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DOE OSTI2013

Invariant distributions on compact homogeneous spaces

In this paper, we study distributions on compact homogeneous spaces, including invariant distributions and also distributions admitting a sub-Riemannian structure. We first consider distributions of dimension 1 and 2 on compact homogeneous spaces. After this, we study the cases of compact homogeneous spaces of dimension 2, 3, and 4 in detail. Invariant distributions on simply connected compact homogeneous spaces are also treated. Bibliography: 18 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

COLOR DEPENDENCE IN THE SIZE DISTRIBUTION OF MAIN BELT ASTEROIDS REVISITED

The size distribution of the asteroid belt is examined with 16956 main belt asteroids detected in data taken from the Canada-France-Hawaii Telescope Legacy Survey in two filters (g' and r'). The cumulative H (absolute magnitude) distribution is examined in both filters, and both match well to simple power laws down to H = 17, with slopes in rough agreement with those reported the literature. This implies that disruptive collisions between asteroids are gravitationally dominated down to at least this size, and probably sub-kilometer scales. The slopes of these distributions appear shallower in the outer belt than the inner belt, and the g' distributions appear slightly steeper than the r'. The slope shallowing in the outer belt may reflect a real compositional difference: the inner asteroid belt has been suggested to consist mostly of stony and/or metallic S-type asteroids, whereas carbonaceous C-types are thought to be more prevalent further from the Sun. No waves are seen in the size distribution above H = 15. Since waves are expected to be produced at the transition from gravitationally-dominated to internal strength-dominated collisions, their absence here may imply that the transition occurs at sub-kilometer scales, much smaller than the H = 17 (diameter {approx} 1.6 km) cutoff of this study.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

The impact of the gas distribution on the determination of dynamical masses of galaxies using unresolved observations

Dynamical mass (M {sub dyn}) is a key property of any galaxy, yet a determination of M {sub dyn} is not straightforward if spatially resolved measurements are not available. This situation occurs in single-dish H I observations of the local universe, but also frequently in high-redshift observations. M {sub dyn} measurements in high-redshift galaxies are commonly obtained through observations of the CO line, the most abundant tracer of the molecular medium. Even though in most cases the CO line width can be determined with reasonable accuracy, a measurement of the size of the emitting region is typically challenging given current facilities. We show how the integrated spectra ('global profiles') of a variety of galaxy models depend on the spatial distribution of the tracer gas as well as its velocity dispersion. We demonstrate that the choice of tracer emission line (e.g., H I tracing extended, 'flat', emission versus CO tracing more compact, 'exponential,' emission) significantly affects the shape of the global profiles. In particular, in the case of high (∼50 km s{sup –1}) velocity dispersions, compact tracers (such as CO) result in Gaussian-like (non-double-horned) profiles, as is indeed frequently seen in high-redshift observations. This leads to significantly different determinations of M {sub dyn} if different distributions of the tracer material ('flat' versus 'exponential') are considered. We determine at which radii the rotation curve reaches the rotation velocity corresponding to the velocity width, and find that for each tracer this happens at a well-defined radius: H I velocity widths typically originate at ∼5 optical scale lengths, while CO velocity widths trace the rotation velocity at ∼2 scale lengths. We additionally explore other distributions to take into account that CO distributions at high redshift likely differ from those at low redshift. Our models, while not trying to reproduce individual galaxies, define characteristic radii that can be used in conjunction with the measured velocity widths in order to define dynamical masses consistent with the assumed gas distribution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

