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2 High Energy Density Astrophysics INTRODUCTION In ancient times, the heavens were thought of as perfect, static, and immutable. Today we see the universe as a place of titanic violence and continuous upheaval. The twin engines of gravitational collapse and nuclear fusion power phenomena on a nearly unimaginable scale. Giant black holes consume the fiery hearts of galaxies, sweeping entire star systems into their immense accretion disks; relativistic particle jets, powered by unknown acceleration mechanisms, focus their extreme energies with incredible precision across millions of light years; supernovae shocks sweep up turbulent plasma and dust, creating the seeds for stellar rebirth; neutron stars the size of Manhattan spin at kilohertz rates, weaving their huge magnetic fields through the surrounding plasma and creating brilliant x-ray lighthouses. Meanwhile, in our own relatively placid corner of the Galaxy, we are pelted by cosmic rays of such immense energy that their very existence is difficult to understand, and the formation, structure, and dynamics of the most massive of our solar companions, the giant planets, remain a mystery. The immense energy densities associated with these phenomena could never be reproduced on Earth. Or could they? Certainly, these conditions can be recreated mathematically using computer models and analytical calculations (if only we had better understanding of the physics!). Perhaps, tiny portions of these extreme environments can be made to flash in and out of existence in accelerator collision chambers, in the focal spots of high-power lasers or particle beams, or at the core of
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magnetic Z-pinch machines. With the aid of such experiments, and through new analytical, computational, and technical breakthroughs, it may soon be possible to gain improved understanding of the physics underlying some of the universe’s most extreme phenomena and to answer some of the fundamental questions outlined in the following sections. Indeed, over the past decade a new genre of laboratory astrophysics has emerged, made possible by the new high energy density (HED) experimental facilities, such as large lasers and Z-pinch generators. On these facilities, macroscopic collections of matter can be created in astrophysically relevant conditions, and their collective properties measured. Examples of processes and issues that can be experimentally addressed include compressible hydrodynamic mixing, strong-shock phenomena, radiative shocks, radiation flow, high-Mach-number jets, complex opacities, photoionized plasmas, equations of state of highly compressed matter, and relativistic plasmas. These processes are relevant to a wide range of astrophysical phenomena, such as supernovae and supernova remnants (see Figure 2.1), astrophysical jets (see Figure 2.2), radiatively driven molecular clouds, accreting black holes, planetary interiors, and gamma-ray bursts. In this chapter these phenomena are discussed in the context of laboratory astrophysics experiments possible on existing and future HED facilities. Key questions in each area will be raised, with the hope and expectation that future experiments on HED facilities will play some role in their resolution. HIGH ENERGY DENSITY DEFINITIONS FOR ASTROPHYSICS Stars are plasma. This state requires energy in excess of the binding energy of molecular or solid matter—which for the most abundant element, hydrogen, corresponds to 4.4 electronvolts or to a gas temperature of about 23,000 K. More extreme conditions abound. They may be classified by equating a thermal kinetic energy (a temperature), or a quantum degeneracy energy (a Fermi energy) to the specified energy. For example, the temperature corresponding to the rest-mass energy of an electron is 6 billion K, and the density at which the electron Fermi energy equals its rest-mass energy is 1 million times that of water. Another set of extremes can be constructed from velocities. Relativistic conditions are energetically extreme: as the velocity of light is approached, the energy of a particle exceeds the rest-mass energy. For typical conditions in the interstellar medium, the sound velocity is about 10 kilometers per second (km/s), while gas motions often exceed this by factors of 10 to 100. Under these conditions, strong shocks, with Mach numbers of 10 to 100, are generated.
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FIGURE 2.1 Crab Nebula in the optical. The Crab Nebula, a supernova remnant whose parent supernova was recorded by Chinese astronomers in the summer of A.D. 1054, is a beautiful example of a relatively young remnant, whose appearance is thought to be largely driven by particle acceleration processes tied to the Crab Pulsar; the observed radiation is due to synchrotron emission from highly relativistic electrons accelerated within the structure seen in this image. The precise nature of the connection between the pulsar and its magnetosphere, and the surroundings, remains uncertain. Courtesy of the European Southern Observatory.
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FIGURE 2.2 Jet formation. Images of the active galaxy M87. Using a variety of high angular resolution observations, astrophysicists have been able to disentangle the spatial structure of jets emanating from the core of active galaxies. Such jets present a wealth of unsolved physics problems, ranging from the precise composition of the material composing the jet itself, to its stability, and—most uncertain—its ultimate origin: acceleration to relativistic energies and remarkable collimation. The “engine” producing these jets is most likely one of the most extreme physical environments encountered in astrophysics, namely, the vicinity of a massive black hole lying near the core of active galaxies (see Figure 2.6 in this chapter). Courtesy of W.Junor, University of New Mexico/Los Alamos National Laboratory; and J.A.Biretta and M.Livio, Space Telescope Science Institute.
