An Extension of the Faddeev-Jackiw Technique to Fields in Curved Spacetimes

The Legendre transformation on singular Lagrangians, e.g. Lagrangians representing gauge theories, fails due to the presence of constraints. The Faddeev-Jackiw technique, which offers an alternative to that of Dirac, is a symplectic approach to calculating a Hamiltonian paired with a well-defined initial value problem when working with a singular Lagrangian. This phase space coordinate reduction was generalized by Barcelos-Neto and Wotzasek to simplify its application. We present an extension of the Faddeev-Jackiw technique for constraint reduction in gauge field theories and non-gauge field theories that are coupled to a curved spacetime that is described by General Relativity. A major difference from previous formulations is that we do not explicitly construct the symplectic matrix, as that is not necessary. We find that the technique is a useful tool that avoids some of the subtle complications of the Dirac approach to constraints. We apply this formulation to the Ginzburg-Landau action and provide a calculation of its Hamiltonian and Poisson brackets in a curved spacetime.Comment: 30 pages, updated to reflect published versio

Star Formation in a Cosmological Simulation of Reionization

We study the luminosity functions of high-redshift galaxies in detailed hydrodynamic simulations of cosmic reionization, which are designed to reproduce the evolution of the Lyman-alpha forest between z=5 and z=6. We find that the luminosity functions and total stellar mass densities are in agreement with observations when plausible assumptions about reddenning at z=6 are made. Our simulations support the conclusion that stars alone reionized the universe.Comment: Accepted for publication in Ap

Neuronal avalanches recorded in the awake and sleeping monkey do not show a power law but can be reproduced by a self-organized critical model

Poster presentation: Self-organized critical (SOC) systems are complex dynamical systems that may express cascades of events, called avalanches [1]. The SOC state was proposed to govern brain function, because of its activity fluctuations over many orders of magnitude, its sensitivity to small input and its long term stability [2,3]. In addition, the critical state is optimal for information storage and processing [4]. Both hallmark features of SOC systems, a power law distribution f(s) for the avalanche size s and a branching parameter (bp) of unity, were found for neuronal avalanches recorded in vitro [5]. However, recordings in vivo yielded contradictory results [6]. Electrophysiological recordings in vivo only cover a small fraction of the brain, while criticality analysis assumes that the complete system is sampled. We hypothesized that spatial subsampling might influence the observed avalanche statistics. In addition, SOC models can have different connectivity, but always show a power law for f(s) and bp = 1 when fully sampled. This may not be the case under subsampling, however. Here, we wanted to know whether a state change from awake to asleep could be modeled by changing the connectivity of a SOC model without leaving the critical state. We simulated a SOC model [1] and calculated f(s) and bp obtained from sampling only the activity of a set of 4 × 4 sites, representing the electrode positions in the cortex. We compared these results with results obtained from multielectrode recordings of local field potentials (LFP) in the cortex of behaving monkeys. We calculated f(s) and bp for the LFP activity recorded while the monkey was either awake or asleep and compared these results to results obtained from two subsampled SOC model with different connectivity. f(s) and bp were very similar for both the experiments and the subsampled SOC model, but in contrast to the fully sampled model, f(s) did not show a power law and bp was smaller than unity. With increasing the distance between the sampling sites, f(s) changed from "apparently supercritical" to "apparently subcritical" distributions in both the model and the LFP data. f(s) and bp calculated from LFP recorded during awake and asleep differed. These changes could be explained by altering the connectivity in the SOC model. Our results show that subsampling can prevent the observation of the characteristic power law and bp in SOC systems, and misclassifications of critical systems as sub- or supercritical are possible. In addition, a change in f(s) and bp for different states (awake/asleep) does not necessarily imply a change from criticality to sub- or supercriticality, but can also be explained by a change in the effective connectivity of the network without leaving the critical state

The Expected Mass Function for Low Mass Galaxies in a CDM Cosmology: Is There a Problem?

It is well known that the mass function for_halos_ in CDM cosmology is a relatively steep power law for low masses, possibly too steep to be consistent with observations. But how steep is the_galaxy_ mass function? We have analyzed the stellar and gas mass functions of the first massive luminous objects formed in a \Lambda CDM universe, as calculated in the numerical simulation described in Gnedin (2000ab). We found that while the dark matter mass function is steep, the stellar and gas mass functions are flatter for low mass objects. The stellar mass function is consistently flat at the low mass end. Moreover, while the gas mass function follows the dark matter mass function until reionization at z~7, between z=7 and z=4, the gas mass function also flattens considerably at the low mass end. At z=4, the gas and stellar mass functions are fit by a Schechter function with \alpha ~ -1.2 +/- 0.1, significantly shallower than the dark matter halo mass function and consistent with some recent observations. The baryonic mass functions are shallower because (a) the dark matter halo mass function is consistent with the Press-Schechter formulation at low masses n(M) M^-2 and (b) heating/cooling and ionization processes appear to cause baryons to collect in halos with the relationship M_b M_d^4 at low masses. Combining (a) and (b) gives n(M_b) M_b^-5/4, comparable to the simulation results. Thus, the well known observational fact that low mass galaxies are underabundant as compared to expectations from numerical dark matter simulations or Press-Schechter modeling of CDM universes emerges naturally from these results, implying that perhaps no ``new physics'' beyond the standard model is needed.Comment: Submitted to ApJ, 17 pages including 6 figure

