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Growth and characterization of binary and pseudo-binary 3-5 compounds exhibiting non-linear optical behavior. Undergraduate research opportunities in microgravity science and technology

In line with the specified objectives, a Bridgman-type growth configuration in which unavoidable end effects - conventionally leading to growth interface relocation - are compensated by commensurate input-power changes is developed; the growth rate on a microscale is predictable and unaffected by changes in heat transfer conditions. To permit quantitative characterization of the growth furnace cavity (hot-zone), a 3-D thermal field mapping technique, based on the thermal image, is being tested for temperatures up to 1100 C. Computational NIR absorption analysis was modified to now permit characterization of semi-insulating single crystals. Work on growth and characterization of bismuth-silicate was initiated. Growth of BSO (B12SiO20) for seed material by the Czochralski technique is currently in progress. Undergraduate research currently in progress includes: ground based measurements of the wetting behavior (contact angles) of semiconductor melts on substrates consisting of potential confinement materials for solidification experiments in a reduced gravity environment. Hardware modifications required for execution of the wetting experiments in a KC-135 facility are developed.

Witt, August F.

High Energy Interactions in Massive Binaries: An Application to a Most Mysterious Binary

Extremely massive stars (50M and above) are exceedingly rare in the local Universe but are believed to have composed the entire first generation of stars, which lived fast, died young and left behind the first generation of black holes and set the stage for the formation of lower mass stars suitable to support life. There are significant uncertainties about how this happened (and how it still happens), mostly due to our poor knowledge of how stars change mass as they evolve. Extremely massive stars give mass back to the ISM via strong radiatively-driven winds and sometimes through sporadic eruptions of the most massive and brightest stars. Such mass loss plays an important role in the chemical and dynamical evolution of the local interstellar medium prior to the supernova explosion. Below we discuss how high energy thermal (and, in some cases, non-thermal) emission, along with modern simulations in 2 and 3 dimensions, can be used to help determine a physically realistic picture of mass loss in a well-studied, mysterious system.

Corcoran, Michael

Primordial main equence binary stars in the globular cluster M71

We report the identification of five short-period variables near the center of the metal-rich globular cluster M71. Our observations consist of multiepoch VI charge coupled device (CCD) images centered on the cluster and covering a 6.3 min x 6.3 min field. Four of these variables are contact eclipsing binaries with periods between 0.35 and 0.41 days; one is a detached or semidetached eclipsing binary with a period of 0.56 days. Two of the variables were first identified as possible eclipsing binaries in an earlier survey by Hodder et al. (1992). We have used a variety of arguments to conclude that all five binary stars are probable members of M71, a result that is consistent with the low number (0.15) of short-period field binaries expected along this line of sight. Based on a simple model of how contact binaries evolve from initially detached binaries, we have determined a lower limit of 1.3% on the frequency of primordial binaries in M71 with initial orbital periods in the range 2.5 - 5 days. This implies that the overall primordial binary frequency, f, is 22(sup +26)(sub -12)% assuming df/d log P = const ( the 'flat' distribution), or f = 57(sup +15)(sub -8)% for df/d log P = 0.032 log P + const as observed for G-dwarf binaries in the solar neighborhood (the 'sloped' distribution). Both estimates of f correspond to binaries with initial periods shorter than 800 yr since any longer-period binaries would have been disrupted over the lifetime of the cluster. Our short-period binary frequency is in excellent agreement with the observed frequency of red-giant binaries observed in globulars if we adopt the flat distribution. For the sloped distribution, our results significantly overestimate the number of red-giant binaries. All of the short-period M71 binaries lie within 1 mag of the luminosity of the cluster turnoff in the color-magnitude diagram despite the fact we should have easily detected similar eclipsing binaries 2 - 2.5 mag fainter than this. We discuss the implications of this on our estimates of the binary frequency in M71 and on the formation of blue stragglers.

