# Gravitational lens and gravitational waves question

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Here's the kind of confirmation I was looking for

http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf

This is a generic feature of circular gravitational wave binaries: the gravitational wave frequency in a circular binary is twice the orbital frequency. In practice what it means is that for each cycle made by the binary motion, the gravitational wave signal goes through two full cycles — there are two maxima and two minima per orbit. For this reason, gravitational waves are called quadrupolar waves

Not a guess, not logic. Physics.

When they say "generic feature" doesn't that imply you have to go back and look at the basic physics of the situation. I wasn't guessing, I was looking at how those waves were being generated, OK it involved logic but are you sure logic is not part of a generic feature?

Definition of generic "characteristic of or relating to a class or group of things; not specific."

Well I'm pleased. I picture it as 2 wavefronts per orbit, due to those two (3D) spirals of gravitational energy traveling through space.

To picture them as 3D spirals is not easy, but it was a necessary part of that tweet. The strength is greatest above and below the orbital plane, so are we getting summation of the waves above and below?

http://www.scienceforums.net/topic/93472-gravitational-lens-and-gravitational-waves-question/page-2#entry909493

It seems like they would lose their distinctiveness perpendicular to the orbital plane even if they were stronger as according to @AstroKatie. I'm putting this down to them orbiting different distances (in most cases) from their CoM.

In one paper it likened GE to the water coming out of an "S" shaped rotating garden sprinkler.

So I'd say there are two streams of water coming out continuously but when a person is standing closeby there are two showers of water per revolution of the sprinkler head.

In the garden sprinkler the water is piped in but where does the "supply" of gravitational energy come from?

Edited by Robittybob1

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In the garden sprinkler the water is piped in but where does the "supply" of gravitational energy come from?

Positions in the gravitational field. Orbits getting closer together.

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Positions in the gravitational field. Orbits getting closer together.

OK as I was saying before if we calculated the amount of PE (that was available from infinity) and halved it does that work out to be 3 solar masses of energy for those two black holes of the masses that they have calculated. Was it 29 and 36 to start with and ended up 62 and 3 were lost as energy.

(I say halved it because some of the energy is going to be in kinetic motion of the BHs.)

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OK as I was saying before if we calculated the amount of PE (that was available from infinity) and halved it does that work out to be 3 solar masses of energy for those two black holes of the masses that they have calculated. Was it 29 and 36 to start with and ended up 62 and 3 were lost as energy.

(I say halved it because some of the energy is going to be in kinetic motion of the BHs.)

By "we" you mean someone other than you?

I don't know what the GR answer is, but the pre-GR answer is basically "how big do you want it to be" since the PE expression diverges for r=0, and ultimately we're dealing with a singularity.

Basically you want to know how big GMm/r is compared to ∆mc^2 for some change in r, where ∆m is the three solar masses.

Assuming my calculation is right, the change in energy from bringing in the masses from far away to ~515 km is equivalent of three solar masses. Going from 515 km to half that will change the PE by the same amount. Rs for these black holes is in the neighborhood of 90 km.

Nothing about these numbers refutes (or brings into question) the notion that this energy release is from changes in orbit.

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By "we" you mean someone other than you?

I don't know what the GR answer is, but the pre-GR answer is basically "how big do you want it to be" since the PE expression diverges for r=0, and ultimately we're dealing with a singularity.

Basically you want to know how big GMm/r is compared to ∆mc^2 for some change in r, where ∆m is the three solar masses.

Assuming my calculation is right, the change in energy from bringing in the masses from far away to ~515 km is equivalent of three solar masses. Going from 515 km to half that will change the PE by the same amount. Rs for these black holes is in the neighborhood of 90 km.

Nothing about these numbers refutes (or brings into question) the notion that this energy release is from changes in orbit.

