Resonance in PSR B1257+12 planetary system

In this paper we present a new method that can be used for analysis of times of arrival (TOAs) of pulsar pulses. It is especially designed to detect quasi-periodic variations of TOAs. We apply our method to timing observations of PSR B1257+12 and demonstrate that by using it, it is possible to detect not only first harmonics of a periodic variations, but also the presence of a resonance effect. The resonance effect detected independently of its physical origin can appear only when there is a nonlinear interaction between two periodic modes. The explanation of TOAs variations as an effect of the existence of planets was, until now, the only known and well-justified explanation. In this context, the existence of the resonance frequency in TOAs is the most significant signature of the gravitational interaction of planets.