Because neutrinos interact only by the weak interaction, a large target volume is necessary to detect them. This is especially true in the case of naturally occurring neutrinos where the flux is low compared to neutrinos from an accelerator beam or from a nuclear reactor. The idea of using a large volume of clear water to detect neutrinos was proposed in 1960 by Greisen [538], Reines [693] and Markov [694]. The Cherenkov light from charged particles produced by interactions of neutrinos would be detected by optical modules in the water, visible from a long distance. Reines distinguished between cosmic neutrinos (by which he meant neutrinos of astrophysical origin) and cosmic ray (i.e. atmospheric) neutrinos. He writes that interest in the possibility of detecting cosmic neutrinos “stems from the weak interaction of neutrinos with matter, which means that they propagate essentially unchanged in direction and energy from their point of origin (except for the gravitational interaction with bulk matter, as in the case of light passing by a star) and so carry information which may be unique in character.” In the same volume of Annual Reviews, Greisen proposed to use a large volume of water in a mine to detect astrophysical neutrinos. Markov proposed using the deep ocean or water in a lake to study atmospheric neutrinos.

The idea developed in two ways. The first, originally motivated by the goal of detecting proton decay, led to the relatively densely instrumented detectors in deep mines, IMB and Kamiokande, which detected the burst of ≈10 MeV neutrinos from SN1987A [401, 403] and set limits on stability of the proton. The second-generation water detectors Super-Kamiokande and SNO (Sudbury Neutrino Observatory) were designed in large part for high-resolution measurements respectively of atmospheric and of solar neutrinos. Super-K confirmed oscillations of atmospheric neutrinos [59] as the cause of the anomalous ratio of νμ/νe found earlier by Kamiokande and IMB. It also set stronger limits on proton decay. SNO, filled with heavy water, measured neutral current interactions of all flavors of neutrinos from the Sun, as well as charged current interactions of νe, thereby confirming oscillations as the explanation of the solar neutrino problem [233, 695].

The other path was motivated by the goal of using high-energy neutrinos as a probe of cosmic ray origin.

There have been many new measurements of primary cosmic rays in the past 25 years over the whole energy range from around a GeV to above 100 EeV (1020 eV). Figure 2.1 is a global overview of the whole range of data from some of these experiments. A remarkable feature of the cosmic ray spectrum is the fact that it can be described by inverse power laws over large intervals of energy. Theoretical understanding of this fact (or lack of it) will be the subject of Chapters 9–12 on propagation, acceleration and sources. For now we simply note that the global spectrum can be divided into four regions. From 10 GeV to 1 PeV (1015 eV) the differential spectral index is α ≈ −2.7. From 10 PeV to 1 EeV (1018 eV) it is −3.1. Above 10 EeV the spectrum again flattens somewhat to α −2.6, and then it apparently cuts off around 1020 eV. Below 10 GeV the spectrum locally is modified by solar modulation from the interstellar index of α ≈ −2.7, as illustrated in Figure 1.5. The transition regions are known as the “knee” (∼ 3 PeV) and the “ankle” (∼ 3 EeV). The former is usually assumed to signal in some way the approaching end of the spectrum of galactic cosmic accelerators, while the ankle is sometimes associated with the emergence of particles of extragalactic origin. This picture is not final, and there are important hints of finer structure within the main regions that we will discuss.

Antiprotons and positrons are included on Figure 2.1 even though they are mostly (if not entirely) “secondary” in the sense that they are produced by collisions of “primary” cosmic ray nuclei during propagation in the interstellar medium. Positrons and antiprotons are therefore discussed in Chapter 11 following the introduction to cosmic ray propagation in Chapters 9 and 10. Although most electrons are “primary” in the sense of coming from cosmic ray acceleration sources, their spectra are significantly affected by propagation, so the discussion of electrons is also postponed until Chapter 11.

Fluxes of primary cosmic ray protons and nuclei are the starting point for all the topics of this book. On the one hand, the incident cosmic rays, by their interactions, generate the atmospheric hadrons, muons and neutrinos that reach the surface of the Earth.

The expressions derived for neutrino fluxes in Chapter 6 apply to atmospheric neutrinos at production. Because of their small cross section, most neutrinos pass through the Earth without absorption, so atmospheric neutrinos from the whole sky can be observed from a single detector. This makes it possible to compare neutrino fluxes over a range of path lengths from ∼ 10 to 10,000 km. If the neutrinos change in some way as they propagate after production, then the fluxes will differ from those obtained by integrating their production spectra from the top of the atmosphere to the ground.

