Gas perturbations in cool cores of galaxy clusters: effective equation of state, velocity power spectra and turbulent heating

We present the statistical analysis of X-ray surface brightness and gas density fluctuations in cool cores of ten, nearby and bright galaxy clusters that have deep Chandra observations and show observational indications of radio-mechanical AGN feedback. Within the central parts of cool cores the total variance of fluctuations is dominated by isobaric and/or isothermal fluctuations on spatial scales ~ 10-60 kpc, which are likely associated with slow gas motions and bubbles of relativistic plasma. Adiabatic fluctuations associated with weak shocks constitute less than 10 per cent of the total variance in all clusters. The typical amplitude of density fluctuations is small, ~ 10 per cent or less on scales of ~ 10-15 kpc. Subdominant contribution of adiabatic fluctuations and small amplitude of density fluctuations support a model of gentle AGN feedback as opposed to periodically explosive scenarios which are implemented in some numerical simulations. Measured one-component velocities of gas motions are typically below 100-150 km/s on scales < 50 kpc, and can be up to ~ 300 km/s on ~ 100 kpc scales. The non-thermal energy is < 12 per cent of the thermal energy. Regardless of the source that drives these motions the dissipation of the energy in such motions provides heat that is sufficient to balance radiative cooling on average, albeit the uncertainties are large. Presented results here support previous conclusions based on the analysis of the Virgo and Perseus Clusters, and agree with the Hitomi measurements. With next generation observatories like Athena and Lynx, these techniques will be yet more powerful.Comment: 16 pages, 11 figures, submitted to MNRA

Witnessing the Growth of the Nearest Galaxy Cluster: Thermodynamics of the Virgo Cluster Outskirts

We present results from Suzaku Key Project observations of the Virgo Cluster, the nearest galaxy cluster to us, mapping its X-ray properties along four long `arms' extending beyond the virial radius. The entropy profiles along all four azimuths increase with radius, then level out beyond $0.5r_{200}$, while the average pressure at large radii exceeds Planck Sunyaev-Zel'dovich measurements. These results can be explained by enhanced gas density fluctuations (clumping) in the cluster's outskirts. Using a standard Navarro, Frenk and White (1997) model, we estimate a virial mass, radius, and concentration parameter of $M_{200}=1.05\pm0.02\times10^{14}$ M$_\odot$, $r_{200}=974.1\pm5.7$ kpc, and $c = 8.8 \pm0.2$, respectively. The inferred cumulative baryon fraction exceeds the cosmic mean at $r\sim r_{200}$ along the major axis, suggesting enhanced gas clumping possibly sourced by a candidate large-scale structure filament along the north-south direction. The Suzaku data reveal a large-scale sloshing pattern, with two new cold fronts detected at radii of 233 kpc and 280 kpc along the western and southern arms, respectively. Two high-temperature regions are also identified 1 Mpc towards the south and 605 kpc towards the west of M87, likely representing shocks associated with the ongoing cluster growth. Although systematic uncertainties in measuring the metallicity for low temperature plasma remain, the data at large radii appear consistent with a uniform metal distribution on scales of $\sim 90\times180$ kpc and larger, providing additional support for the early chemical enrichment scenario driven by galactic winds at redshifts of 2-3.Comment: submitted to MNRA

A uniform metallicity in the outskirts of massive, nearby galaxy clusters

Suzaku measurements of a homogeneous metal distribution of $Z\sim0.3$ Solar in the outskirts of the nearby Perseus cluster suggest that chemical elements were deposited and mixed into the intergalactic medium before clusters formed, likely over 10 billion years ago. A key prediction of this early enrichment scenario is that the intracluster medium in all massive clusters should be uniformly enriched to a similar level. Here, we confirm this prediction by determining the iron abundances in the outskirts ($r>0.25r_{200}$) of a sample of ten other nearby galaxy clusters observed with Suzaku for which robust measurements based on the Fe-K lines can be made. Across our sample the iron abundances are consistent with a constant value, $Z_{\rm Fe}=0.316\pm0.012$ Solar ($\chi^2=28.85$ for 25 degrees of freedom). This is remarkably similar to the measurements for the Perseus cluster of $Z_{\rm Fe}=0.314\pm0.012$ Solar, using the Solar abundance scale of Asplund et al. (2009).Comment: accepted for publication in MNRA

The group approach to AdS space propagators

We show that AdS two-point functions can be obtained by connecting two points in the interior of AdS space with one point on its boundary by a dual pair of Dobrev's boundary-to-bulk intertwiners and integrating over the boundary point.Comment: 23 page

The group approach to AdS space propagators: A fast algorithm

In this letter we show how the method of [4] for the calculation of two-point functions in d+1-dimensional AdS space can be simplified. This results in an algorithm for the evaluation of the two-point functions as linear combinations of Legendre functions of the second kind. This algorithm can be easily implemented on a computer. For the sake of illustration, we displayed the results for the case of symmetric traceless tensor fields with rank up to l=4.Comment: 14 pages, comment adde

The Metallicity of the Intracluster Medium Over Cosmic Time: Further Evidence for Early Enrichment

We use Chandra X-ray data to measure the metallicity of the intracluster medium (ICM) in 245 massive galaxy clusters selected from X-ray and Sunyaev-Zel'dovich (SZ) effect surveys, spanning redshifts $0<z<1.2$. Metallicities were measured in three different radial ranges, spanning cluster cores through their outskirts. We explore trends in these measurements as a function of cluster redshift, temperature, and surface brightness "peakiness" (a proxy for gas cooling efficiency in cluster centers). The data at large radii (0.5--1 $r_{500}$) are consistent with a constant metallicity, while at intermediate radii (0.1-0.5 $r_{500}$) we see a late-time increase in enrichment, consistent with the expected production and mixing of metals in cluster cores. In cluster centers, there are strong trends of metallicity with temperature and peakiness, reflecting enhanced metal production in the lowest-entropy gas. Within the cool-core/sharply peaked cluster population, there is a large intrinsic scatter in central metallicity and no overall evolution, indicating significant astrophysical variations in the efficiency of enrichment. The central metallicity in clusters with flat surface brightness profiles is lower, with a smaller intrinsic scatter, but increases towards lower redshifts. Our results are consistent with other recent measurements of ICM metallicity as a function of redshift. They reinforce the picture implied by observations of uniform metal distributions in the outskirts of nearby clusters, in which most of the enrichment of the ICM takes place before cluster formation, with significant later enrichment taking place only in cluster centers, as the stellar populations of the central galaxies evolve.Comment: 13 pages. Accepted version, to appear in MNRA