Convective dynamos in spherical wedge geometry

Self‐consistent convective dynamo simulations in wedge‐shaped spherical shells are presented. Differential rotation is generated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained only for sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large‐scale fields are found to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesian domains is made (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Head-on Collision of Disk–Sphere Galaxies

Numerical simulations are performed to study the tidal effects of non-merging rapid head-on collision between a disk galaxy and a spherical galaxy. The disk consists of three components – a disk, a bulge and a halo – and the spherical galaxy is a Plummer model. The galaxies have the same dimensions with different mass ratios viz., 2, 1 and 0.5. They move in a rectilinear orbit with a relative velocity of 1000 km s⁻¹. None of the simulations leads to the merger of the galaxies by tidal capture. The results of our simulations indicate that although tidal effects are sensitive to both the mass ratio and the inclination of the disk to the orbital plane, it is the mass ratio which is more important in producing tidal damage to the less massive galaxy. The spherical galaxy undergoes considerable tidal effects if the mass of the disk is same or larger. On the other hand the collisions in which the mass of the spherical galaxy is more, result in the formation of a ring structure after the closest approach and the structure disappears by the end of the simulations.     

Differential rotation and meridional circulation in global models of solar convection

In the outer envelope of the Sun and in other stars, differential rotation and meridional circulation are maintained via the redistribution of momentum and energy by convective motions. In order to properly capture such processes in a numerical model, the correct spherical geometry is essential. In this paper I review recent insights into the maintenance of mean flows in the solar interior obtained from high-resolution simulations of solar convection in rotating spherical shells. The Coriolis force induces a Reynolds stress which transports angular momentum equatorward and also yields latitudinal variations in the convective heat flux. Meridional circulations induced by baroclinicity and rotational shear further redistribute angular momentum and alter the mean stratification. This gives rise to a complex nonlinear interplay between turbulent convection, differential rotation, meridional circulation, and the mean specific entropy profile. I will describe how this drama plays out in our simulations as well as in solar and stellar convection zones. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The haloes of merger remnants

We perform collisionless N -body simulations of 1:1 galaxy mergers, using models which include a galaxy halo, disc and bulge, focusing on the behaviour of the halo component. The galaxy models are constructed without recourse to a Maxwellian approximation. We investigate the effect of varying the galaxies' orientation, their mutual orbit and the initial velocity anisotropy or cusp strength of the haloes upon the remnant halo density profiles and shape, as well as on the kinematics. We observe that the halo density profile (determined as a spherical average, an approximation we find appropriate) is exceptionally robust in mergers, and that the velocity anisotropy of our remnant haloes is nearly independent of the orbits or initial anisotropy of the haloes. The remnants follow the halo anisotropy – local density slope (β–γ) relation suggested by Hansen & Moore in the inner parts of the halo, but β is systematically lower than this relation predicts in the outer parts. Remnant halo axis ratios are strongly dependent on the initial parameters of the haloes and on their orbits. We also find that the remnant haloes are significantly less spherical than those described in studies of simulations which include gas cooling.     

Bending instability of stellar disks: The stabilizing effect of a compact bulge

The saturation conditions for bending modes in inhomogeneous thin stellar disks that follow from an analysis of the dispersion relation are compared with those derived from N-body simulations. In the central regions of inhomogeneous disks, the reserve of disk strength against the growth of bending instability is smaller than that for a homogeneous layer. The spheroidal component (a dark halo, a bulge) is shown to have a stabilizing effect. The latter turns out to depend not only on the total mass of the spherical component, but also on the degree of mass concentration toward the center. We conclude that the presence of a compact (not necessarily massive) bulge in spiral galaxies may prove to be enough to suppress the bending perturbations that increase the disk thickness. This conclusion is corroborated by our N-body simulations in which we simulated the evolution of near-equilibrium, but unstable finite-thickness disks in the presence of spheroidal components. The final disk thickness at the same total mass of the spherical component (dark halo + bulge) was found to be much smaller than that in the simulations where a concentrated bulge is present.     

Black hole stability in multidimensional gravity theory

Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in D-dimensional gravity with a chain of n Ricci-flat internal spaces are considered. Their properties and special cases are discussed. A family of multidimensional dilatonic black-hole solutions is singled out, depending on two integration constants (related to black hole mass and charge) and three free parameters of the theory (the coordinate sphere, internal space dimensions, and the coupling constant). The behaviour of the solutions under small perturbations preserving spherical symmetry, is studied. It is shown that the black-hole solutions without a dilaton field are stable, while other solutions, possessing naked singularities, are catastrophically unstable.     

