Probing the dark matter profile of hot clusters and the M-T relation with XMM-Newton

We present results based on XMM-Newton observations of a small sample of hot galaxy clusters. Making a full use of XMM-Newton's spectro-imaging capabilities, we have extracted the radial temperature profile and gas density profile, and with this information, calculated the total mass profile of each cluster (under the assumption of hydrostatic equilibrium and spherical symmetry). Comparing the individual scaled total mass profiles, we have probed the Universality of rich cluster mass profiles over a wide range of radii (from 0.01 to 0.7 the virial radius). We have also tested the shape of cluster mass profiles by comparing with the predicted profiles from numerical simulations of hierarchical structure formation. We also derived the local mass-temperature (M-T) scaling relation over a range of temperature going from 4 to 9 keV, that we compare with theoretical predictions.Comment: 7 pages, 2 figures, Advances in Space Research in press (proceedings of the COSPAR 2004 Assembly, Paris

Ion Sizes and Finite-Size Corrections for Ionic-Solvation Free Energies

Free energies of ionic solvation calculated from computer simulations exhibit a strong system size dependence. We perform a finite-size analysis based on a dielectric-continuum model with periodic boundary conditions. That analysis results in an estimate of the Born ion size. Remarkably, the finite-size correction applies to systems with only eight water molecules hydrating a sodium ion and results in an estimate of the Born radius of sodium that agrees with the experimental value.Comment: 2 EPS figure

Ion Pair Potentials-of-Mean-Force in Water

Recent molecular simulation and integral equation results alkali-halide ion pair potentials-of-mean-force in water are discussed. Dielectric model calculations are implemented to check that these models produce that characteristic structure of contact and solvent-separated minima for oppositely charged ions in water under physiological thermodynamic conditions. Comparison of the dielectric model results with the most current molecular level information indicates that the dielectric model does not, however, provide an accurate description of these potentials-of-mean-force. We note that linear dielectric models correspond to modelistic implementations of second-order thermodynamic perturbation theory for the excess chemical potential of a distinguished solute molecule. Therefore, the molecular theory corresponding to the dielectric models is second-order thermodynamic perturbation theory for that excess chemical potential. The second-order, or fluctuation, term raises a technical computational issue of treatment of long-ranged interactions similar to the one which arises in calculation of the dielectric constant of the solvent. It is contended that the most important step for further development of dielectric models would be a separate assessment of the first-order perturbative term (equivalently the {\it potential at zero charge} ) which vanishes in the dielectric models but is generally nonzero. Parameterization of radii and molecular volumes should then be based of the second-order perturbative term alone. Illustrative initial calculations are presented and discussed.Comment: 37 pages and 8 figures. LA-UR-93-420

Calibration of the galaxy cluster M_500-Y_X relation with XMM-Newton

The quantity Y_ X, the product of the X-ray temperature T_ X and gas mass M_ g, has recently been proposed as a robust low-scatter mass indicator for galaxy clusters. Using precise measurements from XMM-Newton data of a sample of 10 relaxed nearby clusters, spanning a Y_ X range of 10^13 -10^15 M_sun keV, we investigate the M_500-Y_ X relation. The M_500 - Y_ X data exhibit a power law relation with slope alpha=0.548 \pm 0.027, close to the self-similar value (3/5) and independent of the mass range considered. However, the normalisation is \sim 20% below the prediction from numerical simulations including cooling and galaxy feedback. We discuss two effects that could contribute to the normalisation offset: an underestimate of the true mass due to the HE assumption used in X-ray mass estimates, and an underestimate of the hot gas mass fraction in the simulations. A comparison of the functional form and scatter of the relations between various observables and the mass suggest that Y_ X may indeed be a better mass proxy than T_ X or M_g,500.Comment: 4 pages, 2 figures, accepted for publication in A&

Balancing Local Order and Long-Ranged Interactions in the Molecular Theory of Liquid Water

A molecular theory of liquid water is identified and studied on the basis of computer simulation of the TIP3P model of liquid water. This theory would be exact for models of liquid water in which the intermolecular interactions vanish outside a finite spatial range, and therefore provides a precise analysis tool for investigating the effects of longer-ranged intermolecular interactions. We show how local order can be introduced through quasi-chemical theory. Long-ranged interactions are characterized generally by a conditional distribution of binding energies, and this formulation is interpreted as a regularization of the primitive statistical thermodynamic problem. These binding-energy distributions for liquid water are observed to be unimodal. The gaussian approximation proposed is remarkably successful in predicting the Gibbs free energy and the molar entropy of liquid water, as judged by comparison with numerically exact results. The remaining discrepancies are subtle quantitative problems that do have significant consequences for the thermodynamic properties that distinguish water from many other liquids. The basic subtlety of liquid water is found then in the competition of several effects which must be quantitatively balanced for realistic results.Comment: 8 pages, 6 figure

Quasi-chemical theory with a soft cutoff

In view of the wide success of molecular quasi-chemical theory of liquids, this paper develops the soft-cutoff version of that theory. This development has important practical consequences in the common cases that the packing contribution dominates the solvation free energy of realistically-modeled molecules because treatment of hard-core interactions usually requires special purpose simulation methods. In contrast, treatment of smooth repulsive interactions is typically straightforward on the basis of widely available software. This development also shows how fluids composed of molecules with smooth repulsive interactions can be treated analogously to the molecular-field theory of the hard-sphere fluid. In the treatment of liquid water, quasi-chemical theory with soft-cutoff conditioning doesn't change the fundamental convergence characteristics of the theory using hard-cutoff conditioning. In fact, hard cutoffs are found here to work better than softer ones.Comment: 5 pages, 2 figure