The key to all GW detections whatever their intrinsic strength is a "non-axisymmetric" process/scenario, this in turn being techno-speak for non-zero quadrupolar* radiation. It indeed could well be true that spinning neutron stars are not sufficiently radiating for us to detect at current instrument sensitivity levels. So why bother then ?
- it is still a valid scientific result to discover that ie. generate upper bounds on neutron star geometry. So no signal found ( to some threshold ) does not equal project failure. It is up to nature to behave in some way, we seek to accurately determine what that might be.
- said upper bounds feed back to the knowledge of the equation of state for whatever is posited to be the composition of such bodies. 'Neutron star' is a best guess label and is probably true for at least the outer skin. Who can say what might lie deep within? Most of what I have read does not speak confidently about the central core. It's not like we have a sample to poke and probe in the lab.
- it's not ellipticity ( oblate spheroid ) that is interesting as that is axi-symmetric. There may be mountains or bumps, the "relaxation" of which is hypothecated to cause glitches in the electromagnetic pulsar records. Star quakes if you like. It would also be epic if we could simultaneously record GW and EM changes on the one object.
- strictly speaking E@H is a component of LIGO's Continuous Wave Group. It could well be that nature has scenarios other than pulsars which may produce waves of that type. Who can say ?
- while we all like the idea of Einstein's GR being correct, as it certainly has been shown so far, maybe it isn't sometimes. How would we know if we didn't measure ?
If you like : being a new mode of observation then the approach taken is to look while making the fewest assumptions. To see what the universe will show us. We are not in the realtime/alert loops. We examine or integrate long periods of observations to tease out sufficiently periodic sources that show regularities above noise. Noise here is defined as those inputs which are not matched for a specific software signal template.
Cheers, Mike.
* Can't be monopolar as that breaches conservation of mass/energy. Can't be dipolar as that breaches conservation of momentum. It can be quadrupolar and higher orders in spherical harmonics though ....
( edit ) So no, we don't do the crash-bang stuff here at E@H. We might catch an inspiral perhaps but we are not best tuned for that ( though I'll bet someone is looking back over the records to see if there is any precursor to the particular collision under discussion here ). On the upside we are not examining the 'stochastic background' which is even weaker again, that's kind of like a low murmur of static with the whole universe as the echo chamber.
This helps me a lot to better understand what this project is, and also what it isn't. Thanks.
The other record broken with the recent discovery is that it got 25% of all the world's professional astronomers out of bed focused on the one event at the same time !! :-)))
Source? I could be stretched to believe that 25% of available instruments spent some time on this effort, but not even that simultaneously (they don't all bear at the same time, for one thing), but as the ratio of scientists to instruments is rather large, I'm hard put to imagine what the extra warm bodies would have been doing.
[I'm a parent of a recently but not currently practicing astronomer]
A statement by Mike Landry ( head of LIGO Hanford ) in this LIGO press release :
Quote:
“LIGO and Virgo detected 100 seconds of gravitational waves as these two neutron stars spiraled together in a massive and fiery collision,” he said. “In a sprawling follow-up campaign involving about one-quarter of the world’s professional astronomers, observatories in space and on the Earth have detected radiation in all wavelengths from gamma rays to radio waves. But the LIGO and Virgo detectors were absolutely essential in identifying and pinpointing the event in the sky, allowing this campaign to proceed”, Landry added.
The Caltech seminar Seeing and Hearing the Cataclysmic Universe gives a great informative & entertaining insight into how some of the astronomers promptly responded to the alert using many instrument types. :-)
Of special interest was Virgo's wave reception : it didn't ( much ) ! However there are certain incoming wave directions, different for each instrument ( ie. per location, arm orientations and wave polarisation ) and also varying in time as the Earth rotates, where there will be no response* because a passing wave will deform each interferometer arm equally. Hence there will be no relative phase change in the photons travelling in separate arms, and so no alteration in flux at the photodetectors in the corner station. However knowledge of which sky directions these were for Virgo during the time of the wave's passage enabled crucial disambuguation of candidate sky source positions generated by Hanford and Livingston data. Thus Virgo's 'deafness' or null characteristics was a key clue** in directing other astronomers as to where they should look. I reckon this is a super-cool aspect of the discovery.
Cheers, Mike.
* The puckers in the 'peanut' on the right :
.... are the null directions when we consider the interferometer as a receiving antenna.
** From Silver Blaze, a Sherlock Holmes mystery about a missing racehorse :
Quote:
Gregory (Scotland Yard detective): “Is there any other point to which you would wish to draw my attention?”
Holmes: “To the curious incident of the dog in the night-time.”
