Dark-Halo Cusp: Asymptotic Convergence

We propose a model for how the buildup of dark halos by merging satellites produces a characteristic inner cusp, of a density profile \rho \prop r^-a with a -> a_as > 1, as seen in cosmological N-body simulations of hierarchical clustering scenarios. Dekel, Devor & Hetzroni (2003) argue that a flat core of a<1 exerts tidal compression which prevents local deposit of satellite material; the satellite sinks intact into the halo center thus causing a rapid steepening to a>1. Using merger N-body simulations, we learn that this cusp is stable under a sequence of mergers, and derive a practical tidal mass-transfer recipe in regions where the local slope of the halo profile is a>1. According to this recipe, the ratio of mean densities of halo and initial satellite within the tidal radius equals a given function psi(a), which is significantly smaller than unity (compared to being 1 according to crude resonance criteria) and is a decreasing function of a. This decrease makes the tidal mass transfer relatively more efficient at larger a, which means steepening when a is small and flattening when a is large, thus causing converges to a stable solution. Given this mass-transfer recipe, linear perturbation analysis, supported by toy simulations, shows that a sequence of cosmological mergers with homologous satellites slowly leads to a fixed-point cusp with an asymptotic slope a_as>1. The slope depends only weakly on the fluctuation power spectrum, in agreement with cosmological simulations. During a long interim period the profile has an NFW-like shape, with a cusp of 1<a<a_as. Thus, a cusp is enforced if enough compact satellite remnants make it intact into the inner halo. In order to maintain a flat core, satellites must be disrupted outside the core, possibly as a result of a modest puffing up due to baryonic feedback.Comment: 37 pages, Latex, aastex.cls, revised, ApJ, 588, in pres

On The Reduced Canonical Quantization Of The Induced 2D-Gravity

The quantization of the induced 2d-gravity on a compact spatial section is carried out in three different ways. In the three approaches the supermomentum constraint is solved at the classical level but they differ in the way the hamiltonian constraint is imposed. We compare these approaches establishing an isomorphism between the resulting Hilbert spaces.Comment: 17 pages, plain LaTeX. FTUV/93-15, IFIC/93-10, Imperial-TP/93-94/1

Four Measures of the Intracluster Medium Temperature and Their Relation to a Cluster's Dynamical State

We employ an ensemble of hydrodynamic cluster simulations to create spatially and spectrally resolved images of quality comparable to Chandra's expected performance. Emission from simulation mass elements is represented using the XSPEC mekal program assuming 0.3 solar metallicity, and the resulting spectra are fit with a single-temperature model. Despite significant departures from isothermality in the cluster gas, single-temperature models produce acceptable fits to 20,000 source photon spectra. The spectral fit temperature T_s is generally lower than the mass weighted average temperature T_m due to the influence of soft line emission from cooler gas being accreted as part of the hierarchical clustering process. In a Chandra-like bandpass of 0.5 to 9.5 keV we find a nearly uniform fractional bias of (T_m-T_s)/T_s = 20% with occasional large deviations in smaller clusters. In the more traditional 2.0 to 9.5 keV bandpass, the fractional deviation is scale-dependent and on average follows the relation (T_m-T_s)/T_s = 0.2 log(T_m). This bias results in a spectral mass-temperature relationship with slope about 1.6, intermediate between the virial relation M ~ T_m^{3/2} and the observed relation M_{ICM} ~ T^2. Imaging each cluster in the ensemble at 16 epochs in its evolutionary history, we catalogue merger events with mass ratios exceeding 10% in order to investigate the relationship between spectral temperature and proximity to a major merger event. Clusters that are very cool relative to the mean mass-temperature relationship lie preferentially close to a merger, suggesting a viable observational method to cull a subset of dynamically young clusters from the general population.Comment: 34 pages, including 2 tables and 14 figures (one in color). Compiled using LaTeX 2.09 with graphics package and aaspp4 style. The simulated spectral data files used in this paper are available for public consumption at http://redshift.stanford.edu/bfm

The X-ray Fundamental Plane and LX−TL_X-T Relation of Clusters of Galaxies

We analyze the relations among central gas density, core radius, and temperature of X-ray clusters by plotting the observational data in the three-dimensional ($\log \rho_0$, $\log R$, and $\log T$) space and find that the data lie on a 'fundamental plane'. Its existence implies that the clusters form a two-parameter family. The data on the plane still has a correlation and form a band on the plane. The observed relation $L_{\rm X} \propto T^3$ turns out to be the cross section of the band perpendicular to the major axis, while the major axis is found to describe the virial density. We discuss implications of this two-parameter family nature of X-ray clusters.Comment: 7 pages, 2 figures. To be published in ApJ Letter

Corrections for gravitational lensing of supernovae: better than average?

