Learning GRT: Why the High Frequency Search?

[exmarine]

I am trying to learn GRT so I can answer questions for myself. But I might croak first, so I’ll ask here. That gravity wave interferometer they are building out in Richland, Washington - I obviously haven’t read all the technical papers on their web site, but I am pretty sure one I did read showed a spectrogram or PSD with search frequencies of 40 Hz and above. I understand that the behavior of the Taylor-Hulse binary is the only empirical evidence we have so far of gravity waves - and its orbital period is around 8 hours. Can anyone explain why they are looking at such high frequencies? Shouldn’t we be looking for ultra-low frequency waves with periods like 8 hours (or maybe half that for these type waves)? Do we expect stuff falling into a black hole to emit broad-band high frequency gravity waves? Thanks for any enlightenment.

 

[Vanadium 50]

Because the light is better here.

It's difficult to build a gravity wave detector at such low frequencies. If you half the frequency, you double the wavelength, so your instrument wants to be twice as big.

 

[phyzguy]

The gravitational waves emitted by a binary like the Hulse-Taylor binary are much too weak to measure. The best hope for measuring gravitational waves is to measure two orbiting neutron stars or a neutron star-black hole binary just before they coalesce into a black hole. In the last phase of their coalescence, they are orbiting each other extremely rapidly, and their orbital periods are measured in milliseconds. So 10's of Hertz is about right to see these events.

 

[exmarine]

Wow. How long might such an intense phase last?

Can you recommend a good textbook? Grad schools are too far away for me.

 

[HallsofIvy]

The recent "Scientific American" had an article on how much we can learn by detecting gravity waves. We have been looking for gravity waves for, what, 40 to 50 years, now? And no one has ever detected gravity waves! Yes, the general theory of relativity predicts gravity waves but is there any real evidence they exist? And if they exist but we have not detected them yet do we really know how to detect them?

 

[phyzguy]

Wow. How long might such an intense phase last?

Can you recommend a good textbook? Grad schools are too far away for me.

On the order of 0.1 seconds. This link has a good description of the waveform, and links to other sources.

 

[phyzguy]

The recent "Scientific American" had an article on how much we can learn by detecting gravity waves. We have been looking for gravity waves for, what, 40 to 50 years, now? And no one has ever detected gravity waves! Yes, the general theory of relativity predicts gravity waves but is there any real evidence they exist? And if they exist but we have not detected them yet do we really know how to detect them?

The Hulse-Taylor binary is, IMHO, irrefutable evidence that GWs exist. The Nobel prize committee must agree, since they awarded Hulse and Taylor the Nobel prize for their work. Do we really know how to detect them? I guess we'll see. If the "Advanced LIGO" experiment doesn't detect them in the next five years or so, something is seriously wrong. But I would bet that they will detect them.

 

[HallsofIvy]

I will hold my breath!

 

[Bill_K]

Detection of gravitational waves has been "in just a few years" ever since the 1960's.

 

[phyzguy]

Detection of gravitational waves has been "in just a few years" ever since the 1960's.

So has practical production of fusion energy. So we should give up trying? Put things in perspective. How long has it taken us to understand the night sky? Thousands of years, and we're still learning. Suppose Kepler had said "I've been working for decades to understand the planetary orbits and I still don't get it. I give up!"

 

[Bill_K]

So has practical production of fusion energy. So we should give up trying? Put things in perspective. How long has it taken us to understand the night sky? Thousands of years, and we're still learning. Suppose Kepler had said "I've been working for decades to understand the planetary orbits and I still don't get it. I give up!"

I don't know what I said that you interpret as a suggestion to 'give up'. That seems like a large overreaction. What I do say (and maybe this has changed) is that gravitational wave experiments have in the past harmed their credibility by a lack of candor. A failure, perhaps, to be up front about the difficulty of detection, and the time scale required for success. "In just a few years" should have been more plausibly stated, "in just a few decades".

An example of this was a talk I once attended, at which the following exchange (paraphrased) took place between audience member and speaker:

Q. "Why does your experiment deserve funding, when its sensitivity is two orders of magnitude less than a signal that could be produced by any imaginable astrophysical source?"

