2014ApJ...781...30N

I develop a new model for changes of cyclotron line energy with luminosity based on changes in polar cap dimensions and the direction of photon propagation as well as a shock height. In X0115+63 and V0332+53, the fundamental cyclotron line energy has been observed to decrease with increasing luminosity. This phenomenon has been interpreted as a change of a shock height with luminosity. However, the rates of the observed changes are quite different, in which the line energy in V0332+53 varies slowly with luminosity compared with that in X0115+63. I demonstrate that a new model successfully reproduces the changes of the fundamental cyclotron line energies with luminosity in both X0115+63 and V0332+53. On the other hand, the cyclotron line energies in Her X-1, GX301-2, and GX304-1 were reported to increase with increasing luminosity. I discuss the positive correlation between the cyclotron line energy and luminosity based on changes in a beam pattern for Her X-1, GX301-2, and GX304-1. In addition, I discuss how a switch of the predominant, observed emission region from pole1 to pole2 influences cyclotron line energy for GX304-1 and A0535+26.