Phase-space distribution of unbound dark matter near the Sun

We resolve discrepancies in previous analyses of the flow of collisionless dark matter particles in the Sun's gravitational field. We determine the phase-space distribution of the flow both numerically, tracing particle trajectories back in time, and analytically, providing a simple correct relation between the velocity of particles at infinity and at the Earth. We use our results to produce sky maps of the distribution of arrival directions of dark matter particles on Earth at various times of the year. We assume various Maxwellian velocity distributions at infinity describing the standard dark halo and streams of dark matter. We illustrate the formation of a ring, analogous to the Einstein ring, when the Earth is directly downstream of the Sun.Comment: 17 pages, 10 figures (better rendered in ps than pdf

Uniqueness of collinear solutions for the relativistic three-body problem

Continuing work initiated in an earlier publication [Yamada, Asada, Phys. Rev. D 82, 104019 (2010)], we investigate collinear solutions to the general relativistic three-body problem. We prove the uniqueness of the configuration for given system parameters (the masses and the end-to-end length). First, we show that the equation determining the distance ratio among the three masses, which has been obtained as a seventh-order polynomial in the previous paper, has at most three positive roots, which apparently provide three cases of the distance ratio. It is found, however, that, even for such cases, there exists one physically reasonable root and only one, because the remaining two positive roots do not satisfy the slow motion assumption in the post-Newtonian approximation and are thus discarded. This means that, especially for the restricted three-body problem, exactly three positions of a third body are true even at the post-Newtonian order. They are relativistic counterparts of the Newtonian Lagrange points L1, L2 and L3. We show also that, for the same masses and full length, the angular velocity of the post-Newtonian collinear configuration is smaller than that for the Newtonian case. Provided that the masses and angular rate are fixed, the relativistic end-to-end length is shorter than the Newtonian one.Comment: 18 pages, 1 figure; typos corrected, text improved; accepted by PR

The nature of the dense core population in the Pipe Nebula: A survey of NH3, CCS, and HC5N molecular line emission

Recent extinction studies of the Pipe Nebula (d=130 pc) reveal many cores spanning a range in mass from 0.2 to 20.4 Msun. These dense cores were identified via their high extinction and comprise a starless population in a very early stage of development. Here we present a survey of NH3 (1,1), NH3 (2,2), CCS (2_1,1_0), and HC5N (9,8) emission toward 46 of these cores. An atlas of the 2MASS extinction maps is also presented. In total, we detect 63% of the cores in NH3 (1,1) 22% in NH3 (2,2), 28% in CCS, and 9% in HC5N emission. We find the cores are associated with dense gas (~10^4 cm-3) with 9.5 < T_k < 17 K. Compared to C18O, we find the NH3 linewidths are systematically narrower, implying that the NH3 is tracing the dense component of the gas and that these cores are relatively quiescent. We find no correlation between core linewidth and size. The derived properties of the Pipe cores are similar to cores within other low-mass star-forming regions: the only differences are that the Pipe cores have weaker NH3 emision and most show no current star formation as evidenced by the lack of embedded infrared sources. Such weak NH3 emission could arise due to low column densities and abundances or reduced excitation due to relatively low core volume densities. Either alternative implies that the cores are relatively young. Thus, the Pipe cores represent an excellent sample of dense cores in which to study the initial conditions for star formation and the earliest stages of core formation and evolution.Comment: 35 pages, 10 figures (excluding the appendix). For the complete appendix contact [email protected]. Accepted for publication in ApJ

The ortho-to-para ratio of ammonia in the L1157 outflow

We have measured the ortho-to-para ratio of ammonia in the blueshifted gas of the L1157 outflow by observing the six metastable inversion lines from (J, K) = (1, 1) to (6, 6). The highly excited (5, 5) and (6, 6) lines were first detected in the low-mass star forming regions. The rotational temperature derived from the ratio of four transition lines from (3, 3) to (6, 6) is 130-140 K, suggesting that the blueshifted gas is heated by a factor of ~10 as compared to the quiescent gas. The ortho-to-para ratio of the NH3 molecules in the blueshifted gas is estimated to be 1.3--1.7, which is higher than the statistical equilibrium value. This ratio provides us with evidence that the NH3 molecules have been evaporated from dust grains with the formation temperature between 18 and 25 K. It is most likely that the NH3 molecules on dust grains have been released into the gas phase through the passage of strong shock waves produced by the outflow. Such a scenario is supported by the fact that the ammonia abundance in the blueshifted gas is enhanced by a factor of ~5 with respect to the dense quiescent gas.Comment: 16 pages, including 3 PS figures. To appear in the ApJ (Letters). aastex macro

Collinear solution to the general relativistic three-body problem

The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and always line up. The solution is unstable. Hence it is unlikely that such a simple configuration would exist owing to general relativistic forces dependent not only on the masses but also on the velocity of each body. However, we show that the collinear solution remains true with a correction to the spatial separation between masses. Relativistic corrections to the Sun-Jupiter Lagrange points L1, L2 and L3 are also evaluated.Comment: 12 pages, 2 figures, accepted for publication in PR

