The Effects of Clumping and Substructure on ICM Mass Measurements

We examine an ensemble of 48 simulated clusters to determine the effects of small-scale density fluctuations and large-scale substructure on X-ray measurements of the intracluster medium (ICM) mass. We measure RMS density fluctuations in the ICM which can be characterized by a mean mass-weighted clumping factor C = /^2 between 1.3 and 1.4 within a density contrast of 500 times the critical density. These fluctuations arise from the cluster history of accretion shocks and major mergers, and their presence enhances the cluster's luminosity relative to the smooth case. We expect, therefore, that ICM mass measurements utilizing models which assume uniform density at a given radius carry a bias of order sqrt(C) = 1.16. We verify this result by performing ICM mass measurements on X-ray images of the simulations and finding the expected level of bias. The varied cluster morphologies in our ensemble also allow us to investigate the effects of departures from spherical symmetry on our measurements. We find that the presence of large-scale substructure does not further bias the resulting gas mass unless it is pronounced enough to produce a second peak in the image of at least 1% the maximum surface brightness. We analyze the subset of images with no secondary peaks and find a bias of 9% and a Gaussian random error of 4% in the derived mass.Comment: To appear in ApJ

Teacher perceptions related to technology tools for curriculum alignment: a survey of teachers\u27 response to a curriculum mapping tool

The intent of this descriptive study was to build understanding about the tools, methods and theory behind teacher use of a technology-based tool and process to align K-12 curriculum with state standards. A shift to a standards-driven education policy has created conditions in which teachers are encouraged to align classroom instruction to designated content standards but currently educators lack methods, guidance and appropriate strategies to accomplish this task. Curriculum mapping software is one tool that has been developed to aid in this endeavor. Data from an existing survey instrument was utilized to analyze subsets of teacher perception data and to perform a factor analysis to study the tools, methods and theory of the curriculum mapping process. The research addressed the following three research questions: 1. To what extent are teachers able to use the TechPaths curriculum mapping software in order to create instructional units of study that are internally aligned with prescribed content standards in a northwestern state? 2. To what extent do teachers using TechPaths report increased understanding about how instruction aligned to standards improves practice and influences student achievement? 3. What are the factors that represent the underlying constructs of curriculum mapping and how do they correspond to the elements of organizational change presented in the conceptual framework? The researcher analyzed quantitative results of the survey data and the factor analysis and found that teachers appear to be using the software tool to organize and manage curriculum. While engaging in the method of curriculum mapping it appears teachers are reporting that their instruction is aligned to state content standards. An initial theory about the process of curriculum mapping appears to indicate that teachers need support and communication from administrators about the purposes and processes of curriculum mapping. Teachers need additional tool training in order to utilize advanced software features that may facilitate the production of data reports to be used in collegial conversations about curriculum

Constraints on \Omega_0 and Cluster Evolution Using the ROSAT LogN-LogS

We examine the likelihoods of different cosmological models and cluster evolutionary histories by comparing semi-analytical predictions of X-ray cluster number counts to observational data from the ROSAT satellite. We model cluster abundance as a function of mass and redshift using a Press-Schechter distribution, and assume the temperature T(M,z) and bolometric luminosity L_X(M,z) scale as power laws in mass and epoch, in order to construct expected counts as a function of X-ray flux. The L_X-M scaling is fixed using the local luminosity function while the degree of evolution in the X-ray luminosity with redshift L_X \propto (1+z)^s is left open, with s an interesting free parameter which we investigate. We examine open and flat cosmologies with initial, scale-free fluctuation spectra having indices n = 0, -1 and -2. An independent constraint arising from the slope of the luminosity-temperature relation strongly favors the n = -2 spectrum. The expected counts demonstrate a strong dependence on \Omega_0 and s, with lesser dependence on \lambda_0 and n. Comparison with the observed counts reveals a "ridge" of acceptable models in the \Omega_0 - s plane, roughly following the relation s = 6 \Omega_0 and spanning low-density models with a small degree of evolution to \Omega = 1 models with strong evolution. Models with moderate evolution are revealed to have a strong lower limit of \Omega_0 \gtrsim 0.3, and low-evolution models imply that \Omega_0 < 1 at a very high confidence level. We suggest observational tests for breaking the degeneracy along this ridge, and discuss implications for evolutionary histories of the intracluster medium.Comment: MNRAS LaTeX style format, submitted to MNRAS 3/26/97. Thirteen pages, eleven postscript figures. Uses epsf macros to include figure

Four Measures of the Intracluster Medium Temperature and Their Relation to a Cluster's Dynamical State

