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We know that massive bodies attract gas clouds that become ionized and the resulting acceleration can emit very high energy photons.

In a case where a proton for example is undergoing prolonged constant (or even increasing) acceleration that could take many hours, when is radiation emitted? When the proton collides or it's acceleration in suddenly stopped? or are there intermittent releases of radiation and photons during the many hours of travel?

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The radiation of an accelerated or a decelerated charge particle is called "Bremsstrahlung" radiation, which means (roughly) deceleration radiation. The radiation is a continuous spectra. i.e. it's not the emission of one photon. The charged particle which is accelerating emits continuously photons of different energy depending upon the rate of change of it's own energy at that instant. Now the question is, where does this energy come from? In case of deceleration it is obvious that the kinetic energy of the charged particle is giving rise to the radiation energy. What about accelerating particle? Well, the energy used by the agent to accelerate the charge actually is used in two ways. One part increases it's kinetic energy, the other produces the radiation.

So in your case, when the ionised gas is accelerating for hours it emits radiation continuously, of course the radiation becomes visible only when the acceleration is sufficiently large which is very close to the star or whatever is accreting it.

P.S. Just for fun,consider this extra thought. Einstein's General relativity says that an accelerated frame is completely equivalent to a frame exposed to gravity. But if there is a charge in accelerated frame it should radiate. Does that mean that all static charges in earth radiates?

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  • $\begingroup$ interestingly, a charge sitting stationary in a gravitational field does not radiate and a charge accelerating in free fall which is equivalent to a body with no acceleration in GR radiates. $\endgroup$ – Peter R Nov 24 '15 at 4:40
  • $\begingroup$ @PeterR The radiation is seen in a different, accelerated frame. If you were travelling with the particle you would see no radiation, just as in the first case. $\endgroup$ – Rob Jeffries Nov 24 '15 at 7:11
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    $\begingroup$ The equivalence principle says you can't do a local experiment to distinguish acceleration from a gravitational field. A charge "sitting stationary" in any accelerated frame of reference would not radiate. $\endgroup$ – Rob Jeffries Nov 24 '15 at 7:18
  • $\begingroup$ @Rob Jeffries So the Larmor formula does not apply for acceleration that is equivalent to stationarity in any kind of gravitational field? $\endgroup$ – my2cts Mar 24 at 12:29
  • $\begingroup$ @my2cts To be clear: We could not measure radiation from a charge that is in the same reference frame as we are. $\endgroup$ – Rob Jeffries Mar 24 at 12:36

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