What is the best 3D description of Gravitational waves?

[Robittybob1]

 

I assume because you are using an approximation. These tend to get less accurate at the extremes.

No I'm using the best figures I can find. I read the max frequency of the chirp was 250 Hz. Do you know anything different?

It might be relativistic effects. Does the shape of a event horizon change in a fast moving BH? If it did they could get closer in toward each other without the EH touching. This could make a big difference but I don't see any discussion on this in Google Scholar.

Does the shape of an event horizon change in a fast moving BH? You could imagine it does with time dilation and length contraction kicking in.

Edited March 30, 2016 by Robittybob1

[Strange]

.... thinking .... thunk

 

The equation you are using is for two bodies orbiting one another in circular orbits. It does not apply when black holes are in the process of merging. This paper describes a better approximation for the inspiral phase: http://arxiv.org/pdf/1602.03840v1.pdf

 

This has to take into account things like mass ratio, black holes spins, orientation of those spins, etc.

 

And then they say:

 

As the BHs get closer to each other and their veloci- ties increase, the accuracy of the PN expansion degrades, and eventually the full solution of Einstein’s equations is needed to accurately describe the binary evolution.

 

Overview here:

http://cplberry.com/2016/02/23/gw150914-the-papers/#parameter-estimation

That paper also answers this question:

I now want to investigate the cosmological redshift factor of 0.09. Any suggestions as to how to handle that?

Redshift means we are recording the frequencies slower than they were generated, is that right? Higher frequencies are going to demand even more mass in the BBH.

Edited March 30, 2016 by Strange

[swansont]

If you use the omega value for the GW150914 maximum value of 785.4 radians/sec. You can only get that orbital velocity if the masses add to 91 solar masses

 

 

Again, we know this isn't the value. Instead of running with known incorrect information, this is where you stop and try and figure out why you are getting a different answer, rather than assuming the researchers got it wrong.

[Robittybob1]

 

 

Again, we know this isn't the value. Instead of running with known incorrect information, this is where you stop and try and figure out why you are getting a different answer, rather than assuming the researchers got it wrong.

I have never said the researchers got it wrong. All I'm saying is the formula gives us the wrong (different) answer. I'm sure I'm doing the math as per the formulas correctly. The formula as displayed in Wikipedia on gravitational waves gives us the wrong answer. https://en.wikipedia.org/wiki/Gravitational_wave#Wave_amplitudes_from_the_Earth.E2.80.93Sun_system

I'm looking for clues as to what is going wrong. Strange has given some links and I'll look at them soon.

.... thinking .... thunk

 

The equation you are using is for two bodies orbiting one another in circular orbits. It does not apply when black holes are in the process of merging. This paper describes a better approximation for the inspiral phase: http://arxiv.org/pdf/1602.03840v1.pdf

 

This has to take into account things like mass ratio, black holes spins, orientation of those spins, etc.

 

And then they say:

 

Overview here:

http://cplberry.com/2016/02/23/gw150914-the-papers/#parameter-estimation

That paper also answers this question:

Thanks Strange - when you look at this readout https://christopherplberry.files.wordpress.com/2016/02/c01_reconstruction.png can you pinpoint where the merger changes from infall to ringdown?

At what time along the timeline is the frequency the maximum?

Why I am asking this question is I analysed the omega figures again thinking maybe the peak frequency 250 Hz was not at the time of the final stages of the infall.

This appeared so as the separation of two BHs (62 solar-masses) was more than their Schwarzschild radii so it was possible to increase the frequency further. At a wave frequency of 369.19 Hz was when the Sr radii matched the separation.

Looking through the papers in your link I couldn't see any description of the exact moment when one phase changed to another. So I propose that the ringdown starts a little later than is normally appreciated (because it is undefined).

 

Is the ringdown frequency defined anywhere?

 

This paper gives a very low Hz frequency of 132 Hz at the change over phase!

http://arxiv.org/pdf/1602.03841.pdf

I just can't accept that if the system went to such a high rate (370 Hz) even if momentarily that it would disappear so quickly. Maybe it would have gone to this frequency but the Sr changes shape during the last few orbits and the event horizons fuse before the masses have actually closed the separation fully. Gravitational radiation drops from the peak but the rate of rotation increases.

