# Posts Tagged numerical simulation

## Recent Postings from numerical simulation

### Analysis of the spiral structure in a simulated galaxy

We analyze the spiral structure that results in a numerical simulation of a galactic disk with stellar and gaseous components evolving in a potential that includes an axisymmetric halo and bulge. We perform a second simulation without the gas component to observe how it affects the spiral structure in the disk. To quantify this, we use a Fourier analysis and obtain values for the pitch angle and the velocity of the self-excited spiral pattern of the disk. The results show a tighter spiral in the simulation with gaseous component. The spiral structure is consistent with a superposition of waves, each with a constant pattern velocity in given radial ranges.

### Numerical Simulation of Radio Signal from Extended Air Showers

The burst of radio emission by the extensive air shower provides a promising alternative for detecting ultra-high energy cosmic rays.We have developed an independent numerical program to simulate these radio signals. Our code is based on a microscopic treatment, with both the geosynchrotron radiation and charge excess effect included. Here we make a first presentation of our basic program and its results. The time signal for different polarizations are computed, we find that the pulses take on a bipolar pattern, the spectrum is suppressed towards the lower frequencies.We investigate how the shower at different heights in atmosphere contribute to the total signal, and examine the signal strength and distribution at sites of different elevations. We also study the signal from showers of different inclination angles and azimuth directions. In all these cases we find the charge excess effect important.

### Towards Collisions of Inhomogeneous Shockwaves in AdS [Cross-Listing]

We perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate holographic description of the thermalization of a strongly coupled plasma, which can model the dynamics of heavy ion collisions. The results indicate that previous calculations of the thermalization time may have been underestimates.

### Towards Collisions of Inhomogeneous Shockwaves in AdS

We perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate holographic description of the thermalization of a strongly coupled plasma, which can model the dynamics of heavy ion collisions. The results indicate that previous calculations of the thermalization time may have been underestimates.

### Towards Collisions of Inhomogeneous Shockwaves in AdS

We perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate holographic description of the thermalization of a strongly coupled plasma, which can model the dynamics of heavy ion collisions. The results indicate that previous calculations of the thermalization time may have been underestimates.

### Numerical Simulation of Superhalo Electrons Generated by Magnetic Reconnection in the Solar Wind Source Region

Superhalo electrons appear to be continuously present in the interplanetary medium, even at very quiet times, with a power-law spectrum at energies above $\sim$2 keV. Here we numerically investigate the generation of superhalo electrons by magnetic reconnection in the solar wind source region, using the MHD and test particle simulations for both single X-line reconnection and multiple X-line reconnection. We find that the direct current electric field, produced in the magnetic reconnection region, can accelerate electrons from an initial thermal energy of T $\sim10^5$ K up to hundreds of keV. After acceleration, some of the accelerated electrons, together with the nascent solar wind flow driven by the reconnection, propagate upwards along the newly-opened magnetic field lines into the interplanetary space, while the rest move downwards into the lower atmosphere. Similar to the observed superhalo electrons at 1 AU, the flux of the upward-traveling accelerated electrons versus energy displays a power-law distribution at $\sim$ 2 $-$ 100 keV, $f(E) \sim E^{-\delta}$, with a $\delta$ of $\sim$ 1.5 $-$ 2.4. For single (multiple) X-line reconnection, the spectrum becomes harder (softer) as the anomalous resistivity parameter $\alpha$ (uniform resistivity $\eta$) increases. These modeling results suggest that the acceleration in the solar wind source region may contribute to superhalo electrons.

### Numerical Simulation Of Spectral And Timing Properties Of Galactic Black Holes

A black hole accretion may have both the Keplerian and the sub-Keplerian components. We consider the most general accretion flow configuration, namely, two-component advective flow (TCAF) in which the Keplerian disk is immersed inside a low angular momentum, accreting sub-Keplerian halo component around a black hole. Low energy (soft) photons from the Keplerian component and hot electrons in the sub-Keplerian component exchange their energy through Comptonization or inverse-Comptonization processes. In the sub-Keplerian component, a shock is generally formed due to the centrifugal force. The post-shock region is known as the CENtrifugal pressure dominated BOundary Layer (CENBOL). The spectral and the timing properties of TCAF have been extensively studied using mostly analytical and some time dependent numerical simulations since the model was proposed by Chakrabarti & Titarchuk in 1995. The findings are the key inputs of understanding several observed features of black hole candidates. In this thesis, using numerical simulation, we rigorously prove some of the conjectures of the TCAF model. In the work presented in this thesis, we have considered for the first time the presence of both the Keplerian and the sub-Keplerian flow in a single simulation. The Keplerian disk resides on the equatorial plane and is the standard disk from which low energy photons having multi-color blackbody spectrum is emitted. The hydrodynamics as well as the thermal properties of the sub-Keplerian halo are simulated using a finite difference code which uses the principle of total variation diminishing (TVD). The Comptonization between the photons and the hot electrons is simulated using a Monte Carlo code. These two codes are then coupled and the resulting localized heating and cooling are included in the coupled code. Using this code, we study the spectral and timing properties of the TCAF.

