A complete mathematical model of a plasma requires three basic elements: first, the motion of all particles must be determined for some assumed electric and magnetic field configuration; second, the current and charge densities must be computed from the particle trajectories; and third, the electric and magnetic fields must be self-consistently determined from the currents and charges, taking into account both internal and external sources. To be self-consistent, the electric and magnetic fields obtained from the last step must correspond to the fields used in the first step. It is this self-consistency requirement that makes the analysis of a plasma difficult.

To develop an understanding of the processes occurring in a plasma, a useful first step is to forget about the self-consistency requirement and concentrate on the motion of a single particle in a specified field configuration. This approach can be useful in a variety of situations. If the external fields are very strong and the plasma is sufficiently tenuous, the internally generated fields are sometimes small and can be safely ignored. This situation arises, for example, in radiation belts at high energies and in various electronic devices such as vacuum tubes and traveling wave amplifiers. In other situations the self-consistent electric and magnetic fields may be known from direct measurement. In this case, it is often useful to follow the motion of individual tracer particles in the known electric and magnetic fields in order to gain insight into the physical processes involved, such as particle transport and energization.

A plasma is an ionized gas consisting of positively and negatively charged particles with approximately equal charge densities. Plasmas can be produced by heating an ordinary gas to such a high temperature that the random kinetic energy of the molecules exceeds the ionization energy. Collisions then strip some of the electrons from the atoms, forming a mixture of electrons and ions. Because the ionization process starts at a fairly well-defined temperature, usually a few thousand K, a plasma is often referred to as the “fourth” state of matter. Plasmas can also be produced by exposing an ordinary gas to energetic photons, such as ultraviolet light or X-rays. The steady-state ionization density depends on a balance between ionization and recombination. In order to maintain a high degree of ionization, either the ionization source must be very strong, or the plasma must be very tenuous so that the recombination rate is low.

The definition of a plasma requires that any deviation from charge neutrality must be very small. For simplicity, unless stated otherwise, we will assume that the ions are singly charged. The charge neutrality condition is then equivalent to requiring that the electron and ion number densities be approximately the same. In the absence of a loss mechanism, the overall charge neutrality assumption is usually satisfied because all ionization processes produce equal amounts of positive and negative charge. However, deviations from local charge neutrality can occur.

This textbook is intended for a full year introductory course in plasma physics at the senior undergraduate or first-year graduate level. It is based on lecture notes from courses taught by the authors for more than three decades in the Department of Physics and Astronomy at the University of Iowa and the Department of Applied Physics at Columbia University. During these years, plasma physics has grown increasingly interdisciplinary, and there is a growing realization that diverse applications in laboratory, space, and astrophysical plasmas can be viewed from a common perspective. Since the students who take a course in plasma physics often have a wide range of interests, typically involving some combination of laboratory, space, and astrophysical plasmas, a special effort has been made to discuss applications from these areas of research. The emphasis of the book is on physical principles, less so on mathematical sophistication. An effort has been made to show all relevant steps in the derivations, and to match the level of presentation to the knowledge of students at the advanced undergraduate and early graduate level. The main requirements for students taking this course are that they have taken an advanced undergraduate course in electricity and magnetism and that they are knowledgeable about using the basic principles of vector calculus, i.e., gradient, divergence and curl, and the various identities involving these vector operators. Although extensive use is made of complex variables, no special background is required in this subject beyond what is covered in an advanced calculus course.

Abstract

Observations over the last decade have shown that neutron stars receive a large kick velocity (of order a few hundred to a thousand km s-1) at birth. The physical origin of the kicks and the related supernova asymmetry is one of the central unsolved mysteries of supernova research. We review the physics of different kick mechanisms, including hydrodynamically driven, neutrino — magnetic field driven, and electromagnetically driven kicks. The viabilities of the different kick mechanisms are directly related to the other key parameters characterizing nascent neutron stars, such as the initial magnetic field and the initial spin. Recent observational constraints on kick mechanisms are also discussed.