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THE FUNDAMENTAL QUESTIONS FOR HIGH ENERGY DENSITY ASTROPHYSICS How Does Matter Behave Under Conditions of Extreme Temperature, Pressure, and Density? A fundamental quest of physics is to determine the properties of matter—its equation of state, its opacity, and its transport properties (thermal conductivity, viscosity, particle diffusivity, electrical conductivity, and so on). The universe offers a huge range of conditions for matter, far beyond what can be directly obtained in a terrestrial laboratory setting. Following are some examples of new opportunities for studies of matter under extraordinary conditions, spanning both laboratory and astrophysical settings. The Origin and Evolution of the Giant Planets and Brown Dwarfs and of Planetary Interiors The discovery of extrasolar planets and brown dwarfs represents one of the most exciting astronomical developments of the decade. The newly discovered planets tend to be giant gas planets with small, highly eccentric orbitals. These new “hot giants” raise many questions about existing models for planetary formation and planetary interiors. Models exist for the interiors of the extrasolar planets as well as for the solar planets, but these models rely upon a quantitative understanding of cold, dense matter at extreme pressures. At such high pressures, the matter is pressed so closely together that the outer electronic orbitals overlap, causing pressure ionization. This serves as an energy sink, which affects the compressibility. Such coupled quantum-mechanical-thermodynamic effects are notoriously difficult to calculate theoretically. In order to solve the many fundamental questions of planetary formation, evolution, and structure, it is essential to improve our understanding of hydrogen in the ultrahigh-pressure environment found in the interior of brown dwarfs and giant planets. This environment is characterized by moderate temperatures of order 0.1 to 1 eV, and extreme pressures of order 1 to 10 Mbar. Under these conditions, hydrogen is expected to form a degenerate strongly coupled plasma/fluid. The basic thermodynamic properties of such plasmas are still incompletely characterized. In the specific case of the interior of Jupiter (see Figure 2.3), model calculations predict that molecular hydrogen (H2) dissociates to atomic hydrogen and ionizes in the mantle, changing from a dielectric to a conductor. The relevant pressure and temperature for this transition is 0.5 to 5 Mbar at temperatures of a fraction of an electronvolt. Deeper in the interior of Jupiter, the pressure and temperature increase to above 40 Mbar and a few electronvolts near the center. For reference, the
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FIGURE 2.3 Planetary interiors and their equation of state. The internal structure of the giant gaseous planets, such as Jupiter shown in the top image, is an ongoing puzzle, primarily because of uncertainties regarding the properties of matter at extreme pressures. One of the few ways to explore such questions experimentally is to probe the relevant materials (primarily hydrogen) in lasers and magnetic pinch facilities, which give us access to the relevant physical regimes; an example of such an experiment is shown in the image on the bottom, drawn from an equation-of-state experiment carried out at a laser facility. The ultimate aim of such studies is to be able to discriminate between different planetary formation models. Courtesy (top) of NASA and Space Telescope Science Institute, and (bottom) R. Cauble and G. Collins, Lawrence Livermore National Laboratory.
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corresponding conditions for the brown dwarf GL 229 are similar in the mantle, but 4 orders of magnitude higher in pressures at the core, Pcore ≈ 105 Mbar. The molecular dielectric to atomic metallic transition in hydrogen (H2→H++H+) is important because convection of pressure-ionized, metallic hydrogen is thought to create the 10 to 15 gauss magnetic field of Jupiter. Of particular concern is whether a first-order plasma phase transition exists, as this critically affects the internal structure in the important convection zone and the degree of gravitational energy release due to sedimentation of helium (He) and heavier elements. Jupiter and Saturn’s atmospheres are observed to be helium-poor, and the energy release from helium sedimentation is required to explain Saturn’s intrinsic heat flux. Among the open questions are these: What is the phase diagram of high-pressure hydrogen? Is there a (first-order) plasma phase transition? Does hydrogen form a metallic state at high pressure? What is the solubility of other chemical elements (especially He) in a high-pressure hydrogen plasma? Can H and He become immiscible, with the formation of “He rain,” at high pressure and density? In addition, transport properties in general (such as electrical and thermal conductivity) are poorly understood, but are essential if we are to understand dynamical processes such as magnetic field generation and thermal convection. An improved understanding of hydrogen in the high-pressure regime would directly impact the following fundamental questions of planetary science: What is the structure of a gas giant as a function of depth? Where (and what) is the region within which the magnetic field is generated? Are such planets fully convective? Do these planets form by direct collapse of the solar nebula, or do they form around a preexisting rock-ice core? By inferring the core conditions of Jupiter, can the planetary formation mechanism for the solar system be inferred? What high-pressure chemistry goes on within such planets? While much of the hydrogen equation of state is well known, many of the important questions require accuracy at the 1 percent level in density for a given pressure and temperature. (For example, 1 percent of Jupiter’s mass is 3 Earth masses, comparable to the postulated core mass.) Transport properties are currently much less-well understood, and even a factor-of-2 knowledge of the electric and thermal conductivity would be useful. Miscibilities of various cosmically abundant elements in hydrogen within a factor of 2 would also be a great advance relative to current
