A Study on the Evolution of Emission Altitude with Frequency Among 104 Normal Pulsars

Utilizing the databases from the European Pulsar Network (EPN), the Australia Telescope National Facility (ATNF), and published literature data, a geometric method was used to investigate the multifrequency emission altitude of 104 pulsars. We found that the evolution of emission altitudes with frequency for the majority of pulsars can be fitted using a power-law function with a normalization constant. In this work, it is found that the frequency evolution of pulsar emission altitude can be divided into three groups according to their different frequency dependencies of emission altitude (emission altitude decreases with frequency (Group A, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>η</mi><mo>≤</mo><mo>−</mo><mn>0.1</mn></mrow></semantics></math></inline-formula>), keeps relatively constant with frequency (Group B, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>0.1</mn><mo><</mo><mi>η</mi><mo>≤</mo><mn>0.1</mn></mrow></semantics></math></inline-formula>), and increases with frequency (Group C, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>η</mi><mo>≥</mo><mn>0.1</mn></mrow></semantics></math></inline-formula>)), where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> is the emission altitude variation rate. We also computed the emission altitudes across multiple frequency bands for these pulsars, thereby estimating the approximate range of the pulsar emission regions. We found that most pulsar emissions occur at altitudes of tens to hundreds of kilometers above the polar cap, with differences in emission altitude between the three groups becoming more clear at lower frequencies.