Hugo Martel

Adaptive Smoothed Particle Hydrodynamics: Methodology. II.

Further development and additional details and tests of adaptive smoothed particle hydrodynamics (ASPH), the new version of smoothed particle hydrodynamics (SPH) described in the first paper in this series (Shapiro et al.), 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 also 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 the first paper in this series, based upon the 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 two and three dimensions, including a number of details not previously included in the earlier paper, some of which represent either advances or different choices with respect to the ASPH method detailed in the earlier paper. 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 three dimensions. In the category of different choices, the shock-tracking algorithm described in the earlier paper 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 two and three dimensions is then applied to a series of one-, two-, and three-dimensional test problems, and the results are compared to those of standard SPH applied to the same problems. These include the problem of cosmological pancake collapse, the Riemann shock tube, cylindrical and spherical Sedov blast waves, the collision of two strong shocks, and problems involving shearing disks intended to test the angular momentum conservation properties of the method. These results further support the idea that ASPH has significantly better resolving power than standard SPH for a wide range of problems, including that of cosmological structure formation.

The emergence of the thick disk in a CDM universe. II. Colors and abundance patterns

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 we examine our thick-disk formation scenario in light of the most recent observations of extragalactic thick disks. In agreement, our simulated thick disks are old and relatively metal rich, with V - I colors that do not vary significantly with distance from the plane. Furthermore, 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.

Two Disk Components from a Gas-Rich Disk-Disk Merger

We employ N-body, smoothed particle hydrodynamic simulations, including detailed treatment of chemical enrichment, to follow a gas-rich merger that results in a galaxy with disk morphology. We trace the kinematic, structural, and chemical properties of stars formed before, during, and after the merger. We show that such a merger produces two exponential disk components, with the older, hotter component having a scale length 20% larger than the later forming, cold disk. Rapid star formation during the merger quickly enriches the protogalactic gas reservoir, resulting in high metallicities of the forming stars. These stars form from gas largely polluted by Type II supernovae, which form rapidly in the merger-induced starburst. After the merger, a thin disk forms from gas that has had time to be polluted by Type Ia supernovae. Abundance trends are plotted, and we examine the proposal that increased star formation during gas-rich mergers may explain the high α-to-iron abundance ratios that exist in the relatively high-metallicity, thick-disk component of the Milky Way.

The 21 cm Background from the Cosmic Dark Ages: Minihalos and the Intergalactic Medium before Reionization

The H atoms inside minihalos (i.e., halos with virial temperatures Tvir ≤ 104 K, in the mass range roughly from 104 to 108 M☉) during the cosmic dark ages in a ΛCDM universe produce a redshifted background of collisionally pumped 21 cm line radiation that can be seen in emission relative to the cosmic microwave background (CMB). Previously, we used semianalytical calculations of the 21 cm signal from individual halos of different mass and redshift and the evolving mass function of minihalos to predict the mean brightness temperature of this 21 cm background and its angular fluctuations. Here we use high-resolution cosmological N-body and hydrodynamic simulations of structure formation at high redshift (z 8) to compute the mean brightness temperature of this background from both minihalos and the intergalactic medium (IGM) prior to the onset of Lyα radiative pumping. We find that the 21 cm signal from gas in collapsed, virialized minihalos dominates over that from the diffuse shocked gas in the IGM.

Fragmentation of elongated cylindrical clouds. III, Formation of binary and multiple systems

Using three-dimensional hydrodynamical simulations, the fragmentation of uniform, isothermal, elongated molecular clouds, slowly rotating around an axis perpendicular to their elongation is studied. It is argued that this process could result in the formation of binary and multiple stars. This new method for forming binary stars can explain wide binaries with large eccentricities and various mass ratios. At relatively low initial Jeans numbers (the ratio of the absolute value of gravitational to thermal energies), a simple binary system is formed. For higher initial Jeans numbers, multiple fragmentation occurs between the binary fragments, forming a multiple system

Fragmentation and Evolution of Molecular Clouds. I. Algorithm and First Results

We present a series of simulations of the fragmentation of a molecular cloud, leading to the formation of a cluster of protostellar cores. We use Gaussian initial conditions with a power spectrum P(k) ∝ k-2, assume an isothermal equation of state, and neglect turbulence and magnetic fields. The purpose of these simulations is to address a specific numerical problem called artificial fragmentation, which plagues simulations of cloud fragmentation. We argue that this is a serious problem, and that the only reasonable and practical way to address it within the smoothed particle hydrodynamics (SPH) algorithm is to use a technique called particle splitting. We performed three simulations, with Ngen = 0, 1, and 2 levels of particle splitting. All simulations start up with 643 SPH particles, but their effective resolutions correspond to 643, 1283, and 2563 particles, respectively. The third simulation properly resolves the Jeans mass throughout the entire system, at all times, thus preventing artificial fragmentation. The high resolution of our simulations results in the formation of a large number of protostellar cores, nearly 3000 for the largest simulation. The final mass distribution of cores is lognormal, and the distribution shifts down in mass as the resolution improves. The width of the distribution is about 1.5 (e.g., a factor of 30 in the mass), and the low-mass edge of the distribution corresponds to the lowest core mass that the code can resolve. This result differs from previous claims of a relationship between the mean of the distribution and the initial Jeans mass.

