[...]... discussion of magnetic fields in astrophysics: methods of measurement and their results, and the fundamental ideas of batteries (generating the seeds of astrophysical magnetic fields) as well as of dynamos (amplifying these seeds) These topics are hardly ever found in high-energy astrophysics textbooks, even though they are crucial for an understanding of various phenomena, such as the acceleration of non-thermal... principles of relativistic hydrodynamics and shock waves, and de Laval’s nozzle.1 Hydrodynamics considers a fluid as a macroscopic object, therefore, ideally, as a continuous medium Even when we consider infinitesimal volumes of fluids, elements, or particles of fluid, we will always assume them to be made up of a very large number of molecules The description of a fluid in a state of rest requires knowledge of. .. ∂X/∂t + v · ∇X (1.12) expresses the time variation of any physical quantity X, when we consider its variation not at a fixed position, but for a fixed element of mass In other words, if we concentrate on a certain element of mass and follow it in its motion, DX/Dt expresses the variation of X with time, just as we would see it if we straddled the element of mass in question Because of this, the operator... here knowledge of its equation of state, so that it is necessary to provide only two of the three fundamental thermodynamical quantities (namely, pressure, density, and temperature) A generic fluid not in a state of rest will be therefore described also by the instantaneous speed of motion In the following, we shall suppose that all these quantities (P, ρ, T, v) are continuous functions of space and time,... on an area element dA, where p is the pressure Therefore there is a 4 CHAPTER 1 HYDRODYNAMICS pressure − pdA on a fluid within a volume dV This can be rewritten as − pdA = − pdV (1.7) which, in its turn, can be interpreted as follows: on each element of mass ρdV contained in an element of volume dV a pressure is exerted that equals −∇pdV The equation of motion of this infinitesimal mass is thus ρ Dv... acceleration of nonthermal particles, astrophysical accretion flows, both spherical and disk-shaped, and explosive motions (supernovae and gamma-ray bursts) Chapter 8 presents the basic results of electrodynamics around compact objects The second half of chapter 2, as well as the whole of chapters 7 and 8, present material not usually included in textbooks on high-energy astrophysics The second half of chapter... this is wrong: the expression for jE is incomplete Indeed, it is well known from elementary courses on thermodynamics that the internal energy of a gas can either increase or decrease by a compression or an expansion, respectively, so that under adiabatic conditions we have dE = −pdV (1.29) This compression heating must be included in the law of energy conservation of a fluid in motion Of course, the heating... Equation The first fundamental law of fluids expresses mass conservation Let us consider a volume V containing a fluid mass ρV The law of mass conservation states that mass can neither be created nor destroyed, so that the mass inside V can change only when a certain amount crosses the surface of the volume in question The quantity of mass crossing an infinitesimal element dA of area, per unit time, is ρv... detail—on the thermodynamic state and on the speed of the fluid where the emission takes place Therefore, we can say that a necessary prerequisite for high-energy astrophysics is the study of hydrodynamics and magnetohydrodynamics In this chapter, I shall briefly explain the fundamental principles of hydrodynamics, as well as some key results, which will often be used in the following chapters In particular,... meaning of R emerges when we integrate equation 1.36 on a finite volume We thus obtain d ∂ (ρvi )dV = ∂t dt ρvi dV = − ∂R ik dV = − ∂xk R ik dA k (1.37) The latter expression is the flux of R ik through the surface, whereas the left-hand side is the variation of the ith component of the momentum contained in the volume It follows that R ik is the flux through a surface with its normal in the k direction, of . Pisa, Italy. The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London C  2008 by The University of Chicago All rights reserved. Published 2008 Printed in the. Physics Georg G. Raffelt (1996) Foundations of High-Energy Astrophysics Mario Vietri THE UNIVERSITY OF CHICAGO PRESS Chicago and London MARIO VIETRI is professor of astrophysics at the Scuola Normale. Theoretical Astrophysics titles available from the University of Chicago Press Inner Space / Outer Space Edward Kolb, Michael Turner, Keith Olive, and David Seckel, editors (1985) Theory of Neutron