The connection between cosmic rays and particle physics has experienced a renewal of interest in the past decade. Large detectors, deep underground, sample groups of coincident cosmic ray muons and study atmospheric neutrinos while searching for proton decay, monopoles, neutrino oscillations, etc. Detector arrays at the surface measure atmospheric cascades in the effort to identify sources of the most energetic naturally occurring particles. This book is an introduction to the phenomenology and theoretical background of this field of particle astrophysics. The book is directed to graduate students and researchers, both experimentalists and theorists, with an interest in this growing interdisciplinary field.

The book is divided into an introductory section and three main parts. The two introductory chapters give a brief background of cosmic ray physics and particle physics. Chapters 5 through 8 concern cosmic rays in the atmosphere – hadrons, photons, muons and neutrinos. The second major part (chapters 9–13) is about propagation, acceleration and origin of cosmic rays in the galaxy. Air showers and related topics are the subject of the last four chapters.

I am grateful to many colleagues at Bartol and elsewhere for discussions which have helped me learn about aspects of the field. I thank Alan Watson, Raymond Protheroe, Paolo Lipari, Francis Halzen, David Seckel, Todor Stanev, Floyd Stecker and Carl Fichtel for reading various chapters and offering helpful suggestions.

I thank Leslie Hodson, Jack van der Velde, Jay Perrett and Sergio Petrera for providing me with photographs to illustrate the book.

Supernovae and their remnants play a fundamental role in the production and acceleration of galactic cosmic rays. Supernova remnants provide the necessary power to sustain the observed sea of cosmic rays which are isotropized in galactic magnetic fields. The shocks driven by expanding ejecta from supernovae of all types provide a natural mechanism for acceleration of cosmic rays, as described in the previous chapter. However, the clear identification of individual cosmic ray sources still remains elusive. The study of gamma rays and neutrinos produced in the interaction of cosmic rays in the sources or in the ambient gas has the potential to provide direct insight into the origin of galactic cosmic rays. In this chapter, after a short description of the Milky Way, we describe the supernovae and the evolution of their remnants. We also study binary systems and the role of star-forming regions.

The Milky Way galaxy

As already introduced in Section 9.2, the Milky Way galaxy is a spiral galaxy composed of a thin disk or galactic plane of radius ∼20 kpc and thickness ∼400– 600 pc, a spherical central region with radius ∼2–3 kpc (also known as the “bulge” or “galactic center”), and a halo which extends to more then ∼30 kpc away from the center (Figure 13.1). The majority of standard matter (to be distinguished from dark matter) is concentrated in the thin disk composed of stars and interstellar medium (ISM). The ISM is filled by gas, dust and cosmic rays and it accounts for 10–15% of the total mass of the galactic plane. The gas is very inhomogeneously distributed at small scales, and it is mostly confined to discrete clouds. Only a few per cent of the interstellar volume is occupied by dense accumulation of ISM. The turbulent, ionized component of the ISM is threaded with a magnetic field that plays an important intermediate role connecting cosmic rays with the ISM. To understand the origin of galactic cosmic rays and the energy involved, we review here the ISM and star-forming regions. Of particular interest is the feedback exercised by supernova explosions and their remnants on the ISM and the related triggering of star formation. We also describe the galactic center region and, for completeness, the dark matter halo.

What are cosmic rays?

Cosmic ray particles hit the Earth's atmosphere at the rate of about 1000 per square meter per second. They are ionized nuclei – about 90% protons, 9% alpha particles and the rest heavier nuclei – and they are distinguished by their high energies. Most cosmic rays are relativistic, having energies comparable to or somewhat greater than their masses. A small but very interesting fraction of them have ultrarelativistic energies extending up to 1020 eV (about 20 joules), eleven orders of magnitude greater than the equivalent rest mass energy of a proton. The fundamental question of cosmic ray physics is, “Where do they come from?” and, in particular, “How are they accelerated to such high energies?”

The answer to the question of the origin of cosmic rays is not yet fully known. It is clear, however, that nearly all of them come from outside the solar system, but from within the Galaxy. The relatively few particles of solar origin are characterized by temporal association with violent events on the Sun and consequently by a rapid variability. In contrast, the bulk of cosmic rays show an anti-correlation with solar activity, being more effectively excluded from the solar neighborhood during periods when the expanding, magnetized plasma from the Sun – the solar wind – is most intense. The very highest energy cosmic rays have gyroradii in typical galactic magnetic fields that are larger than the size of the Galaxy. These may be of extragalactic origin.