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knowledge. It is possible that new experiments involving high energy density plasmas may soon be able to answer these questions, while improved astronomical observations will allow us to explore more fully the mass range of extrasolar giant gaseous planets down to values characteristic of such planets in our solar system. Another area of interest is the atmosphere and envelope of white dwarfs. Accreting white dwarfs are thought to be the starting point of Type Ia supernovae, which in turn are used as “standard candles” to map out the expansion of the deep universe. Cooling white dwarfs can be used as “clocks,” or cosmochronometers, to determine the age of regions of the Galaxy. An understanding of the equation of state, opacity, and heat conductivity in the atmospheres and envelopes of white dwarfs would be very beneficial, and may be experimentally accessible, especially with future facilities, as described in this subsection. Experimental techniques are being developed on pulsed-power facilities, lasers, gas guns, and diamond anvil cells to probe the properties of matter under extreme conditions of pressure and compression. The conditions achieved to date cover pressure ranges of 0.1 to 40 Mbar in equation-of-state measurements, planar shock pressures of up to 750 Mbar in a proof-of-principle demonstration experiment, and ≈10 gigabars (Gbar) at the core of an imploding spherical capsule. Using modern pulse shaping techniques on lasers and on magnetic pinch facilities, pressures in the megabar regime under quasi-isentropic compressions have been achieved. In the coming decade, with the advent of the National Ignition Facility and Laser Megajoule (LMJ) lasers, this parameter space will be filled in and extended. On these future facilities, quasi-isentropic compressions of well over 10 Mbar should be possible. These laboratory conditions correspond to the interiors of terrestrial and giant gas planets, brown dwarfs, average mass stars, and the envelopes of white dwarfs. Even the simplest case studied experimentally so far, the equation of state of hydrogen, shows the humbling complexity of the behavior of matter under extreme conditions of compression. To develop and have confidence in theoretical and numerical models that pertain to the interiors of the astronomical objects referred to above will require experimental data to guide the way. Strongly Coupled Plasmas Most of our understanding of plasmas comes from study of tenuous, ionized gases, in which the electromagnetic behavior is a modest modification of the simpler gas behavior. This Debye (weak coupling) limit breaks down as density increases and/or temperature decreases. At the other extreme, we are familiar with the liquid and solid states. The intermediate condition, “strongly coupled” plasmas, is complex and challenging to understand theoretically. It corresponds to the conditions in giant planets, brown dwarf and white dwarf stars, and the progenitors of Type Ia
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supernovae. It occurs naturally in HED plasma experiments, and a fertile interaction between astronomy and HED plasma physics has begun in this area. (See Figure 1.1 in Chapter 1 and Figure 3.3 in Chapter 3 for a summary of relevant regimes.) The line labeled E(coulomb)=kT in Figure 1.1 represents the boundary for strongly coupled plasmas: they lie to the right (at higher density). The Opacities of Stellar Matter Historically, one of the oldest areas of overlap between HED plasma physics and astronomy has been the radiative opacity of matter. The opacity of stellar plasma controls the rate at which energy leaks from stars, that is, their luminosity. If large enough, opacity causes the onset of mixing currents which, in turn, modifies the structure of stars and their evolution. For example, a well-mixed Betelgeuse would be blue, not red. The bumps in the opacity curves (the changes with temperature and density) can drive pulsations and probably mass loss. Cepheid pulsating stars are the other cosmological yardstick. Type Ia supernovae provide a particularly fundamental and important challenge: the luminosity and effective temperature we observe is governed by leakage of light from the plasma, but the expansion is so great that the light is red-shifted between emission and absorption, making the probability of its escape too difficult to solve accurately. Observations of these supernovae seem to imply that the universe is expanding at an accelerated rate, contrary to prediction. This conclusion is based on empirical rules for behavior of relatively nearby supernovae, and involves a light curve shape-luminosity correction based on an opacity hypothesis. An understanding based on laboratory experiment would be much more compelling. For example, measurement of the radiation transport in a rapidly expanding, inhomogeneous, fully three-dimensional target would greatly contribute to our understanding of the behavior of Type Ia supernovae. The error budget for the ages of stellar clusters is dominated by uncertainties in opacity. Continued refinement of our knowledge will allow us to better place a time scale on the formation and development of our Galaxy and nearby galaxies. Degenerate Plasma Convection Type Ia supernovae, novae, and the core helium flash are supposed to be initiated under conditions of strong degeneracy of electrons. Thermonuclear burning begins in a degenerate plasma and proceeds to thermal runaway; as the temperature rises in the flame region, a convective instability develops and eventually proceeds to explosion. Similar convective motions under degenerate plasma conditions—
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albeit without the local nuclear burning and possible runaway—are thought to occur in the outer regions of brown dwarf stars. Unfortunately, there are no experimental data on convection in an (electron) degenerate plasma; thus, unlike the case of, for example, Boussinesq convection, very little is known about degenerate convection. For this reason, both experiments and fundamental theory and simulations directed at convection under degenerate conditions are very important. Physics of Nuclear Burning Historically, the study of nuclear reactions has been based on acceleration of particles and study of their scattering off a target. In a burning plasma, one must also account for the effects of the more complex environment. Instead of bare nuclei, the “projectile” and the “target” have an associated cloud of electrons, and there are other ions and their electrons around. A short term for these additional effects is “screening.” At present, a debate rages over the question of whether plasma screening of reacting nuclei is static or dynamic. As plasmas so often exhibit subtle behavior, even sophisticated physical models can be misleading. In the Sun, the plasma screening only affects the reaction rate at the level of a few percent. However, in progenitors of supernovae, the screening factors are large (a few million), which makes a purely theoretical estimate dubious. A better theory would result from experimental tests, making the necessary extrapolation to more extreme conditions more reliable. Detailed laboratory measurements could settle these important issues. HED experiments promise to allow the study of a nuclear-burning plasma, that is, the source of stellar energy. Accelerator experiments have provided means to study nuclear reactions in a piecemeal way; HED experiments will allow us to place the phenomena into the context of a burning plasma. In estimating the rate of stellar nuclear reactions, some assumptions about the plasma medium must be made; HED experiments will allow these to be tested directly. As Figure 1.1 shows, the experimentally accessible range already overlaps stellar conditions of temperature and density. Well over 99 percent of the stars in the sky are burning hydrogen and/or helium, and there conditions are mostly in the range that is now available to OMEGA and will be available to NIF. Stellar burning is slow because the basic fusion reactions that the stars use are slow. Experiments with burning plasmas that are based on faster reactions are feasible—in fact, that is one way of expressing the goal of thermonuclear ignition for NIF. Burning plasma experiments will allow us to study the same process, if not the identical reactions, that powers the stars.
