Two-Component Fokker-Planck Models for the Evolution of Isolated Globular Clusters

Two-component (normal and degenerate stars) models are the simplest realization of clusters with a mass spectrum because high mass stars evolve quickly into degenerates, while low mass stars remain on the main-sequence for the age of the universe. Here we examine the evolution of isolated globular clusters using two-component Fokker-Planck (FP) models that include heating by binaries formed in tidal capture and in three-body encounters. Three-body binary heating dominates and the postcollapse expansion is self-similar, at least in models with total mass M <= 3 x 10^5 M_\odot, initial half-mass radius r_{h,i} >= 5 pc, component mass ratio m_2/m_1 <= 2, and number ratio N_1/N_2 <= 300 when m_2=1.4 M_\odot. We derive scaling laws for \rho_c, v_c, r_c, and r_h as functions of m_1/m_2, N, M, and time t from simple energy-balance arguments, and these agree well with the FP simulations. We have studied the conditions under which gravothermal oscillations (GTOs) occur. If E_{tot} and E_c are the energies of the cluster and of the core, respectively, and t_{rh} and t_c are their relaxation times, then \epsilon \equiv (E_{tot}/t_{rh})/(E_c/t_{rc}) is a good predictor of GTOs: all models with \epsilon>0.01 are stable, and all but one with \epsilon < 0.01 oscillate. We derive a scaling law for \epsilon against N and m_1/m_2 and compared with our numerical results. Clusters with larger m_2/m_1 or smaller N are stabler.Comment: 15 pages (LaTeX) with 8 figures. To appear in ApJ March 10, 1998 issu

The Local Instability of Steady Astrophysical Flows with non Circular Streamlines with Application to Differentially Rotating Disks with Free Eccentricity

We carry out a general study of the stability of astrophysical flows that appear steady in a uniformly rotating frame. Such a flow might correspond to a stellar pulsation mode or an accretion disk with a free global distortion giving it finite eccentricity. We consider perturbations arbitrarily localized in the neighbourhood of unperturbed fluid streamlines.When conditions do not vary around them, perturbations take the form of oscillatory inertial or gravity modes. However, when conditions do vary so that a circulating fluid element is subject to periodic variations, parametric instability may occur. For nearly circular streamlines, the dense spectra associated with inertial or gravity modes ensure that resonance conditions can always be satisfied when twice the period of circulation round a streamline falls within. We apply our formalism to a differentially rotating disk for which the streamlines are Keplerian ellipses, with free eccentricity up to 0.7, which do not precess in an inertial frame. We show that for small $e,$ the instability involves parametric excitation of two modes with azimuthal mode number differing by unity in magnitude which have a period of twice the period of variation as viewed from a circulating unperturbed fluid element. Instability persists over a widening range of wave numbers with increasing growth rates for larger eccentricities. The nonlinear outcome is studied in a follow up paper which indicates development of small scale subsonic turbulence.Comment: Accepted for publication in Astronomy and Astrophysic

A Weakly nonlinear theory for spiral density waves excited by accretion disc turbulence

We develop an analytic theory to describe spiral density waves propagating in a shearing disc in the weakly nonlinear regime. Such waves are generically found to be excited in simulations of turbulent accretion disks, in particular if said turbulence arises from the magneto-rotational instability (MRI). We derive a modified Burgers equation governing their dynamics, which includes the effects of nonlinear steepening, dispersion, and a bulk viscosity to support shocks. We solve this equation approximately to obtain nonlinear sawtooth solutions that are asymptotically valid at late times. In this limit, the presence of shocks is found to cause the wave amplitude to decrease with time as 1/t^2. The validity of the analytic description is confirmed by direct numerical solution of the full nonlinear equations of motion. The asymptotic forms of the wave profiles of the state variables are also found to occur in MRI simulations indicating that dissipation due to shocks plays a significant role apart from any effects arising from direct coupling to the turbulence

A new approach to the problem of modes in the Mestel disk

We examine the modes admitted by the Mestel disk, a disk with a globally flat rotation curve. In contrast to previous analyses of this problem by Zang (\cite{1976PhDT........26Z}) and Evans & Read (\cite{1998MNRAS.300...83E}, \cite{1998MNRAS.300..106E}), we approximate the orbits to obtain almost closed expressions for the kernel of the integral equation governing the behaviour of the modes. Otherwise we, like them, follow Kalnajs' programme to simultaneously solve the Boltzmann and Poisson equations. We investigate the modes admitted by both the self-consistent and a cut-out Mestel disk, the difference being that in the latter, a part of the matter in the disk is immobilised. This breaks the self-similarity and produces a pronouncedly different picture, both technically and in terms of the disk properties. The self-consistent disk is governed by a Cauchy integral equation, the cut-out disk by an integral equation that can be treated as a Fredholm equation of the second kind. In general, our approximation reproduces the results of the previous works remarkably well, yielding quantities mostly within 5% of the values reported by Zang and Evans & Read and thus also the basic result that in a ``standard'' cut-out disk, only one-armed modes are unstable at the limit of axisymmetric stability. In the self-consistent disk, relatively compact expressions for the kernel allow an intuitive understanding of most of the properties of neutral (non-rotating, non-growing) modes there. We finally show that self-consistent Mestel disks do not admit growing or rotating modes in this sort of stellar-dynamical analysis.Comment: 10 pages, 1 figure; accepted for publication in A&

