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PARTICLE PRODUCTION IN A STRONG, SLOWLY-VARYING MAGNETIC FIELD WITH AN APPLICATION TO ASTROPHYSICS
DI PIAZZA, ANTONINO
2004-04-05
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Contributor(s)
SENATORE, GAETANO
Abstract
In this work I have studied the production from vacuum of electrons, positrons and photons in the presence of strong and slowly-varying magnetic fields. "Strong magnetic fields" here means magnetic fields whose intensity is much larger than Ber = m2c3 / (he) = 4.4 x 1013 gauss corresponding t o the minimum strength of a magnetic field whose energy is enough to create an e- - e+ pair from vacuum. Such intense magnetic fields cannot be created in terrestrial laboratories but, as some indirect evidences and numerical simulations show, they may be present around some astrophysical compact objects (strongly magnetized neutron stars called magnetar or massive black ho l es). For this reason, in the present work I h ave assumed t ha t the sources of the magnetic fields are always such kind of astrophysical compact objects. In particular, I have tried t o apply my results to the so-called Gamma-Ray Bursts ( G RB) an d their energy spectra. G RB are very intense soft gamma-ray pulses that our satellites register on average once a day and that are thought to be originated around astrophysical objects like massive black ho l es or, following some models, magnetars. My point of view is no t astrophysical but theoretical then the models I have used are very simplified versions of the real situation. Nevertheless, some of the photon spectra I have calculated are qualitatively similar to the corresponding experimental G RBs energy spectra. The results of the thesis can be divided into three different parts: the first one concerns the production of e- - e+ pairs in the presence of a strong, slowly-varying magnetic field in various configurations, the second one concerns the production of photons in the presence of a strong and slowly-rotating magnetic field and, finally, the third one concerns how the presence of the gravitational field of the astrophysical compact object affects the production of e- -e+ pairs. In the first part I have calculated the probability per unit volume that an e- - e+ pair is created from vacuum in the presence of a strong, slowly varying magnetic field through the first-order adiabatic perturbation theory. Firstly, I have shown analytically that if the direction of the magnetic field changes with time then production mechanisms are primed that are much more efficient than those primed in the presence of a magnetic field changing only in strength. The physical reason of this fact is the existence of one particle electron and positron states whose energy does not depend on the magnetic field. In fact, these states, called transverse ground states (TGS), have, in the presence of a strong magnetic field, an energy much lower than that of the other states and only if the magnetic field changes in direction it is possible to create a pair in which both the electron and the positron are in a TGS. Another conclusion in this first part concerns the role that the electric field induced by the time variation of the magnetic field plays in the production mechanism. In fact, one sees that the pair creation is possible ( obviously) only if such an electric field is present an d, in particular, t ha t the probability per unit volume is proportional to the square of the electric field itself. Having in mind a possible application of the calculations to G RBs spectra, in the second part of the thesis I have calculated the spectrum of the photons emitted by electrons and positrons in the magnetic field as a consequence of their annihilation or as synchrotron radiation. In both cases the final spectrum has been calculated numerically. While the annihilation spectrum shows a well marked peak around the electron mass, the synchrotron spectrum shows two different behaviours around an energy value rv 1-3 Me V. In general, the form of the synchrotron spectrum is qualitatively similar to some GRBs spectra while the annihilation spectrum is completely different. In particular, analogously to the experimental spectra the low-energy behaviour of the synchrotron spectrum is proportional to the inverse of the photon energy. Finally, I have also calculated the spectrum of the photons emitted directly from vacuum as a consequence of the nonlinear interaction of the vacuum itself with the rotating magnetic field but the results show that the number of photons produced through this mechanism is definitely lower than that of the photons produced through the other mechanisms and their presence can be neglected. As I have said at the beginning, the magnetic fields considered are produced by neutron stars or black holes. For this reason, taking into account the gravitational field produced by the compact object may give relevant results. I have clone this in the last part of the thesis where I have shown how the one particle electron an d positron energies and states and, consequently, the probability production of a pair are modified by the presence of a weak gravitational field treated perturbatively or by the presence of a strong gravitational field treated non perturbatively. In the first case, the most important result is that in the presence of a ( though weak) gravitational field perpendicular to the magnetic field it is possible to create pairs with the electron and the positron both in a TGS even if the magnetic field changes only in strength. Instead, the treatment of the non perturbative case resulted completely different because the electron an d positron one particle energies, unlike in Minkowski spacetime, are characterized by a continuous quantum number independent of the other quantum numbers and of the magnetic field. In this case, I have shown how the effects of the gravitational field on the production probability are really important and that they cannot be neglected. In particular, high-energy electrons an d positrons are more likely produced in the presence of a strong gravitational field than in Minkowski spacetime.
Insegnamento
Publisher
Università degli studi di Trieste
Languages
en
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