Adaptive binning of X-ray galaxy cluster images

We present a simple method for adaptively binning the pixels in an image. The algorithm groups pixels into bins of size such that the fractional error on the photon count in a bin is less than or equal to a threshold value, and the size of the bin is as small as possible. The process is particularly useful for generating surface brightness and colour maps, with clearly defined error maps, from images with a large dynamic range of counts, for example X-ray images of galaxy clusters. We demonstrate the method in application to data from Chandra ACIS-S and ACIS-I observations of the Perseus cluster of galaxies. We use the algorithm to create intensity maps, and colour images which show the relative X-ray intensities in different bands. The colour maps can later be converted, through spectral models, into maps of physical parameters, such as temperature, column density, etc. The adaptive binning algorithm is applicable to a wide range of data, from observations or numerical simulations, and is not limited to two-dimensional data.Comment: 8 pages, 12 figures, accepted by MNRAS (includes changes suggested by referee), high resolution version at http://www-xray.ast.cam.ac.uk/~jss/adbin

Large scale gas sloshing out to half the virial radius in the strongest cool core REXCESS galaxy cluster, RXJ2014.8-2430

We search the cool core galaxy clusters in the REXCESS sample for evidence of large scale gas sloshing, and find clear evidence for sloshing in RXJ2014.8-2430, the strongest cool core cluster in the REXCESS cluster sample. The residuals of the surface brightness distribution from the azimuthal average for RXJ2014 show a prominent swirling excess feature extending out to an abrupt surface brightness discontinuity at 800 kpc from the cluster core (half the virial radius) to the south, which the XMM-Newton observations confirm to be cold, low entropy gas. The gas temperature is significantly higher outside this southern surface brightness discontinuity, indicating that this is a cold front 800 kpc from the cluster core. Chandra observations of the central 200 kpc show two clear younger cold fronts on opposite sides of the cluster. The scenario appears qualitatively consistent with simulations of gas sloshing due to minor mergers which raise cold, low entropy gas from the core to higher radius, resulting in a swirling distribution of opposing cold fronts at increasing radii. However the scale of the observed sloshing is much larger than that which has been simulated at present, and is similar to the large scale sloshing recently observed in the Perseus cluster and Abell 2142.Comment: 5 pages, 5 figures. Accepted for publication in MNRA

Symbolic Computation of Polynomial Conserved Densities, Generalized Symmetries, and Recursion Operators for Nonlinear Differential-Difference Equations

Algorithms for the symbolic computation of polynomial conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of the Fréchet and variational derivatives, as well as discrete Euler and homotopy operators. The algorithms are illustrated for prototypical nonlinear polynomial lattices, including the Kac-van Moerbeke (Volterra) and Toda lattices. Results are shown for the modified Volterra and Ablowitz-Ladik lattices

An XMM-Newton view of the merging activity in the Centaurus cluster

We report the results of XMM-Newton observations of the regions around the core of the Centaurus cluster where evidence for merging activity between the subgroup Cen 45 and the main Centaurus cluster has previously been observed using ASCA and ROSAT data. We confirm the ASCA findings of a temperature excess surrounding Cen 45. We find that this temperature excess can be explained using simple shock heating given the large line of sight velocity difference between Cen 45 and the surrounding main Centaurus cluster. We find that there is a statistically significant excess in metallicity around Cen 45, showing that Cen 45 has managed to retain its gas as it has interacted with the main Centaurus cluster. There is a pressure excess to the east in the direction of the merger, and there is also an entropy excess around the central galaxy of Cen 45. The metallicity between 50-100 kpc to the north of NGC 4696 is higher than to the south, which may be the result of the asymmetric distribution of metals due to previous sloshing of the core, or which may be associated with the filamentary structure we detect between NGC 4696 and NGC 4696B.Comment: 11 pages, 12 figures. Accepted for publication in MNRA

Constraining gas motions in the Centaurus cluster using X-ray surface brightness fluctuations and metal diffusion

We compare two different methods of constraining the characteristic velocity and spatial scales of gas motions in the X-ray bright, nearby Centaurus cluster, using new deep (760ks) Chandra observations. The power spectrum of excess surface brightness fluctuations in the 0.5-6.0 keV band in a sector to the west is measured and compared to theoretical expectations for Kolmogorov index fluctuations. The observed power spectrum is flatter than these expectations, and the surface brightness fluctuations are around the 8 percent level on length scales of 2 kpc. We convert the 2D power spectrum of fluctuations into a 3D power spectrum using the method of Churazov et al., and then convert this into constraints on the one-component velocity of the gas motions as a function of their length scale. We find one-component velocities in the range 100-150 km/s on spatial scales of 4-10 kpc. An independent constraint on the characteristic velocity and length scales of the gas motions is then found by considering the diffusion coefficient needed to explain the distribution of metals in the Centaurus cluster, combined with the need to balance the rate of gas cooling with the rate of heat dissipated by the gas motions. We find that these two methods of constraining the velocity and length scales of the gas motions are in good agreement.Comment: 8 pages, 7 figures. Accepted for publication in MNRA

Approximation of expectation values

Approximation of expectation values by perturbation theor