Thanks Mike i enjoyed this and may i add a thought or three.
Proof that BIG black holes exist. (supermassive BH are known, and stellar BH are known up to about 15 solar masses, but each of the progenitors is unique)
Citations - I had not noticed or thiought much about how papers are prepared before but the meticulous effort it must take to refer the reader to other papers, names and titles right etc. I especially liked seeing on many papers
Quote:
[1] A. Einstein, Sitzungsber. K. Preuss. Akad. Wiss. 1, 688 (1916).
and on some others
Quote:
[6] J. Kepler,Astronomia nova ..., seu physica coelestis, tra-dita commentariis de motibus stellae martis(1609).
[7] I. Newton,Philosophiae Naturalis Principia Mathematica (1687)
The fantastic simulations made it simple and comprehensible for the public, i think Einstein would have liked that, at the time he published SR and GR there probably was only a handful of scholars who could grasp the significance of the equations. Now us mere mortals can visualize and imagine it.
Quote:
Q2 : Could real signals be co-incident b/w two detectors ? Three ? Four ? Assume ( correctly ) that no group of three detectors lie only along a common line. }
Playing devil's advocate a hypothetical GW source located at the earth's centre would arrive at all surface detectors at the same time. Now that would raise a 5 sigma eyebrow.
I still can't believe i have on this PC some of this real GW data. It's a bit like living next door to Galileo and he says "Would you like a look through the perspicillum?"
Thanks Mike i enjoyed this and may i add a thought or three.
Proof that BIG black holes exist. (supermassive BH are known, and stellar BH are known up to about 15 solar masses, but each of the progenitors is unique)
I guess it is looking like nature has several pathways to produce the high mass/energy density required for the formation of an event horizon. Like sharks they can gobble each other up.
Quote:
Citations - I had not noticed or thiought much about how papers are prepared before but the meticulous effort it must take to refer the reader to other papers, names and titles right etc. I especially liked seeing on many papers
Quote:
[1] A. Einstein, Sitzungsber. K. Preuss. Akad. Wiss. 1, 688 (1916).
and on some others
Quote:
[6] J. Kepler,Astronomia nova ..., seu physica coelestis, tra-dita commentariis de motibus stellae martis(1609).
[7] I. Newton,Philosophiae Naturalis Principia Mathematica (1687)
Gravitational physics has a long and distinguished pedigree. It is well worth going to any primary source you can lay your hands on. This is not an exercise in literary history ! Just think of these as old text books which can speak to us now just as any recently written. Don't fall into the trap of the arrogance of contemporary view ie. it's new therefore it must be better than the older one. That's not cleverness but gullibility. Put dates aside and search for merit. Apart perhaps from language idiom I see no problem with those authors ! :-))
Quote:
The fantastic simulations made it simple and comprehensible for the public, i think Einstein would have liked that, at the time he published SR and GR there probably was only a handful of scholars who could grasp the significance of the equations. Now us mere mortals can visualize and imagine it.
Mr Einstein would be absolutely grinning ear to ear ( fit a banana sideways type of smile ) over this discovery.
Quote:
Quote:
Q2 : Could real signals be co-incident b/w two detectors ? Three ? Four ? Assume ( correctly ) that no group of three detectors lie only along a common line. }
Playing devil's advocate a hypothetical GW source located at the earth's centre would arrive at all surface detectors at the same time. Now that would raise a 5 sigma eyebrow.
Your right ! I wasn't thinking of that, but that's correct. OOoooh. No point running for the hills over that one ! :-)
Each detector pair gives a time offset b/w signal arrivals. Thus a cone is defined :
- the axis of the cone is the direct line b/w the interferometers ( extended to infinity ).
- the interferometer of latest arrival at the cone's apex.
- projected onto the celestial sphere this gives a circle.
So with an array of detectors one plays the game pairwise for each and thus the magic question is : where on the celestial sphere do the cones intersect ? But there are error margins to account for. So each cone projects as an annulus onto the sky ie. an area ( measured in square degrees ) bounded by two concentric circles.
Quote:
I still can't believe i have on this PC some of this real GW data. It's a bit like living next door to Galileo and he says "Would you like a look through the perspicillum?"