Objective of this book

The focus of this book is the interface between particle physics and cosmic rays. The two subjects have been closely connected from the beginning, and this remains true today. Until the advent of accelerators, cosmic rays and their interactions were the principal source of new information about elementary particles. The discovery in 1998 of evidence for neutrino oscillations using the neutrino beam produced by interactions of cosmic rays in the atmosphere is reminiscent of the discoveries of the positron, the muon, the pion and the kaon in the 1930s and 40s. Also, the highest energy cosmic rays can still offer clues about particle physics above accelerator energies, and searches for novel fundamental processes are possible, for example with antiparticles in the cosmic radiation. For the most part, however, cosmic rays are of interest now for the astrophysical information they carry, as reflected by the modern term particle astrophysics.

In this chapter we summarize measurements of the spectrum and composition of cosmic rays with energies above 100 TeV and the implications for sources. We noted in Chapter 12 that the knee of the cosmic ray spectrum may coincide with the upper limit of shock acceleration by supernova remnants (SNR). We also noted that, whether the knee reflects the maximum energy of a class of accelerators or a rigidity-dependent change in propagation, the composition should change systematically from light to heavy in the knee region.

Particles with energies greater than 3×1018 eV are generally assumed to be from sources outside of the MilkyWay because they show no sign of the anisotropy that would be expected if they came from sources in the Galactic plane. The hardening of the spectrum at the ankle around this energy is often interpreted as the transition from Galactic to extragalactic cosmic rays [638]. If the knee reflects the upper limit of acceleration by SNR with a maximum energy for protons of ≈ 1015 eV, then the major nuclear groups would follow the Peters cycle in rigidity culminating with Emax(Fe) ≈ 3 × 1016 eV. Interpretation of the ankle as the transition to extragalactic cosmic rays would then require a second kind of Galactic source capable of accelerating protons to ≈ 1017 eV and iron to ≈ 3 × 1018 eV. Hillas [639] suggests this possibility and identifies the contribution of unknown origin as Population B. On the other hand, the population of extragalactic cosmic rays may extend down to lower energy, A 1017 eV, in which case an alternate explanation for the ankle is needed. Berezinsky et al. [308] proposed an extragalactic spectrum dominated by protons to explain the ankle as a pileup effect just below 3 × 1018 eV, the energy above which losses due to e+e− pair production by protons in the CMB become more important than adiabatic expansion (see Figure 10.2).

These conflicting possibilities require a detailed understanding of the spectrum and composition as a function of energy for their resolution.

Partially ionized plasmas have only recently started getting attention as a research topic especially in the context of cosmic objects and environs. More often than not, the neutral particles have been treated as collision partners for the dominant charged components of a plasma. Alternately, there are cases where the neutrals are the dominant component, and therefore they become the main source of inertia in a partially ionized plasma. There is a lot to investigate in the intermediate circumstances. A glimpse of the three-fluid, the two-fluid, the single-fluid pictures, along with the special case of a weakly ionized plasma has been attempted in the previous chapters. The study is far from complete!

In this chapter, a few research problems, in continuation of the subject matter presented in this book are listed chapterwise. These are the research problems I myself would have liked to pursue had I enough resources at my disposal.

The Three-fluid Description The three-fluid description of a partially ionized plasma has been given in Section 2:3 where it was assumed that the plasma consisted of electrons, ions with fixed electric charge Ze and neutrals. It is however, possible, in such a system, that some of the neutrals pick up electric charges due to electron attachment, charge exchange, ionization or acquire an electric dipole moment due to polarization depending upon the temperature of the plasma. The charging of the neutrals is akin to the charging of the dust grains in a dusty plasma and should be included in the set of Eqs (2.119)–(2.134) along with the assurance of the electric charge conservation. Some efforts in this direction have been made, for example, in the context of the stability of cold solar prominence material high up in the atmosphere against the solar gravity.

The Two-fluid Description

The electron fluid and the ion fluids were combined to construct the magnetohydrodynamic (MHD) fluid in Subsection 2.4.1. The MHD fluid and the neutral fluid then form the two-fluid description of a partially ionized plasma.

In this chapter, we shall attempt to introduce the reader to some specific issues arising in partially ionized plasmas as they exist in varied astrophysical sites. We have taken the solar atmosphere as a prime example, as it spans a wide range of plasma parameters which present circumstances for suitable application of the four different descriptions of a partially ionized plasma. A variety of issues such as the equilibrium, the waves and the instabilities giving rise to turbulence, summon our attention. A few examples of the equilibrium states of a partially ionized plasma in its different descriptions have been presented in Chapter 3.

Here, we shall explore in some detail the existence of equilibrium structures, including gravitational, rotational, magnetic and multifluid effects. The Hall equilibrium of the partially ionized plasma, in particular, brings out a new spatial scale which is larger than the ion inertial scale. The double curl nature of the solutions maps the velocity and the magnetic field on short spatial scales. The equilibrium of the partially ionized plasma under the dominance of the ambipolar effect reveals the existence of extremely sharp magnetic structures embedding large current densities. Such structures enable the heating of the plasma through the excitation and saturation of plasma instabilities.

