The relation between gas density and velocity power spectra in galaxy clusters: high-resolution hydrodynamic simulations and the role of conduction

Exploring the ICM power spectrum can help us to probe the physics of galaxy clusters. Using high-resolution 3D plasma simulations, we study the statistics of the velocity field and its relation with the thermodynamic perturbations. The normalization of the ICM spectrum (density, entropy, or pressure) is linearly tied to the level of large-scale motions, which excite both gravity and sound waves due to stratification. For low 3D Mach number M~0.25, gravity waves mainly drive entropy perturbations, traced by preferentially tangential turbulence. For M>0.5, sound waves start to significantly contribute, passing the leading role to compressive pressure fluctuations, associated with isotropic (or slightly radial) turbulence. Density and temperature fluctuations are then characterized by the dominant process: isobaric (low M), adiabatic (high M), or isothermal (strong conduction). Most clusters reside in the intermediate regime, showing a mixture of gravity and sound waves, hence drifting towards isotropic velocities. Remarkably, regardless of the regime, the variance of density perturbations is comparable to the 1D Mach number. This linear relation allows to easily convert between gas motions and ICM perturbations, which can be exploited by Chandra, XMM data and by the forthcoming Astro-H. At intermediate and small scales (10-100 kpc), the turbulent velocities develop a Kolmogorov cascade. The thermodynamic perturbations act as effective tracers of the velocity field, broadly consistent with the Kolmogorov-Obukhov-Corrsin advection theory. Thermal conduction acts to damp the gas fluctuations, washing out the filamentary structures and steepening the spectrum, while leaving unaltered the velocity cascade. The ratio of the velocity and density spectrum thus inverts the downtrend shown by the non-diffusive models, allowing to probe the presence of significant conductivity in the ICM.Comment: Accepted by A&A; 15 pages, 10 figures; added insights and references - thank you for the positive feedbac

Mode Selection in the Spontaneous Motion of an Alcohol Droplet

An alcohol (pentanol) droplet exhibits spontaneous agitation on an aqueous solution, driven by a solutal Marangoni effect. We found that the droplet's mode of motion is controlled by its volume. A droplet with a volume of less than $0.1 \mu\rm{l}$ shows irregular translational motion, whereas intermediate-sized droplets of $0.1-200 \mu\rm{l}$ show vectorial motion. When the volume is above $300 \mu\rm{l}$, the droplet splits into smaller drops. These experimental results regarding mode selection are interpreted in terms of the wave number selection depending on the droplet volume.Comment: 4 pages, 5 figure

Quantifying properties of ICM inhomogeneities

We present a new method to identify and characterize the structure of the intracluster medium (ICM) in simulated galaxy clusters. The method uses the median of gas properties, such as density and pressure, which we show to be very robust to the presence of gas inhomogeneities. In particular, we show that the radial profiles of median gas properties are smooth and do not exhibit fluctuations at locations of massive clumps in contrast to mean and mode properties. It is shown that distribution of gas properties in a given radial shell can be well described by a log-normal PDF and a tail. The former corresponds to a nearly hydrostatic bulk component, accounting for ~99% of the volume, while the tail corresponds to high density inhomogeneities. We show that this results in a simple and robust separation of the diffuse and clumpy components of the ICM. The FWHM of the density distribution grows with radius and varies from ~0.15 dex in cluster centre to ~0.5 dex at 2r_500 in relaxed clusters. The small scatter in the width between relaxed clusters suggests that the degree of inhomogeneity is a robust characteristic of the ICM. It broadly agrees with the amplitude of density perturbations in the Coma cluster. We discuss the origin of ICM density variations in spherical shells and show that less than 20% of the width can be attributed to the triaxiality of the cluster gravitational potential. As a link to X-ray observations of real clusters we evaluated the ICM clumping factor with and without high density inhomogeneities. We argue that these two cases represent upper and lower limits on the departure of the observed X-ray emissivity from the median value. We find that the typical value of the clumping factor in the bulk component of relaxed clusters varies from ~1.1-1.2 at r_500 up to ~1.3-1.4 at r_200, in broad agreement with recent observations.Comment: 16 pages, 12 figure, accepted to MNRA

Determination of nuclear parton distribution functions and their uncertainties at next-to-leading order

