Prospective GW sources
5 Aug 2005 8:08:31 UTC
Topic 189666
(moderation:
What do we expect to find? As I heard - gravity waves from "pulsars" (spinning neutron stars). But why they should emit detectable GW power? Afaik, gravity waves are emitted only by oscillating quadrupole (not even doublet). Why should we think, that neutron stars have sufficient quadrupole momentums? Why they all might not be spherically symmetric?
Prospective GW sources
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Because they are rotating.
RE: RE: Why they all
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Afaik, ellipsoid of revolution also won't emit
A single neutron star won't
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A single neutron star won't be a good source for GW but a binary natutron star, ie two neutron start orbiting each other, would be. An isolated ordinary neutron star is hhard to find but pulsars are easy to find if they happen to be emtting their radio pusles in our direction. Then one could hope that some of these pulsars might also be binaries.
So at least one reason for looking at pulsars is that it actually gives us a way to find neutron stars, which may then turn out be binaries too.
However if the rotation axis
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However if the rotation axis shifts from the symmetry axis the pulsar will generate GWs. The crust of a neutron start is extremely stiff and can not adjust rapidly shifts in structure. This is similar to the way the pulsar's strong magnetic field is not aligned with its spin axis (which is why pulsars pulse). The interaction between the competing forces tries to align the three different axes but it takes a long time to expend the extra energy embedded in the such a system.
Epros, There are a lot of
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Epros,
There are a lot of sources we might find, at varying levels of expectation. Here is a review article which is four years out of date but still a good overview. It was meant for a technical audience, but if you skip over the heavy-going bits and skim the rest you can get a good idea. Spinning neutron stars (or similar things) are the particular source that Einstein@Home is focusing on, because that's where the biggest computational demands are.
It is true that gravitational radiation is generated by changing quadrupole (or higher) moments. There are several ways that spinning neutron stars could have those.
Mark Forester's answer about the symmetry axis and the spin axis is one way. The technical term for that is "free precession" and it is possible because neutron stars have a thin crust on top. (Actually, there are a few meters of liquid gunk on top of the crust, which is about 1km thick out of about 10km total radius of the star.) Americans can visualize free precession as what happens when you screw up passing an American football: The axes don't coincide, so the thing wobbles around some mean direction. If you work out the numbers, though, free precession is almost certainly not detectable by LIGO until early next decade when there have been some big upgrades.
Since neutron stars have solid crusts, they can also have mountains, which will generate some quadrupole asymmetry and radiate as the star spins. The mountain building mechanisms are very different from those on Earth. Young neutron stars should have big mountains because the crust forms around the same time the star is forming in the extremely violent core collapse of a supernova explosion. Older neutron stars can have mountain building if they are accreting matter very rapidly from an ordinary companion star. For reasons of computational cost, Einstein@Home is just looking for isolated pulsars right now, which means that young neutron stars are the best bet.
Actually, neutron stars may not be made (mostly) of neutrons - extrapolating from terrestrial nuclear physics, there are several possibilities for funny things going on in their high-density interiors. In some of those theories, a large part of the star's core may be solid too. In that case, you can have an even bigger quadrupole (the purely liquid core of the standard neutron star model can't contribute). Even though LIGO is not yet quite at its initial design sensitivity, it's already getting to where it has a shot at some of these.
Even if the star is mostly liquid, it turns out there is a way it can generate a detectable quadrupole. There is a type of fluid motion called "r-modes" that in principle can feed off its own radiation and have all sorts of neat effects, although if this happens in reality it is probably in accreting neutron stars in binaries. These are being searched for, but in a more preliminary way than isolated pulsars and not (yet) in Einstein@Home.
Hope this helps,
Ben
P.S. Klasm, you may want to read this post.
P.P.S. Everyone, you can find the answers to several science questions browsing my previous posts, which are linked from my profile (click on my name to the right of this post).
RE: Since neutron stars
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Thank you, Ben.
But I have some doubts about magnitude of mountains: Black holes are formed even under more violent collapse, but afaik they completely lose quadrupole momentum. Considering neutron stars as a kind of "approach" to black holes, I expect they _almost_ lose their quadrupole momentum. Or precise computations show another picture?
epros: In the case of a black
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epros:
In the case of a black hole only gravatational momentum and energy of the multipole moments are availabel to support them. These fields radiate away rapidly. The multipole moments of neutron star have weaker gravatational momentum and energy and a much greater inertial momentum and energy.
