Calibration of the galaxy cluster M_500-Y_X relation with XMM-Newton

The quantity Y_ X, the product of the X-ray temperature T_ X and gas mass M_ g, has recently been proposed as a robust low-scatter mass indicator for galaxy clusters. Using precise measurements from XMM-Newton data of a sample of 10 relaxed nearby clusters, spanning a Y_ X range of 10^13 -10^15 M_sun keV, we investigate the M_500-Y_ X relation. The M_500 - Y_ X data exhibit a power law relation with slope alpha=0.548 \pm 0.027, close to the self-similar value (3/5) and independent of the mass range considered. However, the normalisation is \sim 20% below the prediction from numerical simulations including cooling and galaxy feedback. We discuss two effects that could contribute to the normalisation offset: an underestimate of the true mass due to the HE assumption used in X-ray mass estimates, and an underestimate of the hot gas mass fraction in the simulations. A comparison of the functional form and scatter of the relations between various observables and the mass suggest that Y_ X may indeed be a better mass proxy than T_ X or M_g,500.Comment: 4 pages, 2 figures, accepted for publication in A&

Final state interactions in two-particle interferometry

We reconsider the influence of two-particle final state interactions (FSI) on two-particle Bose-Einstein interferometry. We concentrate in particular on the problem of particle emission at different times. Assuming chaoticity of the source, we derive a new general expression for the symmetrized two-particle cross section. We discuss the approximations needed to derive from the general result the Koonin-Pratt formula. Introducing a less stringent version of the so-called smoothness approximation we also derive a more accurate formula. It can be implemented into classical event generators and allows to calculate FSI corrected two-particle correlation functions via modified Bose-Einstein "weights".Comment: 12 pages RevTeX, 2 ps-figures included, submitted to Phys. Rev.

The hot gas content of fossil galaxy clusters

We investigate the properties of the hot gas in four fossil galaxy systems detected at high significance in the Planck Sunyaev-Zeldovich (SZ) survey. XMM-Newton observations reveal overall temperatures of kT ~ 5-6 keV and yield hydrostatic masses M500,HE > 3.5 x 10e14 Msun, confirming their nature as bona fide massive clusters. We measure the thermodynamic properties of the hot gas in X-rays (out to beyond R500 in three cases) and derive their individual pressure profiles out to R ~ 2.5 R500 with the SZ data. We combine the X-ray and SZ data to measure hydrostatic mass profiles and to examine the hot gas content and its radial distribution. The average Navarro-Frenk-White (NFW) concentration parameter, c500 = 3.2 +/- 0.4, is the same as that of relaxed `normal' clusters. The gas mass fraction profiles exhibit striking variation in the inner regions, but converge to approximately the cosmic baryon fraction (corrected for depletion) at R500. Beyond R500 the gas mass fraction profiles again diverge, which we interpret as being due to a difference in gas clumping and/or a breakdown of hydrostatic equilibrium in the external regions. Overall our observations point to considerable radial variation in the hot gas content and in the gas clumping and/or hydrostatic equilibrium properties in these fossil clusters, at odds with the interpretation of their being old, evolved and undisturbed. At least some fossil objects appear to be dynamically young.Comment: 4 pages, 2 figures. Accepted for publication in A&

Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak

When electron cyclotron (EC) driven current is first applied to the inside of a magnetic island, the current spreads throughout the island and after a short period achieves a steady level. Using a two equation fluid model for the EC current that allows us to examine this early evolution in detail, we analyze high-resolution simulations of a 2/1 classical tearing mode in a low-beta large aspect-ratio circular tokamak. These simulations use a nonlinear 3D reduced-MHD fluid model and the JOREK code. During the initial period where the EC driven current grows and spreads throughout the magnetic island, it is not a function of the magnetic flux. However, once it has reached a steady-state, it should be a flux function. We demonstrate numerically that if sufficiently resolved toroidally, the steady-state EC driven current becomes approximately a flux function. We discuss the physics of this early period of EC evolution and its impact on the size of the magnetic island.Comment: 12 pages, 7 figure

A system of relational syllogistic incorporating full Boolean reasoning

We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related to all B; All A are R-related to some B; All A are R-related to all B. Such primitives formalize sentences from natural language like `All students read some textbooks'. Here A and B denote arbitrary sets (of objects), and R denotes an arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem.Comment: Available at http://link.springer.com/article/10.1007/s10849-012-9165-

The structural and scaling properties of nearby galaxy clusters - II. The M-T relation

Using a sample of ten nearby (z< 0.15), relaxed galaxy clusters in the temperature range [2-9] keV, we have investigated the scaling relation between the mass at various density contrasts (delta=2500,1000,500,200) and the cluster temperature. The masses are derived from NFW-type model fits to mass profiles, obtained under the hydrostatic assumption using precise measurements, with XMM, at least down to delta=1000. The logarithmic slope of the M-T relation is well constrained and is the same at all delta, reflecting the self-similarity of the mass profiles. At delta=500, the slope of the relation for the sub-sample of hot clusters (kT>3.5 keV) is consistent with the standard self-similar expectation: alpha= 1.49\pm0.15. The relation steepens when the whole sample is considered: alpha=1.71\pm0.09. The normalisation of the relation is discrepant (by ~ 30%), at all density contrasts, with the prediction from purely gravitation based models. Models that take into account radiative cooling and galaxy feedback are generally in better agreement with our data. We argue that remaining discrepancies, in particular at low delta, are more likely due to problems with models of the ICM thermal structure rather than to an incorrect estimate of the mass from X-ray data.Comment: 11 pages, 4 figures, A&A in press, updated to match the accepted version (19/08/2005). Minor text clarifications, more detailed analysis of the M-T relations in Sect 3.2, corrected typo in Table 1 (redshift) and on cluster markers in Fig 1 legen

Structural and scaling properties of galaxy clusters: probing the physics of structure formation

We present XMM-Newton studies of the total mass, gas density, temperature and entropy profiles in nearby hot and cool clusters, together with follow-up observations of distant clusters from the SHARC Survey. The observed structural and scaling properties are compared with the predictions of the self-similar model of cluster formation. These data indicate that clusters do form a self-similar population down to low mass and up to high redshift, and give support to the standard picture of structure formation for the dark matter component. However, deviations from the standard scaling laws confirm that the specific physics of the gas component is still insufficiently understood.Comment: 9 pages, 8 figures; to be published in Memorie della Societa' Astronomica Italiana, the Proceedings of the EPIC Consortium (held on Oct 14-16, 2003 in Palermo