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The Nature of Matter at the Extremes The quark-gluon plasma is a new phase of matter—in the sense that it has not yet been detected in the laboratory—whose elementary constituents are the quarks, antiquarks, and gluons that make up the strongly interacting particles. It is also the oldest phase of matter, the form of matter that filled up the early universe, until the first few microseconds after the big bang. Appropriate for this report, quark-gluon plasmas are the densest plasmas in the universe. They may possibly be present deep in the cores of neutron stars, and may even be made in stellar collapse. To probe the densest states of nuclear matter, the nuclear physics community has embarked on a large-scale program of studying collisions of ultrarelativistic heavy ions, at Brookhaven National Laboratory and the European Organization for Nuclear Research (CERN). A major step in the program is the construction of a large colliding beam accelerator at Brookhaven—the Department of Energy’s Relativistic Heavy Ion Collider (RHIC)—which will provide the capability of colliding nuclei as heavy as gold on gold at 100 GeV per nucleon in the center of mass (equivalent to 20 teraelectronvolts [TeV] per nucleon in a fixed target experiment), and should, early in this century, enable one to produce and study quark-gluon plasmas in the laboratory. The basis for expecting a quark-gluon plasma at high densities or temperatures is that quite generally as matter is heated or compressed, its degrees of freedom change from composite to more fundamental. For example, by heating or compressing a gas of atoms, one eventually forms a plasma in which the nuclei become stripped of the electrons, which go into continuum states forming an electron gas. Similarly, when nuclei are squeezed (as happens in the formation of neutron stars in supernovae where the matter is compressed by gravitational collapse), they merge into a continuous fluid of neutrons and protons. Nucleons and the other strongly interacting particles, or hadrons, are made of quarks that are confined to the individual hadrons. One can thus go a step farther and predict that a gas of nucleons, when squeezed or heated, turns into a gas of uniform quark matter, composed of freely roaming quarks, and at a finite temperature, antiquarks and gluons—the mediators of the strong interaction. The physics is basically the same as that leading to the formation of ordinary plasmas. The regions in the phase diagram of matter in the temperature-baryon density plane where quark-gluon plasmas are expected to occur are outside the phase space included in Figure 1.1 in Chapter 1. In the low-temperature-low-baryon-density region, the basic degrees of freedom are hadronic, those of nucleons, mesons, and internally excited states of the nucleon, while in the high-temperature-high-baryon-density regions (temperatures above about 200 MeV, equivalent to a few times 1012 K, and densities of order 5 to 10 times the density of matter inside a large nucleus, approximately 0.16 particles per cubic femtometer [fm−3], equivalent to
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observations. To get reasonable efficiencies, the accelerated-electron-to-total-energy ratio εe~1 must not be far below unity, while the magnetic-to-total-energy ratio εb~<1 depends on whether the synchrotron or the inverse Compton spectral peak represents the observed MeV spectral break. The radiative efficiency and the electron power law minimum Lorentz factor also depends on the fraction ζ<1 of swept-up electrons injected into the acceleration process. While many afterglow-snapshot or multiepoch fits can be done with time-independent values of the shock parameters εb, εe, p, in some cases the fits indicate that the shock physics may be a function of the shock strength. For instance, p, εb, εe or the electron injection fraction ζ may change in time. While these are, in a sense, time-averaged shock properties, specifically time-dependent effects would be expected to affect the electron energy distribution and photon spectral slopes, leading to time-integrated observed spectra that could differ from those in the simple time-averaged picture. The back-reaction of protons accelerated in the same shocks and magnetic fields may also be important, as in supernova remnants. Turbulence may be important for the electron-proton energy exchange, while reactions leading to neutrons and vice versa can influence the escaping proton spectrum. The same shocks responsible for accelerating the electrons can accelerate protons up to energies of order 1020 eV, comparable to the highest-energy cosmic rays measured with the Fly’s Eye and AGASA arrays. New experiments under construction, such as the Pierre Auger Observatory array, will provide much stronger constraints on whether GRBs are associated with such events. Relativistic protons can lead also to neutrinos with energies εv≥1014 eV via interactions with the ≈MeV gamma rays, and with energies εv≥1018 eV via interactions with ultraviolet photons. Protons accelerated in internal shocks in the buried jet while it advances through the star interact with thermal x rays to produce teraelectronvolt neutrinos, for which the detection probability is maximized in cubic kilometer Cherenkov detectors such as ICECUBE or ANTARES. In the laboratory, the most promising means for accessing these relativistic plasma dynamics and flows are with experiments done on ultraintense, short-pulse lasers (see Figure 2.7). Experiments on such lasers have reached intensities of ≈1020 W cm−2 and have yielded many fascinating results. Jets of protons with energies of tens of MeV have been created in a very well collimated “beam.” Also, less-collimated directional outflows of electrons and positrons with energies of up to 100 MeV have been generated. In terms of an effective temperature, the high-energy electrons have a “slope parameter” of 1 to 10 MeV, making these plasmas thermally relativistic, with Te>mec2, corresponding to a “laboratory microfireball.” Similar temperatures are inferred from a fireball analysis of gamma-ray bursts. Another intriguing observation in these ultraintense laser experiments was the generation of ultrastrong magnetic fields. Strong magnetic-field generation (>100 MG=104 T) has
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FIGURE 2.7 A combination of theory, simulation, and laboratory experiments is expected to yield new insights into the physics of gamma-ray bursts (GRB). (a) An example of a current model for gamma-ray bursts; (b) an example of a proposed laboratory experiment exploring aspects of the astrophysical model. SOURCES: Images (a) courtesy of S.Woosley, University of California Observatories/Lick Observatory; and (b) courtesy of S.C.Wilks, Lawrence Livermore National Laboratory.
