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Thread: What accounts more for pulsar orbital decay?

  1. #1
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    What accounts more for pulsar orbital decay?

    I was wondering. Which accounts more for the orbital decay of pulsars, is it the electromagnetic radiation or the gravitational radiation? After all, as the matter cools, it's mass decreases and should detract from the momentum.

    many thanks,
    m74

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    Hi. You need two objects for orbital decay. You mean a binary system? Or do you mean something else? Rotation rate?

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    Quote Originally Posted by PraedSt View Post
    Hi. You need two objects for orbital decay. You mean a binary system? Or do you mean something else? Rotation rate?
    Hmm, yes, I wasn't clear. I did indeed mean a binary pulsar system. I guess they needn't be pulsars either...just a pair of very massive stars.

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    It's gravitational radiation, which removes potential energy from the system and makes the pair spiral towards each other.
    Cool objects are indeed less massive than hot objects, so cooling would remove mass from both stars (the mass-energy being radiated away as thermal photons). However, if I'm analysing this correctly, mass loss from the objects themselves would make the pair spiral farther apart. Their mutual velocity would be too high for the reduced gravitational force binding them together.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    It's gravitational radiation, which removes potential energy from the system and makes the pair spiral towards each other.
    Cool objects are indeed less massive than hot objects, so cooling would remove mass from both stars (the mass-energy being radiated away as thermal photons). However, if I'm analysing this correctly, mass loss from the objects themselves would make the pair spiral farther apart. Their mutual velocity would be too high for the reduced gravitational force binding them together.

    Grant Hutchison
    Ok, I'm a tad confused. Radiating electromagnetic energy increases radii, while radiating gravitational energy does the opposite? I think I understand how both work, but I can't understand why one is one and the other the other.

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    Start with radiating electromagnetic energy.

    Suppose that a body in straight uniform movement is radiating energy and thereby losing mass.

    In a comoving observational frame, it is not moving, has no momentum and has no change of momentum. Its mass is decreasing as it radiates electromagnetic energy in all directions equally. The momentum of electromagnetic rays radiated in different directions cancel to zero.

    In an observational frame where the radiating body is moving, it is losing both mass and momentum. The energy radiated in the forward direction is blueshifted, the energy radiated in the backward direction is redshifted, and energy radiated sidewards is aberred. So the radiation carries away momentum. But the radiating body is not accelerated: its momentum decreases, but its ratio of momentum to mass is constant.

    Now put a small test body radiating electromagnetic rays in an orbit around a massive body. Again, heat is radiated - for a coorbiting observer - isotropically, and therefore the speed and orbit stay unchanged.

    But now let us take a massive central body and a small test body orbiting it. And then let us explode the central body into an empty spherical shell.

    So long as the shell is inside the orbit of the test body, the orbit is unaffected, because the gravitational field of a spherical shell is the same as that of a point mass in the centre, for observer outside.

    If the shell now passes the test body, without friction, then a spherical shell has no field of gravity for an inside observer. The test body will by inertia fly off its orbit on a tangent, and escape to infinity if the shell gets there first.

    Thus, if we have a two body system and a body of significant mass loses any, then the orbit of the system will expand.

    But now consider radiation which is NOT spherically uniform even in a corotating frame, because it is caused by accelerated motion in the first place. such as electromagnetic radiation from an accelerated charge or gravity radiation from an accelerated mass.

    In this case, such a force causes any orbiting test body to spiral in by transferring to successive lower angular momentum states, until it goes to the ground state (if the test body had integer spin) or the lowest empty one (if the test body is a fermion).

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    Quote Originally Posted by PraedSt View Post
    Ok, I'm a tad confused. Radiating electromagnetic energy increases radii, while radiating gravitational energy does the opposite? I think I understand how both work, but I can't understand why one is one and the other the other.
    The energy is removed from different parts of the system.
    Each star has mass-energy in its "rest" mass (the mass you would measure when at rest relative to the star). The system of two stars also has kinetic and potential energy stored in the orbits. Remove the "system" energy, and the stars end up in contact at the bottom of their mutual gravity well; remove the mass-energy of the stars and you reduce their gravitational coupling, so they move outwards.

    I suppose a very rough analogy might be an inflated balloon. Remove gas from the balloon, and the balloon gets smaller; but remove rubber from the balloon (by thinning its walls), and it gets bigger.

    Grant Hutchison

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    Quote Originally Posted by chornedsnorkack View Post
    ...
    Quote Originally Posted by grant hutchison View Post
    ...
    Thanks you two. From a Newtonian perspective I can reconcile the two with a bit of fiddling.

    For gravitational waves:

    1. Assume no mass loss,
    2. Treat this a movement along the fixed orbital energy curve of the system.

    So, the shift from a higher orbital energy level to a lower orbital energy level, results in the simultaneous emission of the excess energy as gravitational waves. This corresponds to letting air out of Grant's balloon.

    For electromagnetic emission:

    1. The mass loss results in
    2. A shift in the entire orbital energy curve of the system.

    So, emission and the loss in mass of both objects means that the value of orbital energy at every radius is lower than it was previously, i.e. a shift lower. At the initial orbital radius and velocities, the system is now in disequilibrium. It will therefore re-equilibriate at a higher orbital radius than before. This corresponds to less rubber in Grant's balloon.

    Will this do?

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