Statistical Analysis of Flat-Spectrum and Steep-Spectrum Pulsars

The radio spectra of pulsars are generally the power-law spectra shapes with a spectral index of approximately –1.6. But people have found that the spectra of some pulsars exhibit flat or steep spectra. Flat spectra refer to radio spectra with spectral indices ranging from –1 to 1, while steep spectra refer to radio spectra with spectral indices less than –2.5. We used the ATNF pulsar catalog and other literature to identify 239 flat-spectrum pulsars and 159 steep-spectrum pulsars, and conducted statistical analysis on the spatial position, magnetic field, spectral index, dispersion measure, and radio luminosity of these pulsars. The research results indicate that flat-spectrum and steep-spectrum pulsars are mainly concentrated near the galactic plane. The average spectral index of flat-spectrum pulsars is –0.62, with an average dispersion measure of 195.7 pc cm−3, while the average spectral index of steep-spectrum pulsars is –2.88, with an average dispersion measure of 96.5 pc cm−3. The characteristic age of flat-spectrum pulsars is also smaller than that of steepspectrum pulsars. There is a certain correlation between the dispersion measure of these two types of pulsars and their ages, rotation period changing rates, and surface magnetic fields, with the stronger correlations observed in flat-spectrum pulsars. In addition, there is a strong correlation between the dispersion measure of flat-spectrum pulsars and their rotational energy loss rates, while no such correlation has been found between the dispersion measure of steep-spectrum pulsars and their rotational energy loss rates. These correlations may indicate that the interstellar medium has a significant impact on the evolution process of flat-spectrum and steep-spectrum pulsars.