Magnetic Fields (and Turbulence) in Galaxy Clusters Dongsu Ryu (UNIST