Nuclear parton distribution functions (NPDFs) are determined by global analyses of experimental data on structure-function ratios F_2^A/F_2^{A'} and Drell-Yan cross-section ratios \sigma_{DY}^A/\sigma_{DY}^{A'}. The analyses are done in the leading order (LO) and next-to-leading order (NLO) of running coupling constant \alpha_s. Uncertainties of the NPDFs are estimated in both LO and NLO for finding possible NLO improvement. Valence-quark distributions are well determined, and antiquark distributions are also determined at x<0.1. However, the antiquark distributions have large uncertainties at x>0.2. Gluon modifications cannot be fixed at this stage. Although the advantage of the NLO analysis, in comparison with the LO one, is generally the sensitivity to the gluon distributions, gluon uncertainties are almost the same in the LO and NLO. It is because current scaling-violation data are not accurate enough to determine precise nuclear gluon distributions. Modifications of the PDFs in the deuteron are also discussed by including data on the proton-deuteron ratio F_2^D/F_2^p in the analysis. A code is provided for calculating the NPDFs and their uncertainties at given x and Q^2 in the LO and NLO.Comment: 15 pages, LaTeX, 22 eps files, to appear in PRC. A code for calculating our nuclear parton distribution functions and their uncertainties can be obtained from http://research.kek.jp/people/kumanos/nuclp.htm

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&

Analysis of electron-positron momentum spectra of metallic alloys as supported by first-principles calculations

Electron-positron momentum distributions measured by the coincidence Doppler broadening method can be used in the chemical analysis of the annihilation environment, typically a vacancy-impurity complex in a solid. In the present work, we study possibilities for a quantitative analysis, i.e., for distinguishing the average numbers of different atomic species around the defect. First-principles electronic structure calculations self-consistently determining electron and positron densities and ion positions are performed for vacancy-solute complexes in Al-Cu, Al-Mg-Cu, and Al-Mg-Cu-Ag alloys. The ensuing simulated coincidence Doppler broadening spectra are compared with measured ones for defect identification. A linear fitting procedure, which uses the spectra for positrons trapped at vacancies in pure constituent metals as components, has previously been employed to find the relative percentages of different atomic species around the vacancy [A. Somoza et al. Phys. Rev. B 65, 094107 (2002)]. We test the reliability of the procedure by the help of first-principles results for vacancy-solute complexes and vacancies in constituent metals.Comment: Submitted to Physical Review B on September 19 2006. Revised version submitted on November 8 2006. Published on February 14 200

The relation between gas density and velocity power spectra in galaxy clusters: qualitative treatment and cosmological simulations

We address the problem of evaluating the power spectrum of the velocity field of the ICM using only information on the plasma density fluctuations, which can be measured today by Chandra and XMM-Newton observatories. We argue that for relaxed clusters there is a linear relation between the rms density and velocity fluctuations across a range of scales, from the largest ones, where motions are dominated by buoyancy, down to small, turbulent scales: $(\delta\rho_k/\rho)^2 = \eta_1^2 (V_{1,k}/c_s)^2$, where $\delta\rho_k/\rho$ is the spectral amplitude of the density perturbations at wave number $k$, $V_{1,k}^2=V_k^2/3$ is the mean square component of the velocity field, $c_s$ is the sound speed, and $\eta_1$ is a dimensionless constant of order unity. Using cosmological simulations of relaxed galaxy clusters, we calibrate this relation and find $\eta_1\approx 1 \pm 0.3$. We argue that this value is set at large scales by buoyancy physics, while at small scales the density and velocity power spectra are proportional because the former are a passive scalar advected by the latter. This opens an interesting possibility to use gas density power spectra as a proxy for the velocity power spectra in relaxed clusters, across a wide range of scales.Comment: 6 pages, 3 figures, submitted to ApJ Letter

Modeling the momentum distributions of annihilating electron-positron pairs in solids

Measuring the Doppler broadening of the positron annihilation radiation or the angular correlation between the two annihilation gamma quanta reflects the momentum distribution of electrons seen by positrons in the material.Vacancy-type defects in solids localize positrons and the measured spectra are sensitive to the detailed chemical and geometric environments of the defects. However, the measured information is indirect and when using it in defect identification comparisons with theoretically predicted spectra is indispensable. In this article we present a computational scheme for calculating momentum distributions of electron-positron pairs annihilating in solids. Valence electron states and their interaction with ion cores are described using the all-electron projector augmented-wave method, and atomic orbitals are used to describe the core states. We apply our numerical scheme to selected systems and compare three different enhancement (electron-positron correlation) schemes previously used in the calculation of momentum distributions of annihilating electron-positron pairs within the density-functional theory. We show that the use of a state-dependent enhancement scheme leads to better results than a position-dependent enhancement factor in the case of ratios of Doppler spectra between different systems. Further, we demonstrate the applicability of our scheme for studying vacancy-type defects in metals and semiconductors. Especially we study the effect of forces due to a positron localized at a vacancy-type defect on the ionic relaxations.Comment: Submitted to Physical Review B on September 1 2005. Revised manuscript submitted on November 14 200