We investigate the possibility of correcting for the magnification due to gravitational lensing of standard candle sources, such as Type Ia supernovae. Our method uses the observed properties of the foreground galaxies along the lines-of-sight to each source and the accuracy of the lensing correction depends on the quality and depth of these observations as well as the uncertainties in translating the observed luminosities to the matter distribution in the lensing galaxies. The current work is limited to cases where the matter density is dominated by the individual galaxy halos. However, it is straightforward to generalize the method to include also gravitational lensing from cluster scale halos. We show that the dispersion due to lensing for a standard candle source at z=1.5 can be reduced from about 7% to ~< 3%, i.e. the magnification correction is useful in reducing the scatter in the Type Ia Hubble diagram, especially at high redshifts where the required long exposure times makes it hard to reach large statistics and the dispersion due to lensing becomes comparable to the intrinsic Type Ia scatter.Comment: Matches accepted version, includes clarifications and additional issues. 28 pages, 7 figures, accepted for publication in Ap

The Galaxy Cluster Luminosity-Temperature Relationship and Iron Abundances - A Measure of Formation History ?

Both the X-ray luminosity-temperature (L-T) relationship and the iron abundance distribution of galaxy clusters show intrinsic dispersion. Using a large set of galaxy clusters with measured iron abundances we find a correlation between abundance and the relative deviation of a cluster from the mean L-T relationship. We argue that these observations can be explained by taking into account the range of cluster formation epochs expected within a hierarchical universe. The known relationship of cooling flow mass deposition rate to luminosity and temperature is also consistent with this explanation. From the observed cluster population we estimate that the oldest clusters formed at z>~2. We propose that the iron abundance of a galaxy cluster can provide a parameterization of its age and dynamical history.Comment: 13 pages Latex, 2 figures, postscript. Accepted for publication in ApJ Letter

Outer Regions of the Cluster Gaseous Atmospheres

We present a systematic study of the hot gas distribution in the outer regions of regular clusters using ROSAT PSPC data. Outside the cooling flow region, the beta-model describes the observed surface brightness closely, but not precisely. Between 0.3 and 1 virial radii, the profiles are characterized by a power law with slope, expressed in terms of the beta parameter, in the range beta=0.65 to 0.85. The values of beta in this range of radii are typically larger by ~0.05 than those derived from the global fit. There is a mild trend for the slope to increase with temperature, from ~0.68 for 3 keV clusters to ~0.8 for 10 keV clusters; however, even at high temperatures there are clusters with flat gas profiles, 0.7. Our values of beta at large radius are systematically higher, and the trend of beta with temperature is weaker than was previously found; the most likely explanation is that earlier studies were affected by an incomplete exclusion of the central cooling flow regions. For our regular clusters, the gas distribution at large radii is quite close to spherically symmetric and this is shown not to be an artifact of the sample selection. The gas density profiles are very similar when compared in the units of cluster virial radius. The radius of fixed mean gas overdensity 1000 (corresponding to the dark matter overdensity 200 for Omega=0.2) shows a tight correlation with temperature, R~T**0.5, as expected from the virial theorem for clusters with the universal gas fraction. At a given temperature, the rms scatter of the gas overdensity radius is only ~7% which translates into a 20% scatter of the gas mass fraction, including statistical scatter due to measurement uncertainties.Comment: ApJ in press, submitted 11/30/9

Diffeomorphisms, Noether Charges and Canonical Formalism in 2D Dilaton Gravity

We carry out a parallel study of the covariant phase space and the conservation laws of local symmetries in two-dimensional dilaton gravity. Our analysis is based on the fact that the Lagrangian can be brought to a form that vanishes on-shell giving rise to a well-defined covariant potential for the symplectic current. We explicitly compute the symplectic structure and its potential and show that the requirement to be finite and independent of the Cauchy surface restricts the asymptotic symmetries.Comment: 14 pages, latex with psfig macro, one figur

Nuclear response functions in homogeneous matter with finite range effective interactions

The question of nuclear response functions in a homogeneous medium is examined. A general method for calculating response functions in the random phase approximation (RPA) with exchange is presented. The method is applicable for finite-range nuclear interactions. Examples are shown in the case of symmetric nuclear matter described by a Gogny interaction. It is found that the convergence of the results with respect to the multipole truncation is quite fast. Various approximation schemes such as the Landau approximation, or the Landau approximation for the exchange terms only, are discussed in comparison with the exact results.Comment: 9 pages, 9 figure