Effects of cold dark matter decoupling and pair annihilation on cosmological perturbations

Weakly interacting massive particles are part of the lepton-photon plasma in the early universe until kinetic decoupling, after which time the particles behave like a collisionless gas with nonzero temperature. The Boltzmann equation for WIMP-lepton collisions is reduced to a Fokker-Planck equation for the evolution of the WIMP distribution including scalar density perturbations. This equation and the Einstein and fluid equations for the plasma are solved numerically including the acoustic oscillations of the plasma before and during kinetic decoupling, the frictional damping occurring during kinetic decoupling, and the free-streaming damping occurring afterwards and throughout the radiation-dominated era. An excellent approximation reduces the solution to quadratures for the cold dark matter density and velocity perturbations. The subsequent evolution is followed through electron pair annihilation and the radiation-matter transition; analytic solutions are provided for both large and small scales. For a 100 GeV WIMP with bino-type interactions, kinetic decoupling occurs at a temperature $T_d=23$ MeV. The transfer function in the matter-dominated era leads to an abundance of small cold dark matter halos; with a smooth window function the Press-Schechter mass distribution is $dn/d\ln M\propto M^{-1/3}$ for $M<10^{-4} (T_d/$10 MeV)$^{-3}$ M$_\odot$.Comment: 18 pages, 12 figures; corrected error in bino decoupling temperature, figures update

Reheating of the Universe and Population III

We note that current observational evidence strongly favors a conventional recombination of ionized matter subsequent to redshift z=1200, followed by reionization prior to redshift z=5 and compute how this would have occurred in a standard scenario for the growth of structure. Extending prior semi-analytic work, we show by direct, high-resolution numerical simulations (of a COBE normalized CDM+Lambda model) that reheating, will occur in the interval 15>z>7, followed by reionization and accompanied by a significant increase in the Jeans mass. However, the evolution of the Jeans mass does not significantly affect star formation in dense, self-shielded clumps of gas, which are detached from the thermal evolution of the rest of the universe. On average, the growth of the Jeans mass tracks the growth of the nonlinear mass scale, a result we suspect is due to nonlinear feedback effects. Cooling on molecular hydrogen leads to a burst of star formation prior to reheating which produces Population III stars with Omega_* reaching 10^{-5.5} and Z/Z_sun reaching 10^{-3.7} by z=14. Star formation subsequently slows down as molecular hydrogen is depleted by photo-destruction and the rise of the temperature. At later times, z<10, when the characteristic virial temperature of gas clumps reach 10,000 degrees, star formation increases again as hydrogen line cooling become efficient. Objects containing Pop III stars accrete mass with time and, as soon as they reach 10,000 K virial temperature, they engage in renewed star formation and turn into normal Pop II objects having an old Pop III metal poor component.Comment: six postscript figures included, submitted to ApJ

Cosmological Reionization by Stellar Sources

I use cosmological simulations that incorporate a physically motivated approximation to three-dimensional radiative transfer that recovers correct asymptotic ionization front propagation speeds for some cosmologically relevant density distributions transfer to investigate the process of the reionization of the universe by ionizing radiation from proto-galaxies. Reionization proceeds in three stages and occupies a large redshift range from z~15 until z~5. During the first, ``pre-overlap'' stage, HII regions gradually expand into the low density IGM, leaving behind neutral high density protrusions. During the second, ``overlap'' stage, that occurs in about 10% of the Hubble time, HII regions merge and the ionizing background rises by a large factor. During the third, ``post-overlap'' stage, remaining high density regions are being gradually ionized as the required ionizing photons are being produced. Residual fluctuations in the ionizing background reach significant (more than 10%) levels for the Lyman-alpha forest absorption systems with column densities above 10^14 - 10^15 cm^-2 at z=3 to 4.Comment: Revised version accepted for publication in ApJ. Color versions of Fig. 3a-h in GIF format, full (unbinned) versions of Fig. 5, 6, and 13, as well as MPEG animations are available at http://casa.colorado.edu/~gnedin/GALLERY/rei_p.htm

Kinematic Density Waves in Accretion Disks

When thin accretion disks around black holes are perturbed, the main restoring force is gravity. If gas pressure, magnetic stresses, and radiation pressure are neglected, the disk remains thin as long as orbits do not intersect. Intersections would result in pressure forces which limit the growth of perturbations. We find that a discrete set of perturbations is possible for which orbits remain non-intersecting for arbitrarily long times. These modes define a discrete set of frequencies. We classify all long-lived perturbations for arbitrary potentials and show how their mode frequencies are related to pattern speeds computed from the azimuthal and epicyclic frequencies. We show that modes are concentrated near radii where the pattern speed has vanishing radial derivative. We explore these modes around Kerr black holes as a possible explanation for the high-frequency quasi-periodic oscillations of black hole binaries such as GRO J1655-40. The long-lived modes are shown to coincide with diskoseismic waves in the limit of small sound speed. While the waves have long lifetime, they have the wrong frequencies to explain the pairs of high-frequency quasi-periodic oscillations observed in black hole binaries.Comment: 28 pages, 6 figures; extended comparison with diskoseismology; added reference to astro-ph/060368

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

Structure Formation With a Long-Range Scalar Dark Matter Interaction

Numerical simulations show that a long-range scalar interaction in a single species of massive dark matter particles causes voids between the concentrations of large galaxies to be more nearly empty, suppresses accretion of intergalactic matter onto galaxies at low redshift, and produces an early generation of dense dark matter halos. These three effects, in moderation, seem to be improvements over the Lambda CDM model predictions for cosmic structure formation. Because the scalar interaction in this model has negligible effect on laboratory physics and the classical cosmological tests, it offers an observationally attractive example of cosmology with complicated physics in the dark sector, notably a large violation of the weak equivalence principle.Comment: 10 pages, 7 figures, revtex4. v2: minor improvements, refs added, version to appear in PR

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

Caustic rings of dark matter

It is shown that the infall of collisionless dark matter onto isolated galaxies produces a series of caustic rings in the halo dark matter distribution. The properties of these caustics are investigated. The density profile of the caustic is derived for a specific case. Bumps in the rotation curve of NGC 3198 are interpreted as due to caustic rings of dark matter.Comment: 12 pages, 1 figure, Latex, minor changes, version to to be published by Phys. Lett.

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

The cloud-in-cloud problem for non-Gaussian density fields

The cloud-in-cloud problem is studied in the context of the extension to non-Gaussian density fields of the Press-Schechter approach for the calculation of the mass function. As an example of a non-Gaussian probability distribution functions (PDFs) we consider the Chi-square, with various degrees of freedom. We generate density fields in cubic boxes with periodic boundary conditions and then determine the number of points considered collapsed at each scale through an hierarchy of smoothing windows. We find that the mass function we obtain differs from that predicted using the Extended Press-Schechter formalism, particularly for low values of $\sigma$ and for those PDFs most distinct from a Gaussian.Comment: 5 pages, LaTex using mn.sty, matches published version, results for the Inverted Chi-square distribution withdraw