### Rotating Solar Jets in Simulations of Flux Emergence with Thermal Conduction

We study the formation of coronal jets through numerical simulation of the emergence of a twisted magnetic flux rope into a pre-existing open magnetic field. Reconnection inside the emerging flux rope in addition to that between the emerging and pre-existing fields give rise to the violent eruption studied. The simulated event closely resembles the coronal jets ubiquitously observed by Hinode/XRT and demonstrates that heated plasma is driven into the extended atmosphere above. Thermal conduction implemented in the model allows us to qualitatively compare simulated and observed emission from such events. We find that untwisting field lines after the reconnection drive spinning outflows of plasma in the jet column. The Poynting flux in the simulated jet is dominated by the untwisting motions of the magnetic fields loaded with high-density plasma. The simulated jet is comprised of spires of untwisting field that are loaded with a mixture of cold and hot plasma and exhibit rotational motion of order 20 km/s and match contemporary observations.

### Restricted phase-space approximation in real-time stochastic quantization

We perform and extend real-time numerical simulation of a scalar quantum field theory using stochastic quantization. After a brief review of the quantization method, we calculate the propagator and the perturbative series and compare with analytical results. This is a first step toward general applications, and we focus only on the vacuum properties of the theory; this enables us to handle the boundary condition by the $i\epsilon$ prescription. Then, we explicitly check the convergence and solve the differential equation in frequency space. For clarity we drop the spatial-derivative terms and make a comparison between our results and the numerically exact results obtained by diagonalization of the Hamiltonian. While we can control stability of the numerical simulation for any coupling strength, our results turn out to flow into an unphysical attractor if the simulation is out of the weak-coupling regime. We propose a simple truncation scheme to incorporate the interaction terms, which we name the "restricted phase-space approximation." With this method, we obtain results with stable simulation at good accuracy. Finally we give a short discussion on the closed-time path formalism.

### Restricted phase-space approximation in real-time stochastic quantization [Cross-Listing]

We perform and extend real-time numerical simulation of a scalar quantum field theory using stochastic quantization. After a brief review of the quantization method, we calculate the propagator and the perturbative series and compare with analytical results. This is a first step toward general applications, and we focus only on the vacuum properties of the theory; this enables us to handle the boundary condition by the $i\epsilon$ prescription. Then, we explicitly check the convergence and solve the differential equation in frequency space. For clarity we drop the spatial-derivative terms and make a comparison between our results and the numerically exact results obtained by diagonalization of the Hamiltonian. While we can control stability of the numerical simulation for any coupling strength, our results turn out to flow into an unphysical attractor if the simulation is out of the weak-coupling regime. We propose a simple truncation scheme to incorporate the interaction terms, which we name the "restricted phase-space approximation." With this method, we obtain results with stable simulation at good accuracy. Finally we give a short discussion on the closed-time path formalism.

### Spinning black hole in the puncture method: Numerical experiments

The strong-field region inside a black hole needs special attention during numerical simulation. One approach for handling the problem is the moving puncture method, which has become an important tool in numerical relativity since it allows long term simulations of binary black holes. An essential component of this method is the choice of the ’1+log’-slicing condition. We present an investigation of this slicing condition in rotating black hole spacetimes. We discuss how the results of the stationary Schwarzschild ’1+log’-trumpet change when spin is added. This modification enables a simple and cheap algorithm for determining the spin of a non-moving black hole for this particular slicing condition. Applicability of the algorithm is verified in simulations of single black hole, binary neutron star and mixed binary simulations.

### Formation of a Flare-Productive Active Region: Observation and Numerical Simulation of NOAA AR 11158

We present a comparison of the Solar Dynamics Observatory (SDO) analysis of NOAA Active Region (AR) 11158 and numerical simulations of flux-tube emergence, aiming to investigate the formation process of this flare-productive AR. First, we use SDO/Helioseismic and Magnetic Imager (HMI) magnetograms to investigate the photospheric evolution and Atmospheric Imaging Assembly (AIA) data to analyze the relevant coronal structures. Key features of this quadrupolar region are a long sheared polarity inversion line (PIL) in the central delta-sunspots and a coronal arcade above the PIL. We find that these features are responsible for the production of intense flares, including an X2.2-class event. Based on the observations, we then propose two possible models for the creation of AR 11158 and conduct flux-emergence simulations of the two cases to reproduce this AR. Case 1 is the emergence of a single flux tube, which is split into two in the convection zone and emerges at two locations, while Case 2 is the emergence of two isolated but neighboring tubes. We find that, in Case 1, a sheared PIL and a coronal arcade are created in the middle of the region, which agrees with the AR 11158 observation. However, Case 2 never builds a clear PIL, which deviates from the observation. Therefore, we conclude that the flare-productive AR 11158 is, between the two cases, more likely to be created from a single split emerging flux than from two independent flux bundles.