A. "Well, yes. But if we did see a signal, just think how remarkable that would be!"

 

[phyzguy]

I don't know what I said that you interpret as a suggestion to 'give up'. That seems like a large overreaction. What I do say (and maybe this has changed) is that gravitational wave experiments have in the past harmed their credibility by a lack of candor. A failure, perhaps, to be up front about the difficulty of detection, and the time scale required for success. "In just a few years" should have been more plausibly stated, "in just a few decades".

An example of this was a talk I once attended, at which the following exchange (paraphrased) took place between audience member and speaker:

Q. "Why does your experiment deserve funding, when its sensitivity is two orders of magnitude less than a signal that could be produced by any imaginable astrophysical source?"

A. "Well, yes. But if we did see a signal, just think how remarkable that would be!"

Bill_K,

I agree completely. You're right, I overreacted, for which I apologize.

 

[exmarine]

Thanks for the replies.

Is there any directionality to the emitted gravitational waves, with respect to the orbital plane of the bodies? And how about the polarization of the waves?

 

[Bill_K]

And how about the polarization of the waves?

Remember that gravitational waves are quadrupole in nature, so instead of a polarization vector like in EM, they have a polarization tensor. The effect of a wave is an alternating compression and extension along axes perpendicular to the propagation. Instead of the two polarization modes being inclined at a 90-degree angle from each other as in EM, the two polarization modes in a gravitational wave are inclined wrt each other at a 45-degree angle.

For a binary star source, for emission in the equatorial plane the polarization tensor is in the latitude-longitude direction. That is, parallel and perpendicular to the equator. For emission in the polar direction, the polarization tensor rotates with the two stars, i.e. circular polarization.

 

[exmarine]

Yes, I called those "n = 2 shell modes" back in engineering. Does anyone know the natural frequency of them in the earth’s crust? And what might be their effective damping? It seems to me that we might be able to detect gravitational waves by looking for global responses of those modes near resonance.

I’ve read that the magnitude of the crust’s response to lunar tides is about 30 inches (not sure if that is amplitude or range - factor of 2). It seems that the damping of such small deflections should be very small, and thus some dynamic amplification of harmonic forcing might be significant.

I’ve also read that, "from direct observation", the lobe of that mode facing the moon does not exactly align with the moon, but lags by 2 to 3 degrees. (What type of observation could detect that with such precision?) This lag information and the natural frequency would allow one to calculate the potential dynamic amplification.

If seismologist can detect effects from major disturbances circling the globe, or the Earth "ringing" after some earthquakes, it seems they could also be looking for near resonant responses to some harmonic forcing from distant gravitational wave sources.

It would require multiple detectors with very accurate time stamps, and then post-processing to look for correlations for source directions, polarizations, etc. And it would of course be complicated by the earth’s rotation, solar orbit, lunar and solar tidal responses, etc.

 

[haael]

I asked this once before, but I'll ask once again: why can't GPS satellites be used to detect gravity waves?

GPS satellites have a good clock source, they track themselves by lasers and they are far away from each other (in fact, the size of the GPS constellation is much bigger than any laboratory we could ever build on Earth).

I'm not speaking about using the GPS geographical location determination. I'm speaking about measuring deformations of the GPS constellation.

We could install laser interferometers on GPS satellites to measure distances between them. This would allow to determine the size and shape of the constellation down to nanometer precision (and it would also have technical and commercial advandages). Then we could check the whole constellation for periodic ellipsoid-like deformations.

I wonder if I'm not missing something here, but I think the GPS constellation is the best gravity wave detector we've already built.

 

[phyzguy]

I asked this once before, but I'll ask once again: why can't GPS satellites be used to detect gravity waves?

GPS satellites have a good clock source, they track themselves by lasers and they are far away from each other (in fact, the size of the GPS constellation is much bigger than any laboratory we could ever build on Earth).

I'm not speaking about using the GPS geographical location determination. I'm speaking about measuring deformations of the GPS constellation.

We could install laser interferometers on GPS satellites to measure distances between them. This would allow to determine the size and shape of the constellation down to nanometer precision (and it would also have technical and commercial advandages). Then we could check the whole constellation for periodic ellipsoid-like deformations.

