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Alan P. Lightman

Bio: Alan P. Lightman is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Compton scattering & Gravitation. The author has an hindex of 33, co-authored 88 publications receiving 8392 citations. Previous affiliations of Alan P. Lightman include Harvard University & Princeton University.


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Book
01 Jan 1979
TL;DR: Inverse square law for a uniformly bright sphere as discussed by the authors is used to define specific intensity and its moments, which is defined as the specific intensity or brightness of a sphere in terms of specific intensity.
Abstract: Chapter 1 Fundamentals of Radiative Transfer 1.1 The Electromagnetic Spectrum Elementary Properties of Radiation 1.2 Radiative Flux Macroscopic Description of the Propagation of Radiation Flux from an Isotropic Source-The Inverse Square Law 1.3 The Specific Intensity and Its Moments Definition of Specific Intensity or Brightness Net Flux and Momentum Flux Radiative Energy Density Radiation Pressure in an Enclosure Containing an Isotropic Radiation Field Constancy of Specific Intensity Along Rays in Free Space Proof of the Inverse Square Law for a Uniformly Bright Sphere 1.4 Radiative Transfer Emission Absorption The Radiative Transfer Equation Optical Depth and Source Function Mean Free Path Radiation Force 1.5 Thermal Radiation Blackbody Radiation Kirchhoff's Law for Thermal Emission Thermodynamics of Blackbody Radiation The Planck Spectrum Properties of the Planck Law Characteristic Temperatures Related to Planck Spectrum 1.6 The Einstein Coefficients Definition of Coefficients Relations between Einstein Coefficients Absorption and Emission Coefficients in Terms of Einstein Coefficients 1.7 Scattering Effects Random Walks Pure Scattering Combined Scattering and Absorption 1.8 Radiative Diffusion The Rosseland Approximation The Eddington Approximation Two-Stream Approximation Problems References Chapter 2 Basic Theory of Radiation Fields 2.1 Review of Maxwell's Equations 2.2 Plane Electromagnetic Waves 2.3 The Radiation Spectrum 2.4 Polarization and Stokes Parameters 62 Monochromatic Waves Quasi-monochromatic Waves 2.5 Electromagnetic Potentials 2.6 Applicability of Transfer Theory and the Geometrical Optics Limit Problems References Chapter 3 Radiation from Moving Charges 3.1 Retarded Potentials of Single Moving Charges: The Lienard-Wiechart Potentials 3.2 The Velocity and Radiation Fields 3.3 Radiation from Nonrelativistic Systems of Particles Larmor's Formula The Dipole Approximation The General Multipole Expansion 3.4 Thomson Scattering (Electron Scattering) 3.5 Radiation Reaction 3.6 Radiation from Harmonically Bound Particles Undriven Harmonically Bound Particles Driven Harmonically Bound Particles Problems Reference Chapter 4 Relativistic Covariance and Kinematics 4.1 Review of Lorentz Transformations 4.2 Four-Vectors 4.3 Tensor Analysis 4.4 Covariance of Electromagnetic Phenomena 4.5 A Physical Understanding of Field Transformations 129 4.6 Fields of a Uniformly Moving Charge 4.7 Relativistic Mechanics and the Lorentz Four-Force 4.8 Emission from Relativistic Particles Total Emission Angular Distribution of Emitted and Received Power 4.9 Invariant Phase Volumes and Specific Intensity Problems References Chapter 5 Bremsstrahlung 5.1 Emission from Single-Speed Electrons 5.2 Thermal Bremsstrahlung Emission 5.3 Thermal Bremsstrahlung (Free-Free) Absorption 5.4 Relativistic Bremsstrahlung Problems References Chapter 6 Synchrotron Radiation 6.1 Total Emitted Power 6.2 Spectrum of Synchrotron Radiation: A Qualitative Discussion 6.3 Spectral Index for Power-Law Electron Distribution 6.4 Spectrum and Polarization of Synchrotron Radiation: A Detailed Discussion 6.5 Polarization of Synchrotron Radiation 6.6 Transition from Cyclotron to Synchrotron Emission 6.7 Distinction between Received and Emitted Power 6.8 Synchrotron Self-Absorption 6.9 The Impossibility of a Synchrotron Maser in Vacuum Problems References Chapter 7 Compton Scattering 7.1 Cross Section and Energy Transfer for the Fundamental Process Scattering from Electrons at Rest Scattering from Electrons in Motion: Energy Transfer 7.2 Inverse Compton Power for Single Scattering 7.3 Inverse Compton Spectra for Single Scattering 7.4 Energy Transfer for Repeated Scatterings in a Finite, Thermal Medium: The Compton Y Parameter 7.5 Inverse Compton Spectra and Power for Repeated Scatterings by Relativistic Electrons of Small Optical Depth 7.6 Repeated Scatterings by Nonrelativistic Electrons: The Kompaneets Equation 7.7 Spectral Regimes for Repeated Scattering by Nonrelativistic Electrons Modified Blackbody Spectra y"1 Wien Spectra y"1 Unsaturated Comptonization with Soft Photon Input Problems References Chapter 8 Plasma Effects 8.1 Dispersion in Cold, Isotropic Plasma The Plasma Frequency Group and Phase Velocity and the Index of Refraction 8.2 Propagation Along a Magnetic Field Faraday Rotation 8.3 Plasma Effects in High-Energy Emission Processes Cherenkov Radiation Razin Effect Problems References Chapter 9 Atomic Structure 9.1 A Review of the Schrodinger Equation 9.2 One Electron in a Central Field Wave Functions Spin 9.3 Many-Electron Systems Statistics: The Pauli Principle Hartree-Fock Approximation: Configurations The Electrostatic Interaction LS Coupling and Terms 9.4 Perturbations, Level Splittings, and Term Diagrams Equivalent and Nonequivalent Electrons and Their Spectroscopic Terms Parity Spin-Orbit Coupling Zeeman Effect Role of the Nucleus Hyperfine Structure 9.5 Thermal Distribution of Energy Levels and Ionization Thermal Equilibrium: Boltzmann Population of Levels The Saha Equation Problems References Chapter 10 Radiative Transitions 10.1 Semi-Classical Theory of Radiative Transitions The Electromagnetic Hamiltonian The Transition Probability 10.2 The Dipole Approximation 10.3 Einstein Coefficients and Oscillator Strengths 10.4 Selection Rules 10.5 Transition Rates Bound-Bound Transitions for Hydrogen Bound-Free Transitions (Continuous Absorption) for Hydrogen Radiative Recombination - Milne Relations The Role of Coupling Schemes in the Determination of f Values 10.6 Line Broadening Mechanisms Doppler Broadening Natural Broadening Collisional Broadening Combined Doppler and Lorentz Profiles Problems References Chapter 11 Molecular Structure 11.1 The Born-Oppenheimer Approximation: An Order of Magnitude Estimate of Energy Levels 11.2 Electronic Binding of Nuclei The H2+ Ion The H2 Molecule 11.3 Pure Rotation Spectra Energy Levels Selection Rules and Emission Frequencies 11.4 Rotation-Vibration Spectra Energy Levels and the Morse Potential Selection Rules and Emission Frequencies 11.5 Electronic-Rotational-Vibrational Spectra Energy Levels Selection Rules and Emission Frequencies Problems References Solutions Index

