The Study on the Frequency Evolution of Pulsar Radiation Heights

We have investigated the multi-frequency radiation altitudes for 104 pulsars collected with multi-frequency observational data from the European Pulsar Network (EPN) and the Australian Telescope National Facility (ATNF), complemented by published literature data. We found that the evolution of radiation altitudes with frequency for the majority of pulsars can be fitted using a power-law function with a constant. In this work, it is found that the frequency evolution of pulsar radiation heights can be divided into three groups according to their different frequency dependencies of radiation heights, radiation altitude decreases with frequency(Group A, η < −0.1), keeps relatively constant with frequency(Group B, −0.1 < η < 0.1), and increases with frequency(Group C, η > 0.1), where η is the radiation height variation rate. We also computed the radiation altitudes across multiple frequency bands for these pulsars and consequently estimated the approximate location of the pulsar radiation region. We found that most pulsar radiation occurs at altitudes of tens to hundreds of kilometers above the polar cap, with differences in radiation heights between the three groups becoming more pronounced at lower frequencies.