In theories in which the cosmological constant Lambda takes a variety of values in different ``subuniverses,'' the probability distribution of its observed values is conditioned by the requirement that there must be someone to measure it. This probability is proportional to the fraction of matter which is destined to condense out of the background into mass concentrations large enough to form observers. We calculate this ``collapsed fraction'' by a simple, pressure-free, spherically symmetric, nonlinear model for the growth of density fluctuations in a flat universe with arbitrary value of the cosmological constant, applied in a statistical way to the observed spectrum of density fluctuations at recombination. From this, the probability distribution for the vacuum energy density rho_V=Lambda/8pi G for Gaussian random density fluctuations is derived analytically. It is shown that the results depend on only one quantity, sigma^3 RHO, where sigma^2 and RHO are the variance and mean value of the fluctuating matter density field at recombination, respectively. To calculate sigma, we adopt the flat CDM model with nonzero cosmological constant and fix the amplitude and shape of the primordial power spectrum in accordance with data on cosmic microwave background anisotropy from the COBE satellite DMR experiment. A comparison of the results of this calculation of the likely values of rho_V with present observational bounds on the cosmological constant indicates that the small, positive value of rho_V (up to 3 times greater than the present cosmic mass density) suggested recently by several lines of evidence is a reasonably likely value to observe, even if all values of rho_V are equally likely a priori.Comment: One single postscript file, gzip-ed, 603392 bytes (2303240 bytes when gunzip-ed

In the standard Cold Dark Matter (CDM) theory of structure formation, virialized minihalos (with T vir 10 4 K) form in abundance at high redshift (z > 6), during the cosmic "dark ages." The hydrogen in these minihalos, the first nonlinear baryonic structures to form in the universe, is mostly neutral and sufficiently hot and dense to emit strongly at the 21-cm line. We calculate the emission from individual minihalos and the radiation background contributed by their combined effect. Minihalos create a "21-cm forest" of emission lines. We predict that the angular fluctuations in this 21-cm background should be detectable with the planned LOFAR and SKA radio arrays, thus providing a direct probe of structure formation during the "dark ages." Such a detection will serve to confirm the basic CDM paradigm while constraining the shape of the power-spectrum of primordial density fluctuations down to much smaller scales than have previously been constrained, the onset and duration of the reionization epoch, and the conditions which led to the first stars and quasars. We present results here for the currently-favored, flat ΛCDM model, for different tilts of the primordial power spectrum.

The recently emerging conviction that thick disks are prevalent in disk galaxies, and their seemingly ubiquitous old ages, means that the formation of the thick disk, perhaps more than any other component, holds the key to unravelling the evolution of the Milky Way, and indeed all disk galaxies. In Paper I, we proposed that the thick disk was formed in an epoch of gas rich mergers, at high redshift. This hypothesis was based on comparing N-body/SPH simulations to a variety of Galactic and extragalactic observations, including stellar kinematics, ages and chemical properties. Here examine our thick disk formation scenario in light of the most recent observations of extragalactic thick disks. In agreement, our simulted thick disks are old and relatively metal rich, with V-I colors that do not vary significantly with distance from the plane. Further, we show that our proposal results in an enhancement of α-elements in thick disk stars as compared with thin disk stars, consistent with observations of the relevant populations of the Milky Way. We also find that our scenario naturally leads to the formation of an old metal weak stellar halo population with high α-element abundances.

Further development and additional details and tests of Adaptive Smoothed ParticleHydrodynamics (ASPH), the new version of Smoothed Particle Hydrodynamics (SPH) described in Shapiro et al. (1996; Paper I) are presented. The ASPH method replaces the isotropic smoothing algorithm of standard SPH, in which interpolation is performed with spherical kernels of radius given by a scalar smoothing length, with anisotropic smoothing involving ellipsoidal kernels and tensor smoothing lengths. In standard SPH the smoothing length for each particle represents the spatial resolution scale in the vicinity of that particle, and is typically allowed to vary in space and time so as to reflect the local value of the mean interparticle spacing. This isotropic approach is not optimal, however, in the presence of strongly anisotropic volume changes such as occur naturally in a wide range of astrophysical flows, including gravitational collapse, cosmological structure formation, cloud-cloud collisions, and radiative shocks. In such cases, the local mean interparticle spacing varies not only in time and space, but in direction as well. This problem is remedied in ASPH, where each axis of the ellipsoidal smoothing kernel for a given particle is adjusted so as to reflect the different mean interparticle spacings along different directions in the vicinity of that particle. By deforming and rotating these ellipsoidal kernels so as to follow the anisotropy of volume changes local to each particle, ASPH adapts its spatial resolution scale in time, space, and direction. This significantly improves the spatial resolving power of the method over that of standard SPH at fixed particle number per simulation.This paper presents an alternative formulation of the ASPH algorithm for evolving anisotropic smoothing kernels, in which the geometric approach of Paper I, based upon 1 Current Address: LLNL, L-16, Livermore, CA 94551 -2the Lagrangian deformation of ellipsoidal fluid elements surrounding each particle, is replaced by an approach involving a local transformation of coordinates to those in which the underlying anisotropic volume changes appear to be isotropic. Using this formulation the ASPH method is presented in 2D and 3D, including a number of details not previously included in Paper I, some of which represent either advances or different choices with respect to the ASPH method detailed in Paper I. Among the advances included here are an asynchronous time-integration scheme with different time steps for different particles and the generalization of the ASPH method to 3D. In the category of different choices, the shock-tracking algorithm described in Paper I for locally adapting the artificial viscosity to restrict viscous heating just to particles encountering shocks, is not included here. Instead, we adopt a different interpolation kernel for use with the artificial viscosity, which has the effect of spatially localizing effects of the artificial viscosity. This version of the ASPH method in 2D and 3D is then applied to a series of 1D, 2D,...

Hydrogen atoms inside virialized minihaloes (with Tvir≤ 104 K) generate a radiation background from redshifted 21‐cm line emission the angular fluctuations of which reflect clustering before and during reionization. We have shown elsewhere that this emission may be detectable with the planned Low‐Frequency Array (LOFAR) and Square Kilometer Array (SKA) in a flat cold dark matter universe with a cosmological constant (ΛCDM). This is a direct probe of structure during the ‘Dark Ages’ at redshifts z≳ 6 and down to smaller scales than have previously been constrained. In our original calculation, we used a standard approximation known as the ‘linear bias’. Here we improve upon that treatment by considering the effect of non‐linear clustering. To accomplish this, we develop a new analytical method for calculating the non‐linear Eulerian bias of haloes, which should be useful for other applications as well. Predictions of this method are compared with the results of ΛCDM N‐body simulations, showing significantly better agreement than the standard linear bias approximation. When applied to the 21‐cm background from minihaloes, our formalism predicts fluctuations that differ from our original predictions by up to 30 per cent at low frequencies (high‐z) and small scales. However, within the range of frequencies and angular scales at which the signal could be observable by LOFAR and SKA as currently planned, the differences are small and our original predictions prove robust. Our results indicate that while a smaller frequency bandwidth of observation leads to a higher signal that is more sensitive to non‐linear effects, this effect is counteracted by the lowered sensitivity of the radio arrays. We calculate the best frequency bandwidth for these observations to be δνobs∼ 2 MHz. Finally we combine our simulations with our previous calculations of the 21‐cm emission from individual minihaloes to construct illustrative radio maps at z= 9.