Evolution of High-energy Electron Distribution in Pulsar Wind Nebulae

TL;DR

This study investigates how high-energy electron distributions in pulsar wind nebulae evolve over time, revealing spectral hardening and magnetic energy decay, using spectral energy distribution modeling of 17 young PWNe.

Contribution

It provides the first detailed analysis of electron spectral evolution in PWNe, showing how spectral indices and magnetic energy change with age based on a uniform modeling approach.

Findings

Electron distributions follow a double power-law with a superexponential cutoff.

High-energy spectral index decreases from ~3.5 to 2.5 as PWNe age.

Magnetic energy decreases with age, while total electron energy remains constant.

Abstract

In this paper, we analyze the spectral energy distributions (SEDs) of 17 powerful (with a spin-down luminosity greater than $10^{35}$ erg s$^{-1}$) young (with an age less than 15000 yrs) pulsar wind nebulae (PWNe) using a simple time-independent one-zone emission model. Our aim is to investigate correlations between model parameters and the ages of the corresponding PWNe, thereby revealing the evolution of high-energy electron distributions within PWNe. Our findings are as follows: (1) The electron distributions in PWNe can be characterized by a double power-law with a superexponential cutoff; (2) As PWNe evolve, the high-energy end of the electron distribution spectrum becomes harder with the index decreasing from approximately 3.5 to 2.5, while the low-energy end spectrum index remains constant near 1.5; (3) There is no apparent correlation between the break energy or cutoff energy and the age of PWNe. (4) The average magnetic field within PWNe decreases with age, leading to a positive correlation between the energy loss timescale of electrons at the break energy or the high-energy cutoff, and the age of the PWN. (5) The total electron energy within PWNe remains constant near $2 \times 10^{48}$ erg, while the total magnetic energy decreases with age.