The Kingdom of Heaven or the New Age

Matthew 25:1-13. Sermon delivered at the chapel, Conrad Grebel College, Univ of Waterloo, November 13, 1996

Equilibrium states and invariant measures for random dynamical systems

Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a consistency conditions for such systems, which admit some proper Markov partitions of connected spaces, are introduced, and further sufficient conditions for them are provided. It is shown that every uniformly continuous Markov system associated with a continuous random dynamical system is consistent if it has a dominating Markov chain. A necessary and sufficient condition for the existence of an invariant Borel probability measure for such a non-degenerate system with a dominating Markov chain and a finite (16) is given. The condition is also sufficient if the non-degeneracy is weakened with the consistency condition. A further sufficient condition for the existence of an invariant measure for such a consistent system which involves only the properties of the dominating Markov chain is provided. In particular, it implies that every such a consistent system with a finite Markov partition and a finite (16) has an invariant Borel probability measure. A bijective map between these measures and equilibrium states associated with such a system is established in the non-degenerate case. Some properties of the map and the measures are given.Comment: The article is published in DCDS-A, but without the 3rd paragraph on page 4 (the complete removal of the paragraph became the condition for the publication in the DCDS-A after the reviewer ran out of the citation suggestions collected in the paragraph

Fermi-LAT upper limits on gamma-ray emission from colliding wind binaries

Context: Colliding wind binaries (CWBs) are thought to give rise to a plethora of physical processes including acceleration and interaction of relativistic particles. Observation of synchrotron radiation in the radio band confirms there is a relativistic electron population in CWBs. Accordingly, CWBs have been suspected sources of high-energy gamma-ray emission since the COS-B era. Theoretical models exist that characterize the underlying physical processes leading to particle acceleration and quantitatively predict the non-thermal energy emission observable at Earth. Aims: We strive to find evidence of gamma-ray emission from a sample of seven CWB systems: WR 11, WR 70, WR 125, WR 137, WR 140, WR 146, and WR 147. Theoretical modelling identified these systems as the most favourable candidates for emitting gamma-rays. We make a comparison with existing gamma-ray flux predictions and investigate possible constraints. Methods: We used 24 months of data from the Large Area Telescope (LAT) on-board the Fermi Gamma Ray Space Telescope to perform a dedicated likelihood analysis of CWBs in the LAT energy range. Results: We find no evidence of gamma-ray emission from any of the studied CWB systems and determine corresponding flux upper limits. For some CWBs the interplay of orbital and stellar parameters renders the Fermi-LAT data not sensitive enough to constrain the parameter space of the emission models. In the cases of WR140 and WR147, the Fermi-LAT upper limits appear to rule out some model predictions entirely and constrain theoretical models over a significant parameter space. A comparison of our findings to the CWB eta Car is made.Comment: 9 pages, 3 figure

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