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Jillian's Guide to Gravitational Waves : SignalsYou will hear the analogy of gravitational waves to sound more often than not, and how when we detect gravitational waves we're hearing the symphony of the cosmos. I think that's a beautiful analogy, even if it does compare gravitational waves to sound (compression) waves. First of all, light rays used to be the only way we could learn about the universe. Ancient astronomers scanned the skies and kept records of the tiny usually still dots of light they saw. Later in life people discovered that the skies held signals of radio waves. Later still they found microwaves and gamma rays. Each step along the way increased our understanding of the universe because of the new light (ye gods, a pun) shed upon it. Each type of signal corresponds to a certain object or event, and people gradually learned about new and interesting astronomical things. There is, however, a problem inherent in electromagnetic signals: degradation. Light rays scatter as they pass through ubiquitous gas clouds, are bent as they encounter gravitational fields, and are absorbed by invisible dust clouds. Light rays bring us a wealth of information about distant suns---but only if we get 'em undistorted. This is where gravity waves come in. While an electromag wave will be scattered by a dust cloud, a gravitational wave will not. Gravity waves pass through nebulae, stars, and gravity wells unaffected and almost nearly undetected! Seems like they're the neutrino of wave signals. How can this be?! It has to do with the basic idea of the wave. Kip Thorne has a wonderful turn of phrase: "Electromagnetic waves are oscillations of the electromagnetic field that propagate through spacetime; gravitational waves are oscillations of the 'fabric' of spacetime itself."1 In this current state of the universe nothing can distort a gravitational wave. Pretty useful if you want a pure signal. Electromagnetic waves are emitted by individual atoms and give information on the composition and thermodynamic state (temperature) of the source. Gravitational waves are emitted by massive bodies accelerating through space. They would give information on the movements of stellar bodies and map out (as it were, anyway) the space of spacetime around those bodies. Kip Thorne noted that the objects people observe in the electromagnetic spectrum would be largely silent in the gravitational spectrum, and likewise the observations of gravitational wave sources would consider objects invisible to the electromagnetic spectrum. Black holes and the until-now-hidden cores supernovae are not the easiest things to study (hah! an understatement!), electromagnetically, just as "light" stars of a few solar masses and nebulae would be impossible to study. So, according to me, there should be all these gravitational waves bouncing around and distorting things for no good reason, right? Mmm, not quite. It's a question of frequency--- both of the signal and of the source emitting the signal. There's an inverse relation of the frequency of the signal to the mass of the source. An ordinary star such as our own (relatively small mass compared to a black hole binary) would have a rather high signal. Apparently "normal" stellar binaries have signals in the 1 microhertz (1 millionth of a hertz) range, while a neutron start would be more in the kilohertz (1 thousand hertz) range, and a galactic core black hole would be in the hertz range2. The greater the mass, the lower the frequency. Why? It has to do with how fast something with that much mass can oscillate. If you've got something that's small, it can really move around and emit high-frequency gravitational waves versus something big and slow and ponderous. Gravitational waves have some problems in common with electromagnetic waves, though, mainly the faintness of distant objects and the redshifting due to expanding spacetime (our jello mold of spacetime is stretching!). Our bowl of jello seen from two miles away is very small; this is a normal occurrence. The curious part is the reason why. Imagine, if you will, the sphere of photons emitted by the jello after 1 second. All those photon crowded together, just like a firework just after it's exploded. Now imagine that sphere a couple seconds later---it's huge! Just like the firework sparkles thin out, the photons from the jello would spread out over a greater area. The greater the distance from the jello, the large the sphere of photons is, thus the fewer photons-per-square meter. The fewer photons per area, the fewer that hit a sensor or an eye; thus the smaller the source seems. For a source emitting photons---or gravitons---there is an additional problem of how many particles are being shot out per second within that square area of the sphere. That determines how faint the source appears. That's why distant stars are so small and faint. Gravitational wave detectors will have this problem with gravitons, making the already-weak signal much weaker over distance! Redshifting due to expanding spacetime? Not only is the frequency of electromagnetic waves decreased by the expansion of our jello-mold-turned-spacetime, but gravitational waves are as well. It makes sense, since gravitational waves are ripples in spacetime. As spacetime expands, the wavelength of the signal increases. Standard physics: the wavelength is inversely proportional to the frequency; thus, the frequency decreases. I've mentioned that certain events in the big bang theory to generate gravitational waves. While it would be cool and informative to have a gravitational version of COBE's results, it's not likely. Those events would have happened a long time ago (heh, when the universe had just been err...born), there would be few gravitons from such a signal, and there is a lot of expanding spacetime crossed by the signal to get to us, making the already-faint signal practically invisible. If we could detect it, chances are it might go unnoticed as static just as the microwave background did. In
a certain Scientific American article
there is a wonderful table of gravitational wave sources, frequencies,
and signal strengths. I'm going to shamelessly reproduce it here because
it's quite useful. However, all credit for work and research goes the
the writers!