We are so lucky to be even vaguely involved. This is the brilliance of distributed computing, the 'citizen scientist' aspect and heaps of muchly thanks to Professor Bruce Allen* for kicking this off.
Cheers, Mike.
* Now that the project is going 'live' as it were for GW's then I'd better tone down the brash/laconic/lout Aussie persona and begin looking suitably respectful !
.
.
.
.
. stifles laughter
.
.
.
NAH ! Only kidding .... :-)
( edit ) If you have the time/energy, then look up stuff about angular momentum in particular. It hovers around these topics quite a bit and goes a long way to explaining why stellar systems evolve as they do. Often it is the key to understanding why one outcome happened and not another. We all have a gut feeling of what linear momentum is and how it works, but angular momentum has some important nuances that are not immediately apparent.
Another great author is Richard Feynman. His lecture series is legendary and he doesn't pull back from disclosing 'secret' stuff and admitting where the limits of understanding are. The content was pitched at mostly first to second year university physics students, but has much that with time you can absorb. I have the three volume 'red' hard copy set from waybackerythen, but I also recurrently listen to the audio recordings of the actual lectures from which they were written. He has a great humor and speaking style that is for me quite heartwarming.
( edit ) For this discovery the absolute minimum of two detectors had data and so a single annulus is the best one can do. Somewhere there is a graphic for that. However given that so much has been gleaned from this case, think of how much more exact will be others to come! The US LIGO's were in engineering mode and fell over it. Much optimisation and further characterisation of the detector response awaits.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Found it ! I was trying to find a reference to a short exchange b/w myself and Bruce Allen in 2009 :
Quote:
After all my time here : It's just hit me ..... how ambitious we are!!! :-)
We are trying to find evidence of a feature smaller than my car's glove compartment ( well, not withstanding the mountain's breadth ), far down in some really, really deep gravity well and who knows how far away.
The numbers are quite staggering. Einstein knew this too. After calculating the probable size of the effect he promptly despaired of ever measuring it.
Cheers, Mike.
Quote:
Keep your chin up! The LIGO instruments routinely measure separation changes in a 4-kilometer baseline which are one thousand times smaller than an atomic nucleus. That's also quite staggering!
Quote:
Ah, I've had one of those epiphany moments in life! Deep breaths. Let us all still go for it though .... get those signals !! :-)
[ It is the comfortable trap of exponents and logarithms. It linearises multiplicative scaling so neatly that it can obscure the real spans. The other big number that I just stare at sometimes ( well, not literally ) is that ratio of EM to gravity coupling : 10 to the 40-ish !! My ears aren't far enough apart to squeeze in the full width of all those significant zeroes .... :-) ]
Cheers, Mike.
We were talking of the millimeter mountains on neutron stars of which the chances of detection are now rather boosted ie. we know they exist and the continuous wave analyses target that.
But we could have equally been chatting about black holes and like stellar sources. So I claim it is correct to assign the word staggering to this description of GW150914 !
Seriously. Make the time to sit somewhere quiet and dim if you can find it. Close your eyes and try to encompass the number 10^[-24] but not as a symbology mathematical thing. Try to either visualise or feel perhaps the span of magnitude from where you are everyday down to where that is. If you either succeed and/or go crazy trying then let us know ! :-0
Cheers, Mike.
( edit ) Of course if 10^[-24] turns out to be a doddle for you then you're good to go for 10^[-42] ....
( edit ) LOL at my own thoughts. Douglas Adams comes to mind here.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Reminds of back in 1985 (I think) watching Professor David Goodstein (C.I.T.) and the 52 episodes of The Mechanical Universe... and Beyond several years after I built my first 10ft satellite dish getting C-band and KU-band back when it still used a LNA and down converter (then the LNB)
Still after all these decades it is my favorite ever on the Dish.
But we did have lots of things discovered since back then.
Hallo!
