Monte-Carlo Simulations of Globular Cluster Evolution - I. Method and Test Calculations

We present a new parallel supercomputer implementation of the Monte-Carlo method for simulating the dynamical evolution of globular star clusters. Our method is based on a modified version of Henon's Monte-Carlo algorithm for solving the Fokker-Planck equation. Our code allows us to follow the evolution of a cluster containing up to 5x10^5 stars to core collapse in < 40 hours of computing time. In this paper we present the results of test calculations for clusters with equal-mass stars, starting from both Plummer and King model initial conditions. We consider isolated as well as tidally truncated clusters. Our results are compared to those obtained from approximate, self-similar analytic solutions, from direct numerical integrations of the Fokker-Planck equation, and from direct N-body integrations performed on a GRAPE-4 special-purpose computer with N=16384. In all cases we find excellent agreement with other methods, establishing our new code as a robust tool for the numerical study of globular cluster dynamics using a realistic number of stars.Comment: 35 pages, including 8 figures, submitted to ApJ. Revised versio

MYRIAD: A new N-body code for simulations of Star Clusters

We present a new C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed using the GRAPE-6 board. Special treatment is used for close encounters, binary and multiple sub-systems that either form dynamically or exist in the initial configuration. The structure of the code is modular and allows the appropriate treatment of more physical phenomena, such as stellar and binary evolution, stellar collisions and evolution of close black-hole binaries. Moreover, it can be easily modified so that the part of the code that uses GRAPE-6, could be replaced by another module that uses other accelerating-hardware like the Graphics Processing Units (GPUs). Appropriate choice of the free parameters give a good accuracy and speed for simulations of star clusters up to and beyond core collapse. Simulations of Plummer models consisting of equal-mass stars reached core collapse at t~17 half-mass relaxation times, which compares very well with existing results, while the cumulative relative error in the energy remained below 0.001. Also, comparisons with published results of other codes for the time of core collapse for different initial conditions, show excellent agreement. Simulations of King models with an initial mass-function, similar to those found in the literature, reached core collapse at t~0.17, which is slightly smaller than the expected result from previous works. Finally, the code accuracy becomes comparable and even better than the accuracy of existing codes, when a number of close binary systems is dynamically created in a simulation. This is due to the high accuracy of the method that is used for close binary and multiple sub-systems.Comment: 24 pages, 29 figures, accepted for publication to Astronomy & Astrophysic

Comparing compact binary parameter distributions I: Methods

Being able to measure each merger's sky location, distance, component masses, and conceivably spins, ground-based gravitational-wave detectors will provide a extensive and detailed sample of coalescing compact binaries (CCBs) in the local and, with third-generation detectors, distant universe. These measurements will distinguish between competing progenitor formation models. In this paper we develop practical tools to characterize the amount of experimentally accessible information available, to distinguish between two a priori progenitor models. Using a simple time-independent model, we demonstrate the information content scales strongly with the number of observations. The exact scaling depends on how significantly mass distributions change between similar models. We develop phenomenological diagnostics to estimate how many models can be distinguished, using first-generation and future instruments. Finally, we emphasize that multi-observable distributions can be fully exploited only with very precisely calibrated detectors, search pipelines, parameter estimation, and Bayesian model inference

The Living Rainforest Sustainable Greenhouses

The Living Rainforest (www.livingrainforest.org) is an educational charity that uses rainforest ecology as a metaphor for communicating general sustainability issues to the public. Its greenhouses and office buildings are to be renovated using the most sustainable methods currently available. This will be realised through construction of a high insulating greenhouse covering with a k-value of less than 2 Wm-2K-1, passive seasonal storage of excess summer solar energy in the ground by a ground source heat exchanger and exploitation of this low grade solar energy for heating in winter by a heat pump. In winter the heat pump will produce cold water to cool the ground allowing a passive cooling function in summer via the GSHE. It will be demonstrated that a GSHE is an alternative for an open aquifer in regions with no aquifer availability. The heat pump will deliver the heating baseload, the peak load will be delivered by a biomass boiler, fired with locally-sourced low-cost wood chips. It is expected that the energy saving will be about 75%, resulting in a major cost reduction. The low k-value of the covering is linked to a light transmission of 75 %. This is high enough for the demands of the vegetation in The Living Rainforest. Because the inner greenhouse climate demands are comparable to that of ornamentals, the results will be applicable to commercial ornamental production. In future low k-value coverings will also be available with high light transmission, allowing wider application of the results. This paper focuses on the correlation between k-value, light transmission and energy demand in order to investigate the trade-off between light transmittance (a major energy gain) and heat loss. The effects of these design parameters on storage and harvesting capacity are also considered but appear to have a low sensitivity. The renovated greenhouse site at The Living Rainforest will show that new greenhouses and ecology can be linked to sustainability and this will be communicated and demonstrated to the public

