Pulsar Sparking: What if mountains on the surface?

TL;DR

This work tackles the puzzle of radio activity in pulsars lying below the traditional death line by introducing a numerical framework that computes the inner vacuum gap height and potential drop while incorporating small polar-cap mountains. The method combines a Ruderman-type inner-gap model with resonant inverse Compton scattering, solving for the mountain-enhanced parallel electric field and resulting gap height via a self-consistent mean-free-path analysis, including a finite-element solution for the field near topographic features. Applying the approach to PSR J0250+5854 and PSR J2144-3933 shows that mountains with steepness around $η \approx 2.1$ can reduce the required gap potential below the maximum unipolar induction potential, effectively re-igniting sparking and radio emission in stars previously considered dormant. The study further argues that stable mountains imply a solid surface state (potentially strangeon matter) and outlines observational tests, notably with FAST, to search for surface-induced sparking signatures and to probe the surface-state hypothesis. The findings link microphysical gap processes to macroscopic surface structure, offering a plausible route to explain irregular sparking, subpulse phenomena, and the behavior of pulsars near or below the death line.

Abstract

A numerical framework to calculate the height and potential of the vacuum inner gap of pulsars is presented here. % The results demonstrate that small mountains on a pulsar's polar cap tend to significantly influence the properties of the inner vacuum gap, making it easier for sparks to form. % In this scenario, the magnetospheric activity observed from the pulsars PSR J0250$+$5854 and PSR J2144$-$3933 which lie below the traditional pulsar death line, and some single-pulse modulation phenomena could also then be understood. % Furthermore, the presence of small mountains should depend on the puzzling state of supranuclear matter inside pulsars. % In order to sustain stable mountains on the surface, pulsars might be made of solid strangeon matter, which is favoured by both the charge neutrality and the flavour symmetry of quarks.

Figures (6)

• Figure 1: The relation between the mean free path of positrons and photons in a strong magnetic field environment of the gap to the upscattered photons energy respectively. The sharp dip of positron mean free path corresponds to the resonance condition $\epsilon_s=2\gamma\epsilon_B$. In the figure, $B=10^{12}\:\mathrm{G},P=1\:\mathrm{s}, T=10^6\:\mathrm{K},\gamma=10^5$ are adopted.
• Figure 2: The electromagnetic field environment and mean free path of positrons and photons. The enlarged inset show the cylindrical vicinity of mountains with equation in the bulk and boundary condition assigned on each surface.
• Figure 3: The distribution of the parallel electric field $E_z$ with respect to the distance to the center of the mountain, i.e. the $x$ coordinate, at different height above the stellar surface. The solid lines are for the scenario with a mountain of height $b=1\:\mathrm{cm}$ and $\eta = 2$, while the dashed line represents the scenario with no mountains. The influence of the mountain on the parallel electric field distribution is localized in the region with distance smaller than half the mountain radius from the origin.
• Figure 4: The $P$-$\dot{P}$ diagram of observed pulsars Manchester+etal+2005 with different categories of pulsars marked by points of different shapes. The red line is the "death line" without mountains, characterized by the maximum unipolar potential difference $5\times 10^{11}\:\mathrm{V}$. The green dashed line represents the death line with unipolar potential $V_\text{max} = 2.5\times 10^{11} \:\mathrm{V}$, i.e. mountain steepness $\eta =2$; the blue dashed line is the death line with $V_\text{max} = 1\times 10^{11}\:\mathrm{V}$, i.e. $\eta =6$
• Figure 5: Orange solid line show the decreasing of the potential drop required by PSR J0250+5854 to form a spark as the mountain steepness increasing, with blue horizontal dashed line marking the maximum potential produced by unipolar induction. When $\eta>2.1$, it hold that $\Delta V<V_\text{max}$