A model for binary-binary close encounters and collisions from a dynamical point of view

The goal of this paper is to provide a model for binary-binary interactions in star clusters, which is based on simultaneous binary collision of a special case of the one-dimensional 4-body problem where four masses move symmetrically about the center of mass. From the theoretical point of view, the singularity due to binary collisions between point masses can be handled by means of regularization theory. Our main tool is a change of coordinates due to McGehee by which we blow-up the singular set associated to total collision and replace it with an invariant manifold which includes binary and simultaneous binary collisions, and then gain a complete picture of the local behavior of the solutions near to total collision via the homothetic orbit.     

Dark matter in the Galactic Bulge: a Microlensing point of view

Microlensing is one of the most promising technique to probe the densityof dark matter in the Galactic Bulge. We review briefly the history ofmicrolensing and comment on the discovery of high optical depthin the direction of the Bulge. This optical depth is several timeslarger than the first theoretical predictions. We will show that someof the discrepancy can be resolved by taking into account the effectof self amplification of stars into the Galactic Bar. We will alsoexplain that the optical depth is contaminated with the contributionof faint unresolved stars. However, we emphasize that a categoryof sources, the bulge giants are bright enough to escape the biasdue to unresolved sources. Finallywe show that even if self amplification in the bar is taken into account, the optical depth to giants is hard to reproduce. We concludeby saying that in the near future this excess in the bulge opticaldepth should be clarified and measured with good accuracy. In particulargood progress should be made when the analyze of the last observationsof Bulge giants will be completed by the MACHO group. The futureimplementation of the image subtraction technique in the data pipelinesshould also help to overcome the bias in the measurement of the opticaldepth to turnoff stars. This revised version was published online in July 2006 with corrections to the Cover Date.     

Gravitational collapse of a dust ball — The external observer's point of view

The problem of collapse of a dust ball has been studied in detail from the point of view of an external observer (O). It is seen that although there is no material pressure from the point of view of the comoving observer, there is a non-vanishing material pressure in the ball from the point of view of O. In the early stages of collapse (w.r.t. O), this pressure is positive everywhere inside the ball, while during the later stages, if one goes outwards from the centre towards the surface of the ball, this pressure is negative up to a certain value of the radial coordinate, and then changes its sign thereafter. On the basis of this pressure, one can understand the physics of the whole scenario of collapse w.r.t. O; in particular, the important feature is that in the ultimate stages an event horizon is formed asymptotically and there is no collapse to a point (as takes place from the point of view of the comoving observer).     

Evidence for common breakup events of the acapulcoites‐lodranites and chondrites

Abstract— Acapulcoites and lodranites are believed to originate on a common parent body and to represent some of the earliest events in the differentiation of the chondritic asteroids. We have conducted isotopic studies of the noble gases He, Ne, Ar, Kr, and Xe, and determinations of the concentrations of the major elements and of the radionuclides ¹⁰Be, ²⁶Al, and ³⁶Cl in an attempt to constrain the cosmic‐ray exposure history of two members of the acapulcoite‐lodranite clan recovered in Antarctica: Frontier Mountain (FRO) 95029 and Graves Nunataks (GRA) 95209. From cosmic‐ray‐produced ³He, ²¹Ne, and ³⁸Ar and appropriate production rates, we derive parent‐body breakup times of 4.59 ± 0.60 and 6.82 ± 0.60 Ma for FOR 95029 and GRA 95209, respectively. These times are consistent with those obtained from the pairs ¹⁰Be‐²¹Ne and ²⁶Al‐²¹Ne; whereas the times inferred from the pair ³⁶Cl‐³⁶Ar are slightly longer, perhaps because the ³⁶Cl activities decreased as a result of decay on Earth. Terrestrial ages up to ～50 ka for the two meteorites are consistent with the measured ³⁶Cl activities of the metal phases. All acapulcoites and lodranites dated until now show cosmic‐ray exposure ages in the range of 4–10 Ma. This is the same range as that found for the major exposure age cluster of the H chondrites. As a common parent body is improbable on the basis of the O‐isotopic systematics, a common set of impactors might have affected the asteroid belt 4–10 Ma ago.     

On the existence of J 2 invariant relative orbits from the dynamical system point of view

