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Amplification of Magnetic Fields by Supernova-Driven Turbulence

Amplification of Magnetic Fields by Supernova-Driven Turbulence. Jongsoo Kim Korea Astronomy and Space Science Institute. Collaborators: Dinshaw Balsara (University of Notre Dame) Mordecai Mac Low (American Museum of Natural History). B-fields at intermediate z.

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Amplification of Magnetic Fields by Supernova-Driven Turbulence

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  1. Amplification of Magnetic Fields by Supernova-Driven Turbulence Jongsoo Kim Korea Astronomy and Space Science Institute Collaborators: Dinshaw Balsara (University of Notre Dame) Mordecai Mac Low (American Museum of Natural History)

  2. B-fields at intermediate z Quasar PKS 1229-021, z=1.038 Kronberg, Perry, & Zukowski 1992 • RM map • VLA at 4520, 4880, and 14965 MHz • Resolution: 0.46arcsec

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

  4. Athreya et al. 1998 • VLA observations of 15 radio galaxies with z>2 • Four gals show intrinsic RMs in excess of 1000 rad m-2 • The environs of the gals at z>2 have B-fields with micro-G strength.

  5. 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

  6. Owen et al. 1990 • RM (gray)+6cm total intensity (contour) in the inner 2kpc of M87, a giant elliptical galaxy • RMs are ~1000 rad m-2 over most of the source. • 40 microG ordered field on the scale of 1 kpc. • In order to explain B-fields in E. gals, we need field amplification mechanisms that are not based on the alpha-omega dynamo.

  7. Seed fields based on astrophysical mechanisms • Radiation-era vorticity (Harrison 1970, 1973) - 10-19G - strong coupling between photons and electrons - week coupling between electrons and protons • Biermann battery effect (Biermann 1950) - 10-21G (Kulsrud et al. 1997) - electron pressure gradient

  8. AGN - Bg ~ 10-6 G : interaction of a jet with the ISM (Daly and Loeb 1990) - BIGM ~ 10-11 G (nAGN/Mpc3) : AGN jets contaminate the protogalactic medium with a magnetic field (Daly and Loeb 1990; Rees 1987, 1994). • Stellar wind (Michel and Yahil 1973; Bisnovatyi-Kogan et al. 1973) B ~ 0.3x10-6G • MRI (Brandenburg’s talk) • Supernovae (Syrovatskii 1970) - number of SN explosions in the Galaxy Nsn ~ 3x108 (one per 30 years) - total volume of the Galaxy Vg ~ 5.7x1011pc3 (=2pi x (15kpc)2 x400pc) - volume per supernova ~ 2x103 pc3 - B-field in the Crab nebula (radius ~ 0.8pc)~3x10-4 G - If the Crab expands to the volume adibatically, then B-field in the ISM B ~ 3x10-4 G (2x103 pc3/ 2pc3)-2/3 ~ 3x10-6 G

  9. 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.

  10. 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.

  11. 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

  12. The results on SNR-turbulence interaction in Balsara, Benjamin and Cox (2001) show that: • Strong SNR shocks interact with turbulent ISM, amplifying the • magnetic field strength. • 2) The post-shock fluid helicity is similarly and strongly amplified. • 3) Both signs of helicity are generated. • 4) Magnetic field amplification correlates with the fluid helicity. • This numerical experiment shows a possible way to amplify B-fields.

  13. We studied field amplification in a turbulence flow driven by SN explosions themselves through numerical experiments. Two Motivations: • SN explosions may release enough energy for the generation of the interstellar turbulent flow. • The interaction of SNRs with the turbulent flow can also amplify the B-field strength.

  14. MHD equations with cooling and heating terms where

  15. 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

  16. 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

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

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

  19. 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.

  20. 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%

  21. 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.

  22. density solenoidal kinetic E. compressible magnetic E. Balsara et al. 2004 • The solenoidal component of velocity PS • overwhelms the compressiblecomponent. • The amplification of B-field is closely • related to the solenoidal component. • The slopes of velocity PS are around • -2, even though it is hard to define • the inertial range, which is due to the strong • shocks. • Magnetic energy PS grow over all scales. • The length scale that gives the peaks • of mag. PS is about 10 pc. • The power in the large scales is also • increasing.

  23. Balsara et al. 2004 • Magnetic helicity shows • a secular increase with • increasing time. magnetic helicity |A dot B| kinetic helicity |v dot curl v|

  24. thermal pressure magnetic pressure kinetic helicity magnetic helicity Balsara et al. 2004 Sliced maps that passes though the recent remnant; t=20Myr; remnant is not spherical; large fluctuation in Hv

  25. B~n0.37 T<103.9 103.9<T<105.5 T>105.5 Balsara & Kim 2005 Histogram of B-field strength Scatter plot of log B vs. log n • As time goes on, a histogram progressively shifts right, which means that field amplification takes place over the whole • range of field strengths. • Intermittency is related to the fact that the fraction with strong B-field is small. Relatively denser and colder gas has strong B-field strength.

  26. Balsara & Kim 2005 How to follow up a line segment • if ds>2dx, new points are added • four-point Lagrangian interpolation was used to assign velocities to the points • second-orderpredictor-corrector method was used for the • temporal evolution of the points: ds t=t2 v t=t1 dx 64 points, 50pc y

  27. Balsara & Kim 2005 • Evolution of a line segment, which is initially aligned with y-axis, in the projected (x,y) plane • The loop-like structure may be formed by interactions of SN shocks with a clumpy turbulent flow and is indicative of Lagrangian motion in a velocity field with a dominant solenoidal component.

  28. e-folding time scale ~ 10 Myr (upper bound for the growth of B-field) Balsara & Kim 2005 • Evolution of the lengths (left panel) and standard deviations (right panel) of three line segments aligned initially x-,y-, and z-axis • standard deviations of radii of points << lengths; line segments are strongly folded. • Line segments grow exponentially, which indicates that magnetic field lines are also stretched exponentially. • Exponential line stretching is one important characteristics of chaos; • Exponential stretching of magnetic field lines is an essential prerequisite for the existence of • a fast dynamo (Vishik 1989)

  29. mean drift Balsara & Kim 2005 Turbulent diffusivity • Drummond, Duane & Hogan (1984) have developed Lagrangian strategy for measuring the diffusivity in a turbulent fluid. • Klessen & Lin (2003) pointed out the • importance of removing the mean drift. • We set up a 643 mesh of particles with inter-particle distance being dx and traced their positions. • diffusion time scale ~(50pc)2/eta_turb ~ Myr • The turbulent diffusion provides an efficient way to mix the elements from SN ejecta. ~6x1026 cgs units

  30. Conclusions • Microgauss levels of the observed B-fields in radio gals at z=2 shorten the time available for dynamo action. • To amplify a seed field by the alpha-omega dynamo mechanism with ~Gyr growth time, the strength of the seed field should be stronger than 10-11 G. • The growth time of B-field by SN-driven turbulence at least at a 100 pc scale is ~ 10 Myr. • SN-driven turbulence may possibly amplify kpc-scale B-fields, which should be confirmed by numerical experiments with a bigger computational domain. • SN-driven turbulence may play an important role in amplifying B-fields in many interesting astrophysical systems.

  31. Movie showing the rendering of isopressure surfaces. SNRs are spherical initially but become progressively non-spherical as the level of self-consistently generated turbulence rises.

  32. Early time Late time Isopressure Surfaces -- SNe-Induced ISM Turbulence

  33. <B2>/<B>2 Balsara & Kim 2005 • As time goes on, the ratio is increasing.

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