Gregory: “The dog did nothing in the night-time.”
Holmes: “That was the curious incident.”
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
So, how large a signal would a neutron star of mass m with a mountain of 10mm height at a distance x would we receive? Sorry this isn't fair - you have a day job.
Luckily after only a modicum of digging I have found Status Of The Continuous Gravitational Wave Searches In The Advanced Detector Era. It was only published last week, was written by a member of the LIGO-Virgo Collaboration ie. on their behalf, and it indirectly addresses your question. So a solid basis for discussion then. :-)
Firstly the precis ( my emphasis ) :
Quote:
Periodic (almost monochromatic) gravitational waves emitted by rotating, asymmetric neutron stars are intriguing potential signals in the sensitivity band of Advanced LIGO and Advanced Virgo detectors. These signals are related to elastic and magnetic stresses in the neutron-star interior, as well as to various possible instabilities, and thus are interesting from the point of view of the largely-unknown neutron star structure. I will describe the main challenges related to these searches, the current state of the data-analysis methods and plans for the future.
.... some hope then.
Quote:
In the following we will focus on rotating, non-axisymmetric neutron stars as sources of continuous periodic gravitational wave emission. Continuous gravitational wave is by definition a long-lived phenomenon, T > Tobs, and its frequency fGW is somehow proportional to the spin frequency of the star f, fGW ∝ f. There are several proposed astrophysical mechanisms providing the necessary asymmetry, which in the case of a rotating star is the source of timevarying quadrupole required for the gravitational-wave emission. Mechanisms include neutronstar ”mountains”, supported by elastic and/or magnetic stresses (fGW = 2f), oscillations (e.g., r-modes, fGW = 4/3f), free precession (fGW ∝ f + fprec) and accretion that drives the deformation from r-modes, thermal gradients and magnetic fields (fGW ~ f).
..... thus several distinctive ways that such large spinning tops might wobble for us to detect. The spacetime strain estimate ( at detector, many assumptions ) is :
which if you strip off all the pfoofle basically sez : it's of the order of 10-25 but this may be modified upwards by ellipticity ( 'fatness' of the equator as it spins ), moment of inertia ( like a flywheel but in humungous units ), frequency of rotation ( to the second power ) and downwards in source distance per 100 parsecs.
I guess what you are really asking is whether E@H has a chance on this. He directly mentions us :
Quote:
All-sky searches are the most demanding types of searches. Source parameters and positions are not known, which makes the parameter space large and the problem becomes very quickly computationally bound. In order to mediate this, hierarchical approaches are being used. Instead of analyzing the whole T0 data span at once, the data is divided into N data segments of length Ts, which are analyzed coherently, and the resulting information is combined incoherently. The expected strain amplitude scales like h0 ∝ SQRT[S/Ts]/N1/4 . The most sophisticated example of the hierarchical approach is the volunteer-driven Einstein@Home project.
.... we are a serious player in this endeavour, and he later mentions that such a search type is "feasible on a typical petaFLOP scale supercomputer" which, my dear folks, is us ( as of today we are at ~ 5.6 PFlops ). He also speaks of future source models "... to search for signals with more complicated, realistic morphology".
No guarantees here, of course. The devil is in the detail. As usual. Personally I'll take the glass-half-full viewpoint on this, but I'm hopelessly & optimistically biased. :-))
Cheers, Mike.
( edit ) In recent times we have been doing more targeted searches especially looking towards the galactic centre, on the principle that since we are located well out to the galaxy's edge there ought be more to find in that inward direction.
( edit ) BTW : You can ( roughly ) think of ellipticity as the ratio of the height of the 'mountain' to the radius of the star. It is reasonable to take a typical neutron star's radius as 10km = 10,000 m = 1,000,000 cm for this discussion. So your 10mm = 1cm bump is 1 part in 1 million here ie. 10-6. A ten centimetre mountain thus brings us up an order to 10-24, all else being equal, etc.
( edit ) FWIW : my gut instinct/hope is that neutron stars are rather more rowdy than we think. They are typically enveloped in an electromagnetic maelstrom and that just has to feed back on regular shifts in the internal structure. I'm particularly thinking of Jupiter's moon Io here and what a working over it gets. Plus all the solar flare stuff. It's possible that the intrinsic GW strength is easily in the Earth based interferometer detection band but we don't have the key waveform type(s), yet, to plug into our searches. Of course I'm a mere mug punter here. My mortgage isn't being paid for via casual guesses in astrophysics. :-))
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
Thank you for the answer Dr Hewson. I am amazed at your background reading.
Your welcome ! But this is only a hobby of mine.
