Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups, Part 3: All Killing fields linearly independent of u^{\alpha} and w^{\alpha}

This is the third and last part of a series of 3 papers. Using the same method and the same coordinates as in parts 1 and 2, rotating dust solutions of Einstein's equations are investigated that possess 3-dimensional symmetry groups, under the assumption that each of the Killing vectors is linearly independent of velocity $u^{\alpha}$ and rotation $w^{\alpha}$ at every point of the spacetime region under consideration. The Killing fields are found and the Killing equations are solved for the components of the metric tensor in every case that arises. No progress was made with the Einstein equations in any of the cases, and no previously known solutions were identified. A brief overview of literature on solutions with rotating sources is given.Comment: One missing piece, signaled after eq. (10.7), is added after (10.21). List of corrections: In (3.7) wrong subscript in vorticity; In (3.10) wrong subscript in last term of g_{23}; In (4.23) wrong formulae for g_{12} and g_{22}; In (7.17) missing factor in velocity; In (7.18) one wrong factor in g_{22}; In (10.9) factor in vorticity; In (10.15) - (10.20) y_0 = 0; In (10.20) wrong second term in y. The rewriting typos did not influence result

Hydrogen and Helium atoms in strong magnetic fields

The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.Comment: 15 pages, 6 figure

Hydrogen molecule in a magnetic field: The lowest states of the Pi manifold and the global ground state of the parallel configuration

The electronic structure of the hydrogen molecule in a magnetic field is investigated for parallel internuclear and magnetic field axes. The lowest states of the $\Pi$ manifold are studied for spin singlet and triplet$(M_s = -1)$ as well as gerade and ungerade parity for a broad range of field strengths $0 \leq B \leq 100 a.u.$ For both states with gerade parity we observe a monotonous decrease in the dissociation energy with increasing field strength up to $B = 0.1 a.u.$ and metastable states with respect to the dissociation into two H atoms occur for a certain range of field strengths. For both states with ungerade parity we observe a strong increase in the dissociation energy with increasing field strength above some critical field strength $B_c$. As a major result we determine the transition field strengths for the crossings among the lowest $^1\Sigma_g$, $^3\Sigma_u$ and $^3\Pi_u$ states. The global ground state for $B \lesssim 0.18 a.u.$ is the strongly bound $^1\Sigma_g$ state. The crossings of the $^1\Sigma_g$ with the $^3\Sigma_u$ and $^3\Pi_u$ state occur at $B \approx 0.18$ and $B \approx0.39 a.u.$, respectively. The transition between the $^3\Sigma_u$ and $^3\Pi_u$ state occurs at $B \approx 12.3 a.u.$ Therefore, the global ground state of the hydrogen molecule for the parallel configuration is the unbound $^3\Sigma_u$ state for $0.18 \lesssim B \lesssim 12.3 a.u.$ The ground state for $B \gtrsim 12.3 a.u.$ is the strongly bound $^3\Pi_u$ state. This result is of great relevance to the chemistry in the atmospheres of magnetic white dwarfs and neutron stars.Comment: submitted to Physical Review

Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress-tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a comoving observer, satisfy an equation of state of the form $p = p(\mu)$, with $\frac{dp}{d\mu} \neq -\frac{1}{3}$, then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.Comment: 13 pages LaTe

The ground state of the Lithium atom in strong magnetic fields

The ground and some excited states of the Li atom in external uniform magnetic fields are calculated by means of our 2D mesh Hartree-Fock method for field strengths ranging from zero up to 2.35 10^8 T. With increasing field strength the ground state undergoes two transitions involving three different electronic configurations: for weak fields the ground state configuration arises from the field-free 1s^22s configuration, for intermediate fields from the 1s^22p_{-1} configuration and in high fields the 1s2p_{-1}3d_{-2} electronic configuration is responsible for the properties of the atom. The transition field strengths are determined. Calculations on the ground state of the Li+ ion allow us to describe the field-dependent ionization energy of the Li atom. Some general arguments on the ground states of multi-electron atoms in strong magnetic fields are provided.Comment: 11 pages, 6 figures, submitted to Physical Review

