I Why binary systems for gravitational waves?

[binbagsss]

So a spherically symmetric object, by Birkhoff's theorem, does not emit gravitational waves.

Is this why we look to binaries, so that there is some rotation of the objects with respect to each other breaking the spherical symmetry? Or mainly because the gravitational radiation is much greater as needed, or is it both reasons?

What single sources, if the sensitivity of detectors was sufficient enough, would emit gravitational waves . Like a single rotating black hole? (or is this spherically symmetric, if it rotates in a certain way)?

Thanks in advance

 

[Vanadium 50]

You need a changing quadrupole moment. A spinning BH does not have a changing quadrupole moment.

 

[binbagsss]

You need a changing quadrupole moment. A spinning BH does not have a changing quadrupole moment.

is this related to the way the mass is distributed?
if the mass is spherically symmetrically distributed about the rotation axis, still spherically symmetric and no quadrople moment?
Can the mass be distributed in such a way relative to the rotation axis that there can be a non-zero quadrople moment?

 

[Ben Niehoff]

is this related to the way the mass is distributed?
if the mass is spherically symmetrically distributed about the rotation axis, still spherically symmetric and no quadrople moment?
Can the mass be distributed in such a way relative to the rotation axis that there can be a non-zero quadrople moment?

Yes. The simplest such non-uniform distribution is when the mass takes the form of a binary system.

 

[Erik 05]

So a spherically symmetric object, by Birkhoff's theorem, does not emit gravitational waves.

Is this why we look to binaries, so that there is some rotation of the objects with respect to each other breaking the spherical symmetry? Or mainly because the gravitational radiation is much greater as needed, or is it both reasons?

What single sources, if the sensitivity of detectors was sufficient enough, would emit gravitational waves . Like a single rotating black hole? (or is this spherically symmetric, if it rotates in a certain way)?

Thanks in advance

Probably not black holes, but it's possible that a single neutron star could be source.

 

[PeterDonis]

if the mass is spherically symmetrically distributed about the rotation axis

It won't be. A stationary rotating system is only axially symmetric, not spherically symmetric. But that's still symmetric enough to prohibit radiating gravitational waves.

 

[PeterDonis]

Probably not black holes, but it's possible that a single neutron star could be source.

No. A single neutron star, or indeed a single object of any type held together by its self-gravity, has the same problem as a black hole: once it settles down to a stationary state, it's too symmetric to radiate gravitational waves.

 

[Keith_McClary]

ligo.org says:

Young neutron stars may be the most likely to emit continuous gravitational waves

 

[Erik 05]

Yes, there is a big difference between black holes and neutron stars. The latter have a solid crust that cracks as the star spins down, and there may be mountains on the surface (a few mm high!) - the question is whether our detectors are sensitive to detect this (likely have to wait for LISA).

 

[PeterDonis]

ligo.org says:

By "young" neutron stars they mean neutron stars that have just formed and have not settled down into a stationary state. There can be "young" black holes by the same criterion--the process of forming a black hole and of the hole settling down into a stationary state can emit gravitational waves. I believe that a black hole would settle down more quickly than a neutron star so a young neutron star might be more likely to have its gravitational waves observed since they would be emitted over a longer period of time.

 

[DrStupid]

A single neutron star, or indeed a single object of any type held together by its self-gravity, has the same problem as a black hole: once it settles down to a stationary state, it's too symmetric to radiate gravitational waves.

Even a Jacobi ellipsoid?

 

[Erik 05]

By "young" neutron stars they mean neutron stars that have just formed and have not settled down into a stationary state. There can be "young" black holes by the same criterion--the process of forming a black hole and of the hole settling down into a stationary state can emit gravitational waves. I believe that a black hole would settle down more quickly than a neutron star so a young neutron star might be more likely to have its gravitational waves observed since they would be emitted over a longer period of time.

Yes, years rather than seconds.

 

[PeterDonis]

Even a Jacobi ellipsoid?

Meaning this?

https://en.wikipedia.org/wiki/Jacobi_ellipsoid

Interesting; such an object would be stationary (more precisely, it would be stationary in the Newtonian case, without gravitational wave emission) but not axisymmetric, so it's possible that the third time derivative of its quadrupole moment would be nonzero, which is the condition for being able to emit gravitational waves.

 

[DrStupid]

Interesting; such an object would be stationary (more precisely, it would be stationary in the Newtonian case, without gravitational wave emission) but not axisymmetric, so it's possible that the third time derivative of its quadrupole moment would be nonzero, which is the condition for being able to emit gravitational waves.

Than the next obvious question is: Can a Neutron star be shaped like that? The Jacobi ellipsoid depends on the mass distribution and it is a classical solution. I don't know if something like that is possile under relativistic conditions.

If yes, the next question would be: How much angular momentum gets lost with the gravitational waves and how long would it take to turn into a spheroid?

 

[PeterDonis]

the next obvious question is: Can a Neutron star be shaped like that?

I would think it would be unlikely because of how strong a neutron star's self-gravity is. But without a detailed understanding of how the equilibrium is maintained in a Jacobi ellipsoid, and whether the equilibrium is still the same in GR as compared with Newtonian physics, it's hard to say for sure.

 

[Erik 05]

In a close binary maybe.