A numerical model for Type II supernovae — The collapse stage

We use the following numerical model for the collapse stage of a Type II supernova of 15 M_⊙. Our electron capture rate includes the effects of the inverse reaction and the neutron-proton mass difference. This decreases the electron density at the collapse stage and led to rather large values of the maximum inward velocity and of the corresponding mass (Umax = 3.06 × 10⁹cm/s, Mmax=0.76 M_⊙). These larger values are more favourable for the propagation of shock after the rebounce and the triggering-off of a Type-II supernova explosion. For neutrino transport, we use a leakage model and an equilibrium diffusion model, respectively, for the thin and thick stages and a grey atmosphere model to assess the effect of neutrino precipitation on the collapse. We found this effect to be small, the energy precipitation to be not more than 10^?5 the neutrino energy loss and the momentum precipitation not more than 10^?6 the gravitational acceleration.     

A numerical model of cohesion in planetary rings

We present a numerical method that incorporates particle sticking in simulations using the N-body code pkdgrav to study motions in a local rotating frame, such as a patch of a planetary ring. Particles stick to form non-deformable but breakable aggregates that obey the (Eulerian) equations of rigid-body motion. Applications include local simulations of planetary ring dynamics and planet formation, which typically feature hundreds of thousands or more colliding bodies. Bonding and breaking thresholds are tunable parameters that can approximately mimic, for example, van der Waals forces or interlocking of surface frost layers. The bonding and breaking model does not incorporate a rigorous treatment of internal fracture; rather the method serves as motivation for first-order investigation of how semi-rigid bonding affects the evolution of particle assemblies in high-density environments.We apply the method to Saturn’s A ring, for which laboratory experiments suggest that interpenetration of thin, frost-coated surface layers may lead to weak cohesive bonding. These experiments show that frost-coated icy bodies can bond at the low impact speeds characteristic of the rings. Our investigation is further motivated by recent simulations that suggest a very low coefficient of restitution is needed to explain the amplitude of the azimuthal brightness asymmetry in Saturn’s A ring, and the hypothesis that fine structure in Saturn’s B ring may in part be caused by large-scale cohesion.This work presents the full implementation of our model in pkdgrav, as well as results from initial tests with a limited set of parameters explored. We find a combination of parameters that yields aggregate size distribution and maximum radius values in agreement with Voyager data for ring particles in Saturn’s outer A ring. We also find that the bonding and breaking parameters define two strength regimes in which fragmentation is dominated either by collisions or other stresses, such as tides. We conclude our study with a discussion of future applications of and refinements to our model.     

A model independent approach to future solar neutrino experiments

We discuss here what model independent information about properties of neutrinos and of the sun can be obtained from future solar neutrino experiments (SNO, Super-Kamiokande). It is shown that in the general case of transitions of solar ν_e's into νμ and/or ντ the initial ⁸B neutrino flux can be measured by the observation of NC events. From the CC measurements the ν_e survival probability can be determined as a function of neutrino energy. The general case of transitions of solar ν_e's into active as well as sterile neutrinos is considered. A number of relations between measurable quantities the test of which will allow to answer the question whether there are sterile neutrinos in the solar neutrino flux on the earth are derived. Transitions of solar ν_e's into active and sterile states due to neutrino mixing and Dirac magnetic moments or into active left-handed neutrinos and active right-handed antineutrinos due to neutrino mixing and Majorana transition magnetic moments are also considered. It is shown that future solar neutrino experiments will allow to distinguish between the cases of Dirac and Majorana magnetic moments.     