Structure, kinematics and chemical enrichment patterns after major gas-rich disc-disc mergers

We used an N-body smoothed particle hydrodynamics algorithm, with a detailed treatment of star formation, supernovae feedback and chemical enrichment, to perform eight simulations of mergers between gas-rich disc galaxies. We vary the mass ratio of the progenitors, their rotation axes and their orbital parameters and analyse the kinematic, structural and chemical properties of the remnants. Six of these simulations result in the formation of a merger remnant with a disc morphology as a result of the large gas fraction of the remnants. We show that stars formed during the merger (a sudden starburst occurs in our simulation and lasts for 0.2-0.3 Gyr) and those formed after the merger have different kinematical and chemical properties. The first ones are located in the thick disc or the halo. They are partially supported by velocity dispersion and have high [alpha/Fe] ratios even at metallicities as high as [Fe/H] = -0.5. The former ones - the young component - are located in a thin disc rotationally supported and have lower [alpha/Fe] ratios. The difference in the rotational support of both components results in the rotation of the thick disc lagging that of the thin disc by as much as a factor of 2, as recently observed. We also find counter-rotating stars in both the old and young populations. A variety of structures are formed during the merger, i.e. most simulations form a ring of young stars and two simulations formed a bar. The scalelength of the thick disc is either equal to that of the thin disc or larger by factors of up to 1.60 and in six out of the eight simulations, the thin and thick discs both have exponential luminosity profiles and are nearly coplanar. We find that, while the kinematic and structural properties of the merger remnant depend strongly upon the orbital parameters of the mergers, there is a remarkable uniformity in the chemical properties of the mergers. This suggests that general conclusions about the chemical signature of gas-rich mergers can be drawn.

LIGHT PROPAGATION IN INHOMOGENEOUS UNIVERSES. I. METHODOLOGY AND PRELIMINARY RESULTS

We describe a numerical algorithm that simulates the propagation of light in inhomogeneous universes. This algorithm computes the trajectories of light rays between the observer, located at redshift z = 0, and distant sources located at high redshift using the multiple lens plane method. The deformation and deflection of light beams as they interact with each lens plane are computed using the filled-beam approximation. We use a particle-particle/particle-mesh (P3M) N-body numerical code to simulate the formation of large-scale structure in the universe. We extend the length resolution of the simulations to submegaparsec scales by using a Monte Carlo method for locating galaxies inside the computational volume according to the underlying distribution of background matter. The observed galaxy two-point correlation function is reproduced. This algorithm constitutes a major improvement over previous methods, which either neglected the presence of large-scale structure, neglected the presence of galaxies, neglected the contribution of distant matter (matter located far from the beam), or used the Zeldovich approximation for simulating the formation of large-scale structure. In addition, we take into account the observed morphology-density relation when assigning morphological types to galaxies, something that was ignored in all previous studies. To test this algorithm, we perform 1981 simulations for three different cosmological models: an Einstein-de Sitter model with density parameter Ω0 = 1, an open model with Ω0 = 0.2, and a flat, low-density model with Ω0 = 0.2 and a cosmological constant of λ0 = 0.8. In all models, the initial density fluctuations correspond to a cold dark matter power spectrum normalized to COBE. In each simulation, we compute the shear and magnification resulting from the presence of inhomogeneities. Our results are the following: (1) The magnification is totally dominated by the convergence, with the shear contributing less than one part in 104. (2) Most of the cumulative shear and magnification is contributed by matter located at intermediate redshifts, z = 1-2. (3) The actual value of the redshift at which the largest contribution to shear and magnification occurs depends on the cosmological model. In particular, the lens planes contributing the most are located at larger redshift for models with smaller Ω0. (4) The number of galaxies directly hit by the beam increases with redshift, while the contribution of lens planes to the shear and magnification decrease with increasing lens plane redshift for z > 2, which indicates that the bulk of the shear and magnification does not originate from direct hits, but rather from the tidal influence of nearby and more distant galaxies and background matter. (5) The average contributions of background matter and nearby galaxies to the shear is comparable for models with small Ω0. For the Einstein-de Sitter model, the contribution of the background matter exceeds the contribution of nearby galaxies by nearly 1 order of magnitude.

Fragmentation And Evolution Of Molecular Clouds. II. The Effect Of Dust Heating

We investigate the effect of heating by luminosity sources in a simulation of clustered star formation. Our heating method involves a simplified continuum radiative transfer method that calculates the dust temperature. The gas temperature is set by the dust temperature. We present the results of four simulations; two simulations assume an isothermal equation of state and the two other simulations include dust heating. We investigate two mass regimes, i.e., 84 M? and 671 M?, using these two different energetics algorithms. The mass functions for the isothermal simulations and simulations that include dust heating are drastically different. In the isothermal simulation, we do not form any objects with masses above 1 M?. However, the simulation with dust heating, while missing some of the low-mass objects, forms high-mass objects (~20 M?) which have a distribution similar to the Salpeter initial mass function. The envelope density profiles around the stars formed in our simulation match observed values around isolated, low-mass star-forming cores. We find the accretion rates to be highly variable and, on average, increasing with final stellar mass. By including radiative feedback from stars in a cluster-scale simulation, we have determined that it is a very important effect which drastically affects the mass function and yields important insights into the formation of massive stars.

Fragmentation of elongated cylindrical clouds. I. Isothermal clouds

We present a numerical study of fragmentation in its simplest possible form : that of elongated, isothermal, axially symmetric clouds. Results have been obtained for different ratios of length to diameter, L/D, and initial Jeans numbers, J 0 (ratio of gravitational to thermal energies). We introduce initial density perturbations on the axis of otherwise uniformly dense cylinders and determine the maximum number of fragments N fmax that can form and grow for combinations of L/D and J 0 .