Lunar Occultation of MACHOs

Lunar occultation can be used to measure the proper motions of some of the long time scale microlensing events, t_{e} \gsim 70 days, now being detected toward the Galactic bulge. The long events are difficult to explain within the context of standard models of the mass distribution and dynamics of the Galaxy. Han & Gould (1995b) have suggested that they may be due to a kinematically cold population near the Sun. To resolve the mass, distance, and velocity of individual events and so to determine their nature, one must measure parallaxes and proper motions. For long events, parallaxes can be often obtained from ground-based measurements, but proper motions can only rarely be determined using conventional methods. Lunar occultations are therefore key to the understanding of the long events. We carry out realistic simulations to estimate the uncertainty of these measurements and show that proper motions could be measured for about one long event per year.Comment: 17 pages, 3 figures, request hard copy of preprint to [email protected]

Luminosity Function of the Perigalactocentric Region

We present H and K photometry of 42,000 stars in an area of 250 arcmin$^{2}$ centered on the Galactic center. We use the photometry to construct a dereddened K band luminosity function (LF) for this region, excluding the excessively crowded inner 2' of the Galaxy. This LF is intermediate between the LF of Baade's window and the LF of inner 2' of the Galactic center. We speculate that the bright stars in this region have an age which is intermediate between the starburst population in the Galactic center and the old bulge population. We present the coordinates and mags for 16 stars with K_{0} < 5 for spectroscopic follow up.Comment: 25 pages. Tarred, gzipped and uuencoded. Includes LaTex source file, Figures 3 to 9 and 5 Tables. Figures 1 and 2 are available at ftp://bessel.mps.ohio-state.edu/pub/vijay . Submitted to Ap

Biased Estimates of Omega from Comparing Smoothed Predicted Velocity Fields to Unsmoothed Peculiar Velocity Measurements

We show that a regression of unsmoothed peculiar velocity measurements against peculiar velocities predicted from a smoothed galaxy density field leads to a biased estimate of the cosmological density parameter Omega, even when galaxies trace the underlying mass distribution and galaxy positions and velocities are known perfectly. The bias arises because the errors in the predicted velocities are correlated with the predicted velocities themselves. We investigate this bias using cosmological N-body simulations and analytic arguments. In linear perturbation theory, for cold dark matter power spectra and Gaussian or top hat smoothing filters, the bias in Omega is always positive, and its magnitude increases with increasing smoothing scale. This linear calculation reproduces the N-body results for Gaussian smoothing radii R_s > 10 Mpc/h, while non-linear effects lower the bias on smaller smoothing scales, and for R_s < 3 Mpc/h Omega is underestimated rather than overestimated. The net bias in Omega for a given smoothing filter depends on the underlying cosmological model. The effect on current estimates of Omega from velocity-velocity comparisons is probably small relative to other uncertainties, but taking full advantage of the statistical precision of future peculiar velocity data sets will require either equal smoothing of the predicted and measured velocity fields or careful accounting for the biases discussed here.Comment: 11 pages including 2 eps figures. Submitted to Ap

Syntheses of Functionalised [2.2]Paracyclophanes: Structure and Reactivity Studies

[2.2]Paracyclophane, a strained sandwich structured molecule, possessing bent benzene rings due to the short ethano bridges, has interested chemists, theoreticians and industrialists over many years. It has found a wide variety of application in stereoselective synthesis, material science, basic organic and supramolecular chemistry are a few to mention. It is also a multi ton industrial product used as a monomer in polymer chemistry. In this thesis, the syntheses of various functionalised [2.2]paracyclophane derivatives possessing different substitution patterns are described. Also a new class of indanono- and indenonophanes have been described. The functionalised cyclophanes structural, chemical, mechanistic and spectroscopic properties have been studied carefully and extensively. These functionalised cyclophanes were also subjected to polymerisation by chemical vapour deposition.[2.2]Paracyclophan, ein gespanntes Molekuel mit sandwichartiger Struktur, welches aufgrund der kurzen Ethanobruecken bootfoermig verzerrte Benzolringe aufweist ist seit Jahren von Interesse für Chemiker, Theoretiker und die Chemische Industrie. Anwendungsbereiche sind unter anderem stereoselektive Synthese, Materialwissenschaften, Organische und Supramolekulare Chemie. Dieses im multi Tonnen Maßstab industriell gefertigte Produkt wird als Monomer in der Polymerchemie verwendet. In dieser Dissertation wird die Synthese einer Vielzahl funktionalisierter [2.2]Paracyclophanderivate mit einem breiten Spektrum an Substitutionsmustern beschrieben. Ebenfalls wird eine neue Klasse von Indanono- und Indenonophanen beschrieben. Die strukturellen, chemischen, mechanistischen und spektroskopischen Eigenschaften der funktionalisierten Cyclophane wurde eingehend untersucht. Darüber hinaus wurden dieser funktionalisierten Cyclophane für die Polymerisation durch Chemical Vapour Deposition genutzt

Bott--Kitaev periodic table and index theory

We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be computed by a topological index. We focus on the spatial dimensions one, two and three, and only consider the bulk theory. In two dimensions, the $\mathbb{Z}$-valued invariants are given by the first Chern number. Meanwhile, $\mathbb{Z}_2$-valued invariants can be computed by the odd topological index and its variations. The Bott-Kitaev periodic table is well-known in the physics literature, we organize the topological invariants in the framework of KR-theory.Comment: 37 page

Lyman-alpha Forest Constraints on the Mass of Warm Dark Matter and the Shape of the Linear Power Spectrum

High resolution N-body simulations of cold dark matter (CDM) models predict that galaxies and clusters have cuspy halos with excessive substructure. Observations reveal smooth halos with central density cores. One possible resolution of this conflict is that the dark matter is warm (WDM); this will suppress the power spectrum on small scales. The Lyman-alpha forest is a powerful probe of the linear power spectrum on these scales. We use collisionless N-body simulations to follow the evolution of structure in WDM models, and analyze artificial Lyman-alpha forest spectra extracted from them. By requiring that there is enough small-scale power in the linear power spectrum to reproduce the observed properties of the Lyman-alpha forest in quasar spectra, we derive a lower limit to the mass of the WDM particle of 750 eV. This limit is robust to reasonable uncertainties in our assumption about the temperature of the mean density gas (T0) at z=3. We argue that any model that suppresses the CDM linear theory power spectrum more severely than a 750 eV WDM particle cannot produce the Lyman-alpha forest.Comment: 13 pages including 4 color Figures and 1 Table, submitted to ApJ Letter