The color–magnitude distribution of small Jupiter Trojans

We present an analysis of survey observations targeting the leading L4 Jupiter Trojan cloud near opposition using the wide-field Suprime-Cam CCD camera on the 8.2 m Subaru Telescope. The survey covered about 38 deg{sup 2} of sky and imaged 147 fields spread across a wide region of the L4 cloud. Each field was imaged in both the g' and the i' band, allowing for the measurement of g – i color. We detected 557 Trojans in the observed fields, ranging in absolute magnitude from H = 10.0 to H = 20.3. We fit the total magnitude distribution to a broken power law and show that the power-law slope rolls over from 0.45 ± 0.05 to 0.36{sub -0.09}{sup +0.05} at a break magnitude of H{sub b}=14.93{sub -0.88}{sup +0.73}. Combining the best-fit magnitude distribution of faint objects from our survey with an analysis of the magnitude distribution of bright objects listed in the Minor Planet Center catalog, we obtain the absolute magnitude distribution of Trojans over the entire range from H = 7.2 to H = 16.4. We show that the g – i color of Trojans decreases with increasing magnitude. In the context of the less-red and red color populations, as classified in Wong et al. using photometric and spectroscopic data, we demonstrate that the observed trend in color for the faint Trojans is consistent with the expected trend derived from extrapolation of the best-fit color population magnitude distributions for bright cataloged Trojans. This indicates a steady increase in the relative number of less-red objects with decreasing size. Finally, we interpret our results using collisional modeling and propose several hypotheses for the color evolution of the Jupiter Trojan population.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

INVARIANT KAPPA DISTRIBUTION IN SPACE PLASMAS OUT OF EQUILIBRIUM

Recent advances in Space Physics theory have shown the connection between non-extensive Statistical Mechanics and space plasmas by providing a theoretical basis for the empirically derived kappa distributions commonly used to describe the phase-space distribution functions of these systems. The non-equilibrium temperature and the kappa index that govern these distributions are the two independent controlling parameters of non-equilibrium systems. The significance of the kappa index is primarily given by its role in identifying the non-equilibrium stationary states and measuring their 'thermodynamic distance' from thermal equilibrium, while its physical meaning is connected to the correlation between the system's particles. The classical, single stationary state at equilibrium is generalized into a whole set of different non-equilibrium stationary states labeled by the kappa index. This paper addresses certain crucial issues about the physical meaning and role of the kappa index in identifying stationary states. The origin of the emerged inconsistencies is that the kappa index is not an invariant physical quantity, but instead depends on the degrees of freedom of the system's particles. This leads in several misleading conclusions, such as (1) only large kappa index, practically infinite, can characterize the many-particle kappa distribution, and (2) the correlation between particles depends on the total number of the system's particles. Here we show that a modified kappa index, invariant for any number of degrees of freedom, can be naturally defined. Then, we develop and examine the relevant corrected formulation of many-particle multidimensional kappa distribution, and discuss the physical meaning of the invariant kappa index.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

THE n-DISTRIBUTION OF ELECTRONS AND DOUBLE LAYERS IN THE ELECTRON-BEAM-RETURN-CURRENT SYSTEM OF SOLAR FLARES

We investigate processes in the electron-beam-return-current system in the impulsive phase of solar flares to answer a question about the formation of the n-electron distribution detected in this phase of solar flares. An evolution of the electron-beam-return-current system with an initial local density depression is studied using a three-dimensional electromagnetic particle-in-cell model. In the system the strong double layer is formed. Its electric field potential increases with the electron beam flux. In this electric field potential, the electrons of background plasma are strongly accelerated and propagate in the return-current direction. The high-energy part of their distribution at the high-potential side of the strong double layer resembles that of the n-distribution. Thus, the detection of the n-distributions, where a form of the high-energy part of the distribution is the most important, can indicate the presence of strong double layers in solar flares. The similarity between processes in solar flare loops and those in the downward current region of the terrestrial aurora, where the double layers were observed by FAST satellite, supports this idea.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

