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

TL;DR

The study tackles the problem that pulsar radio continuum spectra exhibit turnovers whose physical origin can be traced to free-free thermal absorption. It compiles 63 PSR spectra from four prior studies and adopts a homogeneous absorption model reformulated in terms of a characteristic frequency $\nu_{*}$ and flux $S_{*}$, enabling consistent cross-sample comparisons. The analysis finds that turnover frequencies cluster near $\nu_{to} \approx 558$ MHz, with emission measures up to $\sim 10^{5}\,\text{pc cm}^{-6}$; combining these with dispersion measures breaks the degeneracy between absorber density and path length, revealing compact absorbers of $L \sim 0.01$–1 pc and $n_{e} \sim 10^{3}\,\text{cm}^{-3}$ that follow a size–density anticorrelation similar to H II regions. This work provides a framework to probe the line-of-sight ionised medium toward pulsars and supports the interpretation of GHz turnovers as local, clumpy absorbers rather than a diffuse screen, enabling robust PSR–SNR comparisons as well as ISM diagnostics.

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.

Figures (11)

• Figure 1: Radio flux density measurements (coloured filled symbols) vs. frequency for the four PSR subsamples analysed in our study. The panels, from top to bottom, display 15 spectra from K17, 25 from J18, 10 from K21, and 13 from S22. The solid coloured lines represent the best-fit models derived from Eq. \ref{['equation:sast']}, using spectral indices reported in the literature referenced in our work (see Table \ref{['tab:long']} for the parameter values). Asterisk symbols mark the characteristic frequency, $\nu_{\ast}$, for each individual spectrum.
• Figure 2: Normalised radio flux density as a function of normalised frequency for our PSR sample, comprising (from top to bottom) 15 objects reported in K17, 25 in J18, 10 in K21, plus 13 in S22. Each PSR within the subsamples is colour-coded individually. The solid lines represent the fitted models, with parameters listed in Table \ref{['tab:long']}, and the black asterisk indicates the characteristic frequency, $\nu_{\ast}$. This normalisation process highlights the similar exponential drop-off in the spectra associated with $\nu_{\ast}$ values, arranging PSR spectra in increasing order based on the slope of their emission.
• Figure 3: Radio flux density, normalised by the characteristic flux and power-law emission, plotted against normalised frequency for the four subsamples in our study (see labels). Each spectrum was fitted by the respective authors with an exponential drop-off with an exponent $-2.1$. The curved solid line represents the normalised absorption function $A(x)=\mathrm{exp}(-x^{-2.1})$ and the asterisk symbol indicates the characteristic frequency, $\nu_{\ast}$.
• Figure 4: Same PSR data as plotted in Fig. \ref{['figure:fig3']}, with the four subsamples merged (blue symbols). Additionally, data points for the SNRs presented in abadi2024 are reproduced (red symbols). The graph highlights the similarity not only between the PSR spectra but also between the PSR and SNR spectral behaviours. The curved solid line is the normalised absorption $A(x)=\mathrm{exp}(-x^{-2.1})$.
• Figure 5: Relation between the characteristic flux, $S_{\ast}$, and frequency, $\nu_{\ast}$, parameters obtained from fitting the parameterised free-free thermal absorption model (Eq. \ref{['equation:sast']}) for our sample of 63 PSRs. For comparison, parameters calculated from the same model fit applied to 12 SNRs abadi2024 are also included. All data points are shown with the same symbols and colours as in Fig. \ref{['figure:fig4']}. The large solid lines represent the best-fit linear relations for the PSR (blue) and SNR (red) parameters, with logarithmic slopes of $-1.94$ and $-0.52$, respectively. Short lines on each data point indicate the radio spectral index for each object, taken from K17, J18, K21, and S22 for PSRs and from abadi2024 for SNRs. The median values of these spectral indices are consistent with the slopes of the power-law correlation between $S_{\ast}$ and $\nu_{\ast}$. The distribution of $\nu_{\ast}$ values for PSRs and SNRs, with median values indicated by arrows, is shown in the blue and red histograms in the top panel.