On reflection re. this thread it occurs to me that there is a subtlety in the use of the word ellipticity, alas. I may have misled here.
- the first is the sort you would find defined by say mathematicians eg. Wolfram Mathworld as a function involving only the equatorial radius ( distance from centre to any equatorial point ) and the polar radius ( distance from centre to either pole ). This describes either oblate or prolate spheroids, both of which are axi-symmetric and thus ( if of uniform composition ) would not generate gravitational waves as no mass quadrupole exists. So this is a mathematical abstraction referring to shape alone and not physics.
- the second is as above but as a geometric first order approximation, but without the uniformity ( various hypotheses ) and thus a mass quadrupole does come into play. It seems we have a chicken/egg type problem here. If we knew the detailed material behaviour of neutron stars then prediction of the GW waveform follows. But we need a detected wave - where the knowledge of a waveform enhances said discovery - to tell us about the equation of state of the interior of the star !!
.... if I was actually an astrophysicist I could resolve this better for you ....
I'd also add that neutron stars are as about as dense as matter can be while still remaining accessible to electromagnetic study. They are very nearly black holes. Squash/compact them a few kilometers further inwards, or add some mass, and they disappear behind an event horizon leaving only total mass, charge and angular momentum to glean by whatever means. So there is no such thing as examining the structure or mass distribution of a black hole's interior even by gravitational waves. All structural information is radiated away when the horizon forms.
Cheers, Mike.
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
So then why search for gravitational waves sent out by neutron stars, and not by black holes?
I presume you are asking why we aren't looking for continuous waves from black holes ? :-)
Isolated & unperturbed black holes don't emit continuous waves ie. they don't have a mass quadrupole to emit with. I think it was Kip Thorne who showed that during the formation of a black hole, via say the collapse of a star, the closure of spacetime around the imploding mass ( the creation of the event horizon ) all the non axisymmetric aspects would radiate away as gravitational waves.
We have seen this radiation when two black holes collide, it is termed the 'ring-down' phase. It doesn't last long and what remains is a new black hole which then stops radiating, unless of course there is something else about to inspiral/collide/interact with.
So with such isolated/unperturbed beasts one can only measure total mass, angular momentum and electric charge. A Mr John Wheeler said of this : 'black holes have no hair'. This is implied by general relativity and has caused some discomfort in other aspects of physics, in particular thermodynamics which deals with entropy.
{ Entropy is akin to an exercise in counting and the general rule ( if properly stated ) being that the count will almost never decrease. The Universe tends to get messier as it gets older. A black hole appears to diminish entropy by erasing all knowledge ( "counts" get lost ) of what went into it. There is a delicate resolution of this ( Stephen Hawking ), in part depending upon what the ultimate fate of black holes is on immensely long time scales, but not all theorists agree upon it. }
In any event whatever structure there may be inside a black hole can't be perceived on the outside. No one outside of the movies has returned to tell the tale. Those recently discovered neutron stars that collided may have formed a black hole. We don't yet know but it is certainly possible. If so the detected electromagnetic radiation that went along with that event would have either been emitted before horizon formation, or stayed outside of it.
Cheers, Mike.
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
An orthogonal answer to you question ( WARNING : possible overshare ) :
A black hole is not a solid object in the same way that a neutron star is. They were initially called 'frozen stars' before the 'black hole' label was coined. The idea was that, if viewed from a distance, anything that went down near it would appear to slow down and freeze in time. In this description the viewer's position, a long way away, is crucial. Any light that is emitted from an object down near the event horizon and coming outwards to a distant observer has a lowering of it's frequency because of the time dilatation. The phase oscillation becomes soooo slooow that a photon's energy goes to zero by the time it gets to a remote viewer. You may recall that a photon's energy is directly proportional to it's frequency, Planck's constant being the multiplier.
If you like the horizon may be defined as that outermost surface from which no radiation will be received because of time distortion. For an undisturbed hole which does not rotate, that will be of spherical shape. If it rotates then the surface is an oblate spheroid. The horizon is thus black as seen from far away. Recall that material particles always travel slower than light and they have even less opportunity to emerge.
{ In a mild bit of language perversity the slowing of time as seen from one position to another is sometimes called the 'curvature of time'. The meaning here is to analogise with a length ruler, but one that is bent from straightness, and hence measures ordinary physical distances incorrectly. }
The upshot is that to create non-axisymmetric distortion of spacetime some other sufficiently massive object has to disturb the geometry ( time included ) for any GWs to radiate away. Hence the successful detection of merging black holes in recent years.
Cheers, Mike.
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
Mike Hewson schrieb:The key
)
This helps me a lot to better understand what this project is, and also what it isn't. Thanks.