It is not possible to use the formulas to follow the BBH right to the ringdown.

Thanks Strange for the nudges in the right direction.

Edited March 31, 2016 by Robittybob1

[Mordred]

If your looking at ringdown as in chirp frequency your looking at the wrong formula.

Page 10

 

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

 

The formulas you posted are specifically the two polarizations. Whose strength depends on observer placement.

 

Neither determine chirp

Edited March 31, 2016 by Mordred

[Strange]

Thanks Strange - when you look at this readout https://christopherplberry.files.wordpress.com/2016/02/c01_reconstruction.png can you pinpoint where the merger changes from infall to ringdown?

 

I have no idea. I have always assumed it is at the peak amplitude, but I have no reason for that.

 

Why I am asking this question is I analysed the omega figures again thinking maybe the peak frequency 250 Hz was not at the time of the final stages of the infall.

 

 

You may be right. On the other hand, the equation you are using won't work for the last stages of infall. I imagine that means for most of the available signal.

 

 

This paper gives a very low Hz frequency of 132 Hz at the change over phase!

 

Fig 5 appears to show the frequencies at each phase. (I haven't read this in any detail, though.)

[Robittybob1]

if I had the time I would like to go through the whole paper.

 

If your looking at ringdown as in chirp frequency your looking at the wrong formula.
Page 10

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

The formulas you posted are specifically the two polarizations. Whose strength depends on observer placement.

Neither determine chirp

but they gave us the value of the strain and we compared that with what they got at LIGO strain = 1.0E-21

 

I have no idea. I have always assumed it is at the peak amplitude, but I have no reason for that.

 

 

You may be right. On the other hand, the equation you are using won't work for the last stages of infall. I imagine that means for most of the available signal.

 

 

Fig 5 appears to show the frequencies at each phase. (I haven't read this in any detail, though.)

I've given up on it at the moment. I'll still be looking for evidence of relativistic effects on a fast moving event horizon.

Edited March 31, 2016 by Robittybob1

[Mordred]

I'm asking what your referring to as ringdown. Strain and chirp frequency ringdown are two different aspects.

 

Strain occurs every cycle but the chirp frequency determines the number of cycles and frequency rate of those cycles.

[Robittybob1]

I'm asking what your referring to as ringdown. Strain and chirp frequency ringdown are two different aspects.

 

Strain occurs every cycle but the chirp frequency determines the number of cycles and frequency rate of those cycles.

This article describes ringdown as I think ATM. https://www.quora.com/What-is-black-hole-merger-ringdown

 

 

Einstein's theory predicts that when two black holes orbit around each other they will radiate gravitational waves. Over time this will cause a pair of black holes that revolve around each other to lose energy in the gravitational radiation, fall together, and gradually speed up in their rotation as the pair of black holes becomes more deeply bound together.

The end stage of this process goes very fast and is very violent for stellar mass, or above, black holes. The energy carried away in the radiation of gravitational waves first gets bigger and bigger as the system rotates faster and faster.

The eventual result is that the event horizons of the black holes will join together once the two black holes are close enough together. But even after the horizons are joined into one, the system has not yet settled down completely and it will continue to radiate an enormous amount of energy as the event horizon settles towards its final configuration.

As long as there is a changing quadrupole moment in the mass distribution (which here would have to include local energy-momentum of spacetime itself) there will be radiation.

This last phase of the black hole merger, after the event horizons have merged, is called the "ringdown". It's because the system is still "ringing" and radiating, but the radiation is now dropping off towards zero as the merger finishes.

. So from that description ringdown starts when the event horizons first touch ( except in an highly elliptical orbit I could imagine it being intermittent to begin with). The part that contacts is no longer orbiting interesting!

 

With the two equations for strain should we be adding the strains produced at a certain time together? They both can't be producing a strain of full intensity at the same time.

[Mordred]

No drop this "when the event horizons touches."