3,243 citations

Journal ArticleDOI
TL;DR: In this paper, a model for Cygnus X-1, involving an accretion disk around a black hole, is presented, which can explain the observed X-ray spectrum from 8 to 500 keV.
Abstract: We present a model for Cygnus X-1, involving an accretion disk around a black hole, which can explain the observed X-ray spectrum from 8 to 500 keV. In particular we construct a detailed model of the structure of an accretion disk whose inner region is considerably hotter and geometrically thicker than previous disk models. The inner region of the disk is optically thin to absorption, is gas-pressure dominated, and yields, from first principles, electron temperatures of 10/sup 9/ K and ion temperatures 3--300 times hotter. The spectrum above 8 keV is produced by inverse Compton scattering of soft X-ray photons in the two-temperature inner region of the disk. This spectrum is computed by numerical integration of the Kompane'ets equation, modified to account for escape of photons from a region of finite (order unity) electron scattering optical depth. (AIP)

819 citations

Journal ArticleDOI
TL;DR: In this paper, a broad hump between about 10 keV and about 300 keV was predicted for the X-ray spectrum of active galactic nuclei (AGNs), and the predicted amplitude of the hump is about 0.1-0.5.
Abstract: Recent observations and interpretations of the strong UV emission from active galactic nuclei (AGNs) suggest that relatively cold, thermal matter coexists with the hot, X-ray-emitting matter near the centers of these objects. A fraction of the X-rays will be reprocessed by the cold material, and the composite X-ray spectrum should help diagnose the conditions of this material and its energy source. In a variety of situations, reprocessing of the X-rays should lead to a composite X-ray spectrum with a broad hump between about 10 keV and about 300 keV. The lower limit of this energy range is determined by atomic absorption and the upper limit by electron scattering in the cold material. Where available, observed spectra are consistent with such a broad hump; however, the predicted amplitude of the hump is about 0.1-0.5, and observations with smaller error bars are clearly needed. 30 references.

