Introduction

Bremsstrahlung, or free–free emission, appears in many different guises in astrophysics. Applications include the radio emission of compact regions of ionised hydrogen at temperature T ≈ 104 K, the X-ray emission of binary X-ray sources at T ≈ 107 K and the diffuse X-ray emission of intergalactic gas in clusters of galaxies, which may be as hot as T ≈ 108 K. It is also an important loss mechanism for relativistic cosmic ray electrons. Before proceeding to the analysis of the bremsstrahlung of electrons, we need to establish a number of general results concerning the electromagnetic radiation of accelerated charged particles and its spectrum. These results will be of wide applicability to the many radiation processes studied in this book.

The radiation of accelerated charged particles

Relativistic invariants

Gould has provided an excellent introduction to the use of relativistic invariants in the study of electromagnetic processes (Gould, 2005). We will develop a number of these in the course of this exposition. The first of these is the transformation of the energy loss rate by electromagnetic radiation as observed in different inertial frames of reference, that is, how dE/dt changes from one inertial frame of reference to another.

In fact, dE/dt is a Lorentz invariant between inertial frames of reference.