Evidence for neutron star kicks and supernova asymmetry

It has long been recognized that neutron stars (NSs) have space velocities much greater than their progenitors'. A natural explanation for such high velocities is that supernova (SN) explosions are asymmetric, and provide kicks to the nascent NSs. Evidence for NS kicks and NS asymmetry has recently become much stronger. The observations that support (or even require) NS kicks fall into three categories:

Abstract

HETE-2 has confirmed the connection between GRBs and Type Ic supernovae. Thus we now know that the progenitors of long GRBs are massive stars. HETE-2 has also provided strong evidence that the properties of X-Ray Flashes (XRFs) and GRBs form a continuum, and therefore that these two types of bursts are the same phenomenon. We show that both the structured jet and the uniform jet models can explain the observed properties of GRBs reasonably well. However, if one tries to account for the properties of both XRFs and GRBs in a unified picture, the uniform jet model works reasonably well while the structured jet model fails utterly. The uniform jet model of XRFs and GRBs implies that most GRBs have very small jet opening angles (∼ half a degree). This suggests that magnetic fields play a crucial role in GRB jets. The model also implies that the energy radiated in gamma rays is ∼100 times smaller than has been thought. Most importantly, the model implies that there are ∼ 104–105 more bursts with very small jet opening angles for every such burst we see. Thus the rate of GRBs could be comparable to the rate of Type Ic core collapse supernovae. Accurate, rapid localizations of many XRFs, leading to identification of their X-ray and optical afterglows and the determination of their redshifts, will be required in order to confirm or rule out these profound implications.

Abstract

We present the V light curve and optical/infrared spectra of the Type Ic SN 1997B. We show that (1) this SN displayed lines of the He I series; (2)the expansion velocities were higher than those of SNe with traces of H or large He masses in their envelopes (like SN 1993J); the light curve of SN 1997B decayed slower than that of SN 1993J. The smaller mass to kinetic energy ratio and shallower light curve of SN 1997B are inconsistent with it being a He stripped version of some of the best studied Type Ib or II-transition SNe. We infer that Type Ib/c and II-transition SN progenitors come, at least, with two different types of inner structure.

Introduction

A few years ago the presence of He in the atmospheres of Type Ic SNe, the nature of their progenitors, and the relation between Type Ib and Type Ic SNe was subject of debate. On the one hand, empirical evidence and theoretical interpretation supported the view that SNe of Type Ib and Ic are different enough to insure that their progenitors result from different paths of stellar evolution. If so, Type Ic SNe originated in bare C+O cores and were expected not to display He I lines in their spectra. On the other hand, it was stressed that Type Ib and Ic SNe could originate in similar stars evolving as interacting binaries.

Abstract

There are many interesting topics at the intersection of physics and astrophysics we call Supernova Theory. A small subset of them include the origin of pulsar kicks, gravitational radiation signatures of core bounce, and the possible roles of neutrinos and rotation in the mechanism of explosion. In this brief communication we summarize various recent ideas and calculations that bear on these themes.

What is the mechanism of pulsar kicks?

Radio pulsars are observed to have large proper motions that average ∼400–500 km s-1 (Lyne & Lorimer 1994) and whose velocity distribution might be bimodal (Fryer, Burrows, and Benz 1998; Arzomanian, Chernoff, & Cordes 2002). If bimodal, the slow peak would have a mean speed near ∼100 km s-1 and the fast peak would have a mean speed near 500–600 km s-1. A bimodal distribution implies different populations and different mechanisms, but what these populations could be remains highly speculative.

Many arguments suggest that pulsars are given “kicks” at birth (Lai 2000; Lai, Chernoff, and Cordes 2001), and are not accelerated over periods of years or centuries. The best explanation is that these kicks are imparted during the supernova explosion itself. We think that this view is compelling. The two suggested modes of acceleration and impulse are via net neutrino anisotropy during the neutrino emission phase (which lasts seconds) and anisotropic mass motions and aspherical explosion which impart momentum to the residual core.

Abstract

In the popular progenitor scenario, Type Ia supernova are the result of a white dwarf exploding in a binary system. The presence of a nearby companion star could cause a substantial asymmetry in the supernova ejecta — according to the models of Marietta et. al. (2000), the companion carves out an hole in the ejecta. The opening angle of the hole is as large as 40°. Such an asymmetry would leave signatures in the supernova flux and polarization spectra. We explore this possibility using a three-dimensional Monte-Carlo LTE radiative transfer code which includes gamma ray transport and a temperature correction procedure. We calculate synthetic spectra and polarization levels from multiple lines of sight to see how an ejecta hole model compares to observations.

Introduction

While some Type Ia supernovae (SNe Ia) are known to be aspherical, the exact nature of the asymmetry is unknown. The direct evidence of the asphericity is the detection of non-zero intrinsic polarization in, for example, SN 1999by [4] and SN 2001el [17]. In both cases, the polarization level was rather low (∼0.7% for SN 1999by, ∼0.4% for SN 2001el), which indicates a mild asymmetry along the line of sight. In addition, the polarization angle was fairly constant across the majority of line features, indicating that the bulk of the ejecta obeyed a near axial symmetry. The exact shape of the supernova ejecta is an important question, as it must be closely tied to the explosion processes and progenitor systems of SNe Ia.

Abstract

Current massive single star evolution models with rotation, especially when magnetic fields are included, appear to get close in reproducing the spin rates of young neutron stars. This, however, excludes them as progenitors of gamma-ray bursts within the collapsar model. Close binary evolution models with rotation, on the other hand, suggest that the mass receiving star is spun-up appreciably and may retain enough angular momentum in its core until collapse, while the mass donor is spun-down to produce core rotation rates below those of single stars.

Introduction

The evolution of a single star can be strongly influenced by its rotation (e.g., Heger & Langer 2000; Meynet & Maeder 2000), and evolutionary models of rotating stars are now available for many masses and metallicities. While the treatment of the rotational processes in these models is not yet in a final stage (e.g., magnetic dynamo processes are just about to be included; Heger et al. 2003), they provide first ideas of what rotation can really do to a star.

Effects of rotation, as important as they are in single stars, can be much stronger in the components of close binary systems: Estimates of the angular momentum gain of the accreting star in mass transferring binaries show that critical rotation may be reached quickly (Packet 1981; Langer et al. 2000). Therefore, we need binary evolution models which include a detailed treatment of rotation in the stellar interior, as in recent single star models.

Abstract

We study a thermonuclear explosion of a carbon-oxygen white dwarf (WD) using a three-dimensional hydrodynamic model with a simplified mechanism for nuclear reactions and energy release. The explosion begins as a deflagration with the flame front highly distorted by the Rayleigh-Taylor instability. Turbulent combustion and convective flows produce an inhomogeneous mixture of burned and unburned materials that extends from the center to about 0.8 of the radius of the expanding WD. At this stage, a detonation is ignited and propagates through the layers of unburned material with the velocity about 12,000 km/s, which is comparable to the expansion velocities induced in outer layers of the WD by the subsonic burning. During the period of detonation propagation, the density of the expanding unreacted material ahead of the shock can decrease by an order of magnitude compared to its value before the detonation started. Because the detonation burns material to different products at different densities, it can create a large-scale asymmetry in composition if it starts far from the WD center. In contrast to the 3-D deflagration model, the 3-D delayed-detonation model of SN Ia explosions does not leave carbon, oxygen, and intermediate-mass elements in central parts of a WD. This removes the key disagreement between simulations and observations, and confirms that the delayed detonation is currently the most promising mechanism for SN Ia explosions.

Introduction

Type Ia supernovae (SNe Ia) [1–10] result from the most powerful thermonuclear explosions in the Universe.

Abstract

Stellar abundance observations are providing important clues about the relationship between supernovae (SNe) and the rapid neutron capture process (i.e., the r-process). Although the site for the r-process is still not identified, events in and around SNe have long been suspected. Abundances of heavy neutron-capture elements in a number of stars suggest a robust r-process operating over billions of years, constraining astrophysical and nuclear conditions in supernova models. Variations in lighter n-capture element abundances — observed only very recently in any stars — could be explained as a signature of certain supernova models, or might require multiple r-process sites with different mass ranges or frequencies of SNe. Recent observations of elemental abundance scatter in the early Galaxy are consistent with earlier suggestions of a restricted range of SNe responsible for the r-process.

Introduction

The elements heavier than iron are synthesized in neutron processes, either in the (s)-low or (r)-apid process. In the s-process the timescale for neutron capture (τn) is much longer than the electron (beta)-decay (τβ) timescale. For the r-process, however, τn << τβ with many neutrons captured in a very short time period. As a result, neutron captures proceed into very neutron-rich regions far from the stable nuclei, where very little experimental nuclear data is available. This element synthesis is intimately connected to the late stages of stellar evolution, with the s-process occurring in the thermally pulsing helium shells of asymptotic giant branch (AGB) stars of low- and intermediate-mass (M ∼ 0.8–8 M⊙) (see, e.g., the review by Busso, Gallino, & Wasserburg 1999).

Abstract

This paper describes how we have used numerical simulations and laboratory combustion experiments to learn about Type Ia thermonuclear supernova explosions. We discuss detonations, deflagrations, and the transition from deflagrations to detonations, and how these relate to exploding white dwarf stars.