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been experimentally observed on such ultraintense laser experiments, with simulations predicting fields of up to 1 GG (105 T) or more. Such extreme conditions, albeit over small volumes and exceedingly short times, may overlap with aspects of the relativistic fireball dynamics thought to occur in gamma-ray bursts. Pair Plasmas: Pair Creation in Magnetospheres and in the Laboratory The development of petawatt-class lasers opens the door to the study of relativistic and e+e− plasmas in the laboratory. It is well known that lasers with intensities exceeding ≈2×1018 W cm−2 couple most of their energy to superthermal electrons with temperature kT>mc2, where m is the electron rest mass. Pairs can then be created when the relativistic electrons interact with high-Z target ions via the trident and Bethe-Heitler processes. Using particle-in-cell (PIC) simulations, the pair production rate for a thin (few micrometers) gold foil has been estimated, with the conclusion that petawatt lasers with sufficient duration can in principle achieve in situ pair densities as high as ~10−3 of the background electron density, or approximately 1022 cm−3 for solid gold. Detailed numerical simulations have confirmed this result and have further shown that for a thick gold foil (>20 µm), the positron yield may be even higher. Subsequent experiments conducted at Lawrence Livermore National Laboratory using a single petawatt laser hitting 250-µm gold foils showed that the positron yield may be higher than even the theoretical estimates cited above. This demonstrates that petawatt lasers are indeed capable of producing copious pairs and has led to a proposal to use double-sided illumination to partially confine the pairs and to create multiple generations of pairs via reacceleration. PIC simulations show that, after the lasers are turned off, the pairs will expand much faster than the heavier gold ions. Hence a miniature fireball of relativistically expanding pure pairs can be created. This pair fireball can be made to collide with another pair fireball to mimic the internal shock model of gamma-ray bursts, allowing us to study how the expansion energy of pair fireballs can be converted into internal energy and gamma rays. Introduction of external equipartition magnetic fields (≈10 T) may be useful in creating collisionless shocks in such plasmas. Another exotic future application is to study the static pair-balanced plasmas theorized to be the source of the episodic annihilation line flares from black-hole candidates. Two megajoule-class 0.1-petawatt lasers of 10-ns pulse duration, illuminating a gold target on both sides, could in principle create pair densities hundreds of times higher than the background electron density. Such steady-state pair plasmas can then be used to test the BKZS (Bisnovatyi-Kogan, Zel’dovich, Sunyaev) limit of kT≈20 mc2.
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Radiative Blast Waves When a blast wave sweeps up a high-density medium, the optically thin radiative cooling time at the shock front may become shorter than the dynamical time. Such radiative blast waves are expected to occur in the late phase of supernova remnants, gamma-ray burst afterglows, and even young supernova remnants in dense molecular clouds. Such radiative blast waves exhibit over stable radial oscillations when the cooling rate increases sufficiently slowly with temperature. Also the cooled dense shells eventually become unstable against the nonradial thin-shell instability. Numerical simulations in the past two decades consistently found that such thin-shell radiative blast waves in a solar-abundance interstellar medium expand as a power law in time, with an expansion index n (=d ln R/d ln t)≈1/3, significantly below the adiabatic Sedov-Taylor limit of 2/5, but higher than the pressure-driven snowplow limit of 2/7. Hence, radiative blast waves remain a major challenge in astrophysics because they couple the complex plasma radiation processes with hydrodynamics. To simulate radiative blast waves in the laboratory, we need to generate highly radiative yet optically thin shocked gas. Laser experiments with xenon gas first demonstrated that radiative blast waves can indeed be created in the laboratory. Recent experiments using the short-pulse Falcon laser at Lawrence Livermore National Laboratory heating Xe gas jets have allowed probing the detailed physics of radiative blast waves, albeit in a cylindrical, rather than spherical, geometry. The key to such experiments lies in the fact that Xe gas with temperatures around tens to hundreds of electronvolts is highly radiative, yet optically thin for typical laboratory dimensions. The Falcon experiments confirm that Xe radiative blast waves expand as a power law in time, with an index intermediate between the Sedov-Taylor and pressure-driven snowplow limits. It has been proposed that the n≈1/3 numerical simulation results and the Xe data are consistent with the theory that the radiative blast waves with temperatures below the cooling peak only radiate away the thermal component of the postshock energy. This hypothesis remains to be confirmed by further experiments and by numerical simulations with gases of different adiabatic indices. Radiative blast waves with radiatively preheated upstream gas and radiative blast waves with magnetic fields are also being investigated analytically and numerically. They will be priorities for future experiments. Radiatively Driven Molecular Clouds Cold dense molecular clouds illuminated by bright, young, nearby massive stars serve as the stellar incubators of the universe. The intense stellar radiation incident on the cloud creates a high-pressure source at the surface by photoevaporation
