Radio-continuum spectra of pulsars with free-free thermal absorption

The radio continuum spectra of pulsars (PSRs) exhibit a wide variety of shapes, which are interpreted as pure and broken power laws, power laws with turnovers or cutoffs, and logarithmic-parabolic profiles. A notable fraction of these have well-defined power laws with ν −2.1 exponential turnovers, indicative of free-free thermal absorption along the line of sight. We analysed a sample of 63 PSRs with such spectral shapes, compiled from four previously published studies, to investigate their statistical properties. We normalised each spectrum to a characteristic frequency and flux density of its own, facilitating a consistent treatment across the four subsamples. We show that these two fitted parameters are correlated by a power law, with its slope reflecting the median spectral index (∼−2.0) of PSR emission. We find that the turnover frequencies in our sample are typically high, clustering around 558 MHz, which implies notably high emission measures (∼10 5 pc cm −6 ) for an inferred thermal absorbing medium with an electron temperature of 8000 K. Moreover, by combining these emission measures with dispersion measures derived from pulse time delays, we break the degeneracy between the electron density and the path length of the absorbers. This reveals a discrete near-in population of absorbers characterised by small sizes (∼0.1 pc) and high electron densities (∼10 3 cm −3 ), which exhibit a clear size-density anti-correlation reminiscent of that observed in Galactic and extragalactic H ii regions.