According to the ART a Gravitiational Wave is characterized by an amplitude, a frequency and a polarization. In the GW1509:FACTSHEET [Lit. 1] are only stated amplitude and frequency, information about polarization are missed. We know from an interview of Karsten Danzmann (director of AEI Hannover) [Lit. 2], that at minimum four detectors are necessary for gaining this information. So we have to wait another 5 to 10 year, until LIGO India will work properly and deliver the required data. There are at minimum two types of orientation of the polarization + and x, I know from elsewhere. The information about polarization seems to be much less importand than amplitude and frequency. What could we learn from the polarization? Does it carry information about how we are orientated to the plane of rotation and/or any more? [Lit. 3] doesn´t give information about this. In the GW1509:FACTSHEET [Lit. 1] is stated “likely orientation ___ face-on/offâ€. So it´s whether nor, which is most likely? In [Lit. 4] are shown computer simulations of this event. They show by really impressively and colorful pictures the very complicate and highly dynamic of the field structure, but for me, it needs much more accompanying information, to learn in detail what is shown.
Great question ! I'll have a stab at it, but I'm not incredibly sure of this.
As you say there are two polarisation modes. It might be easier to think of them as two mutually independent power channels. That is : one can have a certain ( fraction of the total ) power for one regardless of the other. I say regardless in that at the detector the contributions are "orthogonal", "sum in quadrature" or whatever is your favourite phrase to indicate finding the square root of a weighted sum of squares. To possibly reduce the babble factor here, examine this equation :
flux ~ (constants) * f^2 * (h_+)^2 + (h_x)^2
... for GW flux from a Taylor/Hulse type system ( f is wave frequency ). This is what is being generated at that source, which compared to black hole collisions is very much a low field situation. The flux quoted here is being emitted along the axis of rotation of the system and reduces by a factor of about 8 if considered as radiating away in directions within the equatorial plane ( ie. perpendicular to that rotation axis ). In any event you can see the co-factors of the h_+ and h_x terms are rather different. The upshot is that one could - if suitably instrumentally equipped - deduce a detector array's orientation toward that sort of GW source by examining the relative power in the h_+ and h_x channels, as it were. So I judge that you are right with "carry information about how we are orientated to the plane of rotation" BUT .....
... beware because the above is low field comment/calculation and so the conclusion relies on that. You see in really high fields at source - and this absolutely applies to colliding black holes - one can't sensibly separated 'wave' from 'background'. We are way off first order linear perturbation being even vaguely accurate. It is all highly contorted spacetime deep down in those extremely relativistic systems ie. many dozen solar mass black holes tearing around at half light speed.
So yes we get orientation information ( of source with respect to detector ) but that in Gorrible* Detail depends upon what one thinks is going on at source .... :-)
Cheers, Mike.
* = Gruesomely Horrible ie. get a supercomputer cluster or Go Home.
( edit ) Note that as a general statement GW power goes like the squares of frequency and spacetime strain : ~ f^2 * h^2 but with the caveat of apportioning per polarisation mode.
( edit ) I have an ( electronic ) copy of Bernard Schutz's great book "Gravity From The Ground Up".
Available from all good booksellers etc. Crikey it's a bloody ripper of a book mate ! Very many more people in the world should read it and no doubt for the sake of Mr Schutz : even pay for the copy ! :-))
It has lots of great diagrams like this :
I am currently trying to suck that dry for GW info and is my source for today's post. Of course I could have misunderstood .... :-)
( edit ) Oh and we no longer have to worry about the section in Chapter Twenty-Two "Are Gravitational Waves Real?". :-)
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Hallo Mike!
Thank you for your detailed answer. Sorry for my late response. I was too busy within the last days.
I know, polarization is an inherent characteristic of GWs, but, as Markus Pössel wrote on einstein-online : "xxxxxx the exact appearance of the three-dimensional travelling pattern will depend on the details of their oscillation (on what physicists call the wave's "polarization")." The fact of polarization is not in question for me, but their strength and the ratio beween + and x-polarization etc. and the physics that call for this.
Up to now, I didn´t find about this anywhere an information. Do you have some literature on this or can tell it for me?
EM waves are dipolar and have 2 polarizations. AFAIK GW waves are quadrupolar and should have more polarizations. But, frankly, I am not sure about this.
Tullio
Hallo Tullio!
EM waves is a good example. A linear polarized beam of laserlight can be diminshed or even canceled out by a properly positioned reflecting plate. Similar with a randomly polarized laserlight. This light becomes more linear polarized by a proper placed reflecting plate, as one direction of polarization becomes canceled out. So the effect of reflection is the physical reason for this effect of polarization of EM waves.
