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Numerical Simulations for Astrophysical Turbulent Flows

Numerical Simulations for Astrophysical Turbulent Flows. Jongsoo Kim Korea Astronomy and Space Science Institute. Numerical astrophysics (in Korea) Supersonic interstellar turbulence Interstellar turbulence driven by supernova explosions Star formation in turbulent molecular clouds

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Numerical Simulations for Astrophysical Turbulent Flows

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  1. Numerical Simulations for Astrophysical Turbulent Flows Jongsoo Kim Korea Astronomy and Space Science Institute • Numerical astrophysics (in Korea) • Supersonic interstellar turbulence • Interstellar turbulence driven by supernova explosions • Star formation in turbulent molecular clouds • Conclusions

  2. Why are numerical simulations for astrophysical flows challenging? • Interaction between matter and radiation • - ultimate goal of numerical experiments is to provide information that can be compared with observations • - 5-D (time-space-frequency) problem • Huge dynamic range • - for example, need more than 20 orders-of-magnitude density dynamic range from a MC to a star • Multi-physics • - hydrodynamic, self-gravity, magnetic field, relativistic effect, … • Indeed, numerical simulations are challenging. However, they provide us with a unique laboratory for astrophysical experiments. •  Due to the rapid development of the computer technology, numerical simulations are now quite successful.

  3. Research fields, Researchers, Numerical tools • Cosmology; large-scale structure • Dongsu Ryu (CNU), Hyesung Kang(PNU), Changbum Park, Juhan Kim (KIAS); • HD, N-body • ISM; instabilities, spiral arms, turbulence • Seung Soo Hong, Won-Tae Kim, Yong Sun Park(SNU), Jongsoo Kim (KAO), Sang Min Lee (KISTI), Jungyeon Cho (CNU) • (M)HD, radiative transfer • Stellar, Galactic dynamics: GCs, young *s in Gal. Center • Hyung-Mok Lee (SNU), Hong-Bae Ahn (PNU), Sungsoo Kim(KHU) • N-body, SPH • Numerical Astrophysics is one of major fields in Korea

  4. Barnard 68 observed with 8.2m VLT, ESO

  5. Kim & Hong 2002

  6. Larson’s law; Larson(1981) • The velocity dispersions of interstellar clouds are far broader than the thermal line width, 0.2 km/sec. • A typical Reynolds number of the interstellar gas, VL/nu = 108 > 10-100 • Interstellar clouds are in a supersonic turbulent state.

  7. Decay of turbulence in MCs • - Traditionally, supersonic motions in MCs consist essentially of Alfven waves (Arons & Macs 1975), because • (linear) Alfven waves hardly decays • Alfven speeds of MCs are comparable to turbulent velocity • dispersions • However, decay of all MHD modes is fast (Stone et al. 1998; Mac Low et al. 1998; Padoan & Nordlund 1999). • Compressible and non-compressible modes also decay equally fast (Lazarian & Cho 2003). •  Turbulence in MCs should be continuously driven by some mechanisms.

  8. Stone et al. 1998 • - E: wave (kinetic + magnetic) • energy • - beta: ratio of gas pressure • to magnetic pressure • Due to mostly shock dissipation, the wave energy declines very fast.

  9. Mac Low+Klessen 2004, RvMP Possible Driving Mechanisms • Energy dissipation rate of isothermal, supersonic turbulence (Mac Low 2002) ~3x10-27 erg cm-3 s-1 Energy input rates • MRI (Sellwood & Balbus 1999): ~3x10-29 erg cm-3 s-1 • GI (Wada et al. 2002): ~ 4x10-29 erg cm-3 s-1 • Protostellar outflows: ~ 2x10-28 erg cm-3 s-1 • Supernovae: ~ 4x10-26 erg cm-3 s-1 • Ionizing radiation: ~ 5x10-29 erg cm-3 s-1

  10. MHD equations with cooling and heating terms where

  11. Periodic Boundaries B Randomly placed SN explosions 200.0 pc Magnetized Turbulent ISM forms self- consistently 200.0 pc z y 200.0 pc is covered by 256 cells. x

  12. Initial Conditions • Hydrogen number density: 0.2, 0.4, 0.8, 1.0 cm-3 • -Uniform B-field strengths: 2, 4, 8 and ~1x10-3 microG • SN explosion rates and Positioning • Galactic rate: simulations for Vrms and volume-filling-factors • The Galactic rate (1 SN explosion in 50 years) scales to one • event in 1.2 Myr in our computational box. • 8X Galactic rate: simulations for field amplification • It might be a typical rate for mild starbursts like M82. • - SNe explode one at a time at randomly chosen positions

  13. Late time Early time Isodensity Surfaces -- SNe-Induced ISM Turbulence

  14. Movie showing the rendering of isodensity surfaces. The porosity of the ISM is clearly visible.

  15. perpendicular to B parallel to B • Density averaged Vrms as a function of time for two sets of parameters, (B and n), with the Galactic SN rate. • The velocity dispersions of SN-driven turbulentflows are around 5-10 km/sec. • In the case with a strong field (right panel), Vrms perpendicular to the mean field direction is about 2km/sec higher than that parallel to the mean direction. This is due to magnetosonic waves.