A symmetry-induced model of elliptical galaxy patterns

Sérsic (Atlas de Galaxias Australes, Observatorio Astronómico, 1968) generalized the de Vaucouleurs law which follows the projected (observed) one dimensional radial profile of elliptical galaxies closely and Dehnen (Mon. Not. R. Astron. Soc. 265:250, 1993) proposed an analytical formula of the 3-dimensional light distributions whose projected line profile resembles the de Vaucouleurs law. This paper is involved to recover the Dehnen model and generalize the model to account for galaxy elliptical shapes by means of curvilinear coordinate systems and employing a symmetry principle. The symmetry principle maps an orthogonal coordinate system to a light distribution pattern. The coordinate system for elliptical galaxy patterns turns out to be the one which is formed by the complex-plane reciprocal transformation Z=1/W. The resulting spatial (3-dimensional) light distribution is spherically symmetric and has infinite gradient at its center, which is called spherical-nucleus solution and is used to model galaxy central area. We can make changes of the coordinate system by cutting out some column areas of its definition domain, the areas containing the galaxy center. The resulting spatial (3-dimensional) light distributions are axisymmetric or triaxial and have zero gradient at the center, which are called elliptical-shape solutions and are used to model global elliptical patterns. The two types of logarithmic light distributions are added together to model full elliptical galaxy patterns. The model is a generalization of the Dehnen model. One of the elliptical-shape solutions permits realistic numerical calculation and is fitted to all R-band elliptical images from Frei et al. (Astron. J. 111:174, 1996) galaxy sample. The fitting is satisfactory. This suggests that elliptical galaxy patterns can be represented in terms of a few basic parameters.     

Magnetic helicity in stellar dynamos: new numerical experiments

The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios can give rise to different structures of the mean field which are obtained at early times, but the final saturation field strength is still decreasing with decreasing resistivity. In the presence of shear, cyclic magnetic fields are found whose period is increasing with decreasing resistivity, but the saturation energy of the mean field is in strong super‐equipartition with the turbulent energy. It is shown that artificially induced losses of small scale field of opposite sign of magnetic helicity as the large scale field can, at least in principle, accelerate the production of large scale (poloidal) field. Based on mean field models with an outer potential field boundary condition in spherical geometry, we verify that the sign of the magnetic helicity flux from the large scale field agrees with the sign of α. For solar parameters, typical magnetic helicity fluxes lie around 10⁴⁷ Mx² per cycle.     

Hydrodynamics of hypersonic jets: experiments and numerical simulations

Stars form in regions of the galaxy that are denser and cooler than the mean interstellar medium. These regions are called Giant Molecular Clouds. At the beginning of their life, up to 10⁵–10⁶ years, stars accrete matter from their rich surrounding environment and are origin of a peculiar phenomenon that is the jet emission. Jets from Young Stellar Objects (YSOs) are intensively studied by the astrophysical community by observations at different wavelengths, analytical and numerical modeling and laboratory experiments. Indications about the jet propagation and its resulting morphologies are here obtained by means of a combined study of hypersonic jets carried out both in the laboratory and by numerical simulations.     

A numerical hydrodynamic model of a heated coronal loop

The fluid equations describing a fully ionized single temperature (i.e., electron and proton temperatures assumed identical) hydrogen plasma in a coronal loop subject to a transient heating pulse (2 × 10⁹ ergs cm^–2 s^–1) centred about the loop apex have been solved numerically. An adaptive regriding scheme was used to ensure adequate spatial resolution throughout the transition region, and due regard paid to the numerical time constants. Because of the fine gridding made possible by this scheme these results represent the first reliable simulation of the impact of a downward propagating conduction front on the transition region, and the early stages of the development of the downward moving compression and upward ablation. Intensities in the O v (1371 Å) transition region line were calculated from the model results. Finally estimates have been made of the importance of the downward-streaming collisionless high-energy tail of the distribution in the transition region resulting from the very steep temperature gradients. It is shown that the mass and energy densities are not substantially altered by the non-Maxwellian tail except in so far as they are coupled to higher moments of the distribution function such as the heat flux through the fluid equations.     