We employ an ensemble of hydrodynamic cluster simulations to create spatially and spectrally resolved images of quality comparable to Chandra's expected performance. Emission from simulation mass elements is represented using the XSPEC mekal program assuming 0.3 solar metallicity, and the resulting spectra are fit with a single-temperature model. Despite significant departures from isothermality in the cluster gas, single-temperature models produce acceptable fits to 20,000 source photon spectra. The spectral fit temperature T_s is generally lower than the mass weighted average temperature T_m due to the influence of soft line emission from cooler gas being accreted as part of the hierarchical clustering process. In a Chandra-like bandpass of 0.5 to 9.5 keV we find a nearly uniform fractional bias of (T_m-T_s)/T_s = 20% with occasional large deviations in smaller clusters. In the more traditional 2.0 to 9.5 keV bandpass, the fractional deviation is scale-dependent and on average follows the relation (T_m-T_s)/T_s = 0.2 log(T_m). This bias results in a spectral mass-temperature relationship with slope about 1.6, intermediate between the virial relation M ~ T_m^{3/2} and the observed relation M_{ICM} ~ T^2. Imaging each cluster in the ensemble at 16 epochs in its evolutionary history, we catalogue merger events with mass ratios exceeding 10% in order to investigate the relationship between spectral temperature and proximity to a major merger event. Clusters that are very cool relative to the mean mass-temperature relationship lie preferentially close to a merger, suggesting a viable observational method to cull a subset of dynamically young clusters from the general population.Comment: 34 pages, including 2 tables and 14 figures (one in color). Compiled using LaTeX 2.09 with graphics package and aaspp4 style. The simulated spectral data files used in this paper are available for public consumption at http://redshift.stanford.edu/bfm

A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

Reprocessing of Soft X-ray Emission Lines in Black Hole Accretion Disks

By means of a Monte Carlo code that accounts for Compton scattering and photoabsorption followed by recombination, we have investigated the radiation transfer of Ly alpha, He alpha, and recombination continua photons of H- and He-like C, N, O, and Ne produced in the photoionized atmosphere of a relativistic black hole accretion disk. We find that photoelectric opacity causes significant attenuation of photons with energies above the O VIII K-edge; that the conversion efficiencies of these photons into lower-energy lines and recombination continua are high; and that accounting for this reprocessing significantly (by factors of 21% to 105%) increases the flux of the Ly alpha and He alpha emission lines of H- and He-like C and O escaping the disk atmosphere.Comment: 4 pages including 4 encapsulated postscript figures; LaTeX format, uses aastex.cls and emulateapj5.sty; accepted on 2004 January 13 for publication in The Astrophysical Journa

Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates proportional to their sizes, conserving the total mass. The total number of clusters grows continuously but the full time-dependent distribution can be rescaled over at least 15 decades onto a universal curve which we derive analytically. This curve includes a scale free solution with a scaling exponent of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure

The thermodynamics and roughening of solid-solid interfaces

The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the interface. The solids are allowed to exchange mass by transforming one solid into the other, thermodynamic relations for the transformation of a mass element are derived and a linear stability analysis of the interface is carried out. The stability is shown to depend on the order of the phase transition occurring at the interface. Numerical simulations are performed in the non-linear regime to investigate the evolution and roughening of the interface. It is shown that even small contrasts in the referential densities of the solids may lead to the formation of finger like structures aligned with the principal direction of the far field stress.Comment: (24 pages, 8 figures; V2: added figures, text revisions

Failure of cellulolysis in the rumen of reindeer fed timothy silage

Three male reindeer (Rangifer tarandus tarandus) calves were brought from mountain pastures in April and fed regrowth timothy (Phleum pratense) silage with 76% leaves and 24.0% dry matter (DM) ad libitum. The silage contained (on DM basis) 25.4% cellulose, 12.0% crude protein and 19-6% water soluble carbohydrates. After an initial period of 11 days the daily silage intake rose to almost similar values for all animals, but independently of food intake, body mass (BM) increased by as much as 13.3 kg for animal R3 during the first 21 days, compared to 4.4 kg and 2.8 kg for Rl and R2, respectively. At slaughter the wet weight of the rumen contents of animal R3 constituted 30.2% of the total BM, compared to 18.5% and 19.1% in animals Rl and R2, respectively. A reduced ability of the rumen micro-biota to ferment pure cellulose in vitro was observed in R3. The ruminal pH was 7.07 and the concentration of volatile fatty acids was only 50.0 mM in R3, indicating a low rate of fermentation. The initial rates of in vitro dry matter digestibility of timothy silage and standard hay were also affected by the rumen fermentation failure in animal R3. Depressed rumen cellulolysis, which may be related to natural periods of starvation prior to the feeding experiment, could have caused the low rate of fermentation and the large rumen size observed in this animal