Cold Dark Matter I: The Formation of Dark Halos

We use numerical simulations of critically-closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to $256^3$ particles using the particle-mesh (PM) method and with up to $144^3$ particles using the adaptive particle-particle --particle-mesh (P$^3$M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all $\Omega=1$ CDM models for linear amplitude \sigma_8\gsim 0.5 because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low mass halos. The distribution of halos characterized by their circular velocities for the P$^3$M simulations is in reasonable agreement with the observations for 150\kms\lsim V_{\rm circ} \lsim 350\kms.}}Comment: 41 pages, plain tex, ApJ, 236, in press; postscript figures available in ftp://arcturus.mit.edu/Preprints/CDM1_figs.tar.

Variational Integrators for the Gravitational N-Body Problem

This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the algorithm to handle individual time steps; this introduces fifth-order errors in angular momentum conservation and symplecticity. We show that using adaptive block power of two timesteps does not increase the error in symplecticity. In contrast to other high-order, symplectic, individual timestep, momentum-preserving algorithms, the algorithm takes only forward timesteps. We compare a code integrating an N-body system using the algorithm with a direct-summation force calculation to standard stellar cluster simulation codes. We find that our algorithm has about 1.5 orders of magnitude better symplecticity and momentum conservation errors than standard algorithms for equivalent numbers of force evaluations and equivalent energy conservation errors.Comment: 31 pages, 8 figures. v2: Revised individual-timestepping description, expanded comparison with other methods, corrected error in predictor equation. ApJ, in pres

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

Cold Dark Matter II: Spatial and Velocity Statistics

We examine high-resolution gravitational N-body simulations of the $\Omega=1$ cold dark matter (CDM) model in order to determine whether there is any normalization of the initial density fluctuation spectrum that yields acceptable results for galaxy clustering and velocities. Dense dark matter halos in the evolved mass distribution are identified with luminous galaxies; the most massive halos are also considered as sites for galaxy groups, with a range of possibilities explored for the group mass to light ratios. We verify the earlier conclusions of White et al. (1987) for the low amplitude (high bias) CDM model --- the galaxy correlation function is marginally acceptable but that there are too many galaxies. We also show that the peak biasing method does not accurately reproduce the results obtained using dense halos identified in the simulations themselves. The COBE anisotropy implies a higher normalization, resulting in problems with excessive pairwise galaxy velocity dispersion unless a strong velocity bias is present. Although we confirm the strong velocity bias of halos reported by Couchman \& Carlberg (1992), we show that the galaxy motions are still too large on small scales. We find no amplitude for which the CDM model can reconcile simultaneously the galaxy correlation function, the low pairwise velocity dispersion, and the richness distribution of groups and clusters. With the normalization implied by COBE, the CDM spectrum has too much power on small scales if $\Omega=1$.Comment: 31 pages, plain tex, ApJ, 236, in press; postscript figures available in ftp://arcturus.mit.edu/Preprints/CDM2_figs.tar.

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

Dependence of the Inner DM Profile on the Halo Mass

I compare the density profile of dark matter (DM) halos in cold dark matter (CDM) N-body simulations with 1 Mpc, 32 Mpc, 256 Mpc and 1024 Mpc box sizes. In dimensionless units the simulations differ only for the initial power spectrum of density perturbations. I compare the profiles when the most massive halos are composed of about 10^5 DM particles. The DM density profiles of the halos in the 1 Mpc box show systematically shallower cores with respect to the corresponding halos in the 32 Mpc simulation that have masses, M_{dm}, typical of the Milky Way and are fitted by a NFW profile. The DM density profiles of the halos in the 256 Mpc box are consistent with having steeper cores than the corresponding halos in the 32 Mpc simulation, but higher mass resolution simulations are needed to strengthen this result. Combined, these results indicate that the density profile of DM halos is not universal, presenting shallower cores in dwarf galaxies and steeper cores in clusters. Physically the result sustains the hypothesis that the mass function of the accreting satellites determines the inner slope of the DM profile. In comoving coordinates, r, the profile \rho_{dm} \propto 1/(X^\alpha(1+X)^{3-\alpha}), with X=c_\Delta r/r_\Delta, r_\Delta is the virial radius and \alpha =\alpha(M_{dm}), provides a good fit to all the DM halos from dwarf galaxies to clusters at any redshift with the same concentration parameter c_\Delta ~ 7. The slope, \gamma, of the outer parts of the halo appears to depend on the acceleration of the universe: when the scale parameter is a=(1+z)^{-1} < 1, the slope is \gamma ~ 3 as in the NFW profile, but \gamma ~ 4 at a > 1 when \Omega_\Lambda ~ 1 and the universe is inflating.[abridged]Comment: Accepted for publication in MNRAS. 13 pages, including 11 figures and 2 tables. The revised version has an additional discussion section and work on the velocity dispersion anisotrop

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

Non-uniqueness of the Dirac theory in a curved spacetime

We summarize a recent work on the subject title. The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields leads to an equivalent Hamiltonian operator H, or to an equivalent energy operator E. In this paper, we focus on the standard version of the gravitational Dirac equation, but the non-uniqueness applies also to our alternative versions. We find that the changes which lead to an equivalent operator H, or respectively to an equivalent operator E, are determined by initial data, or respectively have to make some point-dependent antihermitian matrix vanish. Thus, the vast majority of the possible coefficient changes lead neither to an equivalent operator H, nor to an equivalent operator E, whence a lack of uniqueness. We show that even the Dirac energy spectrum is not unique.Comment: 13 pages (standard 12pt article format). Text of a talk given at the 1st Mediterranean Conference on Classical and Quantum Gravity, Kolymbari (Greece), Sept. 14-18, 200

A New Way to Conserve Total Energy for Eulerian Hydrodynamic Simulations with Self-Gravity

We propose a new method to conserve the total energy to round-off error in grid-based codes for hydrodynamic simulations with self-gravity. A formula for the energy flux due to the work done by the the self-gravitational force is given, so the change in total energy can be written in conservative form. Numerical experiments with the code Athena show that the total energy is indeed conserved with our new algorithm and the new algorithm is second order accurate. We have performed a set of tests that show the numerical errors in the traditional, non-conservative algorithm can affect the dynamics of the system. The new algorithm only requires one extra solution of the Poisson equation, as compared to the traditional algorithm which includes self-gravity as a source term. If the Poisson solver takes a negligible fraction of the total simulation time, such as when FFTs are used, the new algorithm is almost as efficient as the original method. This new algorithm is useful in Eulerian hydrodynamic simulations with self-gravity, especially when results are sensitive to small energy errors, as for radiation pressure dominated flow.Comment: 19 pages, 8 figures, 2 tables, add journal information in New Astronom