The ground state of the carbon atom in strong magnetic fields

The ground and a few excited states of the carbon atom in external uniform magnetic fields are calculated by means of our 2D mesh Hartree-Fock method for field strengths ranging from zero up to 2.35 10^9 T. With increasing field strength the ground state undergoes six transitions involving seven different electronic configurations which belong to three groups with different spin projections S_z=-1,-2,-3. For weak fields the ground state configuration arises from the field-free 1s^2 2s^2 2p_0 2p_{-1}, S_z=-1 configuration. With increasing field strength the ground state involves the four S_z=-2 configurations 1s^22s2p_0 2p_{-1}2p_{+1}, 1s^22s2p_0 2p_{-1}3d_{-2}, 1s^22p_0 2p_{-1}3d_{-2}4f_{-3} and 1s^22p_{-1}3d_{-2}4f_{-3}5g_{-4}, followed by the two fully spin polarized S_z=-3 configurations 1s2p_02p_{-1}3d_{-2}4f_{-3}5g_{-4} and 1s2p_{-1}3d_{-2}4f_{-3}5g_{-4}6h_{-5}. The last configuration forms the ground state of the carbon atom in the high field regime \gamma>18.664. The above series of ground state configurations is extracted from the results of numerical calculations for more than twenty electronic configurations selected due to some general energetical arguments.Comment: 6 figures,acc. Phys.Rev.

The Representative XMM-Newton Cluster Structure Survey (REXCESS) of an X-ray Luminosity Selected Galaxy Cluster Sample

The largest uncertainty for cosmological studies using clusters of galaxies is introduced by our limited knowledge of the statistics of galaxy cluster structure, and of the scaling relations between observables and cluster mass. To improve on this situation we have started an XMM-Newton Large Programme for the in-depth study of a representative sample of 33 galaxy clusters, selected in the redshift range z=0.055 to 0.183 from the REFLEX Cluster Survey, having X-ray luminosities above 0.4 X 10^44 h_70^-2 erg s^-1 in the 0.1 - 2.4 keV band. This paper introduces the sample, compiles properties of the clusters, and provides detailed information on the sample selection function. We describe the selection of a nearby galaxy cluster sample that makes optimal use of the XMM-Newton field-of-view, and provides nearly homogeneous X-ray luminosity coverage for the full range from poor clusters to the most massive objects in the Universe. For the clusters in the sample, X-ray fluxes are derived and compared to the previously obtained fluxes from the ROSAT All-Sky Survey. We find that the fluxes and the flux errors have been reliably determined in the ROSAT All-Sky Survey analysis used for the REFLEX Survey. We use the sample selection function documented in detail in this paper to determine the X-ray luminosity function, and compare it with the luminosity function of the entire REFLEX sample. We also discuss morphological peculiarities of some of the sample members. The sample and some of the background data given in this introductory paper will be important for the application of these data in the detailed studies of cluster structure, to appear in forthcoming publications.Comment: 17 pages, 17 figures; to appear in A&A. A pdf version with full-quality figures can be found at ftp://ftp.xray.mpe.mpg.de/people/gwp/xmmlp/xmmlp.pd

Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust

In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that (ii) the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model `irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.Comment: 18 pages. Matches published version in CQ

Turning Points in the Evolution of Isolated Neutron Stars' Magnetic Fields

During the life of isolated neutron stars (NSs) their magnetic field passes through a variety of evolutionary phases. Depending on its strength and structure and on the physical state of the NS (e.g. cooling, rotation), the field looks qualitatively and quantitatively different after each of these phases. Three of them, the phase of MHD instabilities immediately after NS's birth, the phase of fallback which may take place hours to months after NS's birth, and the phase when strong temperature gradients may drive thermoelectric instabilities, are concentrated in a period lasting from the end of the proto--NS phase until 100, perhaps 1000 years, when the NS has become almost isothermal. The further evolution of the magnetic field proceeds in general inconspicuous since the star is in isolation. However, as soon as the product of Larmor frequency and electron relaxation time, the so-called magnetization parameter, locally and/or temporally considerably exceeds unity, phases, also unstable ones, of dramatic changes of the field structure and magnitude can appear. An overview is given about that field evolution phases, the outcome of which makes a qualitative decision regarding the further evolution of the magnetic field and its host NS.Comment: References updated, typos correcte

Isotopic Composition of Light Nuclei in Cosmic Rays: Results from AMS-01

The variety of isotopes in cosmic rays allows us to study different aspects of the processes that cosmic rays undergo between the time they are produced and the time of their arrival in the heliosphere. In this paper we present measurements of the isotopic ratios 2H/4He, 3He/4He, 6Li/7Li, 7Be/(9Be+10Be) and 10B/11B in the range 0.2-1.4 GeV of kinetic energy per nucleon. The measurements are based on the data collected by the Alpha Magnetic Spectrometer, AMS-01, during the STS-91 flight in 1998 June.Comment: To appear in ApJ. 12 pages, 11 figures, 6 table