### Formation of sub-horizon black holes from preheating [Cross-Listing]

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation we compute the probability distribution of curvature fluctuations paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter-space.

### Formation of sub-horizon black holes from preheating [Cross-Listing]

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation we compute the probability distribution of curvature fluctuations paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter-space.

### Formation of subhorizon black holes from preheating [Replacement]

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation, we compute the probability distribution of curvature fluctuations, paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter space.

### Formation of subhorizon black holes from preheating [Replacement]

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation, we compute the probability distribution of curvature fluctuations, paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter space.

### Formation of subhorizon black holes from preheating [Replacement]

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation, we compute the probability distribution of curvature fluctuations, paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter space.

### Formation of sub-horizon black holes from preheating

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation we compute the probability distribution of curvature fluctuations paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter-space.

### Numerical simulation of oscillating magnetospheres with resistive electrodynamics

We present a model of the magnetosphere around an oscillating neutron star. The electromagnetic fields are numerically solved by modeling electric charge and current induced by the stellar torsional mode, with particular emphasis on outgoing radiation passing through the magnetosphere. The current is modeled using Ohm’s law, whereby an increase in conductivity results in an increase in the induced current. As a result, the fields are drastically modified, and energy flux is thereby enhanced. This behavior is however localized in the vicinity of the surface since the induced current disappears outwardly in our model, in which the exterior is assumed to gradually approach a vacuum.

### Synthetic Observations of the Evolution of Starless Cores in a Molecular Cloud Simulation: Comparisons with JCMT Data and Predictions for ALMA

Interpreting the nature of starless cores has been a prominent goal in star formation for many years. In order to characterise the evolutionary stages of these objects, we perform synthetic observations of a numerical simulation of a turbulent molecular cloud. We find that nearly all cores that we detect are associated with filaments and eventually form protostars. We conclude that observed starless cores which appear Jeans unstable are only marginally larger than their respective Jeans masses (within a factor of 3). We note single dish observations such as those performed with the JCMT appear to miss significant core structure on small scales due to beam averaging. Finally, we predict that interferometric observations with ALMA Cycle 1 will resolve the important small scale structure, which has so far been missed by mm-wavelength observations.

### Synthetic Observations of the Evolution of Starless Cores in a Molecular Cloud Simulation: Comparisons with JCMT Data and Predictions for ALMA [Replacement]

Interpreting the nature of starless cores has been a prominent goal in star formation for many years. In order to characterise the evolutionary stages of these objects, we perform synthetic observations of a numerical simulation of a turbulent molecular cloud. We find that nearly all cores that we detect are associated with filaments and eventually form protostars. We conclude that observed starless cores which appear Jeans unstable are only marginally larger than their respective Jeans masses (within a factor of 3). We note single dish observations such as those performed with the JCMT appear to miss significant core structure on small scales due to beam averaging. Finally, we predict that interferometric observations with ALMA Cycle 1 will resolve the important small scale structure, which has so far been missed by mm-wavelength observations.

### Chaos and Turbulent Nucleosynthesis Prior to a Supernova Explosion [Replacement]

Three-dimensional (3D), time dependent numerical simulations, of flow of matter in stars, now have sufficient resolution to be fully turbulent. The late stages of the evolution of massive stars, leading up to core collapse to a neutron star (or black hole), and often to supernova explosion and nucleosynthesis, are strongly convective because of vigorous neutrino cooling and nuclear heating. Unlike models based on current stellar evolutionary practice, these simulations show a chaotic dynamics characteristic of highly turbulent flow. Theoretical analysis of this flow, both in the Reynolds-averaged Navier-Stokes (RANS) framework and by simple dynamic models, show an encouraging consistency with the numerical results. It may now be possible to develop physically realistic and robust procedures for convection and mixing which (unlike 3D numerical simulation) may be applied throughout the long life times of stars. In addition, a new picture of the presupernova stages is emerging which is more dynamic and interesting (i.e., predictive of new and newly observed phenomena) than our previous one.

### Chaos and Turbulent Nucleosynthesis Prior to a Supernova Explosion

Three-dimensional (3D), time dependent numerical simulations, of flow of matter in stars, now have sufficient resolution to be fully turbulent. The late stages of the evolution of massive stars, leading up to core collapse to a neutron star (or black hole), and often to supernova explosion and nucleosynthesis, are strongly convective because of vigorous neutrino cooling and nuclear heating. Unlike models based on current stellar evolutionary practice, these simulations show a chaotic dynamics characteristic of highly turbulent flow. Theoretical analysis of this flow, both in the Reynolds-averaged Navier-Stokes (RANS) framework and by simple dynamic models, show an encouraging consistency with the numerical results. It may now be possible to develop physically realistic and robust procedures for convection and mixing which (unlike 3D numerical simulation) may be applied throughout the long life times of stars. In addition, a new picture of the presupernova stages is emerging which is more dynamic and interesting (i.e., predictive of new and newly observed phenomena) than our previous one.