Well at least the PE is more than the 3 solar masses, so we are looking at least 3 solar masses being lost as GE and 3 as KE. I think your calculation allows for that, in fact we seem to need even more mass loss than that. But there is definitely more than enough energy in the changes of orbit to allow for GE release to be occurring for ages before the final 0.3 sec. Just in the last 0.3 sec you get that final 3 solar mass loss, but what about before that?

At the beginning of that 0.3 sec period how far apart were they? Is there enough PE in that last stage to supply at least 3 solar masses of energy? ().

Can you look at that last 0.3 sec period please?

Edited by Robittybob1
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At the beginning of that 0.3 sec period how far apart were they? Is there enough PE in that last stage to supply at least 3 solar masses of energy? ().

I have read (skimmed) quite a few of the papers related the LIGO result but haven't come across anything that directly relates to your questions. However, as the mass of the final black hole was ~3 solar masses less than the sum of the two black holes. So much of the energy released came from that. What I can't tell you is exactly when that mass was lost.

I think you would have to read a some of the (many) papers that have been written over the years about modelling black hole mergers. (Or find a forum/blog where there is an expert on the subject.)

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At the beginning of that 0.3 sec period how far apart were they? Is there enough PE in that last stage to supply at least 3 solar masses of energy? ().

Can you look at that last 0.3 sec period please?

Let us know when you find out how far apart they were. As far as the energy goes, the answer is most certainly yes, as the changes in PE increase for a given change in distance as r decreases, as it's a 1/r dependence

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Let us know when you find out how far apart they were. As far as the energy goes, the answer is most certainly yes, as the changes in PE increase for a given change in distance as r decreases, as it's a 1/r dependence

I have seen estimates of the distances, so it is just a matter of finding them.

If Caltech has drawn their animation to scale we could get estimates from there

0:23 secs in give a picture of the distances at 0.32 sec.

To get the scale they have drawn the EH of both BHs.

Edited by Robittybob1
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At the beginning of that 0.3 sec period how far apart were they? Is there enough PE in that last stage to supply at least 3 solar masses of energy? ().

Can you look at that last 0.3 sec period please?

The LIGO paper has graphs showing things like frequency and distance against time.

They say:

To reach an orbital frequency of 75 Hz (half the gravitational-wave frequency) the objects must have been very close and very compact; equal Newtonian point masses orbiting at this frequency would be only 350 km apart.

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Found it!

at 36:32 there is a graph showing the separations against time.

The scale for the separation is measured in Rs so which Rs is that? You might be able to pick up on it. Speaker says "Rs of the final merged BH, I think". He said that at 36:28 Funny that he said he thinks!

Are they useful figures?

The LIGO paper has graphs showing things like frequency and distance against time.

They say:

did you have the reference link. Swansont has probably got it already. What time (in seconds before the merger) was this frequency for the frequency is changing all the time.

Edited by Robittybob1
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did you have the reference link. Swansont has probably got it already. What time (in seconds before the merger) was this frequency for the frequency is changing all the time.

Post #29

From Katie Mack's page, I was eventually led to this: http://cplberry.com/2016/02/23/gw150914-the-papers/

An excellent, and really useful, summary of all the papers around the LIGO result. There are papers that go into great detail about every aspect: the detection, modelling the sources, etc. This is a great way to find the ones that are of interest.

The scale for the separation is measured in Rs so which Rs is that? You might be able to pick up on it. Speaker says "Rs of the final merged BH, I think". He said that at 36:28 Funny that he said he thinks!

From the graph in the paper, it looks like Rs of the combined black hole (which is pretty much 2xRs of each of the initial BHs).

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...

From the graph in the paper, it looks like Rs of the combined black hole (which is pretty much 2xRs of each of the initial BHs).

Google "The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light."

Rs = 2GM/(c^2)

Schwarzschild radius is directly proportional to the mass. So we can add the Rs of the smaller BHs multiplied by the factor 62/65 (3 solar masses lost) because of the mass reduction due to GE.

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Swansont has probably got it already.

