We use techniques from nonparametric function estimation theory to extract the density profiles, and their derivatives, from a set of N -body dark matter halos. We consider halos generated from ΛCDM simulations of gravitational clustering, as well as isolated, spherical collapses. The logarithmic density slopes γ ≡ d log ρ/d log r of the ΛCDM halos are found to vary as power-laws in radius, reaching values of γ ≈ −1 at the innermost resolved radii, ∼ 10 −2 r vir . This behavior is significantly different from that of broken power-law models like the NFW profile, but similar to that of models like de Vaucouleurs'. Accordingly, we compare the N -body density profiles with various parametric models to find which provide the best fit. We consider an NFW-like model with arbitrary inner slope; Dehnen & McLaughlin's anisotropic model; Einasto's model (identical in functional form to Sérsic's model but fit to the space density); and the density model of Prugniel & Simien that was designed to match the deprojected form of Sérsic's R 1/n law. Overall, the best-fitting model to the ΛCDM halos is Einasto's, although the Prugniel-Simien and Dehnen-McLaughlin models also perform well. With regard to the spherical collapse halos, both the Prugniel-Simien and Einasto models describe the density profiles well, with an rms scatter some four times smaller than that obtained with either the NFW-like model or the 3-parameter Dehnen-McLaughlin model. Finally, we confirm recent claims of a systematic variation in profile shape with halo mass.

ForewordThe study of the fundamental structure of nuclear matter is a central thrust of physics research in the United States. As indicated in Frontiers of Nuclear Science, the 2007 Nuclear Science Advisory Committee long range plan, consideration of a future Electron-Ion Collider (EIC) is a priority and will likely be a significant focus of discussion at the next long range plan. We are therefore pleased to have supported the ten week program in fall 2010 at the Institute of Nuclear Theory which examined at length the science case for the EIC. This program was a major effort; it attracted the maximum allowable attendance over ten weeks.This report summarizes the current understanding of the physics and articulates important open questions that can be addressed by an EIC. It converges towards a set of "golden" experiments that illustrate both the science reach and the technical demands on such a facility, and thereby establishes a firm ground from which to launch the next phase in preparation for the upcoming long range plan discussions. We thank all the participants in this productive program. In particular, we would like to acknowledge the leadership and dedication of the five co-organizers of the program who are also the co-editors of this report.David Kaplan, Director, National Institute for Nuclear Theory Hugh Montgomery, Director, Thomas Jefferson National Accelerator Facility Steven Vigdor, Associate Lab Director, Brookhaven National Laboratory iii Preface This volume is based on a ten-week program on "Gluons and the quark sea at high energies", which took place at the Institute for Nuclear Theory (INT) in Seattle from September 13 to November 19, 2010. The principal aim of the program was to develop and sharpen the science case for an Electron-Ion Collider (EIC), a facility that will be able to collide electrons and positrons with polarized protons and with light to heavy nuclei at high energies, offering unprecedented possibilities for in-depth studies of quantum chromodynamics. Guiding questions were• What are the crucial science issues?• How do they fit within the overall goals for nuclear physics?• Why can't they be addressed adequately at existing facilities?• Will they still be interesting in the 2020's, when a suitable facility might be realized?The program started with a five-day workshop on "Perturbative and Non-Perturbative Aspects of QCD at Collider Energies", which was followed by eight weeks of regular program and a concluding four-day workshop on "The Science Case for an EIC".More than 120 theorists and experimentalists took part in the program over ten weeks. It was only possible to smoothly accommodate such a large number of participants because of the extraordinary efforts of the INT staff, to whom we extend our warm thanks and appreciation. We thank the INT Director, David Kaplan, for his strong support of the program and for covering a significant portion of the costs for printing this volume. We gratefully acknowledge additional financial support provided by BNL and JLab.The program w...