A numerical model of the Martian polar cap winds

An investigation of the Martian polar cap winds and their response to a variety of factors is carried out by a series of numerical experiments based on a zonally symmetric primitive equation model. These factors are the seasonal thermal forcing, mass exchange between polar caps and atmosphere, large-scale topography, and polar cap size. The thermal forcing sets up a circulation whose surface winds adjust to achieve angular momentum balance, with low-latitude easterlies and high-latitude westerlies. The maximum westerlies occur roughly where the horizontal temperature gradients are largest. This pattern changes when cap and atmosphere exchange mass. Corriolis forces acting on the net outflow or inflow produce easterlies at the surface during spring (outflow) and westerlies during winter (inflow). Topography appears to have a small effect, but cap size does play a role, the circulation intensity increasing with cap size. Peak surface winds occur when outflow or inflow is a maximum and are 20 m sec^?1 during spring and 30 m sec^?1 during winter for the northern hemisphere. The model results show that surface winds near the edge of a retreating polar cap are substantially enhanced, a result which is consistent with the Viking observations of local dust storm activity near the edge of the south polar cap during spring. The results also indicate that the surficial wind indicators near the south pole are formed during spring and those near the north pole during winter. The implication is that the high-latitude dune fields in the northern hemisphere are formed at a time when the terrain is being covered with frost. It is therefore suggested that the saltating particles are “snowflakes” which have formed by the mechanism proposed by Pollack etal. The model results for the winter simulation, which have formed by the mechanism transport by large-scale eddies, compare favorably with general circulation model (GCM) calculations. This suggests that the eddy transports may be less important than those associated with the net mass flow, and that 2-D climate modeling may be more succesful for Mars than Earth.     

Volume scattering model for interpretation of solar radar experiments

It is shown that solar radar experiments carried out at = 8 m can be explained on the assumption that the reflected signal is formed as a result of multiple volume scattering on large-scale (about 1 km) irregularities of the outer corona. The region of effective scattering is located at the heliocentric distancer 2R, i.e., considerably higher than the region of surface mirror reflection. Measured characteristics of reflected signals are in good agreement with the theoretical model.     

A new numerical method for solving radiation driven winds from hot stars

We present a general method for solving the non‐linear differential equation of monotonically increasing steady‐state radiation driven winds. We graphically identify all the singular points before transforming the momentum equation to a system of differential equations with all the gradients explicitly given. This permits a topological classification of all singular points and to calculate the maximum and minimum mass‐loss of the wind. We use our method to analyse for the first time the topology of the non‐rotating frozen‐in ionisation m‐CAK wind, with the inclusion of the finite disk correction factor, and find up to 4 singular points, three of the x‐type and one attractor‐type. The only singular point (and solution passing through) that satisfies the boundary condition at the stellar surface is the standard m‐CAK singular point. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

METEOMOD: A numerical model for the calculation of melting-crystallization relationships in meteoritic igneous systems

Abstract— The METEOMOD model is a computer program designed to calculate melting-crystallization relationships in igneous systems compositionally similar to ordinary chondrites and basaltic achondrites. The core of METEOMOD is a set of empirically calibrated equations, called geothermometers, which describe equilibria between silicate melt and minerals such as olivine, orthopyroxene, pigeonite, augite, plagioclase, and metallic Fe in terms of pressure, temperature, and liquid compositions. The silicate mineral geothermometers are calibrated from a database containing the compositions of melts and minerals produced in melting experiments on 113 meteoritic and 141 synthetic systems. The metallic iron-silicate melt geothermometer is calibrated from a database of 396 melting experiments. The Meteorite Melting Model or METEOMOD calculates crystallization temperatures and contents of major end members in mineral solid solutions with accuracies of ±10–15 °C and ±1–2 mol%, respectively. Input parameters for the program are (1) increment in crystallization degree; (2) one of 12f_O2 buffers routinely used in petrology; (3) shift from the buffer in log units, if any; (4) a choice of equilibrium or fractional crystallization trajectory; (5) terminal crystallization degree; (6) contents of ten major elements in wt%; (7) a set of minor and trace elements in parts per million; (8) the number of initial compositions to be modeled in a single computation run. The output consists of a series of tables that list equilibrium temperatures, O fugacities, and proportions of melt and minerals and their compositions, as a function of the degree of crystallization. The results of application of METEOMOD to modeling of melting-crystallization of the St. Severin LL chondrite are compared with the experimental data of Jurewicz et al. (1995).     

