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Modeling Time Dependent Astrophysical Winds Peter Vitello Lawrence Livermore National Laboratory Livermore, CA 94550-9234 University of Kentucky 01/31/07 This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. Winds are extremely common astrophysical phenomena • Gas pressure driven: – Solar wind (~10-14 Mo/yr - source of interplanetary plasma) – X-ray heated stellar winds in X-ray binaries – X-ray heated stellar and AGN accretion disks (~10-2 Mo/yr) • Radiation pressure driven: – Stellar wind in hot OB stars (10-6 – 10-5 Mo/yr) – Cataclysmic Variable Stellar accretion disks (~10-8 Mo/yr) – Active Galactic Nuclei accretion disks (~1 Mo/yr) • Magnetic pressure driven: – Centrifugally driven outflows in dense molecular clouds collapsing into proto-stellar accretion disks (~10-4 Mo/yr) – X-wind from magnetized proto-star and accretion disk (~10-7 Mo/yr) – Magnetized active Galactic Nuclei accretion disks (~1 Mo/yr) Astrophysical winds are non-spherical • Solar wind originates in open magnetic field lies in coronal holes • Stellar winds from stars rotating near break-up are denser and cooler in the equatorial plane • Winds from accretion disks vary strongly with distance in the disk from the central object • Stellar winds in X-ray binary systems differ on the direction towards and away from the X-ray companion • Non-radial stellar pulsations generate nonuniform photosphere conditions for stellar winds Astrophysical winds are non-steady • Accretion disk winds show stable and unstable regions (turbulent outflow and/or fountain effect) • Line radiation winds inherently unstable at short wavelengths • Wind accretion in binaries to form an accretion disk is turbulent • Velocity shears from non-spherical flows should drive turbulence • Until recently our computational ability to simulate nonspherical, time dependent winds has been extremely limited In a X-ray binary source the X-ray emission is powered by wind accretion and the wind is modified by the X-rays Preliminary 2-D FLASH simulation of Vela X-1 OB star 4.4 10.8 log T (K) 8.3 log n (cm-3) radiatively driven wind 7.3 7.4 log x X-ray source (compact star) v (km s-1) 3500 -1.1 10 Asymmetries affect the predicted X-ray spectrum in ways that cannot be captured by simple models. Mauche LLNL 2006 Disk wind fountain and spiral stellar wind Accretion disk wind fountain Proga & Kallman 2004 Rotating stellar winds from localized emission sites Dessart 2004 Physics involved in modeling astrophysical winds • • • • • • • • Hydrodynamics Gravity Rotation Radiation pressure Heating / Cooling Ionization Radiation transfer Magnetic field • Too much physics is needed to start from scratch and continuously build new computational simulation models Re-use of hydrodynamic codes • Hydrodynamics is one aspect of wind modeling that is shared by many other disciplines • Adopting existing hydrodynamic simulation codes is the basis of wind modeling advances • Early wind modeling used ODE solvers for steady state 1D modeling • Recent modeling has used ZEUS and FLASH which are 2D/3D hydrodynamic codes which were designed to be adaptable to different types of astrophysics problems Evolution of numerical astrophysical modeling • Numerical astrophysical modeling has evolved enormously in the last 30 years – 1D (70’s) -> 2D (80’s) -> 3D (90’s) – Steady state modeling -> time dependent – Low resolution (~100 zones) -> high resolution ( > 108 zones) • 1 mainframe -> massively parallel (>10,000 cpu’s) • A few hours -> millions of cpu hours • Simple mesh -> locally refined mesh (AMR) Computation speed has gone up and cost has gone down • Supercomputers – Cray-1 • LANL in 1976 • 160 MFlop / 8 MB main memory – Blue Gene/L • • • • LLNL in 2005 280 TFlop / 32 TB memory 216 cpu’s (64k) 800 TB storage • Cost per GFlop – 1976 ($55,000,000) • Cray-1 – 1997 ($30,000) • 16 Pentium Pro processor Beowulf cluster – 2006 ($1) • ATI PC add-in graphic card (X1900) Supernova modeling has DOE backing for massive simulations • Univ. of Chicago used 2.7 million hours of supercomputing time to simulation of a supernova from a whole star simulation of a white dwarf with their FLASH code. • CHIMERA code (PRISM collaboration) is one of the proposed ‘peta-applications’ for the next generation PFlop machines. • New 3D simulations which are resulting in many TBytes of data is forcing the development of fast large scale parallel file systems and parallel graphic data visualization tools. FLASH - An Astrophysics Community Code Shortly: Relativistic accretion onto NS Flame-vortex interactions Compressed turbulence Type Ia Supernova The Flash code Gravitational collapse/Jeans instability 1. Parallel, adaptive-mesh simulation code Wave breaking on white dwarfs 2. Can solve a broad range of (astro)physics problems 3. Portable: runs on many massively-parallel systems 4. The largest run on 64k processors Intracluster interactions 6. Not a single code,Laser-driven but component based: shock instabilities Nova outbursts on white dwarfs Rayleigh-Taylor instability combine to form many different applications Helium burning on neutron stars Magnetic Rayleigh-Taylor Cellular detonation Orzag/Tang MHD vortex Lynn Reid ASC Center for Astrophysical Thermonuclear Flashes (University of Chicago) Richtmyer-Meshkov instability FLASH is a Community Code Breakdown of Responses Haven't used yet, plan to in future 8% Not using 17% Primary research tool 41% Sample code/ concept testing/ educational 25% V&V 9% Breakdown of FLASH code research areas for primary