FTIR spectra and conformations of 2′-deoxyuridine in Kr matrices

The Fourier transform infrared spectra in the range 4000–200 cm⁻¹ of pyrimidine nucleoside 2'-deoxyuridine (dU) have been obtained in the low temperature inert Kr matrices. For the first time, instead of a usual flat mirror, a low temperature one-coordinate retroreflector was used as the matrix substrate. Owing to this, the matrix setup is insensitive to dip angle vibrations of the cryostat and is favourable to work with thinner matrix layers. Of two syn-conformers with dU_s1 and dU_s2 (stabilized by the intramolecular hydrogen bond O5'H…O2), only dT_s2 conformer with C2'-endo structure of the ribose ring was uniquely quenched. The height of the interconversion barrier of the minor syn-conformer dU_s1 was estimated to be below 0.7 kcal/mole. It was shown that the energy relaxation of impurities in Kr is slower than in Ar matrices

Planetary Torques as the Viscosity of Protoplanetary Disks

We revisit the idea that density-wave wakes of planets drive accretion in protostellar disks. The effects of many small planets can be represented as a viscosity if the wakes damp locally, but the viscosity is proportional to the damping length. Damping occurs mainly by shocks even for earth-mass planets. The excitation of the wake follows from standard linear theory including the torque cutoff. We use this as input to an approximate but quantitative nonlinear theory based on Burger's equation for the subsequent propagation and shock. Shock damping is indeed local but weakly so. If all metals in a minimum-mass solar nebula are invested in planets of a few earth masses each, dimensionless viscosities [alpha] of order dex(-4) to dex(-3) result. We compare this with observational constraints. Such small planets would have escaped detection in radial-velocity surveys and could be ubiquitous. If so, then the similarity of the observed lifetime of T Tauri disks to the theoretical timescale for assembling a rocky planet may be fate rather than coincidence.Comment: 23 pages, 3 figures. Uses aastex50

Yours ever (well, maybe): Studies and signposts in letter writing

Electronic mail and other digital communications technologies seemingly threaten to end the era of handwritten and typed letters, now affectionately seen as part of snail mail. In this essay, I analyze a group of popular and scholarly studies about letter writing-including examples of pundits critiquing the use of e-mail, etiquette manuals advising why the handwritten letter still possesses value, historians and literary scholars studying the role of letters in the past and what it tells us about our present attitudes about digital communications technologies, and futurists predicting how we will function as personal archivists maintaining every document including e-mail. These are useful guideposts for archivists, providing both a sense of the present and the past in the role, value and nature of letters and their successors. They also provide insights into how such documents should be studied, expanding our gaze beyond the particular letters, to the tools used to create them and the traditions dictating their form and function. We also can discern a role for archivists, both for contributing to the literature about documents and in using these studies and commentaries, suggesting not a new disciplinary realm but opportunities for new interdisciplinary work. Examining a documentary form makes us more sensitive to both the innovations and traditions as it shifts from the analog to the digital; we can learn not to be caught up in hysteria or nostalgia about one form over another and archivists can learn about what they might expect in their labors to document society and its institutions. At one time, paper was part of an innovative technology, with roles very similar to the Internet and e-mail today. It may be that the shifts are far less revolutionary than is often assumed. Reading such works also suggests, finally, that archivists ought to rethink how they view their own knowledge and how it is constructed and used. © 2010 Springer Science+Business Media B.V

Optimal NHS service delivery to care homes: a realist evaluation of the features and mechanisms that support effective working for the continuing care of older people in residential settings

Background Care homes are the institutional providers of long-term care for older people. The OPTIMAL study argued that it is probable that there are key activities within different models of health-care provision that are important for residents’ health care. Objectives To understand ‘what works, for whom, why and in what circumstances?’. Study questions focused on how different mechanisms within the various models of service delivery act as the ‘active ingredients’ associated with positive health-related outcomes for care home residents. Methods Using realist methods we focused on five outcomes: (1) medication use and review; (2) use of out-of-hours services; (3) hospital admissions, including emergency department attendances and length of hospital stay; (4) resource use; and (5) user satisfaction. Phase 1: interviewed stakeholders and reviewed the evidence to develop an explanatory theory of what supported good health-care provision for further testing in phase 2. Phase 2 developed a minimum data set of resident characteristics and tracked their care for 12 months. We also interviewed residents, family and staff receiving and providing health care to residents. The 12 study care homes were located on the south coast, the Midlands and the east of England. Health-care provision to care homes was distinctive in each site. Findings Phase 1 found that health-care provision to care homes is reactive and inequitable. The realist review argued that incentives or sanctions, agreed protocols, clinical expertise and structured approaches to assessment and care planning could support improved health-related outcomes; however, to achieve change NHS professionals and care home staff needed to work together from the outset to identify, co-design and implement agreed approaches to health care. Phase 2 tested this further and found that, although there were few differences between the sites in residents’ use of resources, the differences in service integration between the NHS and care homes did reflect how these institutions approached activities that supported relational working. Key to this was how much time NHS staff and care home staff had had to learn how to work together and if the work was seen as legitimate, requiring ongoing investment by commissioners and engagement from practitioners. Residents appreciated the general practitioner (GP) input and, when supported by other care home-specific NHS services, GPs reported that it was sustainable and valued work. Access to dementia expertise, ongoing training and support was essential to ensure that both NHS and care home staff were equipped to provide appropriate care. Limitations Findings were constrained by the numbers of residents recruited and retained in phase 2 for the 12 months of data collection. Conclusions NHS services work well with care homes when payments and role specification endorse the importance of this work at an institutional level as well as with individual residents. GP involvement is important but needs additional support from other services to be sustainable. A focus on strategies that promote co-design-based approaches between the NHS and care homes has the potential to improve residents’ access to and experience of health care. Funding The National Institute for Health Research Health Services and Delivery Research programme

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