The gravitational-wave memory from eccentric binaries

The nonlinear gravitational-wave memory causes a time-varying but nonoscillatory correction to the gravitational-wave polarizations. It arises from gravitational waves that are sourced by gravitational waves. Previous considerations of the nonlinear memory effect have focused on quasicircular binaries. Here, I consider the nonlinear memory from Newtonian orbits with arbitrary eccentricity. Expressions for the waveform polarizations and spin-weighted spherical-harmonic modes are derived for elliptic, hyperbolic, parabolic, and radial orbits. In the hyperbolic, parabolic, and radial cases the nonlinear memory provides a 2.5 post-Newtonian (PN) correction to the leading-order waveforms. This is in contrast to the elliptical and quasicircular cases, where the nonlinear memory corrects the waveform at leading (0PN) order. This difference in PN order arises from the fact that the memory builds up over a short "scattering" time scale in the hyperbolic case, as opposed to a much longer radiation-reaction time scale in the elliptical case. The nonlinear memory corrections presented here complete our knowledge of the leading-order (Peters-Mathews) waveforms for elliptical orbits. These calculations are also relevant for binaries with quasicircular orbits in the present epoch which had, in the past, large eccentricities. Because the nonlinear memory depends sensitively on the past evolution of a binary, I discuss the effect of this early-time eccentricity on the value of the late-time memory in nearly circularized binaries. I also discuss the observability of large "memory jumps" in a binary's past that could arise from its formation in a capture process. Lastly, I provide estimates of the signal-to-noise ratio of the linear and nonlinear memories from hyperbolic and parabolic binaries.Comment: 25 pages, 8 figures. v2: minor changes to match published versio

Sub-clinical assessment of atopic dermatitis severity using angiographic optical coherence tomography

Measurement of sub-clinical atopic dermatitis (AD) is important for determining how long therapies should be continued after clinical clearance of visible AD lesions. An important biomarker of sub-clinical AD is epidermal hypertrophy, the structural measures of which often make optical coherence tomography (OCT) challenging due to the lack of a clearly delineated dermal-epidermal junction in AD patients. Alternatively, angiographic OCT measurements of vascular depth and morphology may represent a robust biomarker for quantifying the severity of clinical and sub-clinical AD. To investigate this, angiographic data sets were acquired from 32 patients with a range of AD severities. Deeper vascular layers within skin were found to correlate with increasing clinical severity. Furthermore, for AD patients exhibiting no clinical symptoms, the superficial plexus depth was found to be significantly deeper than healthy patients at both the elbow (p = 0.04) and knee (p < 0.001), suggesting that sub-clinical changes in severity can be detected. Furthermore, the morphology of vessels appeared altered in patients with severe AD, with significantly different vessel diameter, length, density and fractal dimension. These metrics provide valuable insight into the sub-clinical severity of the condition, allowing the effects of treatments to be monitored past the point of clinical remission

Secondary resonances of co-orbital motions

The size distribution of the stability region around the Lagrangian point L4 is investigated in the elliptic restricted three-body problem as the function of the mass parameter and the orbital eccentricity of the primaries. It is shown that there are minimum zones in the size distribution of the stability regions, and these zones are connected with secondary resonances between the frequencies of librational motions around L4. The results can be applied to hypothetical Trojan planets for predicting values of the mass parameter and the eccentricity for which such objects can be expected or their existence is less probable.Comment: 9 pages, 7 figures, accepted for publication in MNRA

Solar Wakes of Dark Matter Flows

We analyze the effect of the Sun's gravitational field on a flow of cold dark matter (CDM) through the solar system in the limit where the velocity dispersion of the flow vanishes. The exact density and velocity distributions are derived in the case where the Sun is a point mass. The results are extended to the more realistic case where the Sun has a finite size spherically symmetric mass distribution. We find that regions of infinite density, called caustics, appear. One such region is a line caustic on the axis of symmetry, downstream from the Sun, where the flow trajectories cross. Another is a cone-shaped caustic surface near the trajectories of maximum scattering angle. The trajectories forming the conical caustic pass through the Sun's interior and probe the solar mass distribution, raising the possibility that the solar mass distribution may some day be measured by a dark matter detector on Earth. We generalize our results to the case of flows with continuous velocity distributions, such as that predicted by the isothermal model of the Milky Way halo.Comment: 30 pages, 8 figure

Evolution of gravitational orbits in the expanding universe

The gravitational action of the smooth energy-matter components filling in the universe can affect the orbit of a planetary system. Changes are related to the acceleration of the cosmological scale size R. In a universe with significant dark matter, a gravitational system expands or contracts according to the amount and equation of state of the dark energy. At present time, the Solar system, according to the LambdaCDM scenario emerging from observational cosmology, should be expanding if we consider only the effect of the cosmological background. Its fate is determined by the equation of state of the dark energy alone. The mean motion and periastron precession of a planet are directly sensitive to (d^2 R/d t^2)/R, whereas variations with time in the semi-major axis and eccentricity are related to its time variation. Actual bounds on the cosmological deceleration parameters q_0 from accurate astrometric data of perihelion precession and changes in the third Kepler's law in the Solar system fall short of ten orders of magnitude with respect to estimates from observational cosmology. Future radio-ranging measurements of outer planets could improve actual bounds by five orders of magnitude.Comment: 8 pages; 4 figures; Phys. Rev. D, in pres