ON THE MASS DISTRIBUTION AND BIRTH MASSES OF NEUTRON STARS

We investigate the distribution of neutron star masses in different populations of binaries, employing Bayesian statistical techniques. In particular, we explore the differences in neutron star masses between sources that have experienced distinct evolutionary paths and accretion episodes. We find that the distribution of neutron star masses in non-recycled eclipsing high-mass binaries as well as of slow pulsars, which are all believed to be near their birth masses, has a mean of 1.28 M{sub Sun} and a dispersion of 0.24 M{sub Sun }. These values are consistent with expectations for neutron star formation in core-collapse supernovae. On the other hand, double neutron stars, which are also believed to be near their birth masses, have a much narrower mass distribution, peaking at 1.33 M{sub Sun }, but with a dispersion of only 0.05 M{sub Sun }. Such a small dispersion cannot easily be understood and perhaps points to a particular and rare formation channel. The mass distribution of neutron stars that have been recycled has a mean of 1.48 M{sub Sun} and a dispersion of 0.2 M{sub Sun }, consistent with the expectation that they have experienced extended mass accretion episodes. The fact that only a very small fraction of recycled neutron stars in the inferred distribution have masses that exceed {approx}2 M{sub Sun} suggests that only a few of these neutron stars cross the mass threshold to form low-mass black holes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

A COMPREHENSIVE ANALYSIS OF FERMI GAMMA-RAY BURST DATA. III. ENERGY-DEPENDENT T {sub 90} DISTRIBUTIONS OF GBM GRBs AND INSTRUMENTAL SELECTION EFFECT ON DURATION CLASSIFICATION

The durations (T {sub 90}) of 315 gamma-ray bursts (GRBs) detected with Fermi/GBM (8-1000 keV) up to 2011 September are calculated using the Bayesian Block method. We compare the T {sub 90} distributions between this sample and those derived from previous/current GRB missions. We show that the T {sub 90} distribution of this GRB sample is bimodal, with a statistical significance level comparable to those derived from the BeppoSAX/GRBM sample and the Swift/BAT sample, but lower than that derived from the CGRO/BATSE sample. The short-to-long GRB number ratio is also much lower than that derived from the BATSE sample, i.e., 1:6.5 versus 1:3. We measure T {sub 90} in several bands, i.e., 8-15, 15-25, 25-50, 50-100, 100-350, and 350-1000 keV, to investigate the energy-dependence effect of the bimodal T {sub 90} distribution. It is found that the bimodal feature is well observed in the 50-100 and 100-350 keV bands, but is only marginally acceptable in the 25-50 keV and 350-1000 keV bands. The hypothesis of bimodality is confidently rejected in the 8-15 and 15-25 keV bands. The T {sub 90} distributions in these bands are roughly consistent with those observed by missions with similar energy bands. The parameter T {sub 90} as a function of energy follows T-bar {sub 90}{proportional_to}E{sup -0.20{+-}0.02} for long GRBs. Considering the erratic X-ray and optical flares, the duration of a burst would be even longer for most GRBs. Our results, together with the observed extended emission of some short GRBs, indicate that the central engine activity timescale would be much longer than T {sub 90} for both long and short GRBs and the observed bimodal T {sub 90} distribution may be due to an instrumental selection effect.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

THE THREE-DIMENSIONAL STRUCTURE OF THE M31 SATELLITE SYSTEM; STRONG EVIDENCE FOR AN INHOMOGENEOUS DISTRIBUTION OF SATELLITES

We undertake an investigation into the spatial structure of the M31 satellite system utilizing the distance distributions presented in a previous publication. These distances make use of the unique combination of depth and spatial coverage of the Pan-Andromeda Archaeological Survey to provide a large, homogeneous sample consisting of 27 of M31's satellites, as well as M31 itself. We find that the satellite distribution, when viewed as a whole, is no more planar than one would expect from a random distribution of equal size. A disk consisting of 15 of the satellites is however found to be highly significant, and strikingly thin, with an rms thickness of just 12.34{sup +0.75}{sub -0.43} kpc. This disk is oriented approximately edge-on with respect to the Milky Way and almost perpendicular to the Milky Way disk. It is also roughly orthogonal to the disk-like structure regularly reported for the Milky Way satellite system and in close alignment with M31's Giant Stellar Stream. A similar analysis of the asymmetry of the M31 satellite distribution finds that it is also significantly larger than one would expect from a random distribution. In particular, it is remarkable that 20 of the 27 satellites most likely lie on the Milky Way side of the galaxy, with the asymmetry being most pronounced within the satellite subset forming the aforementioned disk. This lopsidedness is all the more intriguing in light of the apparent orthogonality observed between the satellite disk structures of the Milky Way and M31.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