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(ablation), augmented by the ram pressure from the stellar wind. The result is that the cloud is shock compressed, and subsequently accelerated, as the star clears away the cloud out of which it was born. Well-known examples of such systems are the Eagle Nebula, the Horsehead Nebula, the Rosette Nebula, and NGC 3603. Interest in dense molecular clouds in the vicinity of bright young stars is due in part to the hypothesis that these clouds serve as “cosmic nurseries,” harboring and nurturing regions of active star formation. The Eagle Nebula is intriguing because of its famous columns, the so-called pillars of creation. These “elephant trunk” structures may arise as a result of hydrodynamic instabilities such as the Rayleigh-Taylor instability acting at the photoevaporation front, as first suggested 50 years ago. An alternative explanation, the so-called cometary tail model, attributes the columns to the flow of photoevaporated plasma from and around preexisting dense clumps of matter embedded in the molecular cloud, much like the dynamics that lead to the plasma tail of a comet. Detailed information about the physical conditions in the hot ionized flow and in the cold gaseous cloud interior of the Eagle Nebula has recently been obtained, using both the Hubble Space Telescope and the ground-based millimeter-wavelength BIMA (Berkeley Illinois Maryland Association Array) interferometer array. In particular, hydrodynamic velocities as a function of position inside the cold gas have been determined by recent observations, allowing models of the dynamics of the columns to be tested. The key questions to be answered include these: Are the column shapes seen in the Eagle Nebula and other driven molecular clouds due to hydrodynamic instabilities? Do the radiative shocks launched into the molecular clouds trigger star formation? Do the shapes of these driven molecular clouds record the history of the star turn-on phase? Experimentally, aspects of the dynamics of radiatively driven molecular clouds, and therefore aspects of these questions, can be tested in the laboratory. Using the radiation emitted from tiny radiation cavity “point sources” on large lasers and pulsed-power facilities, it appears possible to reproduce the dominant photoevaporation-front hydrodynamics of radiatively driven molecular clouds. Off-setting and collimating the source of Planckian radiation from the simulant cloud (foam foil) mean that the incoming “drive” photons would be sufficiently directional (quasi-parallel) to reproduce the dominant features of radiatively driven molecular clouds. In particular, new modes of radiative-hydrodynamic instability may arise owing to the directionality of the incident photons, an effect that could in principle
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be reproduced and observed on HED experiments. Also, the strong shock launched into the dense molecular cloud is likely to encounter density inhomogeneities, triggering localized regions of shock-induced turbulent hydrodynamics. Such hydrodynamics can also be reproduced in scaled strong-shock experiments on lasers and Z-pinch facilities. The shock launched into the dense molecular cloud is thought to be radiative. Progress on producing radiative shocks in the laboratory has also been demonstrated on several facilities. A magnetic field embedded in the cloud may be a key component to the dynamics, adding “stiffness” to the compressibility of the cloud. Strong-shock MHD experiments may also be possible on lasers and pulsed-power facilities. The possibility of forming an integrated program of theory, modeling, testbed laboratory experiments, and astronomical observations would be very beneficial, and several groups are moving in that direction. High-Density Plasma in Strong Magnetic Fields and the Study of Surface Emission from Isolated Neutron Stars Background The study of thermal radiation from isolated neutron stars can provide important information on the interior physics, magnetic fields, surface composition, and other properties of neutron stars. Such study has been a long-term goal of neutron star physics/astrophysics since early theoretical works indicated that neutron stars should remain detectable as soft x-ray sources for approximately 105 to 106 years after their birth. The past 35 years have seen significant progress in our understanding of various physical processes responsible for the thermal evolution of neutron stars. The advent of imaging x-ray telescopes in recent years has made it possible to observe isolated neutron stars directly by their surface emission. For example, the ROSAT X-ray Observatory has detected pulsed x-ray emission from about 30 rotation-powered radio pulsars, and some of these clearly show a thermal component in their spectra, indicating emission from the neutron star surface. Several radio-quiet, isolated neutron stars have also been detected in the x-ray and optical bands, and have thermal spectra arising from the neutron star atmosphere. Finally, in the past few years, soft gamma-ray repeaters and anomalous x-ray pulsars have emerged as a possibly new class of neutron stars (“magnetars”) endowed with superstrong magnetic fields, B>1014 G (>109 T). According to the magnetar model, the x-ray luminosity from anomalous x-ray pulsars and the quiescent x-ray emission from soft gamma-ray repeaters are powered by the decay of a superstrong magnetic field. Thermal radiation has already been detected (e.g., by ASCA and Chandra) in several anomalous x-ray pulsars and soft gamma-ray repeaters; fits to the spectra with blackbody or with crude atmosphere models indicate that the thermal x rays can be attributed to magnetar surface emission. Clearly, detailed observational and
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theoretical studies of thermal emission can potentially reveal much about the physical conditions and the true nature of magnetars. The new generation of x-ray telescopes (e.g., Chandra and XMM-Newton currently in orbit, and Constellation-X in the future) are bringing great promise to the study of isolated neutron stars (including radio pulsars, radio-quiet neutron stars, and magnetars). The greatly improved sensitivity and spectral/angular resolution in the x-ray band will lead to detailed spectroscopy (and continuum observation) of neutron star surfaces. In order to interpret the future observations properly, it is crucial to have a detailed understanding of the physical properties of the dense (partially ionized) plasma in the outer layers of neutron stars in the presence of intense magnetic fields (B≈1011 to 1016 G), and to calculate the emergent thermal radiation spectra from the neutron star surfaces. This radiation is determined by