The evidence that atmospheric neutrinos do indeed suffer an identity change during propagation is summarized in Figure 7.1 from the Super-Kamiokande experiment [59]. (See Ref. [220] for a complete review.) Crosses show the data for low energy (top row) and higher energy (bottom row) as a function of zenith angle. The dashed lines show the expected number of events in the absence of oscillation, while the solid lines show the fitted fluxes assuming oscillations. Electron neutrinos are not much affected at these energies, while muon neutrinos show a characteristic behavior in which high-energy downward muons are unaffected while muons that cross the Earth are affected, and the deviation begins already above the horizon for low-energy muon neutrinos. The description of this behavior and its implications for theory are the subject of this chapter. As we will see, the existence of oscillations requires that the neutrinos have a nonzero rest mass.

Neutrino mixing

The hypothesis of neutrino mixing was first anticipated by Pontecorvo in 1957, and a few years later developed by Maki, Nakagawa and Sakata [71] on the basis of a two-neutrino hypothesis. The first evidence for oscillations came from measurements of solar neutrinos by Davis over a 25-year period starting in 1970. The solar neutrino studies began in 1964 with back-to-back papers by Bahcall [221] and Davis [222] predicting the number of electron neutrinos expected from fusion

reactions in the Sun and proposing the experiment using chlorine as the target and looking for

A deficit of electron neutrinos (by a factor of 1/3) was found [223] as measurements continued and ever more detailed calculations were made [224].

In the next three chapters we discuss propagation of cosmic rays in space and production of secondary particles that trace the propagation. We begin in this chapter with a description of the Milky Way galaxy and propagation of primary and secondary nuclei. We also discuss production of secondary positrons and antiprotons. In Chapter 10 we discuss propagation of cosmic rays in intergalactic space, which is essential for understanding the highest energy portion of the cosmic ray spectrum. Then in Chapter 11 we discuss production of gamma rays and neutrinos and how they reflect the propagation of cosmic rays in space.

Two of the most important facts with implications for origin of cosmic rays were already mentioned in Chapter 1:

1. From the ratio of primary to secondary nuclei it can be inferred that, on average, cosmic rays in the GeV range traverse 5–10 g/cm2 equivalent of hydrogen between injection and observation.

2. This effective grammage decreases as energy increases, at least as far as observations extend, as illustrated by the decreasing intensity of the secondary nucleus boron in Figure 1.4 compared to primary nuclei such as carbon and oxygen.

Since the thickness of the disk of the Galaxy is about 10−3 g/cm2, (1) implies that cosmic rays travel distances thousands of times greater than the thickness of the disk during their lifetimes. This suggests diffusion in a containment volume that includes the disk of the Galaxy. The fact that the amount of matter traversed decreases with energy suggests that higher-energy cosmic rays spend less time in the Galaxy than lower-energy ones (although this may be only part of the explanation). It also suggests that cosmic rays are accelerated before most propagation occurs. If, on the contrary, acceleration and propagation occurred together, one would expect a constant ratio of secondary/primary cosmic rays – or even an increasing ratio for some stochastic mechanisms in which it takes longer to accelerate particles to higher energy.

Acceleration and transport of cosmic rays are nevertheless very closely related, particularly in the theory of shock acceleration by supernova blast waves. In that case, diffusive scattering of particles by irregularities in the magnetic field plays a crucial role for acceleration as well as for propagation.

Interest and activity in particle astrophysics has continued to grow. It has now been 25 years since publication of the first edition. A new edition is long overdue, but nevertheless well-motivated in view of the growth of the field and several important discoveries in the interim. The discoveries include flavor oscillations in atmospheric and solar neutrinos, the cutoff of the spectrum of ultra-high-energy cosmic rays, TeV gamma rays from supernova remnants in the Galaxy and from distant active galaxies, an unexpected excess of positrons at high energy (but not of anti-protons) and, most recently, high-energy astrophysical neutrinos.

The discoveries are the result of major investments in the development of new instruments: the major underground experiments, Super-Kamiokande, SNO and Borexino; the giant air shower arrays, Auger and Telescope Array; the imaging atmospheric Cherenkov telescopes VERITAS, H.E.S.S. and MAGIC, and the Fermi Satellite; the particle spectrometers in space, PAMELA and AMS-02, along with balloon-borne detectors ATIC and CREAM; and the neutrino telescopes AMANDA and Baikal, ANTARES and IceCube.

Corresponding developments on the side of particle physics stem from the colliding beam machines at DESY, Fermilab and CERN. These have provided measurements of parton distribution functions over an unprecedented kinematic range, the discovery of the top quark and, most recently, the discovery of the Higgs boson. The LHC is now running at a center of mass energy equivalent to 1017 eV in the lab, well above the knee in the cosmic ray spectrum.