No, that was your job. But Strange did it for you, and the answer is consistent with the numbers I provided.

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As far as I understood, the gravitational waves detected were from 2 black holes that merged.

My question is: the waves were emitted/detectable in all directions, including straight up/down from the orbital plane?

(Scroll down to the "Gravitational Waves From a Pair of Black Holes From Large Distance" video)

"If you look carefully, you'll notice that gravitational waves are emitted in all directions, but that the waves are strongest in the "upward direction", which is normal to the orbital plane of the holes."

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Here is a paper which using the Ligo test results places an upper bound on massive graviton theories.

"which corresponds to a graviton mass

$m_g\le 1.2*10^{-22}eV/c^2$

at 90% confidence

The paper is the pdf on this site.

https://dcc.ligo.org/P1500213/public

Edited by Mordred
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The Maxima/minima determine the TYPE of waveform QUADRUPOLE.

The rate and number of waveforms determine the chirp

When the two masses are inline with our (LIGO) line of site (regardless of their inclination) what part of the GW chirp signal are we seeing?

[minimum or a maximum on the chirp signal are possible answers, I'm picking minimum]

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The binary nature of the orbiting bodies was the similarity. The masses of the bodies involved are different. I read that paper looking to see if the methods they used could be useful to DanMP and I couldn't see how to use their methods. They had multiple recordings to compare timings of hundreds of signals compared to the BBH chirp which only gave approx 10 waves before the merger. Some of these waves could have shown Shapiro delay if there was precession occurring.

In their case they had a system with the lowest recorded angle of inclination whereas GW150914 or GW 150914 was probably very inclined.

OK they were measuring the pulsar signal and Dan would be trying to see the timing of the GW signal (but both signals travel at the speed of light).

The difference, the HUGE, WHOPPING DIFFERENCE, is that a pulsar signal is EM radiation, not gravitational, which makes any similarities moot regarding Shapiro delay.

When the two masses are inline with our (LIGO) line of site (regardless of their inclination) what part of the GW chirp signal are we seeing?

[minimum or a maximum on the chirp signal are possible answers, I'm picking minimum]

It depends on how far away you are. If you're seeing a minimum, move a half wavelength in either direction (closer or further) and it will be a maximum.

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Here this will probably help.

note the distortions on the sinusoidal images. Those are quadrupole waveforms.

A sinusoidal waveform from EM radiation is a dipole waveform.

Chirp frequency the the rate an amplitude of each wave. Not the the wave characteristics.

Edited by Mordred
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The difference, the HUGE, WHOPPING DIFFERENCE, is that a pulsar signal is EM radiation, not gravitational, which makes any similarities moot regarding Shapiro delay.

It depends on how far away you are. If you're seeing a minimum, move a half wavelength in either direction (closer or further) and it will be a maximum.

Imagine being right next to it so we don't have to consider signal transmission times, what phase it it in then?

Either two BHs equidistant to you and two BHs inline with you. Which arrangement gives the minimum?

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See the paper I just posted Robitty.

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Here this will probably help.

note the distortions on the sinusoidal images. Those are quadrupole waveforms.

A sinusoidal waveform from EM radiation is a dipole waveform.

Chirp frequency the the rate an amplitude of each wave. Not the the wave characteristics.

The paper is called "Decoding mode-mixing in black-hole merger ringdown" It seems unlikely to answer my question for I was talking about the phase of the GW before the contact and ringdown.

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The only part you need is the image of a quadrupole waveform.

It is not sinusoidal. But a distorted sinusoidal. The two maxima and minima occurs each chirp cycle.

The maxima being a half cycle, the minima the second half cycle

Edited by Mordred
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The only part you need is the image of a quadrupole waveform.

It is not sinusoidal. But a distorted sinusoidal. The two maxima and minima occurs each chirp cycle.

The maxima being a half cycle, the minima the second half cycle

Which figure number did that quadrupole waveform have? I can't see any in paper that would be helpful, sorry.