 

Gravity waves occur when there is changes in acceleration of the two Blackholes. The event horizons do not need to touch to emit gravity waves.

Strain occurs in every wave. Ringdown is the number of waves and frequency of the collection of waves.

 

It is a different formula than the strain formulas.

[Strange]

No drop this "when the event horizons touches."

 

Gravity waves occur when there is changes in acceleration of the two Blackholes. The event horizons do not need to touch to emit gravity waves.

Strain occurs in every wave. Ringdown is the number of waves and frequency of the collection of waves.

 

Ringdown refers specifically to the period when there is a single, merged black hole settling back into a spherical shape.

[Mordred]

Ah ok I was thinking ringdown in regard to chirp frequency. Though that would be more a ring up lol

Edited March 31, 2016 by Mordred

[Robittybob1]

 

Ringdown refers specifically to the period when there is a single, merged black hole settling back into a spherical shape.

You can't instantly go from two spheres to one enlarged sphere. But the more they overlap the less mass is orbiting, and that could be the ringdown? You would get less GW with time and because the amount of "orbiting" (wobbling) mass is decreasing the frequency is largely stable.

The enlarged BH continues to radiate GWs until the whole thing is a symmetrical spinning shape again.

Ah ok I was thinking ringdown in regard to chirp frequency. Though that would be more a ring up lol

It does NOT go into the ringdown phase.

 

 

With the two equations for strain should we be adding the strains produced at a certain time together? They both can't be producing a strain of full intensity at the same time.

How about answering the bolded question. There must be a change over from h+ to hx at various angles so is it possible e.g. at 45 degrees inclination to be the addition of both types of strain? Have I got that right?

Edited March 31, 2016 by Robittybob1

[swansont]

You can't instantly go from two spheres to one enlarged sphere.

 

 

You don't. The ringdown is the exponentially decreasing part of the oscillating signal. It took a few tens of milliseconds.

[Robittybob1]

 

 

You don't. The ringdown is the exponentially decreasing part of the oscillating signal. It took a few tens of milliseconds.

Was there anything drastically wrong with what I said:

 

 

You can't instantly go from two spheres to one enlarged sphere. But the more they overlap the less mass is orbiting, and that could be the ringdown? You would get less GW with time and because the amount of "orbiting" (wobbling) mass is decreasing the frequency is largely stable.

The enlarged BH continues to radiate GWs until the whole thing is a symmetrical spinning shape again.

I notice the frequency stays around the same, whereas the amplitude during the ringdown is exponentially decreasing.

 

Ringdown refers specifically to the period when there is a single, merged black hole settling back into a spherical shape.

there didn't seem to be the expression of time for combining of the two BHs settling into one spherical shape in Strange's post. Even though what he says is in some of the animations, where the two EH instantly combine to become a larger one.

Edited March 31, 2016 by Robittybob1

[Strange]

You can't instantly go from two spheres to one enlarged sphere. But the more they overlap the less mass is orbiting, and that could be the ringdown? You would get less GW with time and because the amount of "orbiting" (wobbling) mass is decreasing the frequency is largely stable.

The enlarged BH continues to radiate GWs until the whole thing is a symmetrical spinning shape again.

 

They never "overlap". They merge. But you "jellylike" description is probably reasonably good.

[Mordred]

I still think you were using the wrong equation for the ringdown phase.

 

But here you decide.

 

http://www.google.ca/url?q=http://arxiv.org/pdf/1506.00560&sa=U&ved=0ahUKEwjt-JTCtuzLAhVH42MKHb36DhsQFggcMAM&usg=AFQjCNFB0NtD0cy_mhjGnaTAh2RDLNKdIg

See equation 6

Which is the equation to model the ringdown waveform.

 

Note the similarities to the chirp formulas page 10 and 11?

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

 

 

But I guess I don't know what I'm talking about

Edited April 1, 2016 by Mordred

[Robittybob1]

I still think you were using the wrong equation for the ringdown phase.

 

But here you decide.