I wonder if I'm not missing something here, but I think the GPS constellation is the best gravity wave detector we've already built.

This is the concept behind the LISA gravitational wave mission. You say "We could install laser interferometers on GPS satellites to measure distances between them" How would you do this? Mount a special mission to fly to all of the GPS satellites to install these interferometers? How much do you think this would cost? Also, some of the GPS satellites can't see each other because the Earth is in the way, and their orbits are distorted due to the non-uniform gravitational field of the Earth. Far easier and cheaper to mount a dedicated mission in an orbit where the Earth doesn't interfere. This is what LISA is.

 

[haael]

OK, I accept you answer, but I still think GPS is a better option. Installing interferometers would have not only scientific applications, but also technological and commercial. It could be done by gradually replacing old satellites with upgraded ones. I also would argue if LISA approach is cheaper.

Also, some of the GPS satellites can't see each other because the Earth is in the way

From the GPS' satellite perspective Earth is very small and would cover only one or two satellites at once.

and their orbits are distorted due to the non-uniform gravitational field of the Earth

It doesn't matter, since we look only for periodic changes of specific frequency and shape. Does Earth emit some disturbances that could be mistaken for gravity waves for orbit experiments? How is LISA free from that?

 

[phyzguy]

OK, I accept you answer, but I still think GPS is a better option. Installing interferometers would have not only scientific applications, but also technological and commercial. It could be done by gradually replacing old satellites with upgraded ones. I also would argue if LISA approach is cheaper.

Doing it by gradually replacing old satellites might be feasible.

From the GPS' satellite perspective Earth is very small and would cover only one or two satellites at once.

You're probably right on this.

It doesn't matter, since we look only for periodic changes of specific frequency and shape. Does Earth emit some disturbances that could be mistaken for gravity waves for orbit experiments? How is LISA free from that?

LISA would go in a trailing heliocentric orbit, so Earth would be extremely distant (about 1 AU). I think the reason they chose this orbit is to avoid the gravitational influence of any nearby bodies like the Earth or moon. You need to be able to sense changes in position on the order of 1E-12 meter on time scales of 100's to 1000's of seconds. I think the distortions of the orbits caused by the Earth's non-uniform gravitational field would swamp these signals, but I'm not really sure.

 

[exmarine]

I've wondered the same thing about our GPS satellites, but using their very accurate altitude measurements above the Earth's surface - they are already installed. As with ground based observatories, you would be looking for phases between the satellites' (or gravimeters' on the surface) response to the incident gravity wave and the Earth's response to the same wave. I recognize that the sources are probably very weak, so that's why I think we should be looking for situations where some dynamic amplification could exist. I.e., very small deflections, thus very small damping, and HARMONIC forcing near a resonance. Polar regions would be important observation sites, as I think tidal variations there due to lunar, solar, other planets' influence are small.

 

[Creator]

I've wondered the same thing about our GPS satellites, but using their very accurate altitude measurements above the Earth's surface - they are already installed. As with ground based observatories, you would be looking for phases between the satellites' (or gravimeters' on the surface) response to the incident gravity wave and the Earth's response to the same wave. I recognize that the sources are probably very weak, so that's why I think we should be looking for situations where some dynamic amplification could exist. I.e., very small deflections, thus very small damping, and HARMONIC forcing near a resonance. Polar regions would be important observation sites, as I think tidal variations there due to lunar, solar, other planets' influence are small.

Good thinking...

Actually the Earth itself would be a more feasible detector and has actually been used in the past (using gravimeters which are actually accelerometers) based upon calculations provided by Freeman Dyson...but his calcs on were based in large part on some model assumption about Earth's interior. (I was in the LSU physics dept. at the time when they were reving up to replicate Weber bar oscillators). Using Earth as a resonator (antenna) was a great idea because of the large size compared to wavelength. With Dyson's assumptions these expected seismic variations of Earth's fundamental harmonic modes from possible gravitational waves were still calculated to be too small compared to the Earth's 'background' seismic noise, but uncertainties in estimates made it feasible. It involves lots of signal processing and filtering of background.
Nevertheless, I remember reading some published papers of Israeli professors in the early 70's doing experimental measurements with gravimeters and, incredibly, got some clear diurnal variations (in accelerations) using low frequency...(like at 1 or 1.5 htz) which were thought to correspond to the then newly discovered pulsars...