### Numerical simulation of the electron capture process in a magnetar interior

In a superhigh magnetic field, direct Urca reactions can proceed for an arbitrary proton concentration. Since only the electrons with high energy $E$ ($E > Q$, $Q$ is the threshold energy of inverse $\beta-$decay) at large Landau levels can be captured, we introduce the Landau level effect coefficient $q$ and the effective electron capture rate $\Gamma_{\rm eff}$. By using $\Gamma_{\rm eff}$, the values of $L_{\rm X}$ and $L_{\rm \nu}$ are calculated, where and $L_{\rm \nu}$, $L_{\rm X}$ are the average neutrino luminosity of Anomalous X-ray Pulsars (AXPs) and the average X-ray luminosity of AXPs, respectively. The complete process of electron capture inside a magnetar is simulated numerically.

### GLAMER Part II: Multiple Plane Gravitational Lensing

We present an extension to multiple planes of the gravitational lensing code {\small GLAMER}. The method entails projecting the mass in the observed light-cone onto a discrete number of lens planes and inverse ray-shooting from the image to the source plane. The mass on each plane can be represented as halos, simulation particles, a projected mass map extracted form a numerical simulation or any combination of these. The image finding is done in a source oriented fashion, where only regions of interest are iteratively refined on an initially coarse image plane grid. The calculations are performed in parallel on shared memory machines. The code is able to handle different types of analytic halos (NFW, NSIE, power-law, etc.), haloes extracted from numerical simulations and clusters constructed from semi-analytic models ({\small MOKA}). Likewise, there are several different options for modeling the source(s) which can be distributed throughout the light-cone. The distribution of matter in the light-cone can be either taken from a pre-existing N-body numerical simulations, from halo catalogs, or are generated from an analytic mass function. We present several tests of the code and demonstrate some of its applications such as generating mock images of galaxy and galaxy cluster lenses.

### Nonlinear transport of Cosmic Rays in turbulent magnetic field

Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall present the nonlinear results for cosmic ray transport, in particular, the cross field transport of CRs and demonstrate that the concept of cosmic ray subdiffusion in general does not apply and the perpendicular motion is well described by normal diffusion with M_A^4 dependence. Moreover, on scales less than injection scale of turbulence, CRs’ transport becomes super-diffusive. Quantitative predictions for both the normal diffusion on large scale and super diffusion are confronted with recent numerical simulations. Implication for shock acceleration is briefly discussed.

### Nonlinear transport of Cosmic Rays in turbulent magnetic field [Replacement]

Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall present the nonlinear results for cosmic ray transport, in particular, the cross field transport of CRs and demonstrate that the concept of cosmic ray subdiffusion in general does not apply and the perpendicular motion is well described by normal diffusion with M_A^4 dependence. Moreover, on scales less than injection scale of turbulence, CRs’ transport becomes super-diffusive. Quantitative predictions for both the normal diffusion on large scale and super diffusion are confronted with recent numerical simulations. Implication for shock acceleration is briefly discussed.

### Numerical Simulation of Spectral and Timing Properties of a Two Component Advective Flow around a Black Hole

We study the spectral and timing properties of a two component advective flow (TCAF) around a black hole by numerical simulation. Several cases have been simulated by varying the Keplerian disk rate and the resulting spectra and lightcurves have been produced for all the cases. The dependence of the spectral states and quasi-periodic oscillation (QPO) frequencies on the flow parameters is discussed. We also find the earlier explanation of arising of QPOs as the resonance between infall time scale and cooling time scale remain valid even for Compton cooling.

### A new GPU-accelerated hydrodynamical code for numerical simulation of interacting galaxies

In this paper a new scalable hydrodynamic code GPUPEGAS (GPU-accelerated PErformance Gas Astrophysic Simulation) for simulation of interacting galaxies is proposed. The code is based on combination of Godunov method as well as on the original implementation of FlIC method, specially adapted for GPU-implementation. Fast Fourier Transform is used for Poisson equation solution in GPUPEGAS. Software implementation of the above methods was tested on classical gas dynamics problems, new Aksenov’s test and classical gravitational gas dynamics problems. Collisionless hydrodynamic approach was used for modelling of stars and dark matter. The scalability of GPUPEGAS computational accelerators is shown.

### Probing the structure of local magnetic field of solar features with helioseismology

Motivated by the problem of local solar subsurface magnetic structure, we have used numerical simulation to investigate the propagation of waves through monolithic magnetic flux tubes of different size. A cluster model can be a good approximation to simulate sunspots as well as solar plage regions which are composed of an ensemble of compactly packed thin flux tubes. Simulations of this type is a powerful tool to probe the structure and the dynamic of various solar features which are related directly to solar magnetic field activity.

### Numerical Simulation of Establishment of thermodynamic equilibrium in cosmological model with an arbitrary acceleration

Results of numerical simulation constructed before strict mathematical model of an establishment of thermodynamic equilibrium in originally nonequilibrium cosmological ultrarelativistic plasma for the Universe with any acceleration in the assumption of restoration of a scalling of interactions of elementary particles are presented at energies above a unitary limit. Limiting parametres of residual nonequilibrium distribution of nonequilibrium relic particles of ultrahigh energies are found.