419 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the steady state distribution and consumption rate of stars orbiting a massive object at the center of a spherical, N-body stellar system and employed an approximate, analytic analysis of the two-dimensional Fokker-Planck equation describing diffusion in energy E and angular momentum J. The distribution of stars is determined by the consumption of low angular momentum stars which pass within a small distance r/sub t/ of the central mass M and by the relaxation processes associated with gravitational stellar encounters.
Abstract: We consider the steady-state distribution and consumption rate of stars orbiting a massive object at the center of a spherical, N-body stellar system. The distribution of stars is determined by the consumption of low angular momentum stars which pass within a small distance r/sub t/ of the central mass M and by the relaxation processes associated with gravitational stellar encounters. Our method employs an approximate, analytic analysis of the two-dimensional Fokker--Planck equation describing diffusion in energy E and angular momentum J. The basic results are the following: (1) Consumption of low angular momentum stars which have entered the ''loss-cone'' J > greater than or equal to r/sub t/, at which the root mean square angular momentum transferred to a star via stellar encounters in one orbital period equals J/sub min/. (2) The total consumption rate of stars by M is roughly the number of stars inside r/sub crit/ divided by the relaxation time at r/sub crit/. (3) A self-consistent solution can be found in which the distribution of stars is almost isotropic for high-J stars and varies only more » logarithmically with J for low-J stars. (4) The density of core stars has the following form: n(r) approx. =n (r/sub a/)(1+(r/sub a//r)/sup l/), wher the accretion radius r/sub a/ approx. GM/ >> r/sub t/, is the mean-squared velocity dispersion in the core outside r/sub a/, and l decreases slowly from approx. 1.75 at >> r/sub crit/ to approx. 1.60 at r approx. 10r/sub t/. Neglect of loss-cone effects gives a consumption rate too small by roughly the ratio r/sub t//r/sub crit/ and a constant exponent l = 1.75 for >> r/sub t/. These results are applied to massive black holes at the centers of globular clusters and galactic nuclei. (AIP) « less

351 citations


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TL;DR: A review of dark energy can be found in this paper, where the authors present the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.
Abstract: Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, \ensuremath{\Lambda}; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evolving dark-energy density approaching its natural value, zero, and small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a millielectron volt associated with a constant \ensuremath{\Lambda}. Dark energy may have been detected by recent cosmological tests. These tests make a good scientific case for the context, in the relativistic Friedmann-Lema\^{\i}tre model, in which the gravitational inverse-square law is applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one-quarter of the critical Einstein--de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-energy density; a positive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.

4,783 citations

Journal ArticleDOI
TL;DR: The current status of particle dark matter, including experimental evidence and theoretical motivations, including direct and indirect detection techniques, is discussed in this paper. But the authors focus on neutralinos in models of supersymmetry and Kaluza-Klein dark matter in universal extra dimensions.

4,614 citations

Journal ArticleDOI
TL;DR: A comprehensive survey of recent work on modified theories of gravity and their cosmological consequences can be found in this article, where the authors provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a selfcontained, comprehensive and up-to-date introduction to the subject as a whole.

3,674 citations

Journal ArticleDOI
TL;DR: Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging.
Abstract: The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

3,394 citations

Journal ArticleDOI
TL;DR: In this article, the authors describe radio-loud active galactic nuclei (AGN) and summarize the evidence for anisotropic emission, and outline the two most plausible unified schemes.
Abstract: The appearance of active galactic nuclei (AGN) depends so strongly on orientation that our current classification schemes are dominated by random pointing directions instead of more interesting physical properties. Light from the centers of many AGN is obscured by optically thick circumnuclear matter and in radio-loud AGN, bipolar jets emanating from the nucleus emit light that is relativistically beamed along the jet axes. Understanding the origin and magnitude of radiation anisotropies in AGN allows us to unify different classes of AGN; that is, to identify each single, underlying AGN type that gives rise to different classes through different orientations. This review describes the unification of radio-loud AGN, which include radio galaxies, quasars, and blazars. We describe the classification and properties of AGN and summarize the evidence for anisotropic emission. We outline the two most plausible unified schemes for radio-loud AGN, one linking quasars and luminous radio galaxies and another linking BL~Lac objects and less luminous radio galaxies. Using the formalism appropriate to samples biased by relativistic beaming, we show the population statistics for two schemes are in accordance with available data. We analyze the possible connections between low- and high-luminosity radio-loud AGN. We review potential difficulties with unification and conclude that none currently constitutes a serious problem. We discuss likely complications to unified schemes that are suggested by realistic physical considerations; these will be important to consider when more comprehensive data for larger complete samples become available. We conclude with a list of the ten questions we believe are the most pressing in this field.

3,135 citations