However, some guys in California (maybe Cal Tech) tried to duplicate and couldn't,, and I was surprised that not much follow up was attempted later, especially since California is a way too seismic volatile area to try to reliably replicate. I think some of the disinterest also came from the fact that at the time pulsars were not thought to be good GW emitters...but only later were shown to be with high GW flux from rapid spin and elongated (ellipsoidal) physical shape providing the changing quadrupole moment.

I still think there is a possibility to use the Earth's large diameter to detect such signals, especially since we have today a much higher degree of precession in signal processing & filtering technology, but unfortunately attention seems to have remained fixated on laser interferometric techniques.

Here's the report by Dyson: http://adsabs.harvard.edu/full/1969ApJ...156..529D

Creator

 

[exmarine]

"Actually the Earth itself would be a more feasible detector..."

Yes - see my earlier posts. And thanks, I'll be studying Dyson's paper! I've been doing some modeling / estimating / approximations too.

And I realize that, while a very optimistic dynamic amplification factor of several orders of magnitude is fantastic for engineering applications, it my still be insufficient for this astronomical application.

 

[phyzguy]

The use of the Earth itself as a gravitational wave detector is basically what people are trying to do with Pulsar Timing Arrays. Many people think that this technique will detect gravitational waves before any of the ground-based detectors like LIGO.

 

[Creator]

"Actually the Earth itself would be a more feasible detector..."

Yes - see my earlier posts. And thanks, I'll be studying Dyson's paper! I've been doing some modeling / estimating / approximations too.

.

Sorry; I missed your previous post. also, mistake on my post...the guys that did the experiment in the 70's used sensitive seismometers; vertical acceleration is what was being measured if I'm not mistaken...wish I could find that report...I have a hard copy somewhere among the gazillion papers.
Creator

 

[Creator]

The use of the Earth itself as a gravitational wave detector is basically what people are trying to do with Pulsar Timing Arrays. Many people think that this technique will detect gravitational waves before any of the ground-based detectors like LIGO.

Thanks;; interesting technique for pulsars. I am still convinced we can engineer appropriately to capture low frequency pulsars...seem to be best candidates IMHO.
Creator

 

[haael]

What about the Earth-Moon system? There is already a ranging experiment. How much will Moon change distance for a gravity wave from a typical source?

 

[Bill_K]

What about the Earth-Moon system? There is already a ranging experiment. How much will Moon change distance for a gravity wave from a typical source?

According to Wikipedia, the expected amplitude for a gravitational wave is 10^-20. With the Earth-Moon distance about 400,000 km, the distance change is predicted to be 10^-12 m, or 1000 nuclear diameters.

 

[yuiop]

According to Wikipedia, the expected amplitude for a gravitational wave is 10^-20. With the Earth-Moon distance about 400,000 km, the distance change is predicted to be 10^-12 m, or 1000 nuclear diameters.

From the Wikipedia article on Lunar laser ranging

As of 2002 work is progressing on increasing the accuracy of the Earth-Moon measurements to near millimeter accuracy, though the performance of the reflectors continues to degrade with age.[4]

That means the laser ranging measurement has to be at least 9 orders of magnitude more accurate to be able to discern a gravity wave from background noise.

 

[Creator]

What about the Earth-Moon system? There is already a ranging experiment. How much will Moon change distance for a gravity wave from a typical source?

Lunar laser ranging is typically thought not to have the required accuracy. However, planting a detector on lunar surface specifically designed for such a mission similar to my earlier discussion of seismograph on Earth (in the 0.1 to 10 hertz range) could be advantageous to pulsar GW detection, especially since the moon is thought to be seismically quiet (compared to earth).
Here are some preliminary thoughts from a JPL workshop on that topic, placing it in the sensitivity range of LIGO and LISA, and even includes an idea for sensitive displacement detector using a free floating superconductor.
http://www.ligo.caltech.edu/~veronica/CaJAGWR/info/general/paik02.pdf
Creator

 

[haael]

OK, gravity waves aside, is it technically possible now to measure distance to the Moon using interferometer? If not using light, then at least radio waves?

