On the Diversity of Pulsar's Frequency-Dependent Circular Polarization

TL;DR

The paper tackles the long-standing problem of understanding coherent pulsar radio emission by testing a wave mode coupling model in the limiting polarization region against high-quality FAST single-pulse measurements of frequency-dependent circular polarization. A Bayesian framework is used to fit the model to 24 data points per pulse from three pulsars, yielding constraints on plasma multiplicity $κ$ in the range $10^{0}$–$10^{2}$ and Lorentz factor $γ$ in the range $10^{0.5}$–$10^{2}$, though not all pulses are quantitatively described due to additional mode-mixing effects. The results show the model can reproduce a rich diversity of $V/P$ spectra, including handedness changes with frequency, and reveal a positive correlation between $κγ$ and radio luminosity $L$, with implications for where particle acceleration and energy deposition occur in the magnetosphere. The work provides a systematic, data-driven framework to connect pulsar emission theories with observations and highlights the need for more complex treatments to capture PA-jump and orthogonal-mode phenomena. Overall, this approach advances quantitative diagnostics of pulsar magnetospheric plasmas and sets the stage for applying similar analyses to more pulsars as high-quality data become available.

Abstract

The nature of coherent radio emission is still challenging even after more than half a century of pulsar discovery, but it is generally a consensus that single-pulse observations are essential for probing the magnetospheric dynamics, especially with the largest single-dish telescope FAST (Five-hundred-meter Aperture Spherical radio Telescope). The frequency-dependent circular polarization of single pulses, with high signal-to-noise ratios, is recorded by the FAST, which shows great diversity, and we are trying an effort to understand such circular polarization based on the wave mode coupling in the limiting polarization region, and consequently to constrain the dynamical parameters. By quantitatively comparing models with data using Bayesian analysis, it is found that the plasma multiplicity is approximately between $10^0$ and $10^{2}$, while the Lorentz factor of the particles between $10^{0.5}$ and $10^{2}$. This study presents a systematic framework for integrating pulsar emission theories with observational data.

Figures (9)

• Figure 1: (i) The distributions of maximum-likelihood parameters of MCMC results for three pulsars. The third panels of three plots are distributions of multiplicity times Lorentz factor (logarithmic). In each $\lg(\gamma\cdot\kappa)$ distributions: the red vertical line represent the maximum potential drop in polar cap region, times unit charge $e$ divided by electron rest energy $m_{e}c^{2}$; the blue vertical dashed line is the inner gap potential drop $\times e/(m_{e}c^{2})$ given in rs1975; the green vertical dotted line is the charge starvation zone potential drop $\times e/(m_{e}c^{2})$ given in as1979. For details please refer to Section \ref{['sec:kappa_discussion']}. (ii) the common logarithmic values of reduced chi-square distributions for the fittings of three pulsars, in the form of histograms. For the horizontal axis, The (-1,4) range is divided into 20 bins. (iii) The correlation between averaged $\kappa\gamma$ and radio luminosity $L$ for three pulsars. For details please refer to Section \ref{['sec:kappa_discussion']}.
• Figure 2: Six pulses (18 $V/P$ - $\nu$ curves) with fitting results. The pulsar name and the pulse number after # are marked in every figure. For every subfigure, the left panels are polarization profiles of single pulses, and the right plots are $V/P$ - $\nu$ curves of three chosen pulse longitudes (blue dots with errorbars: observation data points; orange dots: modeling points with maximum-likelihood parameters). The maximum-likelihood parameters, and the $\chi^{2}_{r}$s for fitting the three phases are marked out in the right plots. In the "Intensity" panel: Black line---total intensity ($I$); red dashed line---linear polarization intensity ($L=\sqrt{Q^{2}+U^{2}}$); blue line---circular polarization intensity ($V$). $I$, $L$ and $V$ are normalized by the maximum total intensity of the respective profiles. The horizontal axis is the pulse phase (0 to 1 in a period). Red dots in "$P/I$" panel with errorbars---polarization degrees. Green dots in "$\psi$" panel with errorbars---polarization position angles (PA, $\psi=0.5\arctan(U/Q)$). Magenta dots in "$\chi$" panel with errorbars---ellipticity angel (EA, $\chi=0.5\arcsin(V/{\sqrt{Q^{2}+U^{2}+V^{2}}})$).
• Figure 3: Posterior PDFs of four pulses in Figure \ref{['fig:well_fitted1']}. The pulsar names and pulse numbers are marked in each plot. The blue curves are marginal PDFs of parameters, and the grey contours are two-dimensional PDFs of each two parameters. The contour profiles mark the credibility regions of probabilities 50%, 80%, and 94%. The orange stars represent the maximum-likelihood parameters.
• Figure 4: Left two plots: the correlations between standard deviations of posterior PDFs of five modeling parameters and the maximum circular polarization fractions in pulses (left), or the maximum standard deviations of circular polarization fraction spectra in pulses (right). The Spearman rank correlation coefficients $\rho$ and the p-value of permutation tests are marked in all panels. For details please refer to the main text. Right two plots: the maximum $|V/P|$ and the maximum $\sigma(V/P)$ calculated from the mode coupling model, for pairs of $(\lg\kappa, \lg\gamma)$. The calculation details are given in the text. The blank regions in the plots are parameter spaces where $Rc/\omega\ll 1$ is violated.
• Figure 5: The $P$ - $\dot{P}$ diagram. The grey dots are from the psrcatpsrcat website (https://www.atnf.csiro.au/research/pulsar/psrcat/). The red triangle, blue dot, and green square mark the three pulsars chosen for our study.