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

More examples of structure formation in the Lemaitre-Tolman model

In continuing our earlier research, we find the formulae needed to determine the arbitrary functions in the Lemaitre-Tolman model when the evolution proceeds from a given initial velocity distribution to a final state that is determined either by a density distribution or by a velocity distribution. In each case the initial and final distributions uniquely determine the L-T model that evolves between them, and the sign of the energy-function is determined by a simple inequality. We also show how the final density profile can be more accurately fitted to observational data than was done in our previous paper. We work out new numerical examples of the evolution: the creation of a galaxy cluster out of different velocity distributions, reflecting the current data on temperature anisotropies of CMB, the creation of the same out of different density distributions, and the creation of a void. The void in its present state is surrounded by a nonsingular wall of high density.Comment: LaTeX 2e with eps figures. 30 pages, 11 figures, 30 figure files. Revision matches published versio

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

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

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

Milne-Eddington inversions of the He I 10830 {\AA} Stokes profiles: Influence of the Paschen-Back effect

The Paschen-Back effect influences the Zeeman sublevels of the He I multiplet at 10830 {\AA}, leading to changes in strength and in position of the Zeeman components of these lines. We illustrate the relevance of this effect using synthetic Stokes profiles of the He I 10830 {\AA} multiplet lines and investigate its influence on the inversion of polarimetric data. We invert data obtained with the Tenerife Infrared Polarimeter (TIP) at the German Vacuum Tower Telescope (VTT). We compare the results of inversions based on synthetic profiles calculated with and without the Paschen-Back effect being included. We find that when taking into account the incomplete Paschen-Back effect, on average 16% higher field strength values are obtained. We also show that this effect is not the main cause for the area asymmetry exhibited by many He I 10830 Stokes V-profiles. This points to the importance of velocity and magnetic field gradients over the formation height range of these lines.Comment: Accepted for publication in A&A on Jun 12th 200

Constraining f(R) Gravity as a Scalar Tensor Theory

We search for viable f(R) theories of gravity, making use of the equivalence between such theories and scalar-tensor gravity. We find that models can be made consistent with solar system constraints either by giving the scalar a high mass or by exploiting the so-called chameleon effect. However, in both cases, it appears likely that any late-time cosmic acceleration will be observationally indistinguishable from acceleration caused by a cosmological constant. We also explore further observational constraints from, e.g., big bang nucleosynthesis and inflation.Comment: 15 pages, 5 figure