the physical properties of the surface layers, but the surface composition of the neutron star is unknown. The atmosphere could consist of iron-peak elements formed at the neutron star birth, or it could be composed of light elements such as H and He due to accretion and fallback. The immense gravity of the neutron star makes the atmosphere very thin (0.1 to 10 cm) and dense (0.1 to 100 g cm−3), so that the atmospheric matter is highly nonideal, with interactions between particles nonnegligible. If the surface temperature is not too high, light atoms, molecules, and metal grains or droplets may form in the envelope; if the magnetic field is sufficiently strong, the envelope may transform into a condensed phase with very little gas above it. A superstrong magnetic field will also make quantum electrodynamic effects (e.g., vacuum polarization) important in calculating the surface radiation spectrum. All of these problems present significant challenges to the theoretical astrophysics and dense plasma physics communities. The following subsections provide a few more detailed examples of the kinds of new physics problems that one confronts when studying these extreme objects. Microscopic Calculations of Atoms, Molecules, and Dense Matter in Strong Magnetic Fields It is well known that a strong magnetic field can dramatically change the properties of atoms, molecules, and condensed matter. For B≫B0=me2e3c/ℏ3=2.351×109 G, the cyclotron energy of the electron, ℏ ωc=ℏ (eB/mec)=11.58 B12 keV [where B12=B/1012 G], is much larger than the coulomb energy. Thus, the coulomb forces act as a perturbation to the magnetic forces on the electrons, and at typical temperatures of isolated neutron stars, the electrons settle into the ground Landau level. Because of the extreme confinement of electrons in the transverse direction, the atom attains a cylindrical shape and a large binding energy. Moreover, it is possible for these elongated atoms to form molecular chains by covalent bonding along the field direction. Interactions between the linear chains can then lead to the formation of three-dimensional condensate. Much work remains to be done to understand the
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electronic structure of various forms of matter in strong magnetic fields. In particular, the atomic structure of heavy atoms has only been studied for a limited range of field strengths, the excitation energies of molecules (and chains) have only been considered qualitatively, and the cohesive properties of three-dimensional condensed matter are only understood in certain limiting field regimes. Equation of State and Opacities of Dense Plasma in Strong Magnetic Fields A crucial ingredient in modeling neutron star atmospheres and surfaces is the equation of state (including the ionization-recombination equilibrium) of dense plasma in strong magnetic fields. Besides the usual difficulties associated with strong coulomb interactions in dense, zero-field plasmas, there are additional subtleties related to the nontrivial coupling between the center-of-mass motion and the internal structure of atoms and molecules. So far, only very crude models for the equation of state of dense plasma in strong magnetic fields have been constructed. To apply to neutron star atmospheres, various atomic and molecular opacities must be estimated or calculated. For sufficiently high magnetic fields and low temperatures (but still realistic for neutron stars), the condensed phase is more stable than the atoms and molecules, and there is a first-order phase transition from the nondegenerate gas to the macroscopic condensed state. With increasing field strength and decreasing temperature, the saturation vapor density and pressure of the condensate are expected to decrease, and eventually the optical depth of the vapor becomes less than unity. Therefore, thermal radiation can directly emerge from the nearly degenerate condensed metallic liquid. So far these issues have only been studied using very crude approximations. Radiative Transfer in Strong Magnetic Fields Recent study of radiative transfer in strong magnetic fields has focused on transport of photon modes in ionized plasma. Incorporating neutral species self-consistently in the atmosphere models is an important challenge for the future. Even for ionized models (valid for sufficiently high temperatures, T>a few×106 K), several important issues related to the superstrong field regime (B>1014 G) remain to be studied. One of these concerns the effect of ion cyclotron resonance at photon energy 0.63(Z/A)B14 keV, where B14≡B/1014 G, and Z and A are the charge and mass numbers of the ion, respectively. Another concerns the effect of vacuum polarization. Polarization of the vacuum due to virtual e+e− pairs becomes important when B>BQ=me2c3/eℏ=4.414×1013 G. Vacuum polarization modifies the dielectric property of the medium and the polarization of photon modes, thereby altering the radiative opacities. Of particular interest is the “vacuum resonance” phenomenon, which occurs when the effects of vacuum and plasma on the linear polarization of the modes cancel each other, giving rise to a “resonant” feature in the absorption and scattering opacities. The
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vacuum resonance is located at photon energy EV(ρ)≈1.0(Yeρ)1/2B14−1f(B) keV, where ρ is the density (in g cm−3), Ye=Z/A is the electron fraction, and f(B) is a slowly varying function of B [f(B)≈1 for B<BQ, and ranges from 1 to a few for B≈1014 to 1016 G]. Because EV depends on density (which spans a wide range in the atmosphere), proper treatment of this vacuum resonance feature presents a significant challenge for the atmosphere modeling. Another related effect is the resonant mode conversion: a photon propagating down the density gradient in the atmosphere can change its mode characteristics (e.g., an extraordinary mode photon gets converted to ordinary mode) at the density where vacuum resonance occurs; such mode conversion is particularly effective for photons with energies greater than a few kiloelectronvolts. Since the two modes have very different opacities in strong magnetic fields, mode conversion can have a significant effect on the radiative transport and the emergent spectra from