Introduction

This paper is for Craig Wheeler (aka Professor J. Craig Wheeler, Captain, ISS Bunbry, often stationed in the Virgo Cluster), who has been a good friend and fellow traveler for many years. Craig is wonderfully enthusiastic, persistently curious, and always asking those painfully “simple” questions for which we have no answers. He has motivated and driven research programs that have brought combustion science to astrophysics.

A cursory study of the multivolume Proceedings of the Combustion Institute shows that combustion can now be loosely defined as the result of fluid dynamics combined with exothermic reactions, and everything this implies. The definition has expanded with the understanding of the controlling phenomena and the range of applications. In the early 1900's, there was combustion and detonation, and the concepts seemed separated. Combustion was defined as oxidation with energy release, with an emphasis on specific chemical reactions. Detonation studies emphasized the fluid dynamics with shocks and explosions. Now these fields have merged and expanded. We now consider exothermic reactions, including the physics, chemistry, structure and dynamics of flames and detonations, including the production products such as pollutants, soot, diamonds, fullerenes, microparticles, and nanoparticles.

The purpose of this paper is to introduce some aspects of combustion and the combustion community to astrophysicists.

Abstract

I use photometry and spectroscopy data for 24 Type II plateau supernovae to examine their observed and physical properties. This dataset shows that these objects encompass a wide range in their observed properties (plateau luminosities, tail luminosities, and expansion velocities) and their physical parameters (explosion energies, ejected masses, initial radii, and 56Ni yields). Several regularities emerge within this diversity, which reveal (1) a continuum in the properties of Type II plateau supernovae, (2) a one parameter family (at least to first order), (3) evidence that stellar mass plays a central role in the physics of core collapse and the fate of massive stars.

Introduction

Type II supernovae (SNe II, hereafter) are exploding stars characterized by strong hydrogen spectral lines and their proximity to star forming regions, presumably resulting from the gravitational collapse of the cores of massive stars (MZAMS > 8 M⊙). SNe II display great variations in their spectra and lightcurves depending on the properties of their progenitors at the time of core collapse and the density of the medium in which they explode. Nearly 50% of all SNe II belong to the plateau subclass (SNe IIP) which constitutes a well-defined family distinguished by 1) a characteristic “plateau” lightcurve (Barbon et al. 1979), 2) Balmer lines exhibiting broad P-Cygni profiles, and 3) low radio emission (Weiler et al. 2002).

Abstract

The six galactic supernovae within the last millennium are critical to all work on the relationships between supernovae and their remnants. Yet this field has been dogged by controversy and discarded arguments. Even during the Wheeler Symposium, we had successive speakers give different type assignments to individual events. In an effort to at least define the confusion, I have polled a group of leading experts as to their current thinking on the types for each of the historical events. This complements a similar poll made a decade ago. We must realize that these results are not voting-on-the-truth, but is rather an expression of community opinion. The recent poll has the following results. SN1006 is universally agreed to be a Type Ia event. SN1054 (the Crab) is puzzling in many ways, but it must be from some sort of a core collapse event. SN1181 is thought to be a core collapse event primarily on the basis of its remnant being a plerion like the Crab. SN1572 (Tycho's) is agreed to be a Type Ia event. SN1604 (Kepler's) has no consensus, with all types being claimed and denied. Cas A is unanimously agreed to not be a Type Ia event, but after that all possibilities find their champions.

The polls

The six galactic supernovae within the last millennium (SN1006, SN1054, SN1181, SN1572, SN1604, and Cas A) all have very well observed remnants. A key question for understanding these remnants is the type of the original explosion.

Abstract

Combining sub-arcsec imaging with moderate spectral resolution and high throughput, the Chandra X-ray Observatory enables spectacular views of Galactic supernova remnants as well as X-ray studies of compact remnants, young extragalactic supernovae, and gamma-ray burst afterglows. In this contribution, I briefly review the capabilities of Chandra and then describe some recent observations of supernovae and supernova remnants made with Chandra.

The Chandra X-ray observatory — an overview

Chandra (see, e.g., Weisskopf et al. 2002) was launched from space shuttle Columbia 23 July 1999 and is now late into the fourth year of its ten year mission. The heart of the facility is the High-Resolution Mirror Assembly consisting of 4 nested mirror pairs with a 120 cm outer shell diameter. The mirrors provide about 800 cm2 of collecting area at 1 keV and about 400 cm2 at 5 keV. Most importantly, the mirror design results in less than 0.″5 on-axis spatial resolution; an order-of-magnitude higher resolution than any other X-ray facility yet flown. This corresponds to a resolution of ∼100 AU at the distance of the Crab Nebula; making Chandra ideal for probing the fine structure of supernova remnants on spatial scales comparable to that achievable by some of the best ground-based optical telescopes. Equally important, high spatial resolution improves the sensitivity of X-ray measurements by concentrating source photons into a small area thereby minimizing the contribution from the underlying background. There are two types of focal plane instrument onboard Chandra.