Degenerate matter such as the stuff of a neutron star crust is far stiffer than any kind of normal matter. Only extremely energetic events can modify small regions of such material. Most events spread themselves out over large portions of the body.
There is evidence of the extreme events occuring in pulsars. These are in the form of sudden shifts in the phase and frequency of the pulses. At least some of these events are interpreted as seismic events resulting from collapse of the mountain that Ben mentioned.
epros
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epros wrote:
I suppose you could think of neutron stars as an approach to black holes, but they're an approach that has stalled. A collapsing star that will wind up as a black hole has to lose its quadrupole moment very quickly (a fraction of a second for the mass range LIGO is going for), but a neutron star can sit there just fine until the universe ends. The fact that it is made of very stable matter makes a big difference from a black hole, which is made of vacuum.
The End of May Report (ahem - yes it really is coming) will have some pointers to some articles on this, but the brief answer is this: As far as we know, a "standard" neutron star could have a quadrupole moment up to about 10^-6 times its moment of inertia, or almost 10^39 grams cm^2. A "hybrid star" with some quarks mixed in might have a solid core and up to 10^-5; that is more speculative but a decent possibility. Out on the wacky end (but not impossible) is a strange quark star, which might be solid and have a quadrupole upwards of 10^-4 times the moment of inertia. (There is a range of theories because observations have not constrained them very well - yet.)
Are the solid parts of neutron stars stiff or not? Actually, that gets back to the discussion of dimensionless numbers the other day. If you think of stiffness in terms of the shear modulus and see that the inner parts of the crust can get up to 10^30 erg/cm^3, you say "Wow that's a big number and means it's really stiff." I think that's where Mark Forester is coming from. But if you look at a dimensionless number like the ratio of the shear modulus to the pressure, that's 10^-3 in the inner crust. Or those dimensionless numbers in the previous paragraph (quadrupole over moment of inertia) are even smaller.
So the way I'd think of it, this stuff is not very stiff. In terms of how it responds (pressure waves vs shear waves) if you whack it, this stuff is more like Jell-O than anything else. Jell-O that is several times the density of an atomic nucleus, superconducts and carries a magnetic field millions of times the terrestrial one, and is a superfluid at a hundred million degrees.
As Mark said, there is evidence from pulsar observations that a fair chunk of a neutron star is solid, and has nasty seismic events from time to time. Einstein@Home wouldn't pick up the mountain collapsing (although other LIGO searches might), but it could pick up the radiation from the mountain spinning around for ages before the big quake.
Hope this helps,
Ben
Ben: I was looking for a
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Ben:
I was looking for a discriptive term that would describe a material that can withstand gravatational force 10^11 times higher than Earth's without yielding. What would you suggest in place of "stiff"?
Mark Forester
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Mark Forester wrote:
The thing is, you can put two kinds of stress on matter: shear and compression. Compression is when you squeeze stuff, shear is when you move bits of it past each other in different directions without compression (or expansion).
Materials can respond very differently to shear and compression. Air goes with whatever you do to it, very little resistance. Water moves readily if you shear it, but squeeze all you like and it doesn't give. So it's a fluid, but an incompressible one. Rock resists both compression and shear.
Coming back to neutron stars, for gravitational wave emission we want to know how well the stuff holds up mountains. That means computing the "shear modulus", which is basically how much energy it takes to shear it a certain amount. Holding up (not compressing further) under 10^11 gees is impressive, but could be done by a fluid and is a separate issue from shear.
Think of the ocean, where the water at the bottom of the Marianas Trench is holding up under more pressure than in the deepest mines. But the shear modulus is zero, so it's a fluid. Or think of rock. As you go deeper in the Earth's crust, the rock acts more and more like a fluid. The shear modulus is staying about constant, but the pressure goes up enormously. What determines how "solid" something is, in the sense of resisting shear as much as resisting compression, is the ratio of the shear modulus to the pressure.
In the solid parts of neutron stars, that ratio should be around 10^-3. So the solid parts can hold up mountains, but they'll be relatively short. On Earth the highest mountain is 1/600 of the radius, but on a neutron star the highest mountain is probably no more than 1/10^6, certainly no more than 1/10^4.
So I wouldn't call the crust "stiff" because mechanically it almost acts like a fluid. Indeed, most of the stuff underneath is fluid, and it's resisting even higher pressure than the stuff on top (like ocean depths under the ice pack, or the Earth's fluid mantle under its crust).
I guess in the end I wouldn't use a single word, because no single word in English is appropriate. As Terry Pratchett once said:
Hope this helps,
Ben