the magnetar atmosphere. Plasma physics with ultrahigh magnetic-field strengths becomes particularly interesting at B>B0=me2e3c/ℏ3~109 G. At these field strengths, the orbitals of bound electrons become strongly perturbed by the applied magnetic field, that is, (ℏωc)/Eb≥1, where ℏωc is the energy of the electron at the cyclotron frequency due to the magnetic field, and Eb is the electron coulomb binding energy. The details of plasma emission and absorption spectra will be significantly affected, which could be relevant to emission spectra from neutron star atmospheres. With the new genre of ultraintense, short-pulse lasers, magnetic-field strengths in plasmas of order ~109 G have already been demonstrated, with the promise of higher field strengths on future facilities. If such fields could be sufficiently well understood and controlled, it might become feasible to measure emission spectral modifications due to such strong fields. THE ROLE OF COMPUTING IN HIGH ENERGY DENSITY ASTROPHYSICS An essential aspect of numerical modeling in the context of HED astrophysics is that the range of spatial and temporal scale that typically needs to be spanned far exceeds what can be plausibly computed. Another way of looking at this difficulty is that the dimensionless control parameters characterizing astrophysical systems (e.g., Reynolds number, Rayleigh number, and so on) are typically much larger than what can be simulated on existing (or even imagined) computing platforms. In this sense, computing plays a very different role in HED astrophysics than in HED laboratory physics. HED astrophysics computing is used for the following purposes: To develop models for spatially or temporally unresolved physics. Astrophysics-focused simulations invariably use subgrid models in order to describe
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processes not captured by the simulations themselves; common examples of such modeling include the insertion of turbulent viscosity and (in the case of collisionless plasmas) magnetic diffusivity. An important role for joint laboratory and simulation studies is the validation of such (astrophysical) subgrid models. To validate ideas about physical processes thought to take place in an astrophysical context, but which can be explored under less restrictive conditions. In many instances, physical processes arising under astrophysical conditions have counterparts under laboratory conditions—mixing instabilities such as Rayleigh-Taylor exemplify such processes. In such cases, laboratory experiments can be used to validate astrophysics simulation codes; this is a necessary condition for ensuring that such simulations properly describe the astrophysical situation (albeit not a sufficient condition). To explore and develop intuition for highly nonlinear physical processes. The challenging problems in astrophysics are largely related to processes that operate in a fully nonlinear regime. In this regime, reasoning based on the behavior of systems in the linear regime usually proves to be very inadequate, but our physical intuitions are generally based on linear theory. For this reason, there is a broad need to inform practitioners about the complexity of possible behaviors in the nonlinear limit; the numerical exploration of the fully nonlinear development of magnetic dynamos is an excellent example of this type of study. The preceding discussion makes clear that the size (both in memory requirements and computation time) and complexity (in the level of detail of the physics description) of HED astrophysics-oriented simulations are typically set primarily by what is possible: computational HED astrophysicists are rarely heard to say, “We do not need more memory size or computation time.” Thus, computational HED astrophysics drives some of the largest simulations that are typically attempted on leading-edge computing platforms. By the same token, computational HED astrophysics has a profound need for access to state-of-the-art computational resources— thus, it is widely believed that major advances in problems such as Type Ia and Type II (core collapse) supernovae will relate to advances in high-end computational capabilities. For example, it is now possible to do two-dimensional hydrodynamic simulations of Type II supernovae, with nuclear reactions and neutrino transport, on a modern personal computer; it will take days to weeks. But full three-dimensional simulations with good resolution are necessary in order to see the development of low-order modes of instability and at the same time to resolve the boundary between the collapsed core and the ejecta. An obvious estimate of the additional computational resources needed is scaling according to the number of zones needed for the
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new third dimension: roughly 500 to 1,000 personal computers. This translates to at least days or weeks of dedicated time on an ASCI-level parallel system. The Type Ia supernova problem seems to be worse. In addition to demands such as those just mentioned, at least two other issues arise: subgrid models for burning, and grid distortion in the strongly differentially rotating system of a binary merger. These crucial roles played by computations in HED astrophysics have been recognized by the Department of Energy (DOE) and strongly supported within the DOE National Nuclear Security Administration’s ASCI Alliances program and the DOE Office of Science’s Science Discovery through Advanced Computing (SciDAC) program. CONCLUSIONS In summary, there is a wide variety of areas in which theory, numerical simulations, and experiments on HED facilities can address aspects of astrophysical phenomena. Areas of promising overlap include the physics of supernova explosions and supernova remnant evolution, high-Mach-number astrophysical jets, planetary interiors, photoevaporation-front hydrodynamics of molecular clouds, photoionized plasmas around accreting black holes, and relativistic plasmas in gamma-ray burster fireballs. This selection of topics may well be just the “tip of the iceberg” as more experience is obtained in carrying out both large-scale numerical simulations and scaled HED experiments in support of astrophysics.
Representative terms from entire chapter: