APOD: A Message from the Gravitational... (2023 Jun 29)

[VictorBorun]

The process of accretion involves accelerated mass. So it produces gravitational radiation. (Accretion always involves inspiraling matter.) It is the acceleration that matters. Spin a barbell and you produce gravitational radiation, despite the fact that the two masses remain at a fixed distance from each other.

Just to be clear, the outspiraling Moon is also giving rise to GWs, right? That is, there's acceleration happening there too.

And I presume that "decretion" of matter such as what occurs when stars blow off their layers for various reasons will also cause GW?

There is acceleration happening anytime a body isn't moving in a straight line.

If a body blows off mass in a spherically symmetric way, it won't create gravitational radiation.

I wonder whether a 100 million suns BH, if it orbits a 1 billion suns BH and have its spin wobble, would generate higher GW amplitudes at the frequency of its wobbling that at the frequency of its orbiting

[johnnydeep]

The process of accretion involves accelerated mass. So it produces gravitational radiation. (Accretion always involves inspiraling matter.) It is the acceleration that matters. Spin a barbell and you produce gravitational radiation, despite the fact that the two masses remain at a fixed distance from each other.

Just to be clear, the outspiraling Moon is also giving rise to GWs, right? That is, there's acceleration happening there too.

And I presume that "decretion" of matter such as what occurs when stars blow off their layers for various reasons will also cause GW?

There is acceleration happening anytime a body isn't moving in a straight line.

If a body blows off mass in a spherically symmetric way, it won't create gravitational radiation.

Alright. Perhaps I'll have to not understand that. If the body blowing off mass is doing so symmetrically (spherically or maybe radially in a single plane?) IT won't experience any acceleration, but the blown off matter certainly will, and so, won't IT create GWs?

Finally, one last hypothetical: if a body blows off matter symmetrically and that matter falls back symmetrically, I might guess that the main body would emit GWs due solely to the fluctuation in mass. But that's probably not right either. It's back to the "attempt to understand GWs" drawing board for me!

[Chris Peterson]

Just to be clear, the outspiraling Moon is also giving rise to GWs, right? That is, there's acceleration happening there too.

And I presume that "decretion" of matter such as what occurs when stars blow off their layers for various reasons will also cause GW?

There is acceleration happening anytime a body isn't moving in a straight line.

If a body blows off mass in a spherically symmetric way, it won't create gravitational radiation.

Alright. Perhaps I'll have to not understand that. If the body blowing off mass is doing so symmetrically (spherically or maybe radially in a single plane?) IT won't experience any acceleration, but the blown off matter certainly will, and so, won't IT create GWs?

It's not a matter of what individual particles are doing. You need to look at the system, which is a spherically symmetric, non-varying mass. That is true if it pulses in and out in size (which some bodies actually do). If you want the gruesome details, you can check out Birkhoff's theorem, which describes spherically symmetric cases in GR.

Finally, one last hypothetical: if a body blows off matter symmetrically and that matter falls back symmetrically, I might guess that the main body would emit GWs due solely to the fluctuation in mass. But that's probably not right either. It's back to the "attempt to understand GWs" drawing board for me!

Again, there is no "main body", there's just a spherically symmetric mass which is oscillating while maintaining that symmetry. Not sure it's physically accurate, but by analogy you could imagine that if you're observing this from a distance, a blob of mass moving towards you is exactly offset by a blob of the same mass moving away from you.

[johnnydeep]

There is acceleration happening anytime a body isn't moving in a straight line.

If a body blows off mass in a spherically symmetric way, it won't create gravitational radiation.

Alright. Perhaps I'll have to not understand that. If the body blowing off mass is doing so symmetrically (spherically or maybe radially in a single plane?) IT won't experience any acceleration, but the blown off matter certainly will, and so, won't IT create GWs?