Mike Hewson wrote:The other
)
Source? I could be stretched to believe that 25% of available instruments spent some time on this effort, but not even that simultaneously (they don't all bear at the same time, for one thing), but as the ratio of scientists to instruments is rather large, I'm hard put to imagine what the extra warm bodies would have been doing.
[I'm a parent of a recently but not currently practicing astronomer]
A statement by Mike Landry (
)
A statement by Mike Landry ( head of LIGO Hanford ) in this LIGO press release :
The Caltech seminar Seeing and Hearing the Cataclysmic Universe gives a great informative & entertaining insight into how some of the astronomers promptly responded to the alert using many instrument types. :-)
Of special interest was Virgo's wave reception : it didn't ( much ) ! However there are certain incoming wave directions, different for each instrument ( ie. per location, arm orientations and wave polarisation ) and also varying in time as the Earth rotates, where there will be no response* because a passing wave will deform each interferometer arm equally. Hence there will be no relative phase change in the photons travelling in separate arms, and so no alteration in flux at the photodetectors in the corner station. However knowledge of which sky directions these were for Virgo during the time of the wave's passage enabled crucial disambuguation of candidate sky source positions generated by Hanford and Livingston data. Thus Virgo's 'deafness' or null characteristics was a key clue** in directing other astronomers as to where they should look. I reckon this is a super-cool aspect of the discovery.
Cheers, Mike.
* The puckers in the 'peanut' on the right :
.... are the null directions when we consider the interferometer as a receiving antenna.
** From Silver Blaze, a Sherlock Holmes mystery about a missing racehorse :
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
Kavanagh wrote:So, how large
)
Luckily after only a modicum of digging I have found Status Of The Continuous Gravitational Wave Searches In The Advanced Detector Era. It was only published last week, was written by a member of the LIGO-Virgo Collaboration ie. on their behalf, and it indirectly addresses your question. So a solid basis for discussion then. :-)
Firstly the precis ( my emphasis ) :
.... some hope then.
..... thus several distinctive ways that such large spinning tops might wobble for us to detect. The spacetime strain estimate ( at detector, many assumptions ) is :
which if you strip off all the pfoofle basically sez : it's of the order of 10-25 but this may be modified upwards by ellipticity ( 'fatness' of the equator as it spins ), moment of inertia ( like a flywheel but in humungous units ), frequency of rotation ( to the second power ) and downwards in source distance per 100 parsecs.
I guess what you are really asking is whether E@H has a chance on this. He directly mentions us :
.... we are a serious player in this endeavour, and he later mentions that such a search type is "feasible on a typical petaFLOP scale supercomputer" which, my dear folks, is us ( as of today we are at ~ 5.6 PFlops ). He also speaks of future source models "... to search for signals with more complicated, realistic morphology".
No guarantees here, of course. The devil is in the detail. As usual. Personally I'll take the glass-half-full viewpoint on this, but I'm hopelessly & optimistically biased. :-))
Cheers, Mike.
( edit ) In recent times we have been doing more targeted searches especially looking towards the galactic centre, on the principle that since we are located well out to the galaxy's edge there ought be more to find in that inward direction.
( edit ) BTW : You can ( roughly ) think of ellipticity as the ratio of the height of the 'mountain' to the radius of the star. It is reasonable to take a typical neutron star's radius as 10km = 10,000 m = 1,000,000 cm for this discussion. So your 10mm = 1cm bump is 1 part in 1 million here ie. 10-6. A ten centimetre mountain thus brings us up an order to 10-24, all else being equal, etc.
( edit ) FWIW : my gut instinct/hope is that neutron stars are rather more rowdy than we think. They are typically enveloped in an electromagnetic maelstrom and that just has to feed back on regular shifts in the internal structure. I'm particularly thinking of Jupiter's moon Io here and what a working over it gets. Plus all the solar flare stuff. It's possible that the intrinsic GW strength is easily in the Earth based interferometer detection band but we don't have the key waveform type(s), yet, to plug into our searches. Of course I'm a mere mug punter here. My mortgage isn't being paid for via casual guesses in astrophysics. :-))
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
Thank you for the answer Dr
)
Thank you for the answer Dr Hewson. I am amazed at your background reading.
Richard
Kavanagh wrote:Thank you for
)
Your welcome ! But this is only a hobby of mine.
On reflection re. this thread it occurs to me that there is a subtlety in the use of the word ellipticity, alas. I may have misled here.