The present paper addresses the existence of J ₂ invariant relative orbits with arbitrary relative magnitude over the infinite time using the Routh reduction and Poincaré techniques in the J ₂ Hamiltonian problem. The current research also proposes a novel numerical searching approach for J ₂ invariant relative orbits from the dynamical system point of view. A new type of Poincaré mapping is defined from different central manifolds of the pseudo-circular orbits (parameterized by the Jacobi energy E, the polar component of momentum H _z and the measure of distance Δr between the fixed point and its central manifolds) to the nodal periods T _d and the drifts of longitude of the ascending node during one period (ΔΩ), which differs from Koon et al.’s (AIAA 2001) definition on central manifolds parameterized by the same fixed point. The Poincaré mapping is surjective because it compresses the three-dimensional variables into two-dimensional images, and the mapping degenerates into a bijective mapping in consideration of the fixed points. An iteration algorithm to the degenerated bijective mapping is proposed from the continuation procedure to perform the ergodic representation of E- and H _z -contour maps on the space of T _d –ΔΩ. For the surjective mapping with Δr ≠ 0, different pseudo-circular or elliptical orbits may share the same images. Hence, the inverse surjective mapping may achieve non-unique variables from a single image, which makes the generation of J ₂ invariant relative orbits possible. The pseudo-circular or elliptical orbits generated from the surjective mapping will be defined in different meridian planes. Hence, the critical contribution of the present paper is the assignment of J ₂ invariant relative orbits to different invariant parameters E and H _z depending on the E- and H _z -contour map, which will hold J ₂ invariant relative orbits for extended durations. To investigate the high-order nonlinearity neglected by previous studies, a formation configuration with a large magnitude of 500 km is successfully generated from the theory developed in the present work, which is beyond the scope of the linear conditions of J ₂ invariant relative orbits. Therefore, the existence of J ₂ invariant relative orbit with an arbitrary relative magnitude over the infinite time is achieved from the dynamical system point of view.     

Black hole dynamics: A survey of black hole physics from the point of view of perturbation theory

This article is a brief survey of the contribution of perturbative studies to our understanding of black hole physics. For natural reasons, I will not be able to discuss all details required for an exhaustive understanding of a field that has been active for the last forty years. Neither will — I be able to cover all problem areas where perturbation theory has been applied. My aim is simply to provide the interested reader with a few pointers that can serve as useful starting points for an odyssey through the literature.     

Tissemouminites: A new group of primitive achondrites spanning the transition between acapulcoites and winonaites

The Northwest Africa (NWA) 090 meteorite, initially classified as an acapulcoite, presents petrological, chemical, and isotopic characteristics comparable to a group of seven primitive winonaites: Dhofar 1222, NWA 725, NWA 1052, NWA 1054, NWA 1058, NWA 1463, and NWA 8614. Five of these samples were previously classified as acapulcoites or ungrouped achondrites before being reclassified as winonaites based on their oxygen isotopic compositions. These misclassifications are indicative of the particular compositional nature of these primitive achondrites. All contain relict chondrules and a lower closure temperature of metamorphism of 820 ± 20 °C compared to other typical winonaites, as well as mineral elemental compositions similar to those of acapulcoites. The oxygen isotopic signature of these samples, δ¹⁷O of 1.18 ± 0.17‰, δ¹⁸O of 3.18 ± 0.30‰, and Δ¹⁷O of −0.47 ± 0.02, is in fact resolvable from both acapulcoites and winonaites. We investigate the relationship between these eight primitive achondrites, typical winonaites, and acapulcoites, to redefine petrological, mineralogical, and geochemical criteria of primitive achondrite classification. Distinguishing between winonaites, acapulcoites, and this group of eight primitive achondrites can be unambiguously done using a combination of several mineralogical and chemical criteria. A combination of olivine fayalite content and FeO/MnO ratio, as well as plagioclase potassium content allow us to separate these three groups without the absolute necessity of oxygen isotope analyses. NWA 090 as well as the other seven primitive achondrites, although related to winonaites, are most likely derived from a parent body distinct from winonaites and acapulcoites–lodranites, and define a new group of primitive achondrites that can be referred to as tissemouminites.     

Hydrostatic,isothermal planetary models from the point of view of dynamical systems: “Determination of explicit formulas for the point of critical mass”

We investigate a planetary model in spherical symmetry, which consists of a solid core and an envelope of ideal and isothermal gas, embedded in a gaseous nebula. The model equations describe equilibrium states of the envelope. So far, no analytical expressions for their solutions exist, but of course, numerical results have been computed. The point of critical mass, above which no more static solutions for the envelope exist, could not be determined analytically until now. We derive explicit formulas for the core mass and the gas density at the core surface, for the point of critical mass. The critical core mass is also an indicator for the ability of a core to keep its envelope when the surrounding nebula is removed, because at this point, the core's influence extends up to the outer boundary at the Hill radius.     

Potential energy of continuous and discrete distributions of matter from the point of view of the application of the virial theorem

The potential energy of clusters of stars in which the distribution of matter is taken to be continuous is compared with that of static model clusters in which the distribution of matter is discrete, the comparison being made from the point of view of applying the virial theorem to estimate the masses of the clusters. There is good agreement on the average between the two cases as long as the stellar distribution is random. Systematic differences occur whenever there is any departure from randomness. However, reduction of the mass of a cluster as estimated by means of the virial theorem by even as much as a factor of 2 on the average would seem to require even greater departures from randomness in the stellar distribution than are considered here. As might be expected there are sometimes very large fluctuations in the potential energy from one cluster to the next in the discrete case.Contributions of the Louisiana State University Observatory, No. 30.     