### Using 3D Voronoi grids in radiative transfer simulations

Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate discretization is crucial. Adaptive grids with cuboidal cells such as octrees have proven very popular, however several recently introduced hydrodynamical and RT codes are based on a Voronoi tessellation of the spatial domain. Such an unstructured grid poses new challenges in laying down the rays (straight paths) needed in RT codes. We show that it is straightforward to implement accurate and efficient RT on 3D Voronoi grids. We present a method for computing straight paths between two arbitrary points through a 3D Voronoi grid in the context of a RT code. We implement such a grid in our RT code SKIRT, using the open source library Voro++ to obtain the relevant properties of the Voronoi grid cells based solely on the generating points. We compare the results obtained through the Voronoi grid with those generated by an octree grid for two synthetic models, and we perform the well-known Pascucci RT benchmark using the Voronoi grid. The presented algorithm produces correct results for our test models. Shooting photon packages through the geometrically much more complex 3D Voronoi grid is only about three times slower than the equivalent process in an octree grid with the same number of cells, while in fact the total number of Voronoi grid cells may be lower for an equally good representation of the density field. We conclude that the benefits of using a Voronoi grid in RT simulation codes will often outweigh the somewhat slower performance.

### Filaments in Simulations of Molecular Cloud Formation [Replacement]

We report on the filaments that develop self-consistently in a new numerical simulation of cloud formation by colliding flows. As in previous studies, the forming cloud begins to undergo gravitational collapse because it rapidly acquires a mass much larger than the average Jeans mass. Thus, the collapse soon becomes nearly pressureless, proceeding along its shortest dimension first. This naturally produces filaments in the cloud, and clumps within the filaments. The filaments are not in equilibrium at any time, but instead are long-lived flow features, through which the gas flows from the cloud to the clumps. The filaments are long-lived because they accrete from their environment while simultaneously accreting onto the clumps within them; they are essentially the locus where the flow changes from accreting in two dimensions to accreting in one dimension. Moreover, the clumps also exhibit a hierarchical nature: the gas in a filament flows onto a main, central clump, but other, smaller-scale clumps form along the infalling gas. Correspondingly, the velocity along the filament exhibits a hierarchy of jumps at the locations of the clumps. Two prominent filaments in the simulation have lengths ~15 pc, and masses ~600 Msun above density n ~ 10^3 cm-3 (~2×10^3 Msun at n > 50 cm-3). The density profile exhibits a central flattened core of size ~0.3 pc and an envelope that decays as r^-2.5, in reasonable agreement with observations. Accretion onto the filament reaches a maximum linear density rate of ~30 Msun Myr^-1 pc^-1.

### Filaments in Simulations of Molecular Cloud Formation [Replacement]

We report on the filaments that develop self-consistently in a new numerical simulation of cloud formation by colliding flows. As in previous studies, the forming cloud begins to undergo gravitational collapse because it rapidly acquires a mass much larger than the average Jeans mass. Thus, the collapse soon becomes nearly pressureless, proceeding along its shortest dimension first. This naturally produces filaments in the cloud, and clumps within the filaments. The filaments are not in equilibrium at any time, but instead are long-lived flow features, through which the gas flows from the cloud to the clumps. The filaments are long-lived because they accrete from their environment while simultaneously accreting onto the clumps within them; they are essentially the locus where the flow changes from accreting in two dimensions to accreting in one dimension. Moreover, the clumps also exhibit a hierarchical nature: the gas in a filament flows onto a main, central clump, but other, smaller-scale clumps form along the infalling gas. Correspondingly, the velocity along the filament exhibits a hierarchy of jumps at the locations of the clumps. Two prominent filaments in the simulation have lengths ~15 pc, and masses ~600 Msun above density n ~ 10^3 cm-3 (~2×10^3 Msun at n > 50 cm-3). The density profile exhibits a central flattened core of size ~0.3 pc and an envelope that decays as r^-2.5, in reasonable agreement with observations. Accretion onto the filament reaches a maximum linear density rate of ~30 Msun Myr^-1 pc^-1.

### Filaments in Simulations of Molecular Cloud Formation [Replacement]

We report on the filaments that develop self-consistently in a new numerical simulation of cloud formation by colliding flows. As in previous studies, the forming cloud begins to undergo gravitational collapse because it rapidly acquires a mass much larger than the average Jeans mass. Thus, the collapse soon becomes nearly pressureless, proceeding along its shortest dimension first. This naturally produces filaments in the cloud, and clumps within the filaments. The filaments are not in equilibrium at any time, but instead are long-lived flow features, through which the gas flows from the cloud to the clumps. The filaments are long-lived because they accrete from their environment while simultaneously accreting onto the clumps within them; they are essentially the locus where the flow changes from accreting in two dimensions to accreting in one dimension. Moreover, the clumps also exhibit a hierarchical nature: the gas in a filament flows onto a main, central clump, but other, smaller-scale clumps form along the infalling gas. Correspondingly, the velocity along the filament exhibits a hierarchy of jumps at the locations of the clumps. Two prominent filaments in the simulation have lengths ~15 pc, and masses ~600 Msun above density n ~ 10^3 cm-3 (~2×10^3 Msun at n > 50 cm-3). The density profile exhibits a central flattened core of size ~0.3 pc and an envelope that decays as r^-2.5, in reasonable agreement with observations. Accretion onto the filament reaches a maximum linear density rate of ~30 Msun Myr^-1 pc^-1.

### Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics [Replacement]

Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through use of integer spin weighted spherical harmonics we present a method which allows for the implementation of arbitrary tensorial evolution equations. Our method combines two numerical techniques that were originally developed with different applications in mind. The first is Huffenberger and Wandelt’s spectral decomposition algorithm to perform the mapping from physical to spectral space. The second is the application of Luscombe and Luban’s method, to convert numerically divergent linear recursions into stable nonlinear recursions, to the calculation of reduced Wigner d-functions. We give a detailed discussion of the theory and numerical implementation of our algorithm. The properties of our method are investigated by solving the scalar and vectorial advection equation on the sphere, as well as the 2+1 Maxwell equations on a deformed sphere.

### Realistic Simulations of Stellar Surface Convection with ANTARES: I. Boundary Conditions and Model Relaxation [Replacement]

We have implemented open boundary conditions into the ANTARES code to increase the realism of our simulations of stellar surface convection. Even though we greatly benefit from the high accuracy of our fifth order numerical scheme (WENO5), the broader stencils needed for the numerical scheme complicate the implementation of boundary conditions. We show that the effective temperature of a numerical simulation cannot be changed by corrections at the lower boundary since the thermal stratification does only change on the Kelvin-Helmholtz time scale. Except for very shallow models, this time scale cannot be covered by multidimensional simulations due to the enormous computational requirements. We demonstrate to what extent numerical simulations of stellar surface convection are sensitive to the initial conditions and the boundary conditions. An ill-conceived choice of parameters for the boundary conditions can have a severe impact. Numerical simulations of stellar surface convection will only be (physically) meaningful and realistic if the initial model, the extent and position of the simulation box, and the parameters from the boundary conditions are chosen adequately.

### Nonuniformity effects in the negative effective magnetic pressure instability

Using direct numerical simulations (DNS) and mean-field simulations (MFS), the effects of non-uniformity of the magnetic field on the suppression of the turbulent pressure is investigated. This suppression of turbulent pressure can lead to an instability which, in turn, makes the mean magnetic field even more non-uniform. This large-scale instability is caused by a resulting negative contribution of small-scale turbulence to the effective (mean-field) magnetic pressure. We show that enhanced mean current density increases the suppression of the turbulent pressure. The instability leads to magnetic flux concentrations in which the normalized effective mean-field pressure is reduced to a certain value at all depths within a structure.

### The Burst Mode of Accretion in Primordial Star Formation

We present simulation results for the formation and long-term evolution of a primordial protostellar disk harbored by a first star. Using a 2+1D nonaxisymmetric thin disk numerical simulation, together with a barotropic relation for the gas, we are able to probe ~20 kyr of the disk’s evolution. During this time period we observe fragmentation leading to loosely bound gaseous clumps within the disk. These are then torqued inward and accreted onto the growing protostar, giving rise to a burst phenomenon. The luminous feedback produced by this mechanism may have important consequences for the subsequent growth of the protostar.

### Flavor stability analysis of dense supernova neutrinos with flavor-dependent angular distributions [Cross-Listing]

Numerical simulations of the supernova (SN) neutrino self-induced flavor conversions, associated with the neutrino-neutrino interactions in the deepest stellar regions, have been typically carried out assuming the "bulb-model". In this approximation, neutrinos are taken to be emitted half-isotropically by a common neutrinosphere. In the recent Ref. \cite{Mirizzi:2011tu} we have removed this assumption by introducing flavor-dependent angular distributions for SN neutrinos, as suggested by core-collapse simulations. We have found that in this case a novel multi-angle instability in the self-induced flavor transitions can arise. In this work we perform an extensive study of this effect, carrying out a linearized flavor stability analysis for different SN neutrino energy fluxes and angular distributions, in both normal and inverted neutrino mass hierarchy. We confirm that spectra of different nu species which cross in angular space (where F_{\nu_e}=F_{\nu_x} and F_{\bar\nu_e}=F_{\bar\nu_x}) present a significant enhancement of the flavor instability, and a shift of the onset of the flavor conversions at smaller radii with respect to the case of an isotropic neutrino emission. We also illustrate how a qualitative (and sometimes quantitative) understanding of the dynamics of these systems follows from a stability analysis.