Understanding the PSCz Galaxy Power Spectrum with N-body Simulations

By comparing the PSCz galaxy power spectrum with the results of nested pure dark matter N-body simulations, we try to understand how infrared-selected galaxies populate dark-matter haloes, paying special attention to the method of halo identification in the simulations. We thus test the hypothesis that baryonic physics negligibly affects the distribution of galaxies down to the smallest scales yet observed. We are successful in reproducing the PSCz power spectrum on scales < ~40 h/Mpc, near our resolution limit, by imposing a central density cut-off on simulated haloes, which gives a rough minimum mass and circular velocity of haloes in which PSCz galaxies formed.Comment: 12 pages, 16 figures (one added), conforms to version in MNRA

The Omega Dependence of the Evolution of xi(r)

The evolution of the two-point correlation function, xi(r,z), and the pairwise velocity dispersion, sigma(r,z), for both the matter and halo population, in three different cosmological models: (Omega_M,Omega_Lambda)=(1,0), (0.2,0) and (0.2,0.8) are described. If the evolution of xi is parameterized by xi(r,z)=(1+z)^{-(3+eps)}xi(r,0), where xi(r,0)=(r/r_0)^{-gamma}, then eps(mass) ranges from 1.04 +/- 0.09 for (1,0) to 0.18 +/- 0.12 for (0.2,0), as measured by the evolution of at 1 Mpc (from z ~ 5 to the present epoch). For halos, eps depends on their mean overdensity. Halos with a mean overdensity of about 2000 were used to compute the halo two-point correlation function tested with two different group finding algorithms: the friends of friends and the spherical overdensity algorithm. It is certainly believed that the rate of growth of this xihh will give a good estimate of the evolution of the galaxy two-point correlation function, at least from z ~ 1 to the present epoch. The values we get for eps(halos) range from 1.54 for (1,0) to -0.36 for (0.2,0), as measured by the evolution of xi(halos) from z ~ 1.0 to the present epoch. These values could be used to constrain the cosmological scenario. The evolution of the pairwise velocity dispersion for the mass and halo distribution is measured and compared with the evolution predicted by the Cosmic Virial Theorem (CVT). According to the CVT, sigma(r,z)^2 ~ G Q rho(z) r^2 xi(r,z) or sigma proportional to (1+z)^{-eps/2}. The values of eps measured from our simulated velocities differ from those given by the evolution of xi and the CVT, keeping gamma and Q constant: eps(CVT) = 1.78 +/- 0.13 for (1,0) or 1.40 +/- 0.28 for (0.2,0).Comment: Accepted for publication in the ApJ. Also available at http://manaslu.astro.utoronto.ca/~carlberg/cnoc/xiev/xi_evo.ps.g

Radial Alignment in Simulated Clusters

Observational evidence for the radial alignment of satellites with their dark matter host has been accumulating steadily in the past few years. The effect is seen over a wide range of scales, from massive clusters of galaxies down to galaxy-sized systems, yet the underlying physical mechanism has still not been established. To this end, we have carried out a detailed analysis of the shapes and orientations of dark matter substructures in high-resolution N-body cosmological simulations. We find a strong tendency for radial alignment of the substructure with its host halo: the distribution of halo major axes is very anisotropic, with the majority pointing towards the center of mass of the host. The alignment peaks once the sub-halo has passed the virial radius of the host for the first time, but is not subsequently diluted, even after the halos have gone through as many as four pericentric passages. This evidence points to the existence of a very rapid dynamical mechanism acting on these systems and we argue that tidal torquing throughout their orbits is the most likely candidate.Comment: v2: 13 pages, 10 figures, ApJ in press. Revisions include a new section (4.2) comparing our results with observations, and a few added reference

The Halo Mass Function: High-Redshift Evolution and Universality

We study the formation of dark matter halos in the concordance LCDM model over a wide range of redshifts, from z=20 to the present. Our primary focus is the halo mass function, a key probe of cosmology. By performing a large suite of nested-box N-body simulations with careful convergence and error controls (60 simulations with box sizes from 4 to 256 Mpc/h, we determine the mass function and its evolution with excellent statistical and systematic errors, reaching a few percent over most of the considered redshift and mass range. Across the studied redshifts, the halo mass is probed over 6 orders of magnitude (10^7 - 10^13.5 M_sun/h). Historically, there has been considerable variation in the high redshift mass function as obtained by different groups. We have made a concerted effort to identify and correct possible systematic errors in computing the mass function at high redshift and to explain the discrepancies between some of the previous results. We discuss convergence criteria for the required force resolution, simulation box size, halo mass range, initial and final redshift, and time stepping. Because of conservative cuts on the mass range probed by individual boxes, our results are relatively insensitive to simulation volume, the remaining sensitivity being consistent with extended Press-Schechter theory. Previously obtained mass function fits near z=0, when scaled by linear theory, are in good agreement with our results at all redshifts, although a mild redshift dependence consistent with that found by Reed and collaborators exists at low redshifts.Comment: 20 pages, 15 figures. Minor changes to the text and figures; results and conclusions unchange