Turbulent pressure support and hydrostatic mass bias in the intracluster medium

ABSTRACT The degree of turbulent pressure support by residual gas motions in galaxy clusters is not well known. Mass modelling of combined X-ray and Sunyaev–Zel’dovich observations provides an estimate of turbulent pressure support in the outer regions of several galaxy clusters. Here, we test two different filtering techniques to disentangle bulk from turbulent motions in non-radiative high-resolution cosmological simulations of galaxy clusters using the cosmological hydrocode enzo. We find that the radial behaviour of the ratio of non-thermal pressure to total gas pressure as a function of cluster-centric distance can be described by a simple polynomial function. The typical non-thermal pressure support in the centre of clusters is ∼5 per cent, increasing to ∼15 per cent in the outskirts, in line with the pressure excess found in recent X-ray observations. While the complex dynamics of the intracluster medium makes it impossible to reconstruct a simple correlation between turbulent motions and hydrostatic bias, we find that a relation between them can be established using the median properties of a sample of objects. Moreover, we estimate the contribution of radial accelerations to the non-thermal pressure support and conclude that it decreases moving outwards from 40 per cent (in the core) to 15 per cent (in the cluster’s outskirts). Adding this contribution to one provided by turbulence, we show that it might account for the entire observed hydrostatic bias in the innermost regions of the clusters, and for less than 80 per cent of it at r > 0.8 r200,m.

An analytical model of cymbal transducer dynamics. Radial vibration of a piezoelectric disc

This article represents the first step in an attempt to obtain an analytical model of a cymbal transducer. The structure is considered as two mechanically coupled systems (i.e. a piezoelectric disc producing radial motion and end caps amplifying under the compression caused by this radial behaviour). Therefore, an analytical model of the piezoelectric disc, core driver of the cymbal, and its dynamics under an electrical signal are presented in this article. The function describing the radial motion of the disc, distribution of the electrical potential along the thickness, and displacement along the thickness are obtained analytically. The obtained radial motion function will be used for modelling the end cap amplification as a compressive loading.

Numerical Simulations of Dense Collisional Systems with Extended Distribution of Particle Sizes

The dynamical evolution of dense planetary rings, such as Saturn's rings, is mainly governed by the mutual impacts between macroscopic icy particles. The local equilibrium state is determined by the energy loss in partially inelastic impacts and the viscous gain of energy from the systematic velocity field. Due to frequent impacts the time-scale for the establishment of local energy equilibrium is very short, as compared to the time-scale for radial evolution, which is determined by viscous spreading, and in some cases also by the angular momentum exchange with external satellites. Therefore, local and radial behaviour can, to a large extent be studied separately. This fact is utilized by the local simulation method (Wisdom and Tremaine, 1988; Salo, 1991), following the orbital evolution in a small co-moving region inside the rings with periodic boundary conditions. Compared to previous simulation methods (Salo, 1987) this enables much higher surface density. With the presently attainable number of particles (up to several thousands), realistic modeling of dense regions is possible, taking simultaneously into account the particle size distribution, rotation of particles, as well as vertical self-gravity. By combining several local simulations with different surface densities, it is possible to deduce the expected radial behaviour as well.