Radio-Continuum Spectra of Pulsars with Free-Free Thermal Absorption

Abstract: The radio continuum spectra of pulsars (PSRs) exhibit a wide variety of shapes, that are interpreted as pure and broken power laws, power laws with turnovers or cut-offs, 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-site. We analyse a sample of 63 PSRs with such spectral shapes, compiled from four previously published studies, to investigate their statistical properties. We normalise each spectrum to a characteristic frequency and flux density of its own, facilitating a consistent treatment across the four sub-samples. We show these two fitted parameters are correlated by a power law, with its slope reflecting the median spectral index ($α\sim -2.0$) of PSR emission. We found that the turnover frequencies in our sample are typically high, clustering around 558 MHz, implying notably high emission measures ($EM \sim 10^{5}$ pc cm$^{-6}$) for an inferred thermal absorbing medium with electron temperature of $T_{\mathrm{e}}=8000$ K. Moreover, by combining these $EM$ with dispersion measures (DM) derived from pulse time delays, we break the degeneracy between electron density and path length of the absorbers. This reveals a discrete near-in population of absorbers characterised by small sizes ($L \sim 0.1\,\text{pc}$) and high electron densities $(n_{\mathrm{e}} \sim 10^{3}\,\text{cm}^{-3} $)), which exhibit a clear size-density anticorrelation reminiscent of that observed in Galactic and extragalactic H$_\rm{II}$ regions.