Markov chain reconstruction of the 2dF Galaxy Redshift Survey real-space power spectrum

The real-space power spectrum of L _* galaxies measured from the 2dF Galaxy Redshift Survey (2dFGRS) is presented. Markov chain Monte Carlo (MCMC) sampling was used to fit radial and angular modes resulting from a spherical harmonics decomposition of the 2dFGRS overdensity field (described in a previous paper) with 16 real-space power spectrum values and linear redshift-space distortion parameter  β( L _*, 0)  . The recovered marginalized band powers are compared to previous estimates of galaxy power spectra. Additionally, we provide a simple model for the 17-dimensional likelihood hypersurface in order to allow the likelihood to be quickly estimated given a set of model band powers and β( L _*, 0). The likelihood surface is not well approximated by a multivariate Gaussian distribution with model-independent covariances. Instead, a model is presented in which the distribution of each band power has a Gaussian distribution in a combination of the band power and its logarithm. The relative contribution of each component was determined by fitting the MCMC output. Using these distributions, we demonstrate how the likelihood of a given cosmological model can be quickly and accurately estimated, and we use a simple set of models to compare estimated likelihoods with likelihoods calculated using the full spherical harmonics procedure. All of the data are made publicly available (from http://www.roe.ac.uk/~wjp/ ), enabling the spherical harmonics decomposition of the 2dFGRS of Percival et al. to be easily used as a cosmological constraint.     

Turbulent convection in rapidly rotating spherical shells: A model for equatorial and high latitude jets on Jupiter and Saturn

The origin of zonal jets on the jovian planets has long been a topic of scientific debate. In this paper we show that deep convection in a spherical shell can generate zonal flow comparable to that observed on Jupiter and Saturn, including a broad prograde equatorial jet and multiple alternating jets at higher latitudes. We present fully turbulent, 3D spherical numerical simulations of rapidly rotating convection with different spherical shell geometries. The resulting global flow fields tend to be segregated into three regions (north, equatorial, and south), bounded by the tangent cylinder that circumscribes the inner boundary equator. In all of our simulations a strong prograde equatorial jet forms outside the tangent cylinder, whereas multiple jets form in the northern and southern hemispheres, inside the tangent cylinder. The jet scaling of our numerical models and of Jupiter and Saturn is consistent with the theory of geostrophic turbulence, which we extend to include the effect of spherical shell geometry. Zonal flow in a spherical shell is distinguished from that in a full sphere or a shallow layer by the effect of the tangent cylinder, which marks a reversal in the sign of the planetary β-parameter and a jump in the Rhines length. This jump is manifest in the numerical simulations as a sharp equatorward increase in jet widths—a transition that is also observed on Jupiter and Saturn. The location of this transition gives an estimate of the depth of zonal flow, which seems to be consistent with current models of the jovian and saturnian interiors.     

The problem of the maximum volumes and particle horizon in the Friedmann universe model

The maximum volume of the closed Friedmann universe is further investigated and is shown to be 2² R ³ (t), instead of ² R ³ (t) as found previously. This discrepancy comes from the incomplete use of the volume formula of 3-dimensional spherical space in the astronomical literature. Mathematically, there exists the maximum volume at any cosmic timet in a 3-dimensional spherical case. However, the Friedmann closed universe in expansion reaches its maximum volume only at the timet _m of the maximum scale factorR(t _m ). The particle horizon has no limitation for the farthest objects in the closed Friedmann universe if the proper distance of objects is compared with the particle horizon as it should be. It will lead to absurdity if the luminosity distance of objects is compared with the proper distance of the particle horizon.     

The formation of asteroid satellites in large impacts: results from numerical simulations

We present results of 161 numerical simulations of impacts into 100-km diameter asteroids, examining debris trajectories to search for the formation of bound satellite systems. Our simulations utilize a 3-dimensional smooth-particle hydrodynamics (SPH) code to model the impact between the colliding asteroids. The outcomes of the SPH models are handed off as the initial conditions for N-body simulations, which follow the trajectories of the ejecta fragments to search for the formation of satellite systems. Our results show that catastrophic and large-scale cratering collisions create numerous fragments whose trajectories can be changed by particle-particle interactions and by the reaccretion of material onto the remaining target body. Some impact debris can enter into orbit around the remaining target body, which is a gravitationally reaccreted rubble pile, to form a SMAshed Target Satellite (SMATS). Numerous smaller fragments escaping the largest remnant may have similar trajectories such that many become bound to one another, forming Escaping Ejecta Binaries (EEBs). Our simulations so far seem to be able to produce satellite systems qualitatively similar to observed systems in the main asteroid belt. We find that impacts of 34-km diameter projectiles striking at 3 km s⁻¹ at impact angles of ∼30° appear to be particularly efficient at producing relatively large satellites around the largest remnant as well as large numbers of modest-size binaries among their escaping ejecta.     