  16. Volume filling factors (VFFs) of hot gas whose temperature is higher than 106 K as a function of time with different sets of mean field strength and hydrogen number density. • VFFs are sensitively dependent on hydrogen number density and mildly on field strength • VFFs vary from 1% to 30%

  17. Kronberg, Perry, & Zukowski 1992 The intervener is a spiral galaxy with a bisymmetric B-field. Field Geometry of M81

  18. Available time for dynamo action (or the minimum strength of a seed field) as a function of Omega_m in spatially flat cosmology (Widrow 2002) zf=0 zi=25 10 A~1014 Bi~10-20 G 5 13Gyr 3 • Parameters: • H0=70 km s-1 Mpc-1 • Gamma = 2.5Gyr-1 • (cf. 0.45Gyr-1 • in Ferriere and Schmidt 2000 zf=0.4 A~1011 Bi~10-17 G zi=10 10Gyr As observations (for example, the SKA) detect B-fields at a higher z, the available time for dynamo action should be shortened. zf=2.0 A~105 Bi~10-11 G zi=10 5Gyr

  19. Evolution of magnetic energy and rms density Growth time measured with a 10 Myr sliding window Balsara et al. 2004 • While the rms density quickly saturates, Emag steadily increases, which shows that the growth of Emag is not due to the density fluctuation. • The e-folding time scale of Emag is at most 16Myr for the simulation with 2563 cells. The time scale is much shorter than ~1.8 Gyr growth time estimated by Ferriere & Schmitt (2000) for the alpha-omega dynamo driven by Galactic superbubbles.

  20. Myers et al. 1986 • CO 2.6mm, 150micron, 250micron, • 6cm radio continuum, • H 110alpha recombination • inner Galaxy, -1 deg < b <1 deg, • 12 deg < l < 60deg • 54 molecular cloud complexes • mean SFE = mean Ms/(Ms+Mc)=2%

  21. Observed SFEs • Free-fall timescale of a GMC (typical mass 106Msun) with nH~ 100 cm-3 ~ 4Myr • Observed SFE = Ms/(Ms+Mc) is - 2-3% for the molecular cloud complexes in the inner Galaxy (e.g., Myers et al. 1986) - 10-30% for cluster-forming cores (e.g., Lada & Lada 2003) • SF theories should explain the low SFEs (Zuckerman & Evans 1974).

  22. Magnetically sub- and supercritical masses Scalar virial theorem 0.3 (Mouchovias & Spitzer 1974) 1/(4pi^2) (Nakano & Nakamura 1978)

  23. Two SF Theories ion neutral SF regulated by AD SF regulated by turbulence magnetically supercritical cloud. (B-field is not important ingredient.) magnetically subcritical cloud

  24. subcritial supercritial Bourke et al. 2001 Criticality of MC cores • Almost all observed cores are magnetically supercritical if they have spherical geometry. • Even the case with the sheet geometry (Shu et al. 2001) the average normalized flux-to-mass ratio is 0.4, which is in the supercritical range. • More observations are needed in order to clarify the criticality of cores.

  25. 3D, self-gravitating, driven MHD simulations m =(M/F) /(M/F)c=0.9, 2.8, 8.8, infinite n = 500 cm-3 cs = 0.2 km s-1 L = 4pc B = 45, 15, 5, 0 mG Mtot = 2000 Msun periodic boundaries B uniform density turbulence is driven at a large scale around L/2 Mrms = 10 L=4LJ resolution: 2563 cells

  26. m=2.8 m=8.8 HD core formation m=0.9, subcritical Time evolution of global maximum of density field • dmax < 100n0 for the subcritical case. • Within 0.5 tff, dmax ~104n0 (first cores are formed) for the supercritical cases. •  consequence of the production of locally gravitationally unstable objects by the turbulence

  27. 10 no 100 n0 1000 n0 dt_frame = 0.04Myr Magnetically supercritical case, m=2.8 • A few collapsing cores are formed. • First collapsing object goes from first appearance to a fully collapsed state in less than 1 Myr, twice of the local free-fall time.

  28. Core Formation Efficiency (SFE) 0.12 0.04 M (n>500n0) 0.05 2.8 8.8 0.025 lifetime of cloud: 4Myr (e.g, Hartmann et al. 2001) • CFE is dependent on the seed for random driving • velocity fields (Heitsch et al 2001). • CFEs are lower than 10 % in most cases.

  29. Conclusions • Due to the pretty good computer resources and active astrophysicists, numerical astrophysics is one of the major research fields in Korea. • SN explosions may become one of driving mechanisms of the interstellar turbulence. • CFEs(SFEs) measured in 3D driven simulations of magnetically supercritical MCs is less than 10%, which is consistent with the observed levels. (SEFs measured in 2D decaying subcritical simulations with AD have the same level.)

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