In regard of GWs I assume, the strength of polarization depends upon the direction we are looking onto the plane of rotation of the GW-sources, but I don´t know this. It might be much more complicated or even false.
GW waves have as many polarisations as EM waves, just the angles are different - while you can describe any polarised EM wave as a sum of a "|" and a "-" wave of the same frequency but different amplitude and phase each, it's the sum of a "+" and a "X" wave each for GW waves.
As with EM waves the polarisation you measure depends on the orientation of your detector with respect to the source. A + wave might be detected as a X wave if your detector is rotated by 45 degrees, or as a sum of both + and X wave of same phase but different amplitude if rotated arbitrarily.
And just like EM waves, GW waves can be circularly polarised as well, just add a + and a X wave with the same amplitude but 90° phase difference. That's e.g. what you will measure above/below a pair of coalescing black holes, as shown in this video: https://youtu.be/Xn-4N4JZYKA?t=30s
And between poles and the equator you'll get elliptical polarisation, a mixture of both cases.
Thanks Mike i enjoyed this
)
Thanks Mike i enjoyed this and may i add a thought or three.
Proof that BIG black holes exist. (supermassive BH are known, and stellar BH are known up to about 15 solar masses, but each of the progenitors is unique)
Citations - I had not noticed or thiought much about how papers are prepared before but the meticulous effort it must take to refer the reader to other papers, names and titles right etc. I especially liked seeing on many papers
and on some others
The fantastic simulations made it simple and comprehensible for the public, i think Einstein would have liked that, at the time he published SR and GR there probably was only a handful of scholars who could grasp the significance of the equations. Now us mere mortals can visualize and imagine it.
Playing devil's advocate a hypothetical GW source located at the earth's centre would arrive at all surface detectors at the same time. Now that would raise a 5 sigma eyebrow.
I still can't believe i have on this PC some of this real GW data. It's a bit like living next door to Galileo and he says "Would you like a look through the perspicillum?"
RE: Thanks Mike i enjoyed
)
I guess it is looking like nature has several pathways to produce the high mass/energy density required for the formation of an event horizon. Like sharks they can gobble each other up.
Gravitational physics has a long and distinguished pedigree. It is well worth going to any primary source you can lay your hands on. This is not an exercise in literary history ! Just think of these as old text books which can speak to us now just as any recently written. Don't fall into the trap of the arrogance of contemporary view ie. it's new therefore it must be better than the older one. That's not cleverness but gullibility. Put dates aside and search for merit. Apart perhaps from language idiom I see no problem with those authors ! :-))
Mr Einstein would be absolutely grinning ear to ear ( fit a banana sideways type of smile ) over this discovery.
Your right ! I wasn't thinking of that, but that's correct. OOoooh. No point running for the hills over that one ! :-)
Each detector pair gives a time offset b/w signal arrivals. Thus a cone is defined :
- the axis of the cone is the direct line b/w the interferometers ( extended to infinity ).
- the interferometer of latest arrival at the cone's apex.
- projected onto the celestial sphere this gives a circle.
So with an array of detectors one plays the game pairwise for each and thus the magic question is : where on the celestial sphere do the cones intersect ? But there are error margins to account for. So each cone projects as an annulus onto the sky ie. an area ( measured in square degrees ) bounded by two concentric circles.
We are so lucky to be even vaguely involved. This is the brilliance of distributed computing, the 'citizen scientist' aspect and heaps of muchly thanks to Professor Bruce Allen* for kicking this off.
Cheers, Mike.
* Now that the project is going 'live' as it were for GW's then I'd better tone down the brash/laconic/lout Aussie persona and begin looking suitably respectful !
.
.
.
.
. stifles laughter
.
.
.
NAH ! Only kidding .... :-)
( edit ) If you have the time/energy, then look up stuff about angular momentum in particular. It hovers around these topics quite a bit and goes a long way to explaining why stellar systems evolve as they do. Often it is the key to understanding why one outcome happened and not another. We all have a gut feeling of what linear momentum is and how it works, but angular momentum has some important nuances that are not immediately apparent.
Another great author is Richard Feynman. His lecture series is legendary and he doesn't pull back from disclosing 'secret' stuff and admitting where the limits of understanding are. The content was pitched at mostly first to second year university physics students, but has much that with time you can absorb. I have the three volume 'red' hard copy set from waybackerythen, but I also recurrently listen to the audio recordings of the actual lectures from which they were written. He has a great humor and speaking style that is for me quite heartwarming.
