The Entire Virial Radius of the Fossil Cluster RXJ1159+5531: I. Gas Properties

Previous analysis of the fossil-group/cluster RXJ1159+5531 with X-ray observations from a central Chandra pointing and an offset-North Suzaku pointing indicate a radial intracluster medium (ICM) entropy profile at the virial radius ($R_{\rm vir}$) consistent with predictions from gravity-only cosmological simulations, in contrast to other cool-core clusters. To examine the generality of these results, we present three new Suzaku observations that, in conjunction with the North pointing, provide complete azimuthal coverage out to $R_{\rm vir}$. With two new Chandra ACIS-I observations overlapping the North Suzaku pointing, we have resolved $\gtrsim$50\% of the cosmic X-ray background there. We present radial profiles of the ICM density, temperature, entropy, and pressure obtained for each of the four directions. We measure only modest azimuthal scatter in the ICM properties at $R_{\rm 200}$ between the Suzaku pointings: 7.6\% in temperature and 8.6\% in density, while the systematic errors can be significant. The temperature scatter, in particular, is lower than that studied at $R_{\rm 200}$ for a small number of other clusters observed with Suzaku. These azimuthal measurements verify that RXJ1159+5531 is a regular, highly relaxed system. The well-behaved entropy profiles we have measured for RXJ1159+5531 disfavor the weakening of the accretion shock as an explanation of the entropy flattening found in other cool-core clusters but is consistent with other explanations such as gas clumping, electron-ion non-equilibrium, non-thermal pressure support, and cosmic ray acceleration. Finally, we mention that the large-scale galaxy density distribution of RXJ1159+5531 seems to have little impact on its gas properties near $R_{\rm vir}$.Comment: Accepted for publication in Ap

Nonrepetitive Colourings of Planar Graphs with O(log⁡n)O(\log n) Colours

A vertex colouring of a graph is \emph{nonrepetitive} if there is no path for which the first half of the path is assigned the same sequence of colours as the second half. The \emph{nonrepetitive chromatic number} of a graph $G$ is the minimum integer $k$ such that $G$ has a nonrepetitive $k$-colouring. Whether planar graphs have bounded nonrepetitive chromatic number is one of the most important open problems in the field. Despite this, the best known upper bound is $O(\sqrt{n})$ for $n$-vertex planar graphs. We prove a $O(\log n)$ upper bound

CM relations in fibered powers of elliptic families

Let $E_\lambda$ be the Legendre family of elliptic curves. Given $n$ linearly independent points $P_1,\dots , P_n \in E_\lambda\left(\overline{\mathbb{Q}(\lambda)}\right)$ we prove that there are at most finitely many complex numbers $\lambda_0$ such that $E_{\lambda_0}$ has complex multiplication and $P_1(\lambda_0), \dots ,P_n(\lambda_0)$ are dependent over $End(E_{\lambda_0})$. This implies a positive answer to a question of Bertrand and, combined with a previous work in collaboration with Capuano, proves the Zilber-Pink conjecture for a curve in a fibered power of an elliptic scheme when everything is defined over $\overline{\mathbb{Q}}$.Comment: The formulation of Theorem 2.1 is now correc

Hydrostatic Gas Constraints On Supermassive Black Hole Masses: Implications For Hydrostatic Equilibrium And Dynamical Modeling In A Sample Of Early-Type Galaxies

We present new mass measurements for the supermassive black holes (SMBHs) in the centers of three early-type galaxies. The gas pressure in the surrounding, hot interstellar medium (ISM) is measured through spatially resolved spectroscopy with the Chandra X-ray Observatory, allowing the SMBH mass (M(BH)) to be inferred directly under the hydrostatic approximation. This technique does not require calibration against other SMBH measurement methods and its accuracy depends only on the ISM being close to hydrostatic, which is supported by the smooth X-ray isophotes of the galaxies. Combined with results from our recent study of the elliptical galaxy NGC4649, this brings the number of galaxies with SMBHs measured in this way to four. Of these, three already have mass determinations from the kinematics of either the stars or a central gas disk, and hence join only a handful of galaxies with MBH measured by more than one technique. We find good agreement between the different methods, providing support for the assumptions implicit in both the hydrostatic and the dynamical models. The stellar mass-to-light ratios for each galaxy inferred by our technique are in agreement with the predictions of stellar population synthesis models assuming a Kroupa initial mass function (IMF). This concurrence implies that no more than similar to 10%-20% of the ISM pressure is nonthermal, unless there is a conspiracy between the shape of the IMF and nonthermal pressure. Finally, we compute Bondi accretion rates (M(bondi)), finding that the two galaxies with the highest M(bondi) exhibit little evidence of X-ray cavities, suggesting that the correlation with the active galactic nuclei jet power takes time to be established.NASA NAS5-26555, NNG04GE76G, G07-8083XAstronom

AGN Feedback in Galaxy Groups: the two interesting cases of AWM 4 and NGC 5044

We present AGN feedback in the interesting cases of two groups: AWM 4 and NGC 5044. AWM 4 is characterized by a combination of properties which seems to defy the paradigm for AGN heating in cluster cores: a flat inner temperature profile indicative of a past, major heating episode which completely erased the cool core, as testified by the high central cooling time (> 3 Gyrs) and by the high central entropy level (~ 50 keV cm^2), and yet an active central radio galaxy with extended radio lobes out to 100 kpc, revealing recent feeding of the central massive black hole. A recent Chandra observation has revealed the presence of a compact cool corona associated with the BCG, solving the puzzle of the apparent lack of low entropy gas surrounding a bright radio source, but opening the question of its origin. NGC 5044 shows in the inner 10 kpc a pair of cavities together with a set of bright filaments. The cavities are consistent with a recent AGN outburst as also indicated by the extent of dust and H_alpha emission even though the absence of extended 1.4 GHz emission remains to be explained. The soft X-ray filaments coincident with H_alpha and dust emission are cooler than those which do not correlate with optical and infrared emission, suggesting that dust-aided cooling can contribute to the overall cooling. For the first time sloshing cold fronts at the scale of a galaxy group have been observed in this object.Comment: 4 pages, 1 figure, to appear in proceedings of the conference "The Monster's Fiery Breath: Feedback in Galaxies, Groups, and Clusters", June 2009, Madison Wisconsi