Funny how black hole/black hole binaries aren't in the table. I can conjecture that they would produce signals very similar to the neutron/neutron binaries. Perhaps the frequency would be tad higher (around 20 or more kiloHertz?) because the black holes can move more mass and get closer to one another. Black hole/neutron star binaries? Heh, I should think they'd be somewhere in between! I think these were neglected because people still don't quite believe in the existence of black holes and also I imagine a binary of two black holes would be a very rare thing indeed. Oh, yeah. I didn't mention some of these sources, did I? There are good reasons for that. Take the galaxy formation. I've got very little experience with cosmic strings. I barely know what they are. Take the accreting neutron star. I didn't think that would produce measurable gravitational waves---but look at that signal strength: 10-27 is very weak. The stellar binary? Well, yes, they'd make waves, too; but neuron binaries and black hole binaries are much better at moving large masses very quickly. The only drawback to those prime sources is their distance from us, and the more distant the source, the weaker the signal (and they are already weak enough as it is!). Neutron stars are usually further in towards the core of our own galaxy---or in the halo. Neutron stars are also pretty rare. Black holes of only a few solar masses probably are, too. Their larger cousins exist usually in the center of galaxies, which are not quite as frequent as stars are. Ah, well, no one said detecting these waves would be easy. So, what are these detectors, anyway? I've mentioned gravitational wave signals and detectors, but I haven't actually described how one would go about detecting gravitational waves. One popular method is to use something called a laser interferometers. The LIGO project is a great example of this. Basically put, a laser interferometer looks like two dangling mirrors at the end of two long stretches of tube arranged in an L with lasers constantly bouncing off 'em. That's it. How does this detect a gravitational wave? Well, there's trick to it, you see. It can detect waves that strike it head on---so that the plane of the two tubes is perpendicular to the direction in which the waves travel. Before the wave hits the two lasers are sending out signals that are in synch with each other. Each light ray sent out bounces back in the same time. All's well. Then the wave hits. One leg of the L is suddenly stretched and the other is compressed. The light rays still travel at (heh!) the speed of light, but now there is more space to cross in one of the legs and less space to cross in the other. The signals are no longer in synch and the wave is detected. The only drawback to this scenario is that interferometers encounter interference and noise above 1kHz and below 10 Hz. Another way to measure a gravitational wave is to use a resonant mass detector. There are two basic varieties: spheres and bars. The former version has a sphere of some material with sensors either arrayed on the sphere itself or around it. Those sensors make sure the sphere has its normal dimensions. When a gravitational wave hits the sphere, due to the stretching and squishing effect, the sensors detect the deformation of the sphere. Usually, though, the sensors detect the lingering oscillation (like a jello mold that wiggles a little after it's touched) of the sphere. The latter resonant mass detector, the bar, looks like a large soup can of some material with sensors (either at the front and back or arrayed around the middle of the bar) worried about the front and back "lids." It uses the same basic method of detection, looking for the oscillation of the bar, for finding gravitational waves. The drawback to using a bar is that the detector is no longer unidirectional. A wave striking the sphere from any direction could be detected, but only a wave striking the bar roughly perpendicular could be detected. The laser interferometers have this same directional problem, too. A final note and then on to another section. A curious thing---perhaps THE most curious thing---about gravitational waves is the supporters of the theory. This is not Einstein's now-nearly-universally-accepted theory of relativity. (Side note: according to one of my teachers, every six months---from the time Einstein first published his theories to today---papers are published trying to disprove relativity for various scientific and not-so-scientific reasons.) Gravitational waves are on shakier ground than black holes---and people are still not entirely convinced those exist. People diligently build detectors but have had very little luck in detecting bonna fide gravitational waves. Very, very theoretical. Actually, when gravitational waves are detected (I'm optimistic!), they will go far in proving the existence of black holes. Stars the size of small cities people can accept; empty bent spacetime that has a nasty peculiarity in the center takes a little more faith.
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Stellar Binary
Neutron Star Binary
Accreting Neutron Star
Type 2 Supernova
Vibrating Black Hole
Galaxy Formation (by cosmic strings)
Big Bang