### Data assimilation for stratified convection

We show how the 3DVAR data assimilation methodology can be used in the astrophysical context of a two-dimensional convection flow. We study the way this variational approach finds best estimates of the current state of the flow from a weighted average of model states and observations. We use numerical simulations to generate synthetic observations of a vertical two-dimensional slice of the outer part of the solar convection zone for varying noise levels and implement 3DVAR when the covariance matrices are scalar. Our simulation results demonstrate the capability of 3DVAR to produce error estimates of system states between up to tree orders of magnitude below the original noise level present in the observations. This work exemplifies the importance of applying data assimilation techniques in simulations of the stratified convection.

### Synthetic X-ray spectra for simulations of the dynamics of an accretion flow irradiated by a quasar

Ultraviolet and X-ray observations show evidence of outflowing gas around many active galactic nuclei. Some of these outflows may be driven off gas infalling towards the central black hole. We perform radiative transfer calculations to compute the gas ionization state and X-ray spectra for two- and three-dimensional (3D) hydrodynamical simulations of this outflow-from-inflow scenario. By comparison with observations, our results can be used to test the theoretical models and guide future numerical simulations. We predict both absorption and emission features, most of which are formed in a polar funnel of outflowing gas. This outflow causes strong absorption for observer orientation angles of < 35 degrees. Particularly in 3D, the strength of this absorption varies significantly for different lines-of-sight owing to the fragmentary structure of the gas flow. Although infalling material occupies a large fraction of the simulation volume, we do not find that it imprints strong absorption features since the ionization state is very high. Thus, an absence of observed inflow absorption features does not exclude the models. The main spectroscopic consequence of the infalling gas is a scattered continuum component that partially re-fills the absorption features caused by the outflowing polar funnel. Fluorescence and scattering in the outflow is predicted to give rise to several emission features for all observer orientations. For the hydrodynamical simulations considered we find both ionization states and column densities for the outflowing gas that are too high to be quantitatively consistent with well-observed X-ray absorption systems. Nevertheless, our results are qualitatively encouraging and further exploration of the model parameter space is warranted. (Abridged.)

### The Rossiter-McLaughlin effect for exomoons or binary planets

In this paper we study possible signatures of binary planets or exomoons on the Rossiter-McLaughlin (R-M) effect. Our analyses show that the R-M effect for a binary planet or exomoon during its complete transit phase can be divided into two parts. The first is the conventional one similar to the R-M effect from the transit of a single planet, of which the mass and the projected area are the combinations of the binary components; and the second is caused by the orbital rotation of the binary components, which may add a sine- or linear-mode deviation to the stellar radial velocity curve. We find that the latter effect can be up to several or several ten m/s. By doing numerical simulations as well as analytical analyses, we illustrate that the distribution and dispersion of the latter effects obtained from multiple transit events can be used to constrain the dynamical configuration of the binary planet, such as, how the inner orbit of the binary planet is inclined to its orbit rotating around the central star. We find that the signatures caused by the orbital rotation of the binary components are more likely to be revealed if the two components of binary planet have different masses and mass densities, especially if the heavy one has a high mass density and the light one has a low density. Similar signature on the R-M effect may also be revealed in a hierarchical triple star system containing a dark compact binary and a tertiary star.

### 3D simulations of globules and pillars formation around HII regions: turbulence and shock curvature

We investigate the interplay between the ionization radiation from massive stars and the turbulence inside the surrounding molecular gas thanks to 3D numerical simulations. We used the 3D hydrodynamical code HERACLES to model an initial turbulent medium that is ionized and heated by an ionizing source. Three different simulations are performed with different mean Mach numbers (1, 2 and 4). A non-equilibrium model for the ionization and the associated thermal processes was used. This revealed to be crucial when turbulent ram pressure is of the same order as the ionized-gas pressure. The density structures initiated by the turbulence cause local curvatures of the dense shell formed by the ionization compression. When the curvature of the shell is sufficient, the shell collapse on itself to form a pillar while a smaller curvature leads to the formation of dense clumps that are accelerated with the shell and therefore remain in the shell during the simulation. When the turbulent ram pressure of the cold gas is sufficient to balance the ionized-gas pressure, some dense-gas bubbles have enough kinetic energy to penetrate inside the ionized medium, forming cometary globules. This suggests a direct relation in the observations between the presence of globules and the relative importance of the turbulence compared to the ionized-gas pressure. The probability density functions present a double peak structure when the turbulence is low relative to the ionized-gas pressure. This could be used in observations as an indication of the turbulence inside molecular clouds.

### Black Hole-Neutron Star Mergers: Disk Mass Predictions

Determining the final result of black hole-neutron star mergers, and in particular the amount of matter remaining outside the black hole at late times, has been one of the main motivations behind the numerical simulation of these systems. Black hole-neutron star binaries are amongst the most likely progenitors of short gamma-ray bursts — as long as they result in the formation of massive (at least ~0.1 solar mass) accretion disks around the black hole. Whether this actually happens strongly depends on the physical characteristics of the system, and in particular on the mass ratio, the spin of the black hole, and the radius of the neutron star. We present here a simple two-parameter model, fitted to existing numerical results, for the determination of the mass remaining outside the black hole a few milliseconds after a black hole-neutron star merger. This model predicts the remnant mass within a few percents of the mass of the neutron star, at least for remnant masses up to 20% of the neutron star mass. Results across the range of parameters deemed to be the most likely astrophysically are presented here. We find that, for 10 solar mass black holes, massive disks are only possible for fairly large neutron stars (R>12km), or quasi-extremal black hole spins (a/M>0.9). We also use our model to discuss how the equation of state of the neutron star affects the final remnant, and the strong influence that this can have on the rate of short gamma-ray bursts produced by black hole-neutron star mergers.