The Evolution of Globular Clusters in the Galaxy

We investigate the evolution of globular clusters using N-body calculations and anisotropic Fokker-Planck (FP) calculations. The models include a mass spectrum, mass loss due to stellar evolution, and the tidal field of the parent galaxy. Recent N-body calculations have revealed a serious discrepancy between the results of N-body calculations and isotropic FP calculations. The main reason for the discrepancy is an oversimplified treatment of the tidal field employed in the isotropic FP models. In this paper we perform a series of calculations with anisotropic FP models with a better treatment of the tidal boundary and compare these with N-body calculations. The new tidal boundary condition in our FP model includes one free parameter. We find that a single value of this parameter gives satisfactory agreement between the N-body and FP models over a wide range of initial conditions. Using the improved FP model, we carry out an extensive survey of the evolution of globular clusters over a wide range of initial conditions varying the slope of the mass function, the central concentration, and the relaxation time. The evolution of clusters is followed up to the moment of core collapse or the disruption of the clusters in the tidal field of the parent galaxy. In general, our model clusters, calculated with the anisotropic FP model with the improved treatment for the tidal boundary, live longer than isotropic models. The difference in the lifetime between the isotropic and anisotropic models is particularly large when the effect of mass loss via stellar evolution is rather significant. On the other hand the difference is small for relaxation- dominated clusters which initially have steep mass functions and high central concentrations.Comment: 36 pages, 11 figures, LaTeX; added figures and tables; accepted by Ap

Decision Makers Facing Uncertainty: Theory versus Evidence

We consider three competing normative theories of how to make choices when facing uncertainty: subjective expected utility, maximin utility and minimax regret. In simple decision problems, we compare how decision makers under each of these theories value safe options, freedom of choice and information. We then use these models to predict answers to questions in the European Values Survey and use these predictions via a latent class analysis to estimate the distribution of these behaviors across Europe. We find a larger proportion of Bayesians in the Northern countries than in Southern countries. The opposite is true for maximin utility behavior. Only a few are consistent with minimax regret behavior

SAD phasing of XFEL data depends critically on the error model.

A nonlinear least-squares method for refining a parametric expression describing the estimated errors of reflection intensities in serial crystallographic (SX) data is presented. This approach, which is similar to that used in the rotation method of crystallographic data collection at synchrotrons, propagates error estimates from photon-counting statistics to the merged data. Here, it is demonstrated that the application of this approach to SX data provides better SAD phasing ability, enabling the autobuilding of a protein structure that had previously failed to be built. Estimating the error in the merged reflection intensities requires the understanding and propagation of all of the sources of error arising from the measurements. One type of error, which is well understood, is the counting error introduced when the detector counts X-ray photons. Thus, if other types of random errors (such as readout noise) as well as uncertainties in systematic corrections (such as from X-ray attenuation) are completely understood, they can be propagated along with the counting error, as appropriate. In practice, most software packages propagate as much error as they know how to model and then include error-adjustment terms that scale the error estimates until they explain the variance among the measurements. If this is performed carefully, then during SAD phasing likelihood-based approaches can make optimal use of these error estimates, increasing the chance of a successful structure solution. In serial crystallography, SAD phasing has remained challenging, with the few examples of de novo protein structure solution each requiring many thousands of diffraction patterns. Here, the effects of different methods of treating the error estimates are estimated and it is shown that using a parametric approach that includes terms proportional to the known experimental uncertainty, the reflection intensity and the squared reflection intensity to improve the error estimates can allow SAD phasing even from weak zinc anomalous signal