( edit ) For this discovery the absolute minimum of two detectors had data and so a single annulus is the best one can do. Somewhere there is a graphic for that. However given that so much has been gleaned from this case, think of how much more exact will be others to come! The US LIGO's were in engineering mode and fell over it. Much optimisation and further characterisation of the detector response awaits.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Found it ! I was trying to
)
Found it ! I was trying to find a reference to a short exchange b/w myself and Bruce Allen in 2009 :
We were talking of the millimeter mountains on neutron stars of which the chances of detection are now rather boosted ie. we know they exist and the continuous wave analyses target that.
But we could have equally been chatting about black holes and like stellar sources. So I claim it is correct to assign the word staggering to this description of GW150914 !
Seriously. Make the time to sit somewhere quiet and dim if you can find it. Close your eyes and try to encompass the number 10^[-24] but not as a symbology mathematical thing. Try to either visualise or feel perhaps the span of magnitude from where you are everyday down to where that is. If you either succeed and/or go crazy trying then let us know ! :-0
Cheers, Mike.
( edit ) Of course if 10^[-24] turns out to be a doddle for you then you're good to go for 10^[-42] ....
( edit ) LOL at my own thoughts. Douglas Adams comes to mind here.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Reminds of back in 1985 (I
)
Reminds of back in 1985 (I think) watching Professor David Goodstein (C.I.T.) and the 52 episodes of The Mechanical Universe... and Beyond several years after I built my first 10ft satellite dish getting C-band and KU-band back when it still used a LNA and down converter (then the LNB)
Still after all these decades it is my favorite ever on the Dish.
But we did have lots of things discovered since back then.
One called *Telescope* is next.
(might get Mike making youtube lectures after saying this )
(the old Dish was more fun to me than the new ones pre-Vidiocipher)
http://www.ligo.org/science/Publication-S6VSR24KnownPulsar/
Hallo! According to the ART a
)
Hallo!
According to the ART a Gravitiational Wave is characterized by an amplitude, a frequency and a polarization. In the GW1509:FACTSHEET [Lit. 1] are only stated amplitude and frequency, information about polarization are missed. We know from an interview of Karsten Danzmann (director of AEI Hannover) [Lit. 2], that at minimum four detectors are necessary for gaining this information. So we have to wait another 5 to 10 year, until LIGO India will work properly and deliver the required data. There are at minimum two types of orientation of the polarization + and x, I know from elsewhere. The information about polarization seems to be much less importand than amplitude and frequency. What could we learn from the polarization? Does it carry information about how we are orientated to the plane of rotation and/or any more? [Lit. 3] doesn´t give information about this. In the GW1509:FACTSHEET [Lit. 1] is stated “likely orientation ___ face-on/offâ€. So it´s whether nor, which is most likely? In [Lit. 4] are shown computer simulations of this event. They show by really impressively and colorful pictures the very complicate and highly dynamic of the field structure, but for me, it needs much more accompanying information, to learn in detail what is shown.
Kind regards and happy crunching
Martin
[1]: https://losc.ligo.org/s/events/GW150914/GW150914-FactSheet-BW.pdf
[2]: Der Tagsspiegel, Nr. 22671, dated 15. Feb. 2016, page 16, cited and translated in https://einsteinathome.org/node/198424&postid=152380#152380
[3]: http://www.einstein-online.info/spotlights/gw_waves?set_language=en
[4]: http://www.aei.mpg.de/1824987/?page=2
RE: What could we learn
)
Great question ! I'll have a stab at it, but I'm not incredibly sure of this.