Mid-infrared variability of blazars: a view from NEOWISE survey

We studied mid-infrared (MIR) variability of a large sample of blazars detected by LAT/Fermi (called Fermi-detected blazars) and those not detected by LAT/Fermi (called non-Fermi-detected blazars) in order to investigate any difference in the variability characteristics between them as well as between FSRQs and BL Lacs. Making use of NEOWISE archival data from October 2013 to December 2017, we constructed the long-term 3.4 μm and 4.6 μm light curves of 2,573 blazars and computed their intrinsic variability amplitudes, \(\varPsi \). As a result, we found that (1) Fermi-detected blazars show higher \(\varPsi \) than non-Fermi-detected blazars; (2) Fermi-detected FSRQs show higher \(\varPsi \) than non-Fermi-detected FSRQs; (3) Fermi-detected BL Lacs show higher \(\varPsi \) than non-Fermi-detected BL Lacs; (4) FSRQs show higher \(\varPsi \) than BL Lacs. By comparing their distributions of “\(\mathit{var}\_\mathit{flg}\)” in the ALLWISE database, we also found that Fermi-detected blazars/FSRQs/BL Lacs tend to be more variable than non-Fermi-detected blazars/FSRQs/BL Lacs. For the Fermi-detected blazars, there are highly significant correlations between the flux densities and spectral indices in the MIR and gamma-ray bands. These results imply that the activity in the two bands is connected. Our results are consistent with several earlier results on the differences between Fermi-detected blazars and non-Fermi-detected blazars. We also give some possible explanations about the statistical results.     

Siderophile element characteristics of acapulcoite–lodranites and winonaites: Implications for the early differentiation processes of their parent bodies

We have studied magnetic fractions of five acapulcoites, three lodranites, and two winonaites to investigate chemical compositions of their precursor materials and metallic partial melting processes occurring on their parent bodies. One winonaite metal is similar in composition to low Au, low Ni IAB iron subgroup, indicating genetic relationship between them. Magnetic fractions of chondrule‐bearing acapulcoite and winonaite have intermediate chemical compositions of metals between H chondrites and EL chondrites. This fact indicates that the precursor materials of acapulcoite–lodranites and winonaites were similar to H and/or EL chondrites in chemical compositions. Magnetic fractions in acapulcoite–lodranites have a large variety of chemical compositions. Most of them show enrichments of W, Re, Ir, Pt, Mo, and Rh, and one of them shows clear depletion in Re and Ir relative to those of chondrule‐bearing acapulcoite. Chemical compositional variations among acapulcoite–lodranite metals cannot be explained by a single Fe‐Ni‐S partial melting event, but a two‐step partial melting model can explain it.     

Structure and Evolution of Supergranulation from Local Helioseismology

Supergranulation is visible at the solar surface as a cellular pattern of horizontal outflows. Although it does not show a distinct intensity pattern, it manifests itself indirectly in, for example, the chromospheric network. Previous studies have reported significant differences in the inferred basic parameters of the supergranulation phenomenon. Here we study the structure and temporal evolution of a large sample of supergranules, measured by using local helioseismology and SOHO/MDI data from the year 2000 at solar activity minimum. Local helioseismology with f modes provides maps of the horizontal divergence of the flow velocity at a depth of about 1 Mm. From these divergence maps supergranular cells were identified by using Fourier segmentation procedures in two dimensions and in three dimensions (two spatial dimensions plus time). The maps that we analyzed contain more than 10⁵ supergranular cells and more than 10³ lifetime histories, which makes possible a detailed analysis with high statistical significance. We find that the supergranular cells have a mean diameter of 27.1 Mm. The mean lifetime is estimated to be 1.6 days from the measured distribution of lifetimes (three-dimensional segmentation), with a clear tendency for larger cells to live longer than smaller ones. The pair and mark correlation functions do not show pronounced features on scales larger than the typical cell size, which suggests purely random cell positions. The temporal histories of supergranular cells indicate a smooth evolution from their emergence and growth in the first half of their lives to their decay in the second half of their lives (unlike exploding granules, which reach their maximum size just before they fragment).     

Planck and re-ionization history: a model selection view

We use Bayesian model selection tools to forecast the Planck satellite's ability to distinguish between different models for the re-ionization history of the Universe, using the large angular scale signal in the cosmic microwave background polarization spectrum. We find that Planck is not expected to be able to distinguish between an instantaneous re-ionization model and a two-parameter smooth re-ionization model, except for extreme values of the additional re-ionization parameter. If it cannot, then it will be unable to distinguish between different two-parameter models either. However, Bayesian model averaging will be needed to obtain unbiased estimates of the optical depth to re-ionization. We also generalize our results to a hypothetical future cosmic variance limited microwave anisotropy survey, where the outlook is more optimistic.