this all the time with the work I do at the observatory.  As they get excited, they want to know how many gravitational waves we've detected.  My standard response (as of this date, of course) is, "None, and we didn't expect to either."  And I say this with a smile on my face.  Cue the confused and disappointed expressions...

With Initial LIGO, we were hoping to maybe see a gravitational wave from a pair of dense stars merging together about every ten years or so (based on astronomers' estimates on how many of these system there are out there and what fraction of them will be in this merger stage).  While LIGO has been taking data on and off (we take breaks to improve the detector) since 2002, we only have about 2 years of data when both LIGO detectors (in Louisiana and Washington state) were collecting data at the same time (things like earthquakes, weather, etc. can put one or both offline temporarily).  This gives us about a 20% chance of detecting a gravitational wave with LIGO - not the best odds but better than humans have ever done before!  When the Advanced LIGO upgrades are done and the detectors are running at their design sensitivity, we expect to find one of these "merger" gravitational waves about once a month!

An artist's impression of two stars orbiting each other and progressing (from left to right) to merger with resulting gravitational waves. [Image: NASA]

So, what have we been doing with all this data that has no gravitational waves in it?  Some may think it is worthless but that is far from the truth!  Most people think that when you do an experiment and don't find the thing you are looking for (a null result), the experiment was a failure.  While that can be true if your experiment is inherently flawed, it can also tell you valuable information about the world and Universe around you; now you know how something doesn't work or how rare something is.

Since we know that gravitational waves exist from the observations of the Taylor-Hulse pulsar (1993 Nobel Prize in Physics), we know gravitational waves are real.  So we are left with knowledge on how rare gravitational waves are.  We estimate this by carefully studying how sensitive our detectors are and how well our data analysis methods perform.  Once you know these things, you can combine that with how long you looked for gravitational waves (how much data was taken) and estimate the highest rates that the different kinds of detectable gravitational waves pass by Earth.


THE UPPER-LIMIT FOR BURST GRAVITATIONAL WAVES

I am going to use the example of burst gravitational waves which are short duration gravitational waves from unanticipated sources or from known sources where we can't be sure what the gravitational waves will look like, e.g. supernovae, etc.  (The science summary for this work is here.)  I chose this example because this is the kind of gravitational waves I specialize in.

In order to determine the sensitivity of our data analysis method, we need to put fake signals into real data and measure how many of each kind and strength are found by our data analysis method.  This gives us our efficiency.  When combined with the amount of data collected (giving us a measure of how long we were sensitive to gravitational waves) we can estimate the maximum rate that we would expect a kind of gravitational wave to pass by Earth.  We used many different signals to test the data analysis method, but my favorite is called a sine-Gaussian and looks like this:

Sine-Gaussian signal: a sine-wave (trigonometry) multiplied by a bell-curve (Gaussian function).  The horizontal axis measures time in seconds and the vertical axis measures the strength of the signal.  The spacing between the waves provides a measure of frequency.

Using different strengths and frequencies of this signal, we were able to set an upper-limit on the rate of these kinds of gravitational-wave bursts:

Upper limits on the rate of gravitational wave bursts, determined using the LIGO and Virgo data. The different curves represent signals with different characteristic frequencies; the vertical position of each curve shows what rate should have given us at least one detectable burst with 90% probability, for different assumptions about the strength of the burst (horizontal axis). Since no signal was detected, higher rates are ruled out with good confidence.  [Source: S6 Burst Science Summary]

The current results for the burst upper-limits (from the plot above) are that we expect up to about 1.3 sine-Gaussian-like signals a year in LIGO's most sensitive frequency range (64-1600 Hz) with 90% confidence.  


RESTRICTING PARAMETERS ON OBSERVATIONS

Another thing you can do with data that doesn't contain gravitational waves is restrict the possibilities on how observed events happened.  In 2007, there was a strong gamma-ray burst (GRB) observed by the InterPlanetary Network (IPN).  The area that the source could have originated from also overlapped with an arm of the Andromeda Galaxy:

Bottom left corner box: possible area where GRB 070201 could have originated.  Remaining part of image: close-up of the part of the candidate source area that overlaps the Andromeda Galaxy.  An dwarf spheroidal galaxy, called M110, is also labeled.

This was very exciting to all of us at LIGO because one of the possible causes of gamma-ray bursts is the merger of two neutron stars (like in the first image in this post).  With the Andromeda Galaxy being only about 2.5 million light-years away (LIGO was sensitive to these merger gravitational waves all the way out to several hundred million light-years away), if it really was a merger that caused this GRB then we should have seen it!

After careful analysis of our data before, during, and after this GRB, we did not find any evidence of a gravitational wave.  While it would have been very exciting to see something, this null result tells us that:

1. if the GRB was located in the Andromeda Galaxy, it was not caused by a neutron star pair merger, or
2. if the GRB was created by a neutron star pair merger, it was located far behind the Andromeda Galaxy. 

