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The Lexington Benchmarks for Numerical Simulations of Nebulae

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 Added by Gary J. Ferland
 Publication date 2016
  fields Physics
and research's language is English




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We present the results of a meeting on numerical simulations of ionized nebulae held at the University of Kentucky in conjunction with the celebration of the 70th birthdays of Profs. Donald Osterbrock and Michael Seaton.



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To understand how the circumstellar environments of post-AGB stars develop into planetary nebulae, we initiate a systematic study of 2D axisymmetric hydrodynamic simulations of protoplanetary nebula (pPN) with a modified ZEUS code. The aim of this first work is to compare the structure of prolate ellipsoidal winds into a stationary ambient medium where both media can be either atomic or molecular. We specifically model the early twin-shock phase which generates a decelerating shell. A thick deformed and turbulent shell grows when an atomic wind expands into an atomic medium. In all other cases, the interaction shell region fragments into radial protrusions due to molecular cooling and chemistry. The resulting fingers eliminate any global slip parallel to the shell surface. This rough surface implies that weak shocks are prominent in the excitation of the gas despite the fast speed of advance. This may explain why low excitation molecular hydrogen is found towards the front of elliptical pPN. We constrain molecular dissociative fractions and timescales of fast $mathrm H_2$ winds and the pPN lifetime with wind densities $mathrm{sim10^{5}cm^{-3}}$ and shock speeds of $mathrm{80sim200,km,s^{-1}}$. We identify a variety of stages associated with thermal excitation of H$_2$ near-infrared emission. Generated line emission maps and position-velocity diagrams enable a comparison and distinction with post-AGB survey results. The $mathrm{1to0 , S(1)}$ $&$ $mathrm{2to1 , S(1)}$ lines are lobe-dominated bows rather than bipolar shells.
The diversity of structures in the Universe (from the smallest galaxies to the largest superclusters) has formed under the pull of gravity from the tiny primordial perturbations that we see imprinted in the cosmic microwave background. A quantitative description of this process would require description of motion of zillions of dark matter particles. This impossible task is usually circumvented by coarse-graining the problem: one either considers a Newtonian dynamics of particles with macroscopically large masses or approximates the dark matter distribution with a continuous density field. There is no closed system of equations for the evolution of the matter density field alone and instead it should still be discretized at each timestep. In this work we describe a method of solving the full 6-dimensional Vlasov-Poisson equation via a system of auxiliary Schroedinger-like equations. The complexity of the problem gets shifted into the choice of the number and shape of the initial wavefunctions that should only be specified at the beginning of the computation (we stress that these wavefunctions have nothing to do with quantum nature of the actual dark matter particles). We discuss different prescriptions to generate the initial wave functions from the initial conditions and demonstrate the validity of the technique on two simple test cases. This new simulation algorithm can in principle be used on an arbitrary distribution function, enabling the simulation of warm and hot dark matter structure formation scenarios.
High resolution Very Long Baseline Interferometry (VLBI) observations of Active Galactic Nuclei (AGN) revealed traveling and stationary or quasi-stationary radio-components in several blazar jets. The traveling ones are in general interpreted as shock waves generated by pressure perturbations injected at the jet nozzle. The stationary features can be interpreted as recollimation shocks in non-pressure matched jets if they show a quasi-symmetric bump in the spectral index distribution. In some jets there may be interactions between the two kinds of shocks. These shock--shock interactions are observable with VLBI techniques, and their signature should also be imprinted on the single--dish light curves. We performed relativistic hydrodynamic (RHD) simulations of over-pressured and pressure-matched jets. To simulate the shock interaction we injected a perturbation at the jet nozzle once a steady-state was reached. We computed the non-thermal emission (including adiabatic and synchotron losses) resulting from the simulation. We show that the injection of perturbations in a jet can produce a bump in emission at GHz frequencies previous to the main flare, which is produced when the perturbation fills the jet in the observers frame. The detailed analysis of our simulations and the non-thermal emission calculations show that interaction between a recollimation shock and traveling shock produce a typical and clear signature in both the single--dish light curves and in the VLBI observations: the flaring peaks are higher and delayed with respect to the evolution of a perturbation through a conical jet. This fact can allow to detect such interactions for stationary components lying outside of the region in where the losses are dominated by inverse Compton scattering.
We review the numerical techniques for ideal and non-ideal magneto-hydrodynamics (MHD) used in the context of star formation simulations. We outline the specific challenges offered by modeling star forming environments, which are dominated by supersonic and super-Alfvenic turbulence in a radiative, self-gravitating fluid. These conditions are rather unique in physics and engineering and pose particularly severe restrictions on the robustness and accuracy of numerical codes. One striking aspect is the formation of collapsing fluid elements leading to the formation of singularities that represent point-like objects, namely the proto-stars. Although a few studies have attempted to resolve the formation of the first and second Larson cores, resolution limitations force us to use sink particle techniques, with sub-grid models to compute the accretion rates of mass, momentum and energy, as well as their ejection rate due to radiation and jets from the proto-stars. We discuss the most popular discretisation techniques used in the community, namely smoothed particle hydrodynamics, finite difference and finite volume methods, stressing the importance to maintain a divergence-free magnetic field. We discuss how to estimate the truncation error of a given numerical scheme, and its importance in setting the magnitude of the numerical diffusion. This can have a strong impact on the outcome of these MHD simulations, where both viscosity and resistivity are implemented at the grid scale. We then present various numerical techniques to model non-ideal MHD effects, such as Ohmic and ambipolar diffusion, as well as the Hall effect. These important physical ingredients are posing strong challenges in term of resolution and time stepping. For the latter, several strategies are discussed to overcome the limitations due to prohibitively small time steps (abridged).
Bow shocks and related density enhancements produced by the winds of massive stars moving through the interstellar medium provide important information regarding the motions of the stars, the properties of their stellar winds, and the characteristics of the local medium. Since bow shocks are aspherical structures, light scattering within them produces a net polarization signal even if the region is spatially unresolved. Scattering opacity arising from free electrons and dust leads to a distribution of polarized intensity across the bow shock structure. That polarization encodes information about the shape, composition, opacity, density, and ionisation state of the material within the structure. In this paper we use the Monte Carlo radiative transfer code SLIP to investigate the polarization created when photons scatter in a bow shock-shaped region of enhanced density surrounding a stellar source. We present results assuming electron scattering, and investigate the polarization behaviour as a function of optical depth, temperature, and source of photons for two different cases: pure scattering and scattering with absorption. In both regimes we consider resolved and unresolved cases. We discuss the implication of these results as well as their possible use along with observational data to constrain the properties of observed bow shock systems. In different situations and under certain assumptions, our simulations can constrain viewing angle, optical depth and temperature of the scattering region, and the relative luminosities of the star and shock.
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