The Peculiar Velocity Function of Galaxy Clusters

The peculiar velocity function of clusters of galaxies is determined using an accurate sample of cluster velocities based on Tully-Fisher distances of Sc galaxies (Giovanelli et al 1995b). In contrast with previous results based on samples with considerably larger velocity uncertainties, the observed velocity function does not exhibit a tail of high velocity clusters. The results indicate a low probability of $\lesssim$\,5\% of finding clusters with one-dimensional velocities greater than $\sim$ 600 {\kms}. The root-mean-square one-dimensional cluster velocity is 293$\pm$28 {\kms}. The observed cluster velocity function is compared with expectations from different cosmological models. The absence of a high velocity tail in the observed function is most consistent with a low mass-density ($\Omega \sim$0.3) CDM model, and is inconsistent at $\gtrsim 3 \sigma$ level with $\Omega$= 1.0 CDM and HDM models. The root-mean-square one-dimensional cluster velocities in these models correspond, respectively, to 314, 516, and 632 {\kms} (when convolved with the observational uncertainties). Comparison with the observed RMS cluster velocity of 293$\pm$28 {\kms} further supports the low-density CDM model.Comment: revised version accepted for publication in ApJ Letters, 18 pages, uuencoded PostScript with 3 figures included; complete paper available through WWW at http://www.astro.princeton.edu/~library/prep.htm

The Shape, Multiplicity, and Evolution of Superclusters in LambdaCDM Cosmology

We determine the shape, multiplicity, size, and radial structure of superclusters in the LambdaCDM concordance cosmology from z = 0 to z = 2. Superclusters are defined as clusters of clusters in our large-scale cosmological simulation. We find that superclusters are triaxial in shape; many have flattened since early times to become nearly two-dimensional structures at present, with a small fraction of filamentary systems. The size and multiplicity functions are presented at different redshifts. Supercluster sizes extend to scales of ~ 100 - 200 Mpc/h. The supercluster multiplicity (richness) increases linearly with supercluster size. The density profile in superclusters is approximately isothermal (~ R^{-2}) and steepens on larger scales. These results can be used as a new test of the current cosmology when compared with upcoming observations of large-scale surveys.Comment: 33 pages, 15 figures, accepted to ApJ; minor content changes, some figures removed to shorten pape

Building analytical three-field cosmological models

A difficult task to deal with is the analytical treatment of models composed by three real scalar fields, once their equations of motion are in general coupled and hard to be integrated. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called "extension method". The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is within inflationary models, where the Einstein-Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.Comment: 11 pages, and 3 figures, updated version published in EPJ

Clustering Analyses of 300,000 Photometrically Classified Quasars--II. The Excess on Very Small Scales

We study quasar clustering on small scales, modeling clustering amplitudes using halo-driven dark matter descriptions. From 91 pairs on scales <35 kpc/h, we detect only a slight excess in quasar clustering over our best-fit large-scale model. Integrated across all redshifts, the implied quasar bias is b_Q = 4.21+/-0.98 (b_Q = 3.93+/-0.71) at ~18 kpc/h (~28 kpc/h). Our best-fit (real-space) power index is ~-2 (i.e., $\xi(r) \propto r^{-2}$), implying steeper halo profiles than currently found in simulations. Alternatively, quasar binaries with separation <35 kpc/h may trace merging galaxies, with typical dynamical merger times t_d~(610+/-260)m^{-1/2} Myr/h, for quasars of host halo mass m x 10^{12} Msolar/h. We find UVX quasars at ~28 kpc/h cluster >5 times higher at z > 2, than at z < 2, at the $2.0\sigma$ level. However, as the space density of quasars declines as z increases, an excess of quasar binaries (over expectation) at z > 2 could be consistent with reduced merger rates at z > 2 for the galaxies forming UVX quasars. Comparing our clustering at ~28 kpc/h to a \xi(r)=(r/4.8\Mpch)^{-1.53} power-law, we find an upper limit on any excess of a factor of 4.3+/-1.3, which, noting some caveats, differs from large excesses recently measured for binary quasars, at $2.2\sigma$. We speculate that binary quasar surveys that are biased to z > 2 may find inflated clustering excesses when compared to models fit at z < 2. We provide details of 111 photometrically classified quasar pairs with separations <0.1'. Spectroscopy of these pairs could significantly constrain quasar dynamics in merging galaxies.Comment: 12pages, 3 figures, 2 tables; uses amulateapj; accepted to Ap

High-order boundary conditions for linearized shallow water equations with stratification, dispersion and advection

The two-dimensional linearized shallow water equations are considered in unbounded domains with density stratifications. Wave dispersion and advection effects are slso taken into account. The infinite domain is truncated via a rectangular artificial boundary B, and a high-order Open Boundary Condition (OBC) is imposed on B. Then the problem is solved numerically in the finite domain bounded by B. A recently developed boundary scheme is employed, which is based on a reformulation of the sequence of OBC's originaly proposed by Higdon. The OBCs can easily be used up to any desired order. They are incorporated here in a finite difference scheme. Numerical examples are used to demonstrate the performance and advantages of the computational method, with an emphasis on the effect of stratification

Neural responses to ambiguity involve domain-general and domain-specific emotion processing systems

Extant research has examined the process of decision making under uncertainty, specifically in situations of ambiguity. However, much of this work has been conducted in the context of semantic and low-level visual processing. An open question is whether ambiguity in social signals (e.g., emotional facial expressions) is processed similarly or whether a unique set of processors come on-line to resolve ambiguity in a social context. Our work has examined ambiguity using surprised facial expressions, as they have predicted both positive and negative outcomes in the past. Specifically, whereas some people tended to interpret surprise as negatively valenced, others tended toward a more positive interpretation. Here, we examined neural responses to social ambiguity using faces (surprise) and nonface emotional scenes (International Affective Picture System). Moreover, we examined whether these effects are specific to ambiguity resolution (i.e., judgments about the ambiguity) or whether similar effects would be demonstrated for incidental judgments (e.g., nonvalence judgments about ambiguously valenced stimuli). We found that a distinct task control (i.e., cingulo-opercular) network was more active when resolving ambiguity. We also found that activity in the ventral amygdala was greater to faces and scenes that were rated explicitly along the dimension of valence, consistent with findings that the ventral amygdala tracks valence. Taken together, there is a complex neural architecture that supports decision making in the presence of ambiguity: (a) a core set of cortical structures engaged for explicit ambiguity processing across stimulus boundaries and (b) other dedicated circuits for biologically relevant learning situations involving faces