The pulsar spectral index distribution

The flux-density spectra of radio pulsars are known to be steep and, to first order, described by a power-law relationship of the form S ν ∝ να, where S ν is the flux density at some frequency ν and α is the spectral index. Although measurements of α have been made over the years for several hundred pulsars, a study of the intrinsic distribution of pulsar spectra has not been carried out. From the result of pulsar surveys carried out at three different radio frequencies, we use population synthesis techniques and a likelihood analysis to deduce what underlying spectral index distribution is required to replicate the results of these surveys. We find that in general the results of the surveys can be modelled by a Gaussian distribution of spectral indices with a mean of −1.4 and unit standard deviation. We also consider the impact of the so-called gigahertz-peaked spectrum pulsars proposed by Kijak et al. The fraction of peaked-spectrum sources in the population with any significant turnover at low frequencies appears to be at most 10 per cent. We demonstrate that high-frequency (>2 GHz) surveys preferentially select flatter spectrum pulsars and the converse is true for lower frequency (