Equilibrium of Partially Ionized Structures in the Solar Atmosphere

The solar atmosphere consists of layers which widely differ in their density, temperature and magnetization properties. While the distribution of the atmospheric matter consisting of neutral hydrogen, hydrogen plasma and ions of various elements is essentially a result of the gravitational stratification, the temperature and the magnetic field variations are extremely large being governed by the local energetics. The outermost layer called the solar corona becomes visible only during solar eclipses. It is at a temperature of more than a million degree Kelvin and consists of a fully ionized hydrogen plasma and trace ions, such as iron and calcium, in various states of ionization. The next identifiable layers are respectively the transition region and the chromosphere. The chromosphere has a temperature of tens of thousands of degree Kelvin and rises to a million degree Kelvin in the very narrow transition region. The next lower layer is the photosphere. It is the layer from which we receive the visible radiation. The colour of the visible radiation (a near yellow) tells us that the photosphere is approximately at a temperature of 6000 degree Kelvin.

Retirement is a time to indulge oneself, determine your own deadlines and to meet them at your own pace. The cooking breaks are no brakes! This is how I came to write this book, my second, after my superannuation; the first one is called Plasmas; The First State of Matter.

I was introduced to the topic of partially ionized plasmas by Professor Kumar Chitre who handed me the A. Brandenburg and E. G. Zweibel paper (1995, Ap. J., 448, 734) during my visit to the Tata Institute of Fundamental Research sometime in the year 2000. This resulted in our paper ‘Ambipolar diffusion in the solar atmosphere’.

Partially ionized plasmas again came into my line of sight in the year 2005 when I visited the University of Tokyo campus near Edogawadai to work with Professor Yoshida-sansei. Since then, I have been studying plasma-typical problems in partially ionized plasmas. Around the same time I was also collaborating with Professor Swadesh Mahajan on the role of the Hall effect in diverse circumstances. It turned out that in the weakly ionized plasma model of a partially ionized plasma, the ion inertial scale, a hallmark of the Hall effect, gets multiplied by the inverse of the ionization fraction. As a result, the effective ion inertial scale acquires a much larger value than its counterpart in a fully ionized plasma. This was reported in “Equilibrium structures in partially ionized rotating plasmas within Hall magnetohydrodynamics”. During my visit to Professor S. Masuda's group in Nagoya University, Professor K. Shibata and I discussed the possibility of observing this new inertial scale phenomena on the solar atmosphere with a future solar mission. Additionally, during my visits to the Kyoto University and the National Astronomical Observatory of Japan, Mitaka, Tokyo, I had discussions on the mean field dynamo in partially ionized plasmas with Professor S. Tsuneta's group. The highly positive response from my peers galvanized me into pursuing the area further, and my own desire to present partially ionized plasmas as a subject in its own right resulted in this book.

We have developed the basic mathematical framework to study the dynamics of a partially ionized plasma as the three-fluid, the two-fluid, the single-fluid and the weakly ionized plasma systems in Chapter 2. The various equilibria of these systems have been explored in Chapter 3. We are now set to study the excitation of waves in these systems. The three-fluids in the presence of a magnetic field support a host of waves, depending upon the nature of the restoring forces. These forces come into play when a system is disturbed from its equilibrium state by a very tiny amount. The restoring forces tend to restore the system back to the equilibrium and the oscillations are set in, in the process. For example, a bend in the otherwise uniform magnetic field generates a restoring force which tries to straighten the field lines. Similarly, the compressions and the rarefactions in the system execute oscillations in an attempt to maintain a uniform mass density. The tiny disturbance to the equilibrium state ensures that the resulting oscillations have tiny but finite amplitudes which do not depend on the magnitude of the disturbance. The system is linearized about its equilibrium state. These circumstances generate a linear response of the system and the ensuing waves are said to be the linear waves. The linear response of the system gives the dispersion relation, the phase and the group speeds, the polarization and the relative estimates of the mechanical and the electromagnetic energy densities of the waves. The waves can be studied in each of the four descriptions of a partially ionized plasma given in Chapter 2. We shall begin with the fourth description, namely, the weakly ionized plasma, and then go on to consider the single-fluid (SPIF), the two-fluid and the three-fluid models.

Waves in a Weakly Ionized Plasma

A weakly ionized plasma is well described by the set of Eqs (2.220)–(2.226) along with the final form of the induction Eq. (3.245) including the time dependence. Let us write here the equations required to study the waves.