It's not a matter of what individual particles are doing. You need to look at the system, which is a spherically symmetric, non-varying mass. That is true if it pulses in and out in size (which some bodies actually do). If you want the gruesome details, you can check out Birkhoff's theorem, which describes spherically symmetric cases in GR.

Finally, one last hypothetical: if a body blows off matter symmetrically and that matter falls back symmetrically, I might guess that the main body would emit GWs due solely to the fluctuation in mass. But that's probably not right either. It's back to the "attempt to understand GWs" drawing board for me!

Again, there is no "main body", there's just a spherically symmetric mass which is oscillating while maintaining that symmetry. Not sure it's physically accurate, but by analogy you could imagine that if you're observing this from a distance, a blob of mass moving towards you is exactly offset by a blob of the same mass moving away from you.

Ok, one more: two identical bodies orbiting a common center of gravity emit GWs, correct?

Now, what about a single rotating body, which seem to me quite similar. Is it constantly emitting GWs or not?

[Chris Peterson]

Alright. Perhaps I'll have to not understand that. If the body blowing off mass is doing so symmetrically (spherically or maybe radially in a single plane?) IT won't experience any acceleration, but the blown off matter certainly will, and so, won't IT create GWs?

It's not a matter of what individual particles are doing. You need to look at the system, which is a spherically symmetric, non-varying mass. That is true if it pulses in and out in size (which some bodies actually do). If you want the gruesome details, you can check out Birkhoff's theorem, which describes spherically symmetric cases in GR.

Finally, one last hypothetical: if a body blows off matter symmetrically and that matter falls back symmetrically, I might guess that the main body would emit GWs due solely to the fluctuation in mass. But that's probably not right either. It's back to the "attempt to understand GWs" drawing board for me!

Again, there is no "main body", there's just a spherically symmetric mass which is oscillating while maintaining that symmetry. Not sure it's physically accurate, but by analogy you could imagine that if you're observing this from a distance, a blob of mass moving towards you is exactly offset by a blob of the same mass moving away from you.

Ok, one more: two identical bodies orbiting a common center of gravity emit GWs, correct?

Now, what about a single rotating body, which seem to me quite similar. Is it constantly emitting GWs or not?

Two bodies orbiting each other create waves in the plane of their orbit. A rotating body produces no gravitational radiation if it is spherical. Otherwise it does.

[johnnydeep]

It's not a matter of what individual particles are doing. You need to look at the system, which is a spherically symmetric, non-varying mass. That is true if it pulses in and out in size (which some bodies actually do). If you want the gruesome details, you can check out Birkhoff's theorem, which describes spherically symmetric cases in GR.



Again, there is no "main body", there's just a spherically symmetric mass which is oscillating while maintaining that symmetry. Not sure it's physically accurate, but by analogy you could imagine that if you're observing this from a distance, a blob of mass moving towards you is exactly offset by a blob of the same mass moving away from you.

Ok, one more: two identical bodies orbiting a common center of gravity emit GWs, correct?

Now, what about a single rotating body, which seem to me quite similar. Is it constantly emitting GWs or not?

Two bodies orbiting each other create waves in the plane of their orbit. A rotating body produces no gravitational radiation if it is spherical. Otherwise it does.

And a dumbbell-shaped body rotating about a line through its "handle"? At what point does "two bodies orbiting each other emitting GWs" become "one asymmetrical rotating body not emitting GWs"?

[Chris Peterson]

Ok, one more: two identical bodies orbiting a common center of gravity emit GWs, correct?

Now, what about a single rotating body, which seem to me quite similar. Is it constantly emitting GWs or not?

Two bodies orbiting each other create waves in the plane of their orbit. A rotating body produces no gravitational radiation if it is spherical. Otherwise it does.

And a dumbbell-shaped body rotating about a line through its "handle"? At what point does "two bodies orbiting each other emitting GWs" become "one asymmetrical rotating body not emitting GWs"?

Not sure I understand your geometry. What axis "through its handle"?