Yan, Lin

Formation and Evolution of Binary Systems Containing Collapsed Stars

This research includes theoretical studies of the formation and evolution of five types of interacting binary systems. Our main focus has been on developing a number of comprehensive population synthesis codes to study the following types of binary systems: (i) cataclysmic variables (#3, #8, #12, #15), (ii) low- and intermediate-mass X-ray binaries (#13, #20, #21), (iii) high-mass X-ray binaries (#14, #17, #22), (iv) recycled binary millisecond pulsars in globular clusters (#5, #10, #ll), and (v) planetary nebulae which form in interacting binaries (#6, #9). The numbers in parentheses refer to papers published or in preparation that are listed in this paper. These codes take a new unified approach to population synthesis studies. The first step involves a Monte Carlo selection of the primordial binaries, including the constituent masses, and orbital separations and eccentricities. Next, a variety of analytic methods are used to evolve the primary star to the point where either a dynamical episode of mass transfer to the secondary occurs (the common envelope phase), or the system evolves down an alternate path. If the residual core of the primary is greater than 2.5 solar mass, it will evolve to Fe core collapse and the production of a neutron star and a supernova explosion. In the case of systems involving neutron stars, a kick velocity is chosen randomly from an appropriate distribution and added to the orbital dynamics which determine the state of the binary system after the supernova explosion. In the third step, all binaries which commence stable mass transfer from the donor star (the original secondary in the binary system) to the compact object, are followed with a detailed binary evolution code. Finally, we include all the relevant dynamics of the binary system. For example, in the case of LMXBs, the binary system, with its recoil velocity from the supernova explosion, is followed in time through its path in the Galactic potential. For our globular cluster study, detailed three-body calculations are used to follow the interactions of the binary with passing field stars.

Rappaport, Saul

Efficient algorithms for dilated mappings of binary trees

The problem is addressed to find a 1-1 mapping of the vertices of a binary tree onto those of a target binary tree such that the son of a node on the first binary tree is mapped onto a descendent of the image of that node in the second binary tree. There are two natural measures of the cost of this mapping, namely the dilation cost, i.e., the maximum distance in the target binary tree between the images of vertices that are adjacent in the original tree. The other measure, expansion cost, is defined as the number of extra nodes/edges to be added to the target binary tree in order to ensure a 1-1 mapping. An efficient algorithm to find a mapping of one binary tree onto another is described. It is shown that it is possible to minimize one cost of mapping at the expense of the other. This problem arises when designing pipelined arithmetic logic units (ALU) for special purpose computers. The pipeline is composed of ALU chips connected in the form of a binary tree. The operands to the pipeline can be supplied to the leaf nodes of the binary tree which then process and pass the results up to their parents. The final result is available at the root. As each new application may require a distinct nesting of operations, it is useful to be able to find a good mapping of a new binary tree over existing ALU tree. Another problem arises if every distinct required binary tree is known beforehand. Here it is useful to hardwire the pipeline in the form of a minimal supertree that contains all required binary trees.

Iqbal, M. Ashraf

A m-ary linear feedback shift register with binary logic

A family of m-ary linear feedback shift registers with binary logic is disclosed. Each m-ary linear feedback shift register with binary logic generates a binary representation of a nonbinary recurring sequence, producible with a m-ary linear feedback shift register without binary logic in which m is greater than 2. The state table of a m-ary linear feedback shift register without binary logic, utilizing sum modulo m feedback, is first tubulated for a given initial state. The entries in the state table are coded in binary and the binary entries are used to set the initial states of the stages of a plurality of binary shift registers. A single feedback logic unit is employed which provides a separate feedback binary digit to each binary register as a function of the states of corresponding stages of the binary registers.

Perlman, M.

The evolution of a primordial binary population in a globular cluster

A simple model is presented for the evolution of a primordial binary population in a globular cluster. Monte Carlo simulations are given for an initial population of 50,000 binaries against a fixed background population of 500,000 single stars in a tidally truncated cluster model. Individual histories of all binaries are followed through mass segregation, scattering recoil, escape from the cluster, or coalescence. It is found that most binaries are destroyed by binary-binary interactions, with the rest escaping in the point-mass approximation. In a more realistic model, the majority of the rest merge. At any instant, most of the remaining binaries are drifting in toward the center before their first strong encounter. A typical binary spends most of its active life in or near the cluster core. The few binaries which receive a recoil sufficient to place them in the halo past the half-mass radius remain there long enough to make a significant contribution to the radial binary distribution.

Hut, Piet

Long-Term Stability of Planets in Binary Systems

A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the systems center of mass, are examined. From the results, empirical expressions are developed for both (1) the largest orbit around each of the stars and (2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (10A4 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio mu and the binary eccentricity e, are determined for the range 0.0=e=0.7-0.8 and 0.1=mu=0.9 in both regions and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually interacting system of planets orbiting one star of a binary system is examined, though in less detail.