The formation of asteroid satellites in large impacts: results from numerical simulations

We present results of 161 numerical simulations of impacts into 100-km diameter asteroids, examining debris trajectories to search for the formation of bound satellite systems. Our simulations utilize a 3-dimensional smooth-particle hydrodynamics (SPH) code to model the impact between the colliding asteroids. The outcomes of the SPH models are handed off as the initial conditions for N-body simulations, which follow the trajectories of the ejecta fragments to search for the formation of satellite systems. Our results show that catastrophic and large-scale cratering collisions create numerous fragments whose trajectories can be changed by particle-particle interactions and by the reaccretion of material onto the remaining target body. Some impact debris can enter into orbit around the remaining target body, which is a gravitationally reaccreted rubble pile, to form a SMAshed Target Satellite (SMATS). Numerous smaller fragments escaping the largest remnant may have similar trajectories such that many become bound to one another, forming Escaping Ejecta Binaries (EEBs). Our simulations so far seem to be able to produce satellite systems qualitatively similar to observed systems in the main asteroid belt. We find that impacts of 34-km diameter projectiles striking at 3 km s⁻¹ at impact angles of ∼30° appear to be particularly efficient at producing relatively large satellites around the largest remnant as well as large numbers of modest-size binaries among their escaping ejecta.     

Exact potential–density pairs for flattened dark haloes

Cosmological simulations suggest that dark matter haloes are not spherical, but typically moderately to strongly triaxial systems. We investigate methods to convert spherical potential–density pairs into axisymmetric ones, in which the basic characteristics of the density profile (such as the slope at small and large radii) are retained. We achieve this goal by replacing the spherical radius r by an oblate radius m in the expression of the gravitational potential  Φ( r )  .
We extend and formalize the approach pioneered by Miyamoto & Nagai to be applicable to arbitrary potential–density pairs. Unfortunately, an asymptotic study demonstrates that, at large radii, such models always show a   R ⁻³  disc superposed on a smooth roughly spherical density distribution. As a result, this recipe cannot be used to construct simple flattened potential–density pairs for dynamical systems such as dark matter haloes. Therefore, we apply a modification of our original recipe that cures the problem of the discy behaviour. An asymptotic analysis now shows that the density distribution has the desired asymptotic behaviour at large radii (if the density falls less rapidly than   r ⁻⁴  ). We also show that the flattening procedure does not alter the shape of the density distribution at small radii: while the inner density contours are flattened, the slope of the density profile is unaltered.
We apply this recipe to construct a set of flattened dark matter haloes based on the realistic spherical halo models by Dehnen & McLaughlin. This example illustrates that the method works fine for modest flattening values, whereas stronger flattening values lead to peanut-shaped density distributions.     

Numerical simulation of the gould belt dynamics

The results of numerical simulations of the Gould Belt motion for the 2D (a ring in the Galactic plane) and 3D (a spherical shell outside the Galactic plane) cases are presented. Particles of the expanding shell interact with each other within the framework of the N-body problem. The Galactic potential has been borrowed from Flynn et al. (1996). The total mass of the shell is 1.5 × 10⁶ M_⊙ in accordance with the estimate from Bobylev (2006). The initial mutual distances and velocities of the shell components are chosen in such a way that the shell reaches the present-day sizes of the Gould Belt in 30–60 Myr. In the 2D case, the ring is shown to be stretched with time into a rotating ellipse, which is consistent with the results from Blaauw (1952) obtained by other methods. In the 3D case, the projections of the initially spherical shell onto the Galactic plane are also rotating ellipses. A vertical oscillation of the Gould Belt components relative to the Galactic plane, a flattening of the spherical shell, and its inclination to the Galactic plane after a certain time interval have been revealed.     