THE TWO-DIMENSIONAL PROJECTED SPATIAL DISTRIBUTION OF GLOBULAR CLUSTERS. I. METHOD AND APPLICATION TO NGC 4261

We present a new method for the determination of the two-dimensional (2D) projected spatial distribution of globular clusters (GCs) in external galaxies. This method is based on the K-Nearest Neighbor density estimator of Dressler, complemented by Monte-Carlo simulations to establish the statistical significance of the results. We apply this method to NGC 4261, a ''test galaxy'' where significant 2D anisotropy in the GC distribution has been reported. We confirm that the 2D distribution of GC is not azimuthally isotropic. Moreover, we demonstrate that the 2D distribution departures from the average GC radial distribution results in highly significant spiral-like or broken shell features. Overall, the same perturbations are found in ''red'' and ''blue'' GCs, but with some differences. In particular, we observe a central feature, roughly aligned with the minor axis of NGC 4261, composed of red and most luminous GCs. Blue and fainter GCs are more frequent at large radial distances and follow the spiral-like features of the overall density structure. These results suggest a complex merging history for NGC 4261.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

The neutron star mass distribution

In recent years, the number of pulsars with secure mass measurements has increased to a level that allows us to probe the underlying neutron star (NS) mass distribution in detail. We critically review the radio pulsar mass measurements. For the first time, we are able to analyze a sizable population of NSs with a flexible modeling approach that can effectively accommodate a skewed underlying distribution and asymmetric measurement errors. We find that NSs that have evolved through different evolutionary paths reflect distinctive signatures through dissimilar distribution peak and mass cutoff values. NSs in double NS and NS-white dwarf (WD) systems show consistent respective peaks at 1.33 M {sub ☉} and 1.55 M {sub ☉}, suggesting significant mass accretion (Δm ≈ 0.22 M {sub ☉}) has occurred during the spin-up phase. The width of the mass distribution implied by double NS systems is indicative of a tight initial mass function while the inferred mass range is significantly wider for NSs that have gone through recycling. We find a mass cutoff at ∼2.1 M {sub ☉} for NSs with WD companions, which establishes a firm lower bound for the maximum NS mass. This rules out the majority of strange quark and soft equation of state models as viable configurations for NS matter. The lack of truncation close to the maximum mass cutoff along with the skewed nature of the inferred mass distribution both enforce the suggestion that the 2.1 M {sub ☉} limit is set by evolutionary constraints rather than nuclear physics or general relativity, and the existence of rare supermassive NSs is possible.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Spatial and kinematic distributions of transition populations in intermediate redshift galaxy clusters

We analyze the spatial and velocity distributions of confirmed members in five massive clusters of galaxies at intermediate redshift (0.5 < z < 0.9) to investigate the physical processes driving galaxy evolution. Based on spectral classifications derived from broad- and narrow-band photometry, we define four distinct galaxy populations representing different evolutionary stages: red sequence (RS) galaxies, blue cloud (BC) galaxies, green valley (GV) galaxies, and luminous compact blue galaxies (LCBGs). For each galaxy class, we derive the projected spatial and velocity distribution and characterize the degree of subclustering. We find that RS, BC, and GV galaxies in these clusters have similar velocity distributions, but that BC and GV galaxies tend to avoid the core of the two z ≈ 0.55 clusters. GV galaxies exhibit subclustering properties similar to RS galaxies, but their radial velocity distribution is significantly platykurtic compared to the RS galaxies. The absence of GV galaxies in the cluster cores may explain their somewhat prolonged star-formation history. The LCBGs appear to have recently fallen into the cluster based on their larger velocity dispersion, absence from the cores of the clusters, and different radial velocity distribution than the RS galaxies. Both LCBG and BC galaxies show a high degree of subclustering on the smallest scales, leading us to conclude that star formation is likely triggered by galaxy-galaxy interactions during infall into the cluster.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Size distribution of possible dust carriers for the extended red emission