Holman, Matthew J.

Search for Gravitational Waves from Low Mass Compact Binary Coalescence in LIGO's Sixth Science Run and Virgo's Science Runs 2 and 3

We report on a search for gravitational waves from coalescing compact binaries using LIGO and Virgo observations between July 7, 2009, and October 20. 2010. We searched for signals from binaries with total mass between 2 and 25 Stellar Mass; this includes binary neutron stars, binary black holes, and binaries consisting of a black hole and neutron star. The detectors were sensitive to systems up to 40 Mpc distant for binary neutron stars, and further for higher mass systems. No gravitational-wave signals were detected. We report upper limits on the rate of compact binary coalescence as a function of total mass. including the results from previous LIGO and Virgo observations. The cumulative 90% confidence rate upper limits of the binary coalescence of binary neutron star, neutron star-black hole, and binary black hole systems are 1.3 x 10(exp -4), 3.1 x 10(exp -5), and 6.4 x 10(exp -6)/cu Mpc/yr, respectively. These upper limits are up to a factor 1.4 lower than previously derived limits. We also report on results from a blind injection challenge.

Abadie, J.

The NANOGrav 11yr Data Set: Limits on Supermassive Black Hole Binaries in Galaxies within 500 Mpc

Supermassive black hole binaries (SMBHBs) should form frequently in galactic nuclei as a result of galaxy mergers. At subparsec separations, binaries become strong sources of low-frequency gravitational waves (GWs), targeted by Pulsar Timing Arrays. We used recent upper limits on continuous GWs from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 11 yr data set to place constraints on putative SMBHBs in nearby massive galaxies. We compiled a comprehensive catalog of ∼44,000 galaxies in the local universe (up to redshift ∼0.05) and populated them with hypothetical binaries, assuming that the total mass of the binary is equal to the SMBH mass derived from global scaling relations. Assuming circular equal-mass binaries emitting at NANOGrav's most sensitive frequency of 8 nHz, we found that 216 galaxies are within NANOGrav's sensitivity volume. We ranked the potential SMBHBs based on GW detectability by calculating the total signal-to-noise ratio such binaries would induce within the NANOGrav array. We placed constraints on the chirp mass and mass ratio of the 216 hypothetical binaries. For 19 galaxies, only very unequal-mass binaries are allowed, with the mass of the secondary less than 10% that of the primary, roughly comparable to constraints on an SMBHB in the Milky Way. However, we demonstrated that the (typically large) uncertainties in the mass measurements can weaken the upper limits on the chirp mass. Additionally, we were able to exclude binaries delivered by major mergers (mass ratio of at least 1/4) for several of these galaxies. We also derived the first limit on the density of binaries delivered by major mergers purely based on GW data.

Zaven Arzoumanian

Dynamics of binary-disk interaction. 1: Resonances and disk gap sizes

We investigate the gravitational interaction of a generally eccentric binary star system with circumbinary and circumstellar gaseous disks. The disks are assumed to be coplanar with the binary, geometrically thin, and primarily governed by gas pressure and (turbulent) viscosity but not self-gravity. Both ordinary and eccentric Lindblad resonances are primarily responsible for truncating the disks in binaries with arbitrary eccentricity and nonextreme mass ratio. Starting from a smooth disk configuration, after the gravitational field of the binary truncates the disk on the dynamical timescale, a quasi-equilibrium is achieved, in which the resonant and viscous torques balance each other and any changes in the structure of the disk (e.g., due to global viscous evolution) occur slowly, preserving the average size of the gap. We analytically compute the approximate sizes of disks (or disk gaps) as a function of binary mass ratio and eccentricity in this quasi-equilibrium. Comparing the gap sizes with results of direct simulations using the smoothed particle hydrodynamics (SPH), we obtain a good agreement. As a by-product of the computations, we verify that standard SPH codes can adequately represent the dynamics of disks with moderate viscosity, Reynolds number R approximately 10(exp 3). For typical viscous disk parameters, and with a denoting the binary semimajor axis, the inner edge location of a circumbinary disk varies from 1.8a to 2.6a with binary eccentricity increasing from 0 to 0.25. For eccentricities 0 less than e less than 0.75, the minimum separation between a component star and the circumbinary disk inner edge is greater than a. Our calculations are relevant, among others, to protobinary stars and the recently discovered T Tau pre-main-sequence binaries. We briefly examine the case of a pre-main-sequence spectroscopic binary GW Ori and conclude that circumbinary disk truncation to the size required by one proposed spectroscopic model cannot be due to Linblad resonances, even if the disk is nonviscous.

