Abstract
In this Chapter I will describe the physics that stands behind the problem of CR propagation. Since the battlefield in which CR propagation takes place is the interstellar medium (ISM) of our Galaxy, I will first present a complete description of the Galactic environment and its components, with particular attention to the interstellar gas, the magnetic field (related to CR diffusion and spallation) and the distribution of pulsars and Supernova Remnants (related to CR origin); I will point out the deep interplay that exist between these components that continuously interact one another: the gas triggers star formation, massive stars quickly generate Supernova explosions that accelerate CRs, the gas returns back again in the ISM and the released energy triggers the turbulence that is responsible of the CR random walk.
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Notes
- 1.
The \({\rm H }\) line corresponds to a transition between \(n=3\) and \(n=2\).
- 2.
A quantitative description of these phenomena is based on magneto-hydro-dynamics (MHD). From the MHD equation of motion:
$$\begin{aligned} \rho \left[ \frac{\partial \vec {v}}{\partial t} + (\vec {v} \cdot \vec {\nabla }) \vec {v} \right] = -\vec {\nabla } p + \rho \vec {g} + \frac{1}{4\pi } (\vec {\nabla } \times \vec {B}) \times \vec {B} \end{aligned}$$(2.1)it is possible to derive the Virial theorem:
$$\begin{aligned} \frac{1}{2} \ddot{I} = 2 ( T - T_s ) + M + W \end{aligned}$$(2.2)where
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\(I\) it the momentum of inertia
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\(T\), is defined by the following equation: \(T \equiv \int _V{\left( \frac{3}{2} P_{th} + \frac{1}{2} \rho v^2 \right) {\rm d}V}\) and represents the internal kinetic energy, with a random microscopic component (thermal energy) and a macroscopic contribution (due to turbulent motions) that is often dominant.
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\(T_s\), defined by: \(T_s \equiv \frac{1}{2} \oint _S{P_{ext} \vec {r} \cdot {\rm d}{\vec {S}}}\) takes into account the pressure of the external medium that surrounds the cloud.
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\(W\) is the gravitational energy.
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\(M\) is the magnetic term: \(M = \frac{1}{8 \pi } \int {(B^2-B_0^2){\rm d}V}\), where \(B_0\) is the intensity of the field present in the surrounding medium.
According to which term prevails, the cloud or a part of it is considered self-gravitating (if the internal pressure due to thermal and turbulent motions is balanced by the gravitational field of the cloud itself) or pressure-confined (if the external medium with its pressure does the same job). Star-forming clouds or clumps are generally self-gravitating. When the density gets too high, due to an external perturbation, the gravitational term becomes dominant and the cloud undergoes a collapse, which is the first step of star formation.
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Gaggero, D. (2012). Cosmic Ray Diffusion in the Galaxy. In: Cosmic Ray Diffusion in the Galaxy and Diffuse Gamma Emission. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29949-0_2
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