[alter-ego]

Two bodies orbiting each other create waves in the plane of their orbit. A rotating body produces no gravitational radiation if it is spherical. Otherwise it does.

And a dumbbell-shaped body rotating about a line through its "handle"? At what point does "two bodies orbiting each other emitting GWs" become "one asymmetrical rotating body not emitting GWs"?

Not sure I understand your geometry. What axis "through its handle"?

A non-zero quadrupole rotation component is required for GW generation. A symmetrical dumbbell has two fundamental rotation axes that generally describe all rotation possibilities: Parallel and perpendicular to the dumbbell handle. Only for the special, on-axis (parallel to the handle) rotation will no GWs be generated. Maximum GWs occur when dumbell rotation is perpendicular to the handle (maximum quadrupole moment).

[johnnydeep]

And a dumbbell-shaped body rotating about a line through its "handle"? At what point does "two bodies orbiting each other emitting GWs" become "one asymmetrical rotating body not emitting GWs"?

Not sure I understand your geometry. What axis "through its handle"?

A non-zero quadrupole rotation component is required for GW generation. A symmetrical dumbbell has two fundamental rotation axes that generally describe all rotation possibilities: Parallel and perpendicular to the dumbbell handle. Only for the special, on-axis (parallel to the handle) rotation will no GWs be generated. Maximum GWs occur when dumbell rotation is perpendicular to the handle (maximum quadrupole moment).

Very interesting. Yes, I was referring to an axis perpendicular to the handle, specifically, either X or Y (really, the same case) in the image below, but not Z:

But it still strikes me as odd that a rotating solid sphere generates no GWs, but simply removing a circular slice of arbitrarily small thickness through the center - thereby creating a symmetrical dumb-bell! - will suddenly cause GWs to be created!

[alter-ego]

Not sure I understand your geometry. What axis "through its handle"?

A non-zero quadrupole rotation component is required for GW generation. A symmetrical dumbbell has two fundamental rotation axes that generally describe all rotation possibilities: Parallel and perpendicular to the dumbbell handle. Only for the special, on-axis (parallel to the handle) rotation will no GWs be generated. Maximum GWs occur when dumbell rotation is perpendicular to the handle (maximum quadrupole moment).

Very interesting. Yes, I was referring to an axis perpendicular to the handle, specifically, either X or Y (really, the same case) in the image below, but not Z:


symmetrical dumbbell axes of rotation.jpg


But it still strikes me as odd that a rotating solid sphere generates no GWs, but simply removing a circular slice of arbitrarily small thickness through the center - thereby creating a symmetrical dumb-bell! - will suddenly cause GWs to be created!

You now have no uniform mass distribution.
You may find these links helpful and certainly interesting!
https://van.physics.illinois.edu/ask/listing/204

Simply consider the gravitational force acting on you at some fixed, finite distance from the rotating mass (or mass ensemble). If you expect to feel a varying force over time as some mass gets closer and farther away from you during a rotation perion, then GWs are emitted. It should be intuitive that there are no variations from a rotating uniform sphere, but split it in half and separate them, even infinitesimally, now introduces a varying gravitational field (GWs).
Now there are more complicated GW emission from exotic dynamic mass conditions (time varying mass-currents) and solitons (as I read anyway ), but I believe the discussion here refers to "basic" binary-inspiral-type GWs.

[johnnydeep]

A non-zero quadrupole rotation component is required for GW generation. A symmetrical dumbbell has two fundamental rotation axes that generally describe all rotation possibilities: Parallel and perpendicular to the dumbbell handle. Only for the special, on-axis (parallel to the handle) rotation will no GWs be generated. Maximum GWs occur when dumbell rotation is perpendicular to the handle (maximum quadrupole moment).

Very interesting. Yes, I was referring to an axis perpendicular to the handle, specifically, either X or Y (really, the same case) in the image below, but not Z:


symmetrical dumbbell axes of rotation.jpg


But it still strikes me as odd that a rotating solid sphere generates no GWs, but simply removing a circular slice of arbitrarily small thickness through the center - thereby creating a symmetrical dumb-bell! - will suddenly cause GWs to be created!

