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-nu proportional to nu(alpha), where S-nu is the flux density at some frequency nu and alpha is the spectral index. Although measurements of alpha 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 (<1 GHz) surveys. This implies that any correlations between a and other pulsar parameters (for example age or magnetic field) need to carefully account for selection biases in pulsar surveys. We also expect that many known pulsars which have been detected at high frequencies will have shallow, or positive, spectral indices. The majority of pulsars do not have recorded flux density measurements over a wide frequency range, making it impossible to constrain their spectral shapes. We also suggest that such measurements would allow an improved description of any populations of pulsars with 'non-standard' spectra. Further refinements to this picture will soon be possible from the results of surveys with the Green Bank Telescope and LOFAR.