A global numerical 3-D MHD model of the solar wind

A fully three-dimensional, steady-state global model of the solar corona and the solar wind is developed. A numerical, self-consistent solution for 3-D MHD equations is constructed for the region between the solar photosphere and the Earth's orbit. Boundary conditions are provided by the solar magnetic field observations. A steady-state solution is sought as a temporal relaxation to the dynamic equilibrium in the region of transonic flow near the Sun and then traced to the orbit of the Earth in supersonic flow region. The unique features of the proposed model are: (a) uniform coverage and self-consistent treatment of the regions of subsonic/sub-Alfvénic and supersonic/super-Alfvénic flows, (b) inferring the global structure of the interplanetary medium between the solar photosphere and 1 AU based on large-scale solar magnetic field data. As an experimental test for the proposed technique, photospheric magnetic field data for CR 1682 are used to prescribe boundary condition near the Sun and results of a simulation are compared with spacecraft measurements at 1 AU. The comparison demonstrates a qualitative agreement between computed and observed parameters. While the difference in densities is still significant, the 3-D model better reproduces variations of the solar wind velocity than does the 2-D model presented earlier (Usmanov, 1993).     

A standard format for reporting PILPS experiments

In model inter-comparisons one major obstacle is the format of the reported data. To facilitate the analysis of the results from the different models they should all be reported in the same format. This requires that the format is flexible enough to be easily implemented into the different land surface schemes. It should also be fault tolerant and allow a few consistence checks to avoid erroneous data to be submitted. The present note describes such a format developed for the PILPS project. After discussing the aim of this new format we present the routines which are used to write and read data. Finally two applications are described which allow the user to perform a number of consistency checks on the data.     

A model for X-ray emission from loop prominences

A study is made of X-ray line emission observed during the developing stages of a set of post-flare loop prominences. The time behaviour of the line emission can be described by a model consisting of two flux tubes containing plasma heated impulsively at the flash phase; the plasma cools by radiation and by conduction to the chromosphere. These ideas are extended to the possible formation of H prominences from low-lying hot loops.     

A helicity proxy from horizontal solar flow patterns

Motivated by new observations of solar surface flow patterns of mesogranulation, theoretical computations of the horizontal divergence-vorticity correlation are presented. Because of its close relation to the helicity in rotating turbulence such observations and discussions are of particular importance for the conventional dynamo theory. For the northern hemisphere we find a small, but always negative, divergence-vorticity correlation. Both an analytical Second Order Correlation Approximation for slow rotation as well as a numerical simulation (originally done for accretion disks) for fast rotation yield very similar results.     

The Fresnel imager: instrument numerical model

The methodology used in the end-to-end numerical model of the Fresnel Interferometric Imager is presented. This Instrument Numerical Model (INM) performs plane-to-plane Fresnel propagation, starting from the Fresnel array and ending at the achromatic focal plane, and has been written in c so that it can handle various instrument configurations (sizes of Fresnel arrays from cm to m, from a few Fresnel zones to a few hundred, and for various wavelengths) with a standard desktop computer (a few GHz processor(s) speed, a few GB of memory, execution time per wavelength spanning from few minutes to few hours in the most extreme cases). The INM is used to estimate the performances of the Fresnel Imager: angular resolution, photometric dynamic range, transmission, for on and off-axis sources.     

Catastrophic fragmentation and formation of families: Preliminary results from a new numerical model

Preliminary results of an improved version of the semiempirical model for catastrophic break up processes developed by Paolicchi et al., (1989) are presented. Among the several changes with respect to the old version, the most important seem to be related to the new treatment of gravitational effects, including self-compression and reaccumulation of fragments. In particular, the new model is able to analyze processes involving both cm-sized objects, like those studied by means of laboratory experiments, as well as much larger bodies, for which self-gravitational effects are dominant; moreover, in this latter case the model seems in principle adequate to describe with the same physics very different phenomena, like the formation of plausible asteroid families and the creation of single, rapidly spinning, objects. This fact, if confirmed by refined analyses, may be of high importance for our general understanding of asteroid collisional evolution.     

A new model for X-ray emission from NGC 4151

We present an analysis of the reported spectral features of NGC 4151 in X-rays. It is shown that the origin of X-rays from the source is inconsistent with a single production mechanism. We suggest a new two-component model in which soft X-rays arise from the black-body emission of a tiny hot nucleus withT2×10⁷ K and the hard X-ray photons are generated in an extended region by inverse Compton scattering of electrons with the infrared photons.