With the Earth-Moon distance about 400,000 km, the distance change is predicted to be 10-12 m, or 1000 nuclear diameters.

OK, that falls somewhere in the X rays spectrum. Sounds promising.

My third question is about the gravity waves themselves. Do they affect light? I mean, does the light know it passed through a region of space where are gravity waves?

Suppose some advanced civilization put a laser in the space and a receiver very far away from it. Suppose also the space between them is filled with a bit of dust. Then, a gravity wave passes.
Scenario 1: A "wide" wave passes, causing the laser and the receiver change distance.
Scenario 2: A "narrow" wave passes, not affecting the distance between the laser and the receiver, but disturbing dust between them.

(I understand gravity waves are a bit like radio waves, that means they can have "shape". Am I correct? There can be region in space where there is a gravity wave and a region where it isn't. In particular, two orbiting neutron stars emit gravity waves mostly in their "equatorial" rotation plane and not at the "poles". The wave intensity angular characteristic is similar to that of the dipole antenna radiation pattern. Am I right?)

In scenario 1, we would see the passing wave on the interferometer, right.
Now in scenario 2. Will the wave be visible to the detector? I mean: the spacetime between the source and detector was disturbed, so the light has to be affected, right?

If that is the case then going back to scenario 1: what is the effect of the light disturbance for the distance measurement experiment? Does it amplify distance vibrations, does it damp them or is it negligible?

That said, could we see some effect of gravity waves in some distant stars light characteristics or in some exotic phenomena like gravity lensing pictures?

 

[Bill_K]

In particular, two orbiting neutron stars emit gravity waves mostly in their "equatorial" rotation plane and not at the "poles". The wave intensity angular characteristic is similar to that of the dipole antenna radiation pattern. Am I right?)

Thanks to the quadrupole nature of gravitational waves, dipole waves do not exist. This can also be understood as the result of momentum conservation. For a binary star system, the leading source term is a rotating quadrupole moment.

As I pointed out above in #14, there is radiation in the polar direction as well, although the polarization is different.

 

[Bill_K]

That said, could we see some effect of gravity waves in some distant stars light characteristics or in some exotic phenomena like gravity lensing pictures?

You haven't specified which directions the gravitational wave and the light are traveling, but if they're traveling more or less parallel to each other, the effect most easily observable at a distance will be that the light ray is deflected sideways.

PS - It's helpful to call them by their proper name, gravitational waves. Gravity waves are something else.

 

[haael]

Thanks to the quadrupole nature of gravitational waves, dipole waves do not exist. This can also be understood as the result of momentum conservation. For a binary star system, the leading source term is a rotating quadrupole moment.

As I pointed out above in #14, there is radiation in the polar direction as well, although the polarization is different.

OK, I understand, but please correct me if I'm wrong.

Gravitational waves, just as electromagnetic waves, have amplitude, frequency and polarization. Now: is it possible to arrange such an emitter that radiates waves in non-isotropic way? For example a setup, where the amplitude is maximal near the equator and zero near the poles?

You haven't specified which directions the gravitational wave and the light are traveling, but if they're traveling more or less parallel to each other, the effect most easily observable at a distance will be that the light ray is deflected sideways.

So if we happen to observe two merging stars at least one of is bright, then we would see the effects of the gravitational waves in the image? Have such experiments ever been performed?

 

[Bill_K]

Now: is it possible to arrange such an emitter that radiates waves in non-isotropic way? For example a setup, where the amplitude is maximal near the equator and zero near the poles?

The wave must have a polarization, and so from the viewpoint of the detector, the source must have a preferred direction - it must look asymmetric.

For any source that is cylindrically symmetric, an observer along the polar direction will NOT see a preferred direction, so there can't be any waves coming at him. E.g. if two stars collide directly, this is a cylindrically symmetric situation, and an observer situated right along the collision axis won't see any radiation.

 

[haael]

For any source that is cylindrically symmetric, an observer along the polar direction will NOT see a preferred direction, so there can't be any waves coming at him. E.g. if two stars collide directly, this is a cylindrically symmetric situation, and an observer situated right along the collision axis won't see any radiation.

Thanks, that is the clear answer.