Artymowicz, Pawel

Efficient Merge and Insert Operations for Binary Heaps and Trees

Binary heaps and binary search trees merge efficiently. We introduce a new amortized analysis that allows us to prove the cost of merging either binary heaps or balanced binary trees is O(l), in the amortized sense. The standard set of other operations (create, insert, delete, extract minimum, in the case of binary heaps, and balanced binary trees, as well as a search operation for balanced binary trees) remain with a cost of O(log n). For binary heaps implemented as arrays, we show a new merge algorithm that has a single operation cost for merging two heaps, a and b, of O(absolute value of a + min(log absolute value of b log log absolute value of b. log absolute value of a log absolute value of b). This is an improvement over O(absolute value of a + log absolute value of a log absolute value of b). The cost of the new merge is so low that it can be used in a new structure which we call shadow heaps. to implement the insert operation to a tunable efficiency. Shadow heaps support the insert operation for simple priority queues in an amortized time of O(f(n)) and other operations in time O((log n log log n)/f (n)), where 1 less than or equal to f (n) less than or equal to log log n. More generally, the results here show that any data structure with operations that change its size by at most one, with the exception of a merge (aka meld) operation, can efficiently amortize the cost of the merge under conditions that are true for most implementations of binary heaps and search trees.

Kuszmaul, Christopher Lee

Terrestrial Planet Formation in Binary Star Systems

Most stars reside in binary/multiple star systems; however, previous models of planet formation have studied growth of bodies orbiting an isolated single star. Disk material has been observed around one or both components of various young close binary star systems. If planets form at the right places within such disks, they can remain dynamically stable for very long times. We have simulated the late stages of growth of terrestrial planets in both circumbinary disks around 'close' binary star systems with stellar separations ($a_B$) in the range 0.05 AU $\le a_B \le$ 0.4 AU and binary eccentricities in the range $0 \le e \le 0.8$ and circumstellar disks around individual stars with binary separations of tens of AU. The initial disk of planetary embryos is the same as that used for simulating the late stages of terrestrial planet growth within our Solar System and around individual stars in the Alpha Centauri system (Quintana et al. 2002, A.J., 576, 982); giant planets analogous to Jupiter and Saturn are included if their orbits are stable. The planetary systems formed around close binaries with stellar apastron distances less than or equal to 0.2 AU with small stellar eccentricities are very similar to those formed in the Sun-Jupiter-Saturn, whereas planetary systems formed around binaries with larger maximum separations tend to be sparser, with fewer planets, especially interior to 1 AU. Likewise, when the binary periastron exceeds 10 AU, terrestrial planets can form over essentially the entire range of orbits allowed for single stars with Jupiter-like planets, although fewer terrestrial planets tend to form within high eccentricity binary systems. As the binary periastron decreases, the radial extent of the terrestrial planet systems is reduced accordingly. When the periastron is 5 AU, the formation of Earth-like planets near 1 AU is compromised.

Lissauer, J. J.

Presupernova evolution in massive interacting binaries

The way in which binary interaction affects the presupernova evolution of massive close binaries and the resulting supernova explosions is investigated systematically by means of a Henyey-type stellar evolution code that was modified to allow its application to binary stellar evolution calculations. The code makes it possible to trace the effects of mass and angular momentum loss from the binary, as well as mass transfer within the binary system. It is found that a large number of binary scenarios can be distinguished, depending on the type of binary interaction and the evolutionary stage of the supernova progenitor at the time of the interaction. Monte Carlo simulations are performed to estimate the frequencies of the occurrence of various scenarios. It is found that, because of a previous binary interaction, 15-30 percent of all massive stars (with initial masses greater than about 8 solar masses) become helium stars, and another 5 percent of all massive stars end their lives as blue supergiants rather than as red supergiants.

Podsiadlowski, PH.