We have recently shown that both the Prugniel-Simien model and Sérsic's function (hereafter referred to as the Einasto model when applied to internal density profiles) describe simulated dark matter halos better than a Navarro-Frenk-WhiteYlike model with an equal number of parameters. Here we provide analytical expressions for the logarithmic slopes of these models and compare them with data from real galaxies. Depending on the Einasto parameters of the dark matter halo, one can expect an extrapolated inner (0.01Y1 kpc) logarithmic profile slope ranging from approximately À0.2 to approximately À1.5, with a typical value at 0.1 kpc around À0.7. Application of this (better fitting) model therefore alleviates some of the past disagreement with observations on this issue. In addition, we provide useful expressions for the concentration and assorted scale radii: r s , r À2 , r e , R e , r vir , and r max , the radius where the circular velocity profile has its maximum value. We also present the circular velocity profiles and the radial behavior of (r)/(r) 3 for both the Einasto and Prugniel-Simien models, where (r) is the velocity dispersion associated with the density profile (r). We find this representation of the phase-space density profile to be well approximated by a power law with a slope slightly shallower than À2 near r ¼ r À2 .

Popular models for describing the luminosity‐density profiles of dynamically hot stellar systems (e.g. Jaffe, Hernquist, Dehnen) were constructed with the desire to match the deprojected form of an R1/4 light profile. Real galaxies, however, are now known to have a range of different light‐profile shapes that scale with mass. Consequently, although highly useful, the above models have implicit limitations, and this is illustrated here through their application to a number of real galaxy density profiles. On the other hand, the analytical density profile given by Prugniel & Simien closely matches the deprojected form of Sérsic R1/n light profiles – including deprojected exponential light profiles. It is thus applicable for describing bulges in spiral galaxies, dwarf elliptical galaxies, and both ordinary and giant elliptical galaxies. Moreover, the observed Sérsic quantities define the parameters of the density model. Here we provide simple equations, in terms of elementary and special functions, for the gravitational potential and force associated with this density profile. Furthermore, to match galaxies with partially depleted cores, and better explore the supermassive black hole/galaxy connection, we have added a power‐law core to this density profile and derived similar expressions for the potential and force of this hybrid profile. Expressions for the mass and velocity dispersion, assuming isotropy, are also given. These spherical models may also prove appropriate for describing the dark matter distribution in haloes formed from ΛCDM cosmological simulations.

We present a novel and quite general analysis of the interaction of a high-field chirped laser pulse and a relativistic electron, in which exquisite control of the spectral brilliance of the upshifted Thomson-scattered photon is shown to be possible. Normally, when Thomson scattering occurs at high field strengths, there is ponderomotive line broadening in the scattered radiation. This effect makes the bandwidth too large for some applications and reduces the spectral brilliance. We show that such broadening can be corrected and eliminated by suitable frequency modulation of the incident laser pulse. Further, we suggest a practical realization of this compensation idea in terms of a chirped-beam driven free electron laser oscillator configuration and show that significant compensation can occur, even with the imperfect matching to be expected in these conditions. PACS numbers: 29.20.Ej, 29.25.Bx, 29.27.Bd, 07.85.Fv Sources of electromagnetic radiation relying upon Thomson scattering are increasingly being applied in fundamental physics research [1], and compact acceleratorbased sources specifically designed for potential user facilities have been built [2]. One remarkable feature of the radiation emerging from such sources, compared to bremsstrahlung sources, is the narrowband nature of the radiation produced. For example, applications to Xray structure determination [3], dark-field imaging [4,5], phase contrast imaging [6], and computed tomography [7] have been demonstrated experimentally and take full advantage of the narrow bandwidth of the Thomson source.Given that narrow bandwidth is desired, it is important to know and understand the sources of bandwidth of the scattered radiation and the limitations imposed on the performance of Thomson sources. For applications where the normalized vector potential of the incident laser pulse is much less than one (the low-field regime), the line width of the radiation from a scattering event reproduces the line width of the incident laser pulse. Unfortunately, when the normalized vector potential increases, as is desired for stronger sources, a detuning red-shift arises during the scattering events that tends to spread out the spectrum [8][9][10]. Physically, the scattering electron slows down, by a varying amount, as the incident pulse is traversed.In a recent paper, Ghebregziabher, Shadwick, and Umstadter (GSU) observed that frequency modulation (FM), or "chirping", of the scattering laser pulse can compensate for such ponderomotive line broadening, and suggested a form for this modulation [11]. Motivated by their observation, we present the exact analytic solution for optimal FM, recovering the low-field linewidth even in the high-field regime. The narrowing of the scattered pulse is Fourier-limited only by the duration of the incident pulse.The essence of laser pulse chirping is analogous to free electron laser (FEL) undulator tapering [12][13][14][15][16]. In tapering, as deceleration occurs due to the FEL emission, the field strength is adjusted to preserve the...