 

http://www.google.ca/url?q=http://arxiv.org/pdf/1506.00560&sa=U&ved=0ahUKEwjt-JTCtuzLAhVH42MKHb36DhsQFggcMAM&usg=AFQjCNFB0NtD0cy_mhjGnaTAh2RDLNKdIg

See equation 6

Which is the equation to model the ringdown waveform.

 

Note the similarities to the chirp formulas page 10 and 11?

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

 

 

But I guess I don't know what I'm talking about

No one liked Roy Kerr's spinning black holes to start with either. It is a learning curve for everyone.

[Mordred]

Still lol strain occurs every cycle of a frequency. Ringdown is a measure of frequency changes.

 

That was why I was confused by your use of the polarity formula

Which is handy to visualize a single wave. But frequency involves multiple waves. So does ringdown

[Robittybob1]

Still lol strain occurs every cycle of a frequency. Ringdown is a measure of frequency changes.

 

That was why I was confused by your use of the polarity formula

Which is handy to visualize a single wave. But frequency involves multiple waves. So does ringdown

I used those polarity formulas because they looked do-able and Strange said they would tell me what the 3D structure of the GW would be like. It has been a bit of a diversion, but an interesting one, for I played around with the formulas and got a feeling for what is happening during the inspiral and ringdown phases.

We couldn't see the 3D structure as the equations were simplified and only worked where R is much larger than the wavelength.

[Mordred]

Yes but part of the problem you were having was the radiated mass.

 

In order to calculate the radiated mass you must calculate the total mass of the BINARY SYSTEM. Each wave emits a portion of that total mass.

 

In other words every wave emits a %.

 

So after each wave is emitted you must recalculate the total mass to calculate the emitted mass of the next wave.

Which isn't as easy as it sounds as you need to account for kinetic as well as potential energy of the binary system.

 

This is why you see an increase in amplitude of the waveform page 11

 

The change in frequency is due to chirp frequency including the ringdown phase

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

 

I hope you understand that now.

Edited April 1, 2016 by Mordred

[Robittybob1]

Yes but part of the problem you were having was the radiated mass.

 

In order to calculate the radiated mass you must calculate the total mass of the BINARY SYSTEM. Each wave emits a portion of that total mass.

 

In other words every wave emits a %.

 

So after each wave is emitted you must recalculate the total mass to calculate the emitted mass of the next wave.

Which isn't as easy as it sounds as you need to account for kinetic as well as potential energy of the binary system.

 

This is why you see an increase in amplitude of the waveform page 11

 

The change in frequency is due to chirp frequency including the ringdown phase

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

 

I hope you understand that now.

There were only a few waves so there was only half that number of orbits so it would be real easy for me to set up a macro that would take the mass loss into account and follow the BHs right into the merger, but if I do that it will be next month.

[Mordred]

Understood. Takes time to equate all the needed equations onto an excel spreadsheet.

 

Personally I like Scilab which is similar to mathlab. However the programming lanquage gets complex.

[swansont]

I used those polarity formulas because they looked do-able and Strange said they would tell me what the 3D structure of the GW would be like. It has been a bit of a diversion, but an interesting one, for I played around with the formulas and got a feeling for what is happening during the inspiral and ringdown phases.

We couldn't see the 3D structure as the equations were simplified and only worked where R is much larger than the wavelength.

 

 

"Only" is a curious choice.

 

Since the wavelength is much smaller than our distance to the BBH, the equations are sufficiently accurate for what the waves look like when the signal gets here. Also for >99% of the volume our distance represents. Once you're 10,000 km or so away, it works. That's a tiny distance in astronomical terms.

[Robittybob1]

 

 

"Only" is a curious choice.

 

Since the wavelength is much smaller than our distance to the BBH, the equations are sufficiently accurate for what the waves look like when the signal gets here. Also for >99% of the volume our distance represents. Once you're 10,000 km or so away, it works. That's a tiny distance in astronomical terms.

I was just repeating what the wikipedia article said "If R is much greater than a wavelength,....". I had not specifically tested this aspect. https://en.wikipedia.org/wiki/Gravitational_wave#Wave_amplitudes_from_the_Earth.E2.80.93Sun_system