Bar dissolution in non-spherical halos

Dynamical evolution of N-body bars embedded in spherical and prolate dark matter halos is investigated. In particular, the configuration such that galactic disks are placed in the plane perpendicular to the equatorial plane of the prolate halos is considered. Such a configuration is frequently found in cosmological simulations. N-body disks embedded in a fixed external halo potential were simulated, so that the barred structure was formed via dynamical instability in initially cool disks. In the subsequent evolution, bars in prolate halos dissolved gradually with time, while the bar pattern in spherical halos remained almost unchanged until the end of simulations. The e-folding time of bars suggest that they could be destroyed in a time smaller than a Hubble time. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Reliability of Merger-Trees and the Mass-Growth Histories of Dark Matter Haloes

We have used merger-trees realizations to study the formation of dark matter haloes. The construction of merger-trees is based on three different pictures about the formation of structures in the Universe. These pictures include the spherical collapse (SC), the ellipsoidal collapse (EC) and the non-radial collapse (NR). The reliability of merger-trees has been examined comparing their predictions related to the distribution of the number of progenitors, as well as the distribution of formation times, with the predictions of analytical relations. The comparison yields a very satisfactory agreement. Subsequently, the mass-growth histories (MGH) of haloes have been studied and their formation scale factors have been derived. This derivation has been based on two different definitions that are (a) the scale factor when the halo reaches half its present day mass and (b) the scale factor when the mass-growth rate falls below some specific value. Formation scale factors follow approximately power laws of mass. It has also been shown that MGHs are in good agreement with models proposed in the literature that are based on the results of N-body simulations. The agreement is found to be excellent for small haloes but, at the early epochs of the formation of large haloes, MGHs seem to be steeper than those predicted by the models based on N-body simulations. This rapid growth of mass of heavy haloes is likely to be related to a steeper central density profile indicated by the results of some N-body simulations.     

Constraints on the initial conditions of globular clusters

N -body simulations are made with a variety of initial conditions, in particular clumpy and flattened distributions, to attempt to constrain the possible initial conditions of globular clusters, using the observations that young LMC globular clusters appear relaxed after only 20 to 40 Myr. It is found that violent relaxation is able to erase most of the initial substructure in only ≈ 6 crossing times. However, initially very clumpy distributions (≲ 100 clumps) form clusters that are too concentrated to resemble real globular clusters. Such clusters also often have large clumps in long-lasting (≳ 30 crossing times) orbits which do not appear in observed cluster profiles. It is also found that even modest amounts of initial flattening produce clusters that are too elliptical to resemble real globular clusters. In such a scenario, cloud–cloud collisions and similar energetic processes would be unlikely to produce sufficiently spherical globular clusters. It is suggested that globular clusters form from roughly spherical initial conditions with star formation occurring either smoothly or in many small clumps.     

3-D non-linear evolution of a magnetic flux tube in a spherical shell: The isentropic case

We present recent 3-D MHD numerical simulations of the non-linear dynamical evolution of magnetic flux tubes in an adiabatically stratified convection zone in spherical geometry, using the anelastic spherical harmonic (ASH) code.We seek to understand the mechanism of emergence of strong toroidal fields from the base of the solar convection zone to the solar surface as active regions. We confirm the results obtained in cartesian geometry that flux tubes that are not twisted split into two counter vortices before reaching the top of the convection zone. Moreover, we find that twisted tubes undergo the poleward-slip instability due to an unbalanced magnetic curvature force which gives the tube a poleward motion both in the non-rotating and in the rotating case. This poleward drift is found to be more pronounced on tubes originally located at high latitudes. Finally, rotation is found to decrease the rise velocity of the flux tubes through the convection zone, especially when the tube is introduced at low latitudes. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cylindrical and spherical electron acoustic solitary waves in the presence of superthermal hot electrons

Propagation of cylindrical and spherical electron-acoustic solitary waves in unmagnetized plasmas consisting of cold electron fluid, hot electrons obeying a superthermal distribution and stationary ions are investigated. The standard reductive perturbation method is employed to derive the cylindrical/spherical Korteweg-de-Vries equation which governs the dynamics of electron-acoustic solitons. The effects of nonplanar geometry and superthermal hot electrons on the behavior of cylindrical and spherical electron acoustic soliton and its structure are also studied using numerical simulations.     

Dissipative forces and external resonances

We analyze the process of resonance trapping due to Poynting–Robertson drag and Stokes drag in the frame of the restricted 3-body problem and in the case of external mean motion resonances. The numerical simulations presented are computed by using the 3-dimensional extended Schubart averaging (ESA) integrator developed by Moons (1994) for all mean motion resonances. We complete it by adding the contributions of the dissipative forces. To follow the philosophy of the initial integrator, we average the drag terms, but we do not make any expansion in series of eccentricity or inclination. We show our results, especially capture around asymmetric equilibria, and compare them to those found by Beaué and Ferraz-Mello (1993, 1994) and Liou et al. (1979).