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

Remnants of Sagittarius Dwarf Spheroidal Galaxy around the young globular cluster Palomar 12

Photometry of a large field around the young globular cluster Palomar 12 has revealed the main-sequence of a low surface-brightness stellar system. This main-sequence is indicative of a stellar population that varies significantly in metallicity and/or age, but in the mean is more metal poor than Pal 12. Under different assumptions for the properties of this population, we find distances from the Sun in the range 17-24 kpc, which encompasses the distance to Pal 12, $19.0\pm0.9$ kpc. The stellar system is also detected in a field 2\arcdeg North of Pal 12, which indicates it has a minimum diameter of $\sim0.9$ kpc. The orbit of Pal 12 (Dinescu et al. 2000), the color-magnitude diagram of the stellar system, their positions on the sky, and their distances suggest that they are debris from the tidal disruption of the Sgr dSph galaxy. We discuss briefly the implications for the evolution of Sgr and the Galactic halo.Comment: 16 pages, 2 figures, accepted for ApJ Letters. Some importante changes after revision, including a new figur

Ca impurity in small mixed 4^4He-3^3He clusters

The structure of small mixed helium clusters doped with one calcium atom has been determined within the diffusion Monte Carlo framework. The results show that the calcium atom sits at the $^4$He-$^3$He interface. This is in agreement with previous studies, both experimental and theoretical, performed for large clusters. A comparison between the results obtained for the largest cluster we have considered for each isotope shows a clear tendency of the Ca atom to reside in a deep dimple at the surface of the cluster for $^4$He clusters, and to become fully solvated for $^3$He clusters. We have calculated the absorption spectrum of Ca around the $4s4p \leftarrow 4s^2$ transition and have found that it is blue-shifted from that of the free-atom transition by an amount that depends on the size and composition of the cluster.Comment: 24 pages, 11 figures. Accepted on Journal of Chemical Physic

Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed Texts

We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck

Universality in the partially anisotropic three-dimensional Ising lattice

Using transfer-matrix extended phenomenological renormalization-group methods the critical properties of spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths ${\vec J}=(J',J',J)$ are studied. Universality of both fundamental critical exponents $y_t$ and $y_h$ is confirmed. It is shown that the critical finite-size scaling amplitude ratios $U=A_{\chi^{(4)}}A_\kappa/A_\chi^2$, $Y_1=A_{\kappa^{''}}/A_\chi$, and $Y_2=A_{\kappa^{(4)}}/A_{\chi^{(4)}}$ are independent of the lattice anisotropy parameter $\Delta=J'/J$. By this for the last above invariant of the three-dimensional Ising universality class we give the first quantitative estimate: $Y_2\simeq2.013$ (shape $L\times L\times\infty$, periodic boundary conditions in both transverse directions).Comment: 11 pages in latex; no figure

Scaling Relations of Dwarf Galaxies without Supernova-Driven Winds

Nearby dwarf galaxies exhibit tight correlations between their global stellar and dynamical properties, such as circular velocity, mass-to-light ratio, stellar mass, surface brightness, and metallicity. Such correlations have often been attributed to gas or metal-rich outflows driven by supernova energy feedback to the interstellar medium. We use high-resolution cosmological simulations of high-redshift galaxies with and without energy feedback, as well as analytic modeling, to investigate whether the observed correlations can arise without supernova-driven outflows. We find that the simulated dwarf galaxies exhibit correlations similar to those observed as early as z~10, regardless of whether supernova feedback is included. We also show that the correlations can be well reproduced by our analytic model that accounts for realistic gas inflow but assumes no outflows, and star formation rate obeying the Kennicutt-Schmidt law with a critical density threshold. We argue that correlations in simulated galaxies arise due to the increasingly inefficient conversion of gas into stars in low-mass dwarf galaxies rather than supernova-driven outflows. We also show that the decrease of the observed effective yield in low-mass objects, often used as an indicator of gas and metal outflows, can be reasonably reproduced in our simulations without outflows. We show that this trend can arise if a significant fraction of metals in small galaxies is spread to the outer regions of the halo outside the stellar extent via mixing. In this case the effective yield can be significantly underestimated if only metals within the stellar radius are taken into account. Measurements of gas metallicity in the outskirts of gaseous disks of dwarfs would thus provide a key test of such explanation.Comment: accepted for publication in ApJ, 19 pages, 12 figures, uses emulateapj