All of the discoveries mentioned have given rise to new questions that stimulate continuing interest in particle astrophysics. In writing this expanded edition, we have kept the basic structure of the first edition while adding chapters on new topics stimulated by some of these open questions. Topics of the new chapters include neutrino oscillations, propagation of ultra-high energy cosmic rays in the cosmic microwave background, sources of the highest energy cosmic rays and neutrino astronomy. The chapters on atmospheric muons and neutrinos, and those on acceleration and propagation of cosmic rays, go into greater depth and focus on new results. Most important are the two chapters on particle physics, which are completely new, and are intended to bring the latest results from high-energy physics to bear on cosmic ray physics.

We are grateful to many colleagues who, in one way or another, helped us to understand and explain the material in this book.

The phenomenology of muons and neutrinos underground is important because of its relevance to studies of neutrino properties and searches for astrophysical neutrinos with deep detectors. Formulas for production and fluxes of atmospheric neutrinos were given in Chapter 6. A summary of measurements of the vertical muon flux at sea level is included in Figure 6.2. The classic discussion of highenergy muon fluxes and their measurement deep underground is the review of Barrett, Bollinger, Cocconi, Eisenberg and Greisen in 1952 [254], which is still a useful reference.

There are two contributions to the flux of muons in deep detectors, penetrating atmospheric muons from above and neutrino-induced muons from all directions, as shown in Figure 8.1. The lines in the figure show the angular distribution of muons at various depths underground assuming a flat overburden of uniform density. The calculation for atmospheric muons is made by evaluating the integral flux of muons in each direction from the integral form of Eq. 6.36 evaluated at the energy required to reach the given depth. Equation 8.5 is used to relate slant depth in m.w.e. to energy, as discussed in Section 8.1. The calculation of the neutrinoinduced muons is discussed in Section 8.3.3. The intersections of the muon flux lines with the νμ-induced flux line indicate the zenith angles at which the two contributions are equal for each depth. The data are from the SNO detector, which has a flat overburden under 5.89 km.w.e.

Essential to the phenomenology of both muons and muon neutrinos is energy loss of high-energy muons during propagation. We therefore begin this chapter with a discussion of muon energy loss. We then apply the results both to atmospheric muons that penetrate to deep detectors and to muons produced by charged current interaction of νμ in or near underground detectors. We also describe the signatures of all three neutrino flavors in underground detectors.

Passage of muons through matter

The energy loss equation for muons has the same form as for electrons (Eq. 5.10). The ionization loss rate is nearly constant for relativistic muons, with a broad minimum below 1 GeV of ∼ 1.8 MeV/(g/cm2) in rock and a logarithmic rise at higher energy.

In this chapter we will give an overview of the modern understanding of particle physics, concentrating on aspects that are of direct relevance to the later discussions in this book. Comprehensive introductions to high-energy physics and the Standard Model of particle physics can be found in the textbooks, for example, by Halzen [34], Perkins [35] and Weinberg [36]. An up-to-date compilation of particle properties and related descriptions is provided by the PARTICLE DATA GROUP.

Historical relation of cosmic ray and particle physics

In the 1930s, the early years of particle physics, the observation of cosmic rays was the only means of studying energetic particles. While the first measurements of cosmic rays, such as the ionization rate of air, were of indirect nature, the use of cloud chambers in cosmic ray observations, pioneered by Skobelzyn in 1927, opened the way to image directly tracks of high-energy particles for the first time.

The first discovery of a new particle in the cosmic radiation was that of the positron by Anderson [37]. Using a lead absorber in a cloud chamber that was placed in a strong magnetic field allowed Anderson to determine not only the energy and charge but also the direction of the particle trajectory. After this serendipitous discovery systematic studies of the particle nature of cosmic rays and their interactions were carried out by many groups.

In the early experiments, not more than 2% of all cloud chamber pictures contained cosmic ray tracks. The development of fast electronic circuits that could be used to take pictures of cloud chambers in coincidence with Geiger tubes for triggering increased this efficiency to 80% and allowed systematic studies of particle trajectories. The much larger number of trajectories that could be observed with triggered experiments led to the discovery of e+e- pair production by Blackett and Occhialini [38] and the muon by Neddermeyer and Anderson [39]. Initially the muon was incorrectly identified as the pion predicted in Yukawa's theory of the strong interaction and given the name mesotron. Other particles discovered with cloud chambers are the and baryons [40, 41]. Furthermore, studying the coincidence rate of Geiger tubes placed at large distances from each other led to the discovery of air showers in high-altitude experiments [42–44]. The interpretation within cascade theory showed already at that time that some cosmic rays must have energies of 1015 eV or higher

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.