Evolution of High-energy Electron Distribution in Pulsar Wind Nebulae

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.