Theory of striped dynamic spectra of the Crab pulsar high-frequency interpulse

Abstract

A theory of the spectral "zebra" pattern of the Crab pulsar's high-frequency interpulse (HFIP) radio emission is developed. The observed emission bands are interference maxima caused by multiple ray propagation through the pulsar magnetosphere. The high-contrast interference pattern is the combined effect of gravitational lensing and plasma de-lensing of light rays. The model enables space-resolved tomography of the pulsar magnetosphere, yielding a radial plasma density profile of $n_{e}\propto r^{-3}$, which agrees with theoretical insights. We predict the zebra pattern trend to change at a higher frequency when the ray separation becomes smaller than the pulsar size. This frequency is predicted to be in the range between 42 GHz and 650 GHz, which is within the reach of existing facilities like ALMA and SMA. These observations hold significant importance and would contribute to our understanding of the magnetosphere. Furthermore, they offer the potential to investigate gravity in the strong field regime near the star's surface.

Figures (5)

• Figure 1: Overall geometry of the system.
• Figure 2: The effective index of refraction as a function of distance, for various values of the so-called "reflection radius" parameter $r_{0}=3,\dots, 7$ and $\kappa=3$. All distances are in units of mass $m$, so that $r_{g}=2$ and the Crab pulsar radius is $r_{*}\simeq 4.8$ (indicated by the vertical dashed line). Bright colors denote $n_{\rm eff}>1$ and dark colors correspond to $n_{\rm eff}<1$.
• Figure 3: Deflection of parallel light rays propagating from right to left for various impact parameters, $b=4,\dots,10$, and for $r_{0}=5.5$ and $\kappa=3$. Brighter colors indicate weak deflection, while darker tones represent strongly deflected rays. The $(r,\phi)$ coordinates of the innermost ray, along with its impact parameter, $b$, and the distance of the closest approach, $r_{m}$, are depicted. Also, plotted are: the Schwarzschild radius, $r_{g}=2$ (smallest dashed circle), the non-transparent region when gravitational blue-shift of $\omega$ is accounted for (gray disk), the neutron star size, $r_{*}\simeq4.8$ (solid black circle), and the reflection radius, $r_{0}$, defined by Eq. \ref{['r0']} (large dashed gray circle). All distances are measured in units of the neutron-star mass $m$.
• Figure 4: A schematic representation of the pulsar system, illustrating its equivalence to Young's slits. Variables drawn with blue inc describe light ray propagation, while those in red inc describe two-slit interference.
• Figure 5: The frequency fringe pattern obtained in the double-slit setup with the slit separation, $a(\omega)=2b_{0}$, obtained from Eq. \ref{['ftot']} for $\phi_{\rm tot}=\pi$. Four different values of the power-law index $\kappa=2.8,\ 2.9,\ 3.1,\ 3.2$ are presented. The black dashed line indicates the anticipated dependence for the analytically obtained value of $\kappa=3$, see Eq. \ref{['kappa']}. Other numerical parameters are adjusted so that there approximately $N\simeq30$ fringes in the 5--30 frequency domain (arb. units). The approximate data points from HE+16b are also shown.