Research in Astron. Astrophys. 2010 Vol. 10 No. 10, 1023–1040 http://www.raa-journal.org http://www.iop.org/journals/raa Research in Astronomy and Astrophysics Polarization in cyclotron radiation in strong magnetic fields Luidmila Semionova 1 , Denis Leahy 2 and Jorge Paez 3 1 Department of Physics, Universidad National, Heredia 86–3000, Costa Rica; lsemiono@yahoo.com 2 Department of Physics and Astronomy, University of Calgary, Alberta T2N 1N4, Canada; leahy@iras.ucalgay.ca 3 Space Research Center, University of Costa Rica, San Jose, Costa Rica; paezjorge174@gmail.com Received 2009 July 14; accepted 2010 March 23 Abstract We revisit the problem of radiative transitions of electrons in the presence of a strong magnetic field. We derive fully relativistic cyclotron transition rates for an arbitrary magnetic field, for any orientation of electron spin and for any polarization of the emitted radiation. Also, we obtain the transition rates for any value of the ini- tial electron’s parallel momentum. For very strong magnetic fields, transitions to the ground state predominate. Transition rates summed over the electron’s spin orienta- tion and for unpolarized radiation are also obtained, which confirm previous results by Latal. Transition widths are calculated for different electron spin orientations and different polarizations of radiation. We obtain general expressions for transition rates that reduce to the results for the non-relativistic case and for unpolarized radiation. Additionally we get, for the non-relativistic approximation, the transition rates for any polarization of radiation. As an application, the first five emission lines are evaluated and compared to the X-ray emitting neutron star V0332+53, which has multiple ob- servable cyclotron lines, taking into account gravitational redshift. The most probable polarization is ˆ ε (2) . Key words: stars: neutron — radiation mechanisms: non-thermal — stars: magnetic fields — polarization 1 INTRODUCTION Cyclotron transition rates in strong magnetic fields are of great interest for emission from neutron stars and some other exotic magnetized stellar objects, and have been discussed many times pre- viously. Particularly, the effect of initial electron’s spin orientation on cyclotron radiation has been analyzed by Herold et al. (1982). In that work, the transition rates are summed over the final spin state and polarization of the emitted radiation. Harding & Preece (1987) discussed the behavior of cyclotron transition rates as a function of electron spin for both initial and final states, unpolarized radiation, and the case of zero initial electron parallel momentum. Bezchastnov & Pavlov (1991) discuss cyclotron emission in plasmas including quantum and relativistic effects, but summed over electron spin. A study of the effects of polarization of the emitted photon can be found in Sina (1996), in which the angular distribution of radiation for two linear polarizations was analyzed, but