The Binary Zoo: The Calculation of Production Rates of Binaries Through 2+1 Encounters in Globular Clusters

In studying encounters between binaries and single stars, one is interested in three classes of events: exchanges of stars, hardening of the original binary by a third star, and the production of merged objects. We present a means for computing cross sections for these three outcomes for an arbitrary binary and single star as might be found in the core of a globular cluster. The cross sections for a number of binaries in various stellar populations are then computed. We consider multiple encounters and the ultimate fate of a population of binaries fed into the cores of different globular cluster models. We see that the presence of only a relatively small number of binaries (containing 10\% of the stars) will boost the production rate of astrophysically-interesting objects by a factor of at least a few over the rates expected from encounters between single stars. In particular, the ratio of smothered neutron stars to low-mass X-ray binaries (LMXBs) may be greatly increased, possibly explaining, in part, the excess of millisecond pulsars compared to LMXBs.Comment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

Spectral Pollution

We discuss the problems arising when computing eigenvalues of self-adjoint operators which lie in a gap between two parts of the essential spectrum. Spectral pollution, i.e. the apparent existence of eigenvalues in numerical computations, when no such eigenvalues actually exist, is commonplace in problems arising in applied mathematics. We describe a geometrically inspired method which avoids this difficulty, and show that it yields the same results as an algorithm of Zimmermann and Mertins.Comment: 23 page

Space photography and the exploration of Mars

A general exposition of the scientific potentialities and analytic framework of space photography is presented using the photography of Mars from flybys and orbiters as the principal example. Space photography is treated here as a communication process in which planetary scene information is communicated to the eye-brain receiver of earth-based interpreters. The salient parameters of this process are: (1) total information returned, (2) surface resolution, and (3) a priori knowledge regarding the planetary surface observed

Close Approach during Hard Binary--Binary Scattering

We report on an extensive series of numerical experiments of binary--binary scattering, analysing the cross--section for close approach during interactions for a range of hard binary parameters of interest in globular cluster cores. We consider the implied rate for tidal interactions for different globular clusters and compare our results with previous, complementary estimates of stellar collision rates in globular clusters. We find that the collision rate for binary--binary encounters dominates in low density clusters if the binary fraction in the cluster is larger than $0.2$ for wide main--sequence binaries. In dense clusters binary--single interactions dominate the collision rate and the core binary fraction must be \ltorder 0.1 per decade in semi--major axis or too many collisions take place compared to observations. The rates are consistent if binaries with semi--major axes $\sim 100 AU$ are overabundant in low density clusters or if breakup and ejection substantially lowers the binary fraction in denser clusters. Given reasonable assumptions about fractions of binaries in the cores of low density clusters such as NGC~5053, we cannot account for all the observed blue stragglers by stellar collisions during binary encounters, suggesting a substantial fraction may be due to coalescence of tight primordial binaries.Comment: 13 pages including 13 ps figures. MNRAS in pres

Infrared diode laser spectroscopy of the fundamental band of NF(a1Δ)

Thirty-one lines of the fundamental vibration–rotation band of the NF free radical in its a 1 state have been detected in absorption near 8.6 µm using a tunable infrared diode laser. Linewidths were Doppler limited and several transitions were accompanied by resolved hyperfine structure due to fluorine and nitrogen nuclear moments. Wave number calibration using accurately determined N2O lines yielded v0 = 1165.952±0.001 cm^−1 for the band center. Rotational and centrifugal distortion constants for both v = 0 and 1 states have also been determined

A numerical investigation of the solution of a class of fourth-order eigenvalue problems

This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are summarized and their implications for numerical approximation are discussed. In particular, the asymptotic behaviour of the first eigenfunction is studied since it is known that this has an unbounded number of oscillations when approaching certain types of corners on domain boundaries. Recent computational results of Bjorstad & Tjostheim, using a highly accurate spectral Legendre-Galerkin method, have demonstrated that a number of these sign changes may be accurately computed on a square domain provided sufficient care is taken with the numerical method. We demonstrate that similar accuracy is also achieved using an unstructured finite-element solver which may be applied to problems on domains with arbitrary geometries. A number of results obtained from this mixed finite-element approach are then presented for a variety of domains. These include a family of circular sector regions, for which the oscillatory behaviour is studied as a function of the internal angle, and another family of (symmetric and non-convex) domains, for which the parity of the least eigenfunction is investigated. The paper not only verifies existing asymptotic theory, but also allows us to make a new conjecture concerning the eigenfunctions of the biharmonic operator

SINFONI's take on Star Formation, Molecular Gas, and Black Hole Masses in AGN

We present some preliminary (half-way) results on our adaptive optics spectroscopic survey of AGN at spatial scales down to 0.085arcsec. Most of the data were obtained with SINFONI which provides integral field capability at a spectral resolution of R~4000. The themes on which we focus in this contribution are: star formation around the AGN, the properties of the molecular gas and its relation to the torus, and the mass of the black hole.Comment: 5 pages, 2 figures. To appear in Science Perspectives for 3D Spectroscopy. ESO Astrophysics Symposia. Ed by M. Kissler-Patig, M. Roth and J. Wals

The effect of stellar-mass black holes on the structural evolution of massive star clusters

We present the results of realistic N-body modelling of massive star clusters in the Magellanic Clouds, aimed at investigating a dynamical origin for the radius-age trend observed in these systems. We find that stellar-mass black holes, formed in the supernova explosions of the most massive cluster stars, can constitute a dynamically important population. If a significant number of black holes are retained (here we assume complete retention), these objects rapidly form a dense core where interactions are common, resulting in the scattering of black holes into the cluster halo, and the ejection of black holes from the cluster. These two processes heat the stellar component, resulting in prolonged core expansion of a magnitude matching the observations. Significant core evolution is also observed in Magellanic Cloud clusters at early times. We find that this does not result from the action of black holes, but can be reproduced by the effects of mass-loss due to rapid stellar evolution in a primordially mass segregated cluster.Comment: Accepted for publication in MNRAS Letters; 2 figures, 1 tabl