# On the broad-band synchrotron spectra of pulsar wind nebulae

## TL;DR

This paper models the broad-band synchrotron spectra of pulsar wind nebulae using MHD turbulence theories, highlighting the role of adiabatic stochastic acceleration in shaping observed spectral features.

## Contribution

It introduces a new analytical model linking MHD turbulence-driven re-acceleration to the spectral characteristics of PWNe, aligning well with observations.

## Key findings

- Analytical spectra match observed radio and X-ray spectra of PWNe.
- Spectral break constrains acceleration timescale and magnetic field strength.
- Re-acceleration explains flat radio and steep X-ray spectra.

## Abstract

As shown by broad-band observations, pulsar wind nebulae (PWNe) are characterized by a broken power-law spectrum of synchrotron emission. Based on the modern magnetohydrodynamic (MHD) turbulence theories, we investigate the re-acceleration of electrons in the PWN through the adiabatic stochastic acceleration (ASA), which arises from fundamental dynamics of MHD turbulence. The ASA acts to flatten the injected energy spectrum of electrons at low energies, while synchrotron cooling results in a steep spectrum of electrons at high energies. Their dominance in different energy ranges leads to a flat radio spectrum ($F_\nu$) and a steep X-ray spectrum. Our analytical spectral shapes generally agree well with the observed synchrotron spectra of radio- and X-ray-bright PWNe. The spectral break corresponding to the balance between the ASA and synchrotron losses provides a constraint on the acceleration timescale of the ASA and the magnetic field strength in the PWN.