As you say there are two polarisation modes. It might be easier to think of them as two mutually independent power channels. That is : one can have a certain ( fraction of the total ) power for one regardless of the other. I say regardless in that at the detector the contributions are "orthogonal", "sum in quadrature" or whatever is your favourite phrase to indicate finding the square root of a weighted sum of squares. To possibly reduce the babble factor here, examine this equation :
flux ~ (constants) * f^2 * (h_+)^2 + (h_x)^2
... for GW flux from a Taylor/Hulse type system ( f is wave frequency ). This is what is being generated at that source, which compared to black hole collisions is very much a low field situation. The flux quoted here is being emitted along the axis of rotation of the system and reduces by a factor of about 8 if considered as radiating away in directions within the equatorial plane ( ie. perpendicular to that rotation axis ). In any event you can see the co-factors of the h_+ and h_x terms are rather different. The upshot is that one could - if suitably instrumentally equipped - deduce a detector array's orientation toward that sort of GW source by examining the relative power in the h_+ and h_x channels, as it were. So I judge that you are right with "carry information about how we are orientated to the plane of rotation" BUT .....
... beware because the above is low field comment/calculation and so the conclusion relies on that. You see in really high fields at source - and this absolutely applies to colliding black holes - one can't sensibly separated 'wave' from 'background'. We are way off first order linear perturbation being even vaguely accurate. It is all highly contorted spacetime deep down in those extremely relativistic systems ie. many dozen solar mass black holes tearing around at half light speed.
So yes we get orientation information ( of source with respect to detector ) but that in Gorrible* Detail depends upon what one thinks is going on at source .... :-)
Cheers, Mike.
* = Gruesomely Horrible ie. get a supercomputer cluster or Go Home.
( edit ) Note that as a general statement GW power goes like the squares of frequency and spacetime strain : ~ f^2 * h^2 but with the caveat of apportioning per polarisation mode.
( edit ) I have an ( electronic ) copy of Bernard Schutz's great book "Gravity From The Ground Up".
Available from all good booksellers etc. Crikey it's a bloody ripper of a book mate ! Very many more people in the world should read it and no doubt for the sake of Mr Schutz : even pay for the copy ! :-))
It has lots of great diagrams like this :
I am currently trying to suck that dry for GW info and is my source for today's post. Of course I could have misunderstood .... :-)
( edit ) Oh and we no longer have to worry about the section in Chapter Twenty-Two "Are Gravitational Waves Real?". :-)
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Hallo Mike! Thank you for
)
Hallo Mike!
Thank you for your detailed answer. Sorry for my late response. I was too busy within the last days.
I know, polarization is an inherent characteristic of GWs, but, as Markus Pössel wrote on einstein-online : "xxxxxx the exact appearance of the three-dimensional travelling pattern will depend on the details of their oscillation (on what physicists call the wave's "polarization")." The fact of polarization is not in question for me, but their strength and the ratio beween + and x-polarization etc. and the physics that call for this.
Up to now, I didn´t find about this anywhere an information. Do you have some literature on this or can tell it for me?
Kind regards and happy crunching
Martin
EM waves are dipolar and have
)
EM waves are dipolar and have 2 polarizations. AFAIK GW waves are quadrupolar and should have more polarizations. But, frankly, I am not sure about this.
Tullio
Hallo Tullio! EM waves is a
)
Hallo Tullio!
EM waves is a good example. A linear polarized beam of laserlight can be diminshed or even canceled out by a properly positioned reflecting plate. Similar with a randomly polarized laserlight. This light becomes more linear polarized by a proper placed reflecting plate, as one direction of polarization becomes canceled out. So the effect of reflection is the physical reason for this effect of polarization of EM waves.
In regard of GWs I assume, the strength of polarization depends upon the direction we are looking onto the plane of rotation of the GW-sources, but I don´t know this. It might be much more complicated or even false.
Kind regads and happy crunching
Martin
GW waves have as many
)
GW waves have as many polarisations as EM waves, just the angles are different - while you can describe any polarised EM wave as a sum of a "|" and a "-" wave of the same frequency but different amplitude and phase each, it's the sum of a "+" and a "X" wave each for GW waves.
As with EM waves the polarisation you measure depends on the orientation of your detector with respect to the source. A + wave might be detected as a X wave if your detector is rotated by 45 degrees, or as a sum of both + and X wave of same phase but different amplitude if rotated arbitrarily.
And just like EM waves, GW waves can be circularly polarised as well, just add a + and a X wave with the same amplitude but 90° phase difference. That's e.g. what you will measure above/below a pair of coalescing black holes, as shown in this video: https://youtu.be/Xn-4N4JZYKA?t=30s
And between poles and the equator you'll get elliptical polarisation, a mixture of both cases.