Abstract

The death of massive stars and the processes which govern the formation of compact remnants are not fully understood. Observationally, this problem may be addressed by studying different classes of cosmic explosions and their energy sources. Here we discuss recent results on the energetics of γ-ray bursts (GRBs) and Type Ib/c Supernovae (SNe Ib/c). In particular, radio observations of GRB 030329, which allow us to undertake calorimetry of the explosion, reveal that some GRBs are dominated by mildly relativistic ejecta such that the total explosive yield of GRBs is nearly constant, while the ultra-relativistic output varies considerably. On the other hand, SNe Ib/c exhibit a wide diversity in the energy contained in fast ejecta, but none of those observed to date (with the exception of SN 1998bw) produced relativistic ejecta. We therefore place a firm limit of 3% on the fraction of SNe Ib/c that could have given rise to a GRB. Thus, there appears to be clear dichotomy between hydrodynamic (SNe) and engine-driven (GRBs) explosions.

The death of massive stars

The death of massive stars (M ≳ 8M⊙) is a chapter of astronomy that is still being written. Recent advances in modeling suggests that a great diversity can be expected. Indeed, such diversity has been observed in the neutron star remnants: radio pulsars, AXPs, and SGRs. We know relatively little about the formation of black holes.

The compact objects form following the collapse of the progenitor core.

Abstract

It is the conventional wisdom that overluminous Type Ia supernovae have an overproduction of their elemental powerhouse, 56Ni, leading to broader light curves, higher temperatures, higher ionization states, and peculiar spectra similar to that of SN1991T. However, this simple picture is incomplete: we show that a broad lightcurve width does not necessarily predict spectroscopic peculiarity, nor does a spectrum resembling SN1991T guarantee a broad lightcurve. There is circumstantial evidence that asymmetry may play a role in the explanation of the diverse properties of broad lightcurve and SN1991T-like SNe Ia.

As an illustrative example, we present optical and NIR light curves, and Lick 3m and HST STIS spectra of the SN Ia with the broadest light curve observed to date, SN 2001ay. SN 2001ay has Δm15(B) = 0.6 and stretch s = 1.6, yet at maximum light is fairly spectroscopically normal. The exception is an extremely high Si velocity, v = 15,000 km s–1. The secondary peak in the I-band lightcurve is higher than the primary peak, and the Js and H lightcurves remain flat over the entire 55 days of observation. SN 2001ay also does not appear to obey lightcurve shape-luminosity relationships, at least as they are currently formulated. Despite its broad lightcurve, the SN has normal absolute magnitudes after correction for Milky Way and host galaxy extinction. Thus, if a stretch or Δm15(B) correction is applied, the resulting magnitude would be overcorrected by ∼1 mag.

Abstract

We present a brief summary of asphericity effects in thermonuclear and core collapse supernovae (SN), and how to distinguish the underlying physics by their observable signatures. Electron scattering is the dominant process to produce polarization which is one of the main diagnostical tools. Asphericities result in a directional dependence of the luminosity which has direct implications for the use of SNe in cosmology. For core collapse SNe, the current observations and their interpretations suggest that the explosion mechanism itself is highly aspherical with a well defined axis and, typically, axis ratios of 2 to 3. Asymmetric density/chemical distributions and off-center energy depositions have been identified as crucial for the interpretation of the polarization P. For thermonuclear SNe, polarization turned out to be an order of magnitude smaller strongly supporting rather spherical, radially stratified envelopes. Nevertheless, asymmetries have been recognized as important signatures to probe A) for the signatures of the progenitor system, B) the global asymmetry with well defined axis, likely to be caused by rotation of an accreting white dwarf or merging WDs, and C) possible remains of the deflagration pattern.

Introduction

During the last decade, advances in observational, theoretical and computational astronomy have provided new insights into the nature and physics of SNe and gamma-ray bursts. Due to the extreme brightness of these events, they are expected to continue to play important role in cosmology. SNe Ia allowed good measurements of the Hubble constant both by statistical methods and theoretical models.