You now have no uniform mass distribution.
You may find these links helpful and certainly interesting!
https://van.physics.illinois.edu/ask/listing/204

Simply consider the gravitational force acting on you at some fixed, finite distance from the rotating mass (or mass ensemble). If you expect to feel a varying force over time as some mass gets closer and farther away from you during a rotation perion, then GWs are emitted. It should be intuitive that there are no variations from a rotating uniform sphere, but split it in half and separate them, even infinitesimally, now introduces a varying gravitational field (GWs).
Now there are more complicated GW emission from exotic dynamic mass conditions (time varying mass-currents) and solitons (as I read anyway ), but I believe the discussion here refers to "basic" binary-inspiral-type GWs.

Thanks. Your "whether an observer will experience a time-variable gravitational field" explanation is certainly a much clearer way of understanding this! But it would also imply that an accreting black hole would emit GWs "merely" because it is getting more massive over time, right? And even if it is NOT rotating, though that is probably virtually impossibly unlikely to happen in reality.

As for the link to further reading, I'll have to add that to my pile.

[Chris Peterson]

Very interesting. Yes, I was referring to an axis perpendicular to the handle, specifically, either X or Y (really, the same case) in the image below, but not Z:


symmetrical dumbbell axes of rotation.jpg


But it still strikes me as odd that a rotating solid sphere generates no GWs, but simply removing a circular slice of arbitrarily small thickness through the center - thereby creating a symmetrical dumb-bell! - will suddenly cause GWs to be created!

You now have no uniform mass distribution.
You may find these links helpful and certainly interesting!
https://van.physics.illinois.edu/ask/listing/204

Simply consider the gravitational force acting on you at some fixed, finite distance from the rotating mass (or mass ensemble). If you expect to feel a varying force over time as some mass gets closer and farther away from you during a rotation perion, then GWs are emitted. It should be intuitive that there are no variations from a rotating uniform sphere, but split it in half and separate them, even infinitesimally, now introduces a varying gravitational field (GWs).
Now there are more complicated GW emission from exotic dynamic mass conditions (time varying mass-currents) and solitons (as I read anyway :?: :idea:), but I believe the discussion here refers to "basic" binary-inspiral-type GWs.

Thanks. Your "whether an observer will experience a time-variable gravitational field" explanation is certainly a much clearer way of understanding this! But it would also imply that an accreting black hole would emit GWs "merely" because it is getting more massive over time, right? And even if it is NOT rotating, though that is probably virtually impossibly unlikely to happen in reality.

An accreting black hole doesn't emit GWs. The accreting material does because it isn't a perfectly homogeneous disc.

[johnnydeep]

You now have no uniform mass distribution.
You may find these links helpful and certainly interesting!
https://van.physics.illinois.edu/ask/listing/204

Simply consider the gravitational force acting on you at some fixed, finite distance from the rotating mass (or mass ensemble). If you expect to feel a varying force over time as some mass gets closer and farther away from you during a rotation period, then GWs are emitted. It should be intuitive that there are no variations from a rotating uniform sphere, but split it in half and separate them, even infinitesimally, now introduces a varying gravitational field (GWs).
Now there are more complicated GW emission from exotic dynamic mass conditions (time varying mass-currents) and solitons (as I read anyway ), but I believe the discussion here refers to "basic" binary-inspiral-type GWs.

Thanks. Your "whether an observer will experience a time-variable gravitational field" explanation is certainly a much clearer way of understanding this! But it would also imply that an accreting black hole would emit GWs "merely" because it is getting more massive over time, right? And even if it is NOT rotating, though that is probably virtually impossibly unlikely to happen in reality.

An accreting black hole doesn't emit GWs. The accreting material does because it isn't a perfectly homogeneous disc.

All right.