### The thick disk rotation-metallicity correlation as a fossil of an "inverse chemical gradient" in the early Galaxy

The thick disk rotation–metallicity correlation, \partial V_\phi/\partial[Fe/H] =40\div 50 km s^{-1}dex^{-1} represents an important signature of the formation processes of the galactic disk. We use nondissipative numerical simulations to follow the evolution of a Milky Way (MW)-like disk to verify if secular dynamical processes can account for this correlation in the old thick disk stellar population. We followed the evolution of an ancient disk population represented by 10 million particles whose chemical abundances were assigned by assuming a cosmologically plausible radial metallicity gradient with lower metallicity in the inner regions, as expected for the 10-Gyr-old MW. Essentially, inner disk stars move towards the outer regions and populate layers located at higher |z|. A rotation–metallicity correlation appears, which well resembles the behaviour observed in our Galaxy at a galactocentric distance between 8 kpc and 10 kpc. In particular,we measure a correlation of \partial V_\phi/\partial[Fe/H]\simeq 60 km s^{-1}dex^{-1} for particles at 1.5 kpc < |z| < 2.0 kpc that persists up to 6 Gyr. Our pure N-body models can account for the V_\phi vs. [Fe/H] correlation observed in the thick disk of our Galaxy, suggesting that processes internal to the disk such as heating and radial migration play a role in the formation of this old stellar component. In this scenario, the positive rotation-metallicity correlation of the old thick disk population would represent the relic signature of an ancient "inverse" chemical (radial) gradient in the inner Galaxy, which resulted from accretion of primordial gas.

### Temporal Evolution of Velocity and Magnetic Field in and around Umbral Dots

We study the temporal evolution of umbral dots (UDs) using measurements from the CRISP imaging spectropolarimeter at the Swedish 1-m Solar Telescope. Scans of the magnetically sensitive 630 nm iron lines were performed under stable atmospheric conditions for 71 min with a cadence of 63 s. These observations allow us to investigate the magnetic field and velocity in and around UDs at a resolution approaching 0.13". From the analysis of 339 UDs, we draw the following conclusions: (1)UDs show clear hints of upflows, as predicted by magnetohydrodynamic (MHD) simulations. By contrast, we could not find systematic downflow signals. Only in very deep layers we detect localized downflows around UDs, but they do not persist in time. (2) We confirm that UDs exhibit weaker and more inclined fields than their surroundings, as reported previously. However, UDs that have strong fields above 2000 G or are in the decay phase show enhanced and more vertical fields. (3)There are enhanced fields at the migration front of UDs detached from penumbral grains, as if their motion were impeded by the ambient field. (4) Long-lived UDs travel longer distances with slower proper motions. Our results appear to confirm some aspects of recent numerical simulations of magnetoconvection in the umbra (e.g., the existence of upflows in UDs), but not others (e.g., the systematic weakening of the magnetic field at the position of UDs.)

### A Mexican Hat with holes: calculating low resolution power spectra from data with gaps

A simple method for calculating a low-resolution power spectrum from data with gaps is described. The method is a modification of the $\Delta$-variance method previously described by Stutzki and Ossenkopf. A Mexican Hat filter is used to single out fluctuations at a given spatial scale and the variance of the convolved image is calculated. The gaps in the image, defined by the mask, are corrected for by representing the Mexican Hat filter as a difference between two Gaussian filters with slightly different widths, convolving the image and mask with these filters and dividing the results before calculating the final filtered image. This method cleanly compensates for data gaps even if these have complicated shapes and cover a significant fraction of the data. The method was developed to deal with problematic 2D images, where irregular detector edges and masking of contaminating sources compromise the power spectrum estimates, but it can also be straightforwardly applied to 1D timing analysis or 3D data cubes from numerical simulations.

### Dark Matter Subhalos in the Ursa Minor Dwarf Galaxy

Through numerical simulations, we study the dissolution timescale of the Ursa Minor cold stellar clump, due to the combination of phase-mixing and gravitational encounters with compact dark substructures in the halo of Ursa Minor. We compare two scenarios; one where the dark halo is made up by a smooth mass distribution of light particles and one where the halo contains 10% of its mass in the form of substructures (subhalos). In a smooth halo, the stellar clump survives for a Hubble time provided that the dark matter halo has a big core. In contrast, when the point-mass dark substructures are added, the clump survives barely for \sim 1.5 Gyr. These results suggest a strong test to the \Lambda-cold dark matter scenario at dwarf galaxy scale.

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