A LOT FROM SEEMINGLY NOTHING...

As of today (14 June 2012), LIGO has submitted 64 papers for publication.  You can also read the public science summaries for the latest published papers here.  This a quite a lot of papers based on data without any gravitational waves!

Q: How Can Gravitational Waves Help Mankind, Part II: Spin-Off Technology

Previously, I have blogged about how gravitational waves can help mankind.  In that post, I noted that observing gravitational waves will allow us to perform unprecedented astronomy, investigate physics in extreme situations that cannot be replicated on Earth, and allow us to further test general relativity.  I also noted that there have been huge advances in technology developed by LIGO scientists and engineers just to make LIGO work.  LIGO has started to document these spin-off technologies on a new webpage: LIGO Technology Development and Migration.

The page describes many methods of how new technology and techniques move from the LIGO research environment to industry or other research applications.  These modes include patents to serendipity (among many others).  I found the descriptions here interesting myself; as a scientist in the thick of it, I am not always aware of how the things I and my colleagues are developing are affecting the world outside of my own little universe.  Also documented on the LIGO Technology Development and Migration page are descriptions of some of the spin-off technology LIGO has produced.

I want to take this opportunity to tell you about just few of the spin-offs that I am most familiar with: 

HOW DO YOU HANG MASSIVE OBJECT FROM A THIN GLASS WIRE?

One of the new additions to Advanced LIGO will be that the mirrors used to measure gravitational waves will be suspended like pendula from glass wires (the pendulum suspension isn't new, it is the glass wire that is new).  It turns out that the metal wires we use like to vibrate right around our most sensitive region in LIGO (about 320 Hz).  This frequency is due to the fact the the wires are made of metal.  If we use wires made from the same material as our mirror is made of (fused silica) then the frequency that they like to vibrate at is outside of our "sweet spot" region (between 100-1000 Hz).  But, our new mirror will be about 40 kg (~88 lb).  It may be surprising, but the glass wires are strong enough to support this weight (which is also the weight of a small child).

Silica fibers bonded to "ears" that are attached to a glass mass

But how do you connect these delicate glass wires (they may be strong, but they are brittle)?  That is the work of Sheila Rowan, James Hough, and Eoin John Eliffe from the University of Glasgow and Stanford University.  They has developed and patented a new technology that not only bonds the wire to the mass, but also minimized contamination of the collected gravitational wave data from glass' thermal noise.  This technology has already been transferred to several optical industry vendors!

Read more about this here!

HOW CAN YOU KEEP THE SHAPE OF A LENS FROM CHANGING WHEN A LASER PASSES THROUGH IT?

In LIGO, it is very important to keep the shape of our mirrors controlled so that we can keep the laser light bounding back and forth in an arm many times before it recombines with the light from the other arms (this makes the light think that our arms are 70-100 times larger than they are and that gives a gravitational wave more time to affect the light in the arm).  Even though our mirrors are nearly perfectly reflecting, a small amount of the light gets absorbed by the mirror and this causes it to heat up.  When the mirror heats up, it warps its shape and this distortion can make it VERY difficult to keep the light focused between two mirrors that are 4 km (~2.5 mi) apart.  What to do?

The solution to this is the heat the mirror in a controlled way so that you can cause your own distortions that compensate for the warping that the laser is causing.  LIGO has spent much effort perfecting techniques light this (I even have a friend who did his Ph.D. research on this).  This also has wider application in industrial and military environments since higher power lasers are being introduced all the time (such applications include welding and material cutting).  The ability to control the shape of the optics that control and direct a laser beam is becoming increasingly important.

Read more about this here!


HOW CAN YOU USE LIGO DATA ANALYSIS METHODS TO ANALYZE OTHER KINDS OF DATA?


This one is dear to my heart since I specialize in LIGO data analysis!  It is not just physical technology that can be reapplied for other purposes; techniques and software can as well.  Of the many different analysis methods that LIGO executes, the one used to search for continuous (long duration with consistent frequency) gravitational waves produced by things light neutron stars with a "mountain" on it (I put "mountain" in quotation marks because a neutron star is so perfectly spherical, that a deformation of less than an inch is considered a "mountain"!).  This is the analysis that is performed by Einstein@Home (which I blogged about previously here).  

Arecibo Radio Telescope (image from Wikipedia)

The data analysis challenge for these gravitational waves turns out to be similar to the challenge faced by astronomers looking for pulsars that emit either radio waves or gamma rays.  This data is collected by the Arecibo radio telescope in Puerto Rico and the Fermi gamma-ray satellite, respectively.  Using Einstein@Home, the continuous gravitational wave data analysis techniques are applied to data from these two detectors to great effect!  The number of known gamma ray pulsars (that don't produce radio waves) has been increased by a third thanks to discoveries made using the same data analysis Einstein@Home uses.  Radio pulsars are also being discovered on a regular basis with Einstein@Home; since the beginning of 2012, 22 new radio pulsars have been discovered!

Read more about this here!