Are you saying as shown in Wikipedia on gravitational waves? https://en.wikipedia.org/wiki/Gravitational_wave#Effects_of_passing

The oscillations depicted in the animation are exaggerated for the purpose of discussion — in reality a gravitational wave has a very small amplitude (as formulated in linearized gravity). However, they help illustrate the kind of oscillations associated with gravitational waves as produced, for example, by a pair of masses in a circular orbit. In this case the amplitude of the gravitational wave is constant, but its plane of polarization changes or rotates at twice the orbital rate and so the time-varying gravitational wave size (or 'periodic spacetime strain') exhibits a variation as shown in the animation.[29] If the orbit of the masses is elliptical then the gravitational wave's amplitude also varies with time according to Einstein's quadrupole formula.[30]

.What I was trying to do is establish what phase of the BBH orbit produces the minimum strain, say when the test particles (in one arm of the LIGO interferometer) are pulled together horizontally (on the x axis). Was that caused by the two masses being equidistant (parallel to the x axis) or inline with the detector arm (parallel to the y axis)?

A minimum on the chirp waveform is "no strain" so it is slightly different than just thinking about one arm of the LIGO at once.

Edited by Robittybob1
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Do you understand the term waveform cycle? The period of a wave is the amount of time it takes to complete one cycle. Frequency is the number of complete cycles that a wave completes in a given amount of time.

With say an alternator one cycle is one complete rotation and will produce a Dipolar (sinusoidal waveform). One maxima one minima.

GW are not true sinusoidal waveforms they are distorted. However other than that article above I can't find good quadrupole waveform images (at least non digital) plenty of digital quadrupole.

The complete 2 maxima and 2 minima occurs every cycle. Of each wave.

Edited by Mordred
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How does some range of delays to electromagnetic radiation relate to the creation of gravitational waves?

And how does that equate to gravitational waves (a) being radiated in all directions and (b) shrinking and stretching objects in orthogonal directions (i.e. having a particular polarization) and ( c) increasing in frequency?

You are effectively making an analogy equivalent to one BH alternately eclipsing and being eclipsed by the other. But that is inaccurate and doesn't tell us anything about the nature of gravitational waves.

If we had the situation as in your second paragraph Dan is enquiring what effect that would have on the signal received by the LIGO.

By eclipse that refers to LIGO only. The BBH would still be producing GWs but would LIGO be able to detect a signal change that corresponds to the timing of the eclipse?

Example is the Sun is still shining during a solar eclipse but the signal (light) on Earth is different.

So the BBHs will during their binary phase be producing GWs regardless of whether LIGO sees an eclipse. - I hope Dan agrees with that.

Do you understand the term waveform cycle? The period of a wave is the amount of time it takes to complete one cycle. Frequency is the number of complete cycles that a wave completes in a given amount of time.

With say an alternator one cycle is one complete rotation and will produce a Dipolar (sinusoidal waveform). One maxima one minima.

GW are not true sinusoidal waveforms they are distorted. However other than that article above I can't find good quadrupole waveform images (at least non digital) plenty of digital quadrupole.

The complete 2 maxima and 2 minima occurs every cycle. Of each wave.

OK that was all correct and understandable, but taking your alternator example, they can relate the different positions of the armature to the waveform produced. Can the same thing be done for a quadrupole wave?

What position (or arrangement) of the accelerating masses creates a maximum and a minimum?

A maximum would be defined as maximum distance between the test particles in the x axis.

What position (or arrangement) of the accelerating masses in relation to the x axis creates a maximum separation in the test particles along the x axis?

Can anyone answer that question for that is where we will see the change in the chirp waveform if it is going to show a Shapiro time delay by delaying the onset or making the onset earlier of the maximum or the minimum part of the waveform. Or it may even show up as a widening of one part of the curve.

Edited by Robittybob1

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