- the first is the sort you would find defined by say mathematicians eg. Wolfram Mathworld as a function involving only the equatorial radius ( distance from centre to any equatorial point ) and the polar radius ( distance from centre to either pole ). This describes either oblate or prolate spheroids, both of which are axi-symmetric and thus ( if of uniform composition ) would not generate gravitational waves as no mass quadrupole exists. So this is a mathematical abstraction referring to shape alone and not physics.
- the second is as above but as a geometric first order approximation, but without the uniformity ( various hypotheses ) and thus a mass quadrupole does come into play. It seems we have a chicken/egg type problem here. If we knew the detailed material behaviour of neutron stars then prediction of the GW waveform follows. But we need a detected wave - where the knowledge of a waveform enhances said discovery - to tell us about the equation of state of the interior of the star !!
.... if I was actually an astrophysicist I could resolve this better for you ....
I'd also add that neutron stars are as about as dense as matter can be while still remaining accessible to electromagnetic study. They are very nearly black holes. Squash/compact them a few kilometers further inwards, or add some mass, and they disappear behind an event horizon leaving only total mass, charge and angular momentum to glean by whatever means. So there is no such thing as examining the structure or mass distribution of a black hole's interior even by gravitational waves. All structural information is radiated away when the horizon forms.
Cheers, Mike.
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
So then why search for
)
So then why search for gravitational waves sent out by neutron stars, and not by black holes?
Hallo Hans! " ... why search
)
Hallo Hans!
" ... why search for gravitational waves sent out by neutron stars ... ?"
Because these events allow a test of the ART at very strong gravitional fields and for theories about the inner conditions in neutron stars.
Kind regards and happy crunching
Martin
Hans_31 wrote:So then why
)
I presume you are asking why we aren't looking for continuous waves from black holes ? :-)
Isolated & unperturbed black holes don't emit continuous waves ie. they don't have a mass quadrupole to emit with. I think it was Kip Thorne who showed that during the formation of a black hole, via say the collapse of a star, the closure of spacetime around the imploding mass ( the creation of the event horizon ) all the non axisymmetric aspects would radiate away as gravitational waves.
We have seen this radiation when two black holes collide, it is termed the 'ring-down' phase. It doesn't last long and what remains is a new black hole which then stops radiating, unless of course there is something else about to inspiral/collide/interact with.
So with such isolated/unperturbed beasts one can only measure total mass, angular momentum and electric charge. A Mr John Wheeler said of this : 'black holes have no hair'. This is implied by general relativity and has caused some discomfort in other aspects of physics, in particular thermodynamics which deals with entropy.
{ Entropy is akin to an exercise in counting and the general rule ( if properly stated ) being that the count will almost never decrease. The Universe tends to get messier as it gets older. A black hole appears to diminish entropy by erasing all knowledge ( "counts" get lost ) of what went into it. There is a delicate resolution of this ( Stephen Hawking ), in part depending upon what the ultimate fate of black holes is on immensely long time scales, but not all theorists agree upon it. }
In any event whatever structure there may be inside a black hole can't be perceived on the outside. No one outside of the movies has returned to tell the tale. Those recently discovered neutron stars that collided may have formed a black hole. We don't yet know but it is certainly possible. If so the detected electromagnetic radiation that went along with that event would have either been emitted before horizon formation, or stayed outside of it.
Cheers, Mike.
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
An orthogonal answer to you
)
An orthogonal answer to you question ( WARNING : possible overshare ) :
A black hole is not a solid object in the same way that a neutron star is. They were initially called 'frozen stars' before the 'black hole' label was coined. The idea was that, if viewed from a distance, anything that went down near it would appear to slow down and freeze in time. In this description the viewer's position, a long way away, is crucial. Any light that is emitted from an object down near the event horizon and coming outwards to a distant observer has a lowering of it's frequency because of the time dilatation. The phase oscillation becomes soooo slooow that a photon's energy goes to zero by the time it gets to a remote viewer. You may recall that a photon's energy is directly proportional to it's frequency, Planck's constant being the multiplier.
If you like the horizon may be defined as that outermost surface from which no radiation will be received because of time distortion. For an undisturbed hole which does not rotate, that will be of spherical shape. If it rotates then the surface is an oblate spheroid. The horizon is thus black as seen from far away. Recall that material particles always travel slower than light and they have even less opportunity to emerge.
{ In a mild bit of language perversity the slowing of time as seen from one position to another is sometimes called the 'curvature of time'. The meaning here is to analogise with a length ruler, but one that is bent from straightness, and hence measures ordinary physical distances incorrectly. }
The upshot is that to create non-axisymmetric distortion of spacetime some other sufficiently massive object has to disturb the geometry ( time included ) for any GWs to radiate away. Hence the successful detection of merging black holes in recent years.
Cheers, Mike.
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