# Scintillation Arc Brightness and Electron Density for an Analytical Noodle Model

## TL;DR

This paper models scintillation arcs caused by narrow plasma filaments, or "noodles," showing how their electron density fluctuations and geometry influence pulsar signal scattering, with implications for observational resolution and plasma scales.

## Contribution

It introduces an analytical model for scintillation arcs based on a noodle-like plasma structure, distinguishing between ray and wave optics regimes, and relates observations to plasma filament properties.

## Key findings

- Scintillation arcs can be explained by narrow plasma filaments with minimal density fluctuations.
- Optimal scattering occurs when filament width matches one Fresnel zone pair.
- Observed data suggests noodles have a minimum radius of about 650 km.

## Abstract

We show that narrow filaments or sheets of over- or under-dense plasma, or "noodles," with fluctuations of scattering phase of less than a radian, can form the scintillation arcs seen for many pulsars. The required local fluctuations of electron density are indefinitely small. We assume a cosine profile for the electron column and find the scattered field by analytic Kirchhoff integration. For a large electron column, corresponding to large amplitude of phase variation, the stationary-phase approximation is accurate; we call this regime "ray optics". For smaller-amplitude phase variation, the stationary-phase approximation is inaccurate or inapplicable; we call this regime "wave optics". We show that scattering is most efficient when the width of the strip equals that of one pair of Fresnel zones, and in the wave-optics regime. We show that the resolution of present observations is about 100 Fresnel zones on the scattering screen. Incoherent superposition of strips within a resolution element tends to increase the scattered field. We find that observations match a single noodle per resolution element with phase of up to 12 radians; or many noodles per resolution element with arbitrarily small phase variation each, for net phase of less than a radian. Observations suggest a minimum radius for noodles of about 650 km, comparable to the ion inertial scale or the ion cyclotron radius in the scattering plasma.