research tool users Variety of User Expertise • Complete beginners - execute only • More advance - Generate new problems, analyze - Change parameters in text files - Generate new simulations with initial conditions, parameters - Write alternate API routines for specialized output • Expert - New research - Can override any aspect of the code - Can install completely new algorithms or meshes - Can contribute to core functionality - Still benefits from framework and infrastructure, verification What happens in wind modeling when the spatial resolution increases? • A consequence of high resolution time dependent 2D/3D modeling is the appearance of fine scale hydrodynamic instabilities • Nature loves chaos and finds ways to mix gradients in flows whenever it can. • Several of the classic flow instabilities (Kelvin-Helmholtz, Rayleigh-Taylor, and Richtmyer-Meshkov) are clearly evident in numerical models of astrophysical winds. • Other flow instabilities can come from magnetic stress and radiation pressure. • These instabilities lead to turbulent flow which can strongly modify density, velocity and temperature structures in winds. Kelvin-Helmholtz velocity shear instability • Kelvin-Helmholtz instability occurs when two fluids of different density flow past each other at different speeds. A KHI on Saturn caused by the interaction between two bands of the planet's atmosphere. Wave clouds forming over Mount Duval. Rayleigh-Taylor gravity accelerated density shear instability • The Rayleigh-Taylor instability occurs any time a dense, heavy fluid is being accelerated by light fluid. Hydrodynamics simulation of the RTI RTI fingers evident in the Crab Nebula in which hot gas from the explosion is ramming into the surrounding Interstellar medium. Richtmyer-Meshkov accelerated density shear instability • The Richtmyer-Meshkov instability occurs when an interface between fluids of differing density is impulsively accelerated, e.g. by the passage of a shock wave. Time Experiment observing the shock-acceleration of a thin, perturbed layer of heavy gas embedded in a lowerdensity gas show new combinations of the three primary flow topologies discovered recently. 1996 APS-DFD Gallery of Fluid Motion by Paul Rightley, Robert Benjamin and Peter Vorobieff. The wind tunnel problem shows the complexity of flows with even simple internal structures • The problem uses a twodimensional rectangular domain with an internal step. • On the left-hand side we use a supersonic inflow. • This problem was run using FLASH with 5 levels of adaptive mesh refinement (AMR). Detail of the KHI at the slip line behind the Mach stem for 2, 3, 4, and 5 levels of refinement 2-D Rayleigh-Taylor / Kelvin-Helmholtz Instability • 2 and 3-D RTI calculations were carried out as part of the validation program for the FLASH code (Kevin Olson) • The images show a narrow spike of dense fluid falling under the influence of gravity, and bubbles of light fluid rising up on the sides. • The small features are the result of a KelvinHelmholtz instability at the interface of the fluids. • With 10 levels of refinement, the effective uniform grid resolution of this calculation is 16,384 x 4,096. Density field of the 2-D Rayleigh-Taylor simulation at a late stage in the calculation Resolution study of the accretion flow in the vicinity of the neutron star. (from ~7x109 to 3x107 cm) Earlier simulation log density r/R log density (g/cm3) 8 OB star 10 r/R Blondin et al. (1990–1995) 14 5x1012 cm 1x1011 cm Recent simulation Mauche LLNL 2006 15 Resolution study of the accretion flow in the vicinity of the neutron star. (from ~7x109 to 3x107 cm) Applying FLASH to “simple” thermally driven stellar winds • The simplist form of astrophysical wind is the thermally (gas pressure) driven wind • For steady state, spherical initial conditions analytic solutions exist • Looking at high resolution at winds with even simple, smoothly varying conditions at the base of the wind can lead to turbulent flow 2D simulation of a thermally driven wind from a star with a perturbed photosphere • Boundary conditions – Stellar mass: 2 Mo – Stellar radius: 0.1 Ro – Photosphere temperature: • Cosine variation: 2x107- 4 x107 K ( T = To + T1cos(6pq) ) – Radiation pressure: • Cosine variation: G = 0.45 – 0.55 (G = Go + G1cos(6pq) ) • AMR mesh – 8 levels of refinement – 1.4x106 mesh zones – Maximum resolution • 3.3x104 radial zones x 512 angular zones • 1.7x107 zones if uniform mesh used Wind flow is stable if temperature and radiation pressure reinforce each other Vr Boundary conditions T = 2x107 - 2x106 cos(6pq) G = 0.5 - 0.05 cos(6pq) log10(den) Temperature Wind stability mode is dependent upon initial conditions Vr Boundary conditions T = 2x107 - 2x106 cos(6pq) G = 0.5 + 0.05 cos(6pq) log10(den) Temperature Radial velocity evolution Larger temperature perturbation leads to a more chaotic flow Initial temperature profile Boundary conditions T = 3x107 - 1x107 cos(6pq) G = 0.5 + 0.05 cos(6pq) Final temperature profile Density profile evolution Initial log10(den) profile Boundary conditions T = 3x107 - 1x107 cos(6pq) G = 0.5 - 0.05 cos(6pq) Final log10(den) profile Velocity profile evolution Initial vr Final vr Final vq Conclusion • Simulations of astrophysical winds today can be done with spatial resolution that was impossible even a few years ago • This increased resolution unfortunately leads to a lot of computational effort being used to deal with hydrodynamic instabilities • What is needed to be done next is to be able to advance the level of physics in the models