Power-law size distributions expected to be applicable to possible carriers of extended red emission (ERE) have been examined using Monte Carlo (MC) simulations. Si nanoparticles and some polycyclic aromatic hydrocarbon complexes such as oligoacene and oligorylenes with energy gaps close to 2 eV have been considered. In the simplest case of unit quantum efficiency, the MC-generated size distributions are used to obtain photoluminescence (PL) spectra that are then corrected for dust extinction and reddening effects for comparison with observed ERE spectra. It is shown that a power-law size distribution with a decay exponent of α = 7/2, which closely agrees with starlight extinction data, fails to produce an ERE-like spectrum. However, size distributions with decay exponents of α = 19/12 and 3/2 are found to lead to acceptable spectra. Results indicate that energetic photon-induced breakup and competing aggregation effects dominate collisional effects in producing the observed steady-state mass distribution. It is shown that the peak wavelength of emission critically depends on the band gap, rather than cluster mass, which for oligoacenes and oligorylenes is widely different. The peak wavelength is also shown to be insensitive to dust attenuation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

PROBING THE ROLE OF DYNAMICAL FRICTION IN SHAPING THE BSS RADIAL DISTRIBUTION. I. SEMI-ANALYTICAL MODELS AND PRELIMINARY N-BODY SIMULATIONS

We present semi-analytical models and simplified N-body simulations with 10{sup 4} particles aimed at probing the role of dynamical friction (DF) in determining the radial distribution of blue straggler stars (BSSs) in globular clusters. The semi-analytical models show that DF (which is the only evolutionary mechanism at work) is responsible for the formation of a bimodal distribution with a dip progressively moving toward the external regions of the cluster. However, these models fail to reproduce the formation of the long-lived central peak observed in all dynamically evolved clusters. The results of N-body simulations confirm the formation of a sharp central peak, which remains as a stable feature over time regardless of the initial concentration of the system. In spite of noisy behavior, a bimodal distribution forms in many cases, with the size of the dip increasing as a function of time. In the most advanced stages, the distribution becomes monotonic. These results are in agreement with the observations. Also, the shape of the peak and the location of the minimum (which, in most of cases, is within 10 core radii) turn out to be consistent with observational results. For a more detailed and close comparison with observations, including a proper calibration of the timescales of the dynamical processes driving the evolution of the BSS spatial distribution, more realistic simulations will be necessary.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

LONG GRBs ARE METALLICITY-BIASED TRACERS OF STAR FORMATION: EVIDENCE FROM HOST GALAXIES AND REDSHIFT DISTRIBUTION

We investigate the mass distribution of long gamma-ray burst (GRB) host galaxies and the redshift distribution of long GRBs by considering that long GRBs occur in low-metallicity environments. We calculate the upper limit on the stellar mass of a galaxy which can produce long GRBs by utilizing the mass-metallicity (M-Z) relation of galaxies. After comparing with the observed GRB host galaxies masses, we find that the observed GRB host galaxy masses can fit the predicted masses well if GRBs occur in low-metallicity 12 + log (O/H){sub KK04} < 8.7. GRB host galaxies have low metallicity, low mass, and high star formation rate compared with galaxies of seventh data release of the Sloan Digital Sky Survey. We also study the cumulative redshift distribution of the latest Swift long GRBs by adding dark GRBs and 10 new GRBs redshifts from the TOUGH survey. The observed discrepancy between the GRB rate and the star formation history can be reconciled by considering that GRBs tend to occur in low-metallicity galaxies with 12 + log (O/H){sub KK04} < 8.7. We conclude that the metallicity cutoff that can produce long GRBs is about 12 + log (O/H){sub KK04} < 8.7 from the host mass distribution and redshift distribution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Pseudorapidity distributions of charged particles in pp($\bar p$), p(d)A and AA collisions using Tsallis thermodynamics

The pseudorapidity distributions of charged particles measured in p + p($\overline{\text{p}}$) collisions for energies ranging from $\sqrt{{s}_{\mathrm{N}\mathrm{N}}}=23.6$ GeV to 13 TeV and A + A collisions at RHIC and LHC are investigated in the fireball model with Tsallis thermodynamics. We assume that the rapidity axis is populated with fireballs following q-Gaussian distribution and the charged particles follow the Tsallis distribution in the fireball. We also extend the fireball model to asymmetric collision systems, i.e. d + Au collisions at $\sqrt{{s}_{\mathrm{N}\mathrm{N}}}=200$ GeV and p + Pb collisions at $\sqrt{{s}_{\mathrm{N}\mathrm{N}}}=5.02$ TeV, by taking into account the asymmetric geometry configuration. The model can fit the experimental data well for all the collision systems and centralities investigated. The collision energy and centrality dependence of the model parameters for the symmetric (asymmetric) collision system, i.e. the central position y 0 (y 0a , y 0A ) and its width σ (σ a , σ A ) of the fireball distribution, are also investigated and discussed. Furthermore, our results suggest that the fireball model with Tsallis thermodynamics can be used as a universal framework for the pseudorapidity distributions of charged particles in high energy collisions at RHIC and LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

The rates and time-delay distribution of multiply imaged supernovae behind lensing clusters

Time delays of gravitationally lensed sources can be used to constrain the mass model of a deflector and determine cosmological parameters. We here present an analysis of the time-delay distribution of multiply imaged sources behind 17 strong lensing galaxy clusters with well-calibrated mass models. We find that for time delays less than 1000 days, at z = 3.0, their logarithmic probability distribution functions are well represented by P(log Δt) = 5.3 × 10{sup −4}Δt{sup β-tilde}/M{sub 250}{sup 2β-tilde}, with β-tilde = 0.77, where M{sub 250} is the projected cluster mass inside 250 kpc (in 10{sup 14}M{sub ☉}), and β-tilde is the power-law slope of the distribution. The resultant probability distribution function enables us to estimate the time-delay distribution in a lensing cluster of known mass. For a cluster with M{sub 250} = 2 × 10{sup 14}M{sub ☉}, the fraction of time delays less than 1000 days is approximately 3%. Taking Abell 1689 as an example, its dark halo and brightest galaxies, with central velocity dispersions σ≥500kms{sup −1}, mainly produce large time delays, while galaxy-scale mass clumps are responsible for generating smaller time delays. We estimate the probability of observing multiple images of a supernova in the known images of Abell 1689. A two-component model of estimating the supernova rate is applied in this work. For a magnitude threshold of m{sub AB} = 26.5, the yearly rate of Type Ia (core-collapse) supernovae with time delays less than 1000 days is 0.004±0.002 (0.029±0.001). If the magnitude threshold is lowered to m{sub AB} ∼ 27.0, the rate of core-collapse supernovae suitable for time delay observation is 0.044±0.015 per year.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Anisotropic dark matter distribution functions and impact on WIMP direct detection

Dark matter N-body simulations suggest that the velocity distribution of dark matter is anisotropic. In this work we employ a mass model for the Milky Way whose parameters are determined from a fit to kinematical data. Then we adopt an ansatz for the dark matter phase space distribution which allows to construct self-consistent halo models which feature a degree of anisotropy as a function of the radius such as suggested by the simulations. The resulting velocity distributions are then used for an analysis of current data from dark matter direct detection experiments. We find that velocity distributions which are radially biased at large galactocentric distances (up to the virial radius) lead to an increased high velocity tail of the local dark matter distribution. This affects the interpretation of data from direct detection experiments, especially for dark matter masses around 10 GeV, since in this region the high velocity tail is sampled. We find that the allowed regions in the dark matter mass-cross section plane as indicated by possible hints for a dark matter signal reported by several experiments as well as conflicting exclusion limits from other experiments shift in a similar way when the halo model is varied. Hence, it is not possible to improve the consistency of the data by referring to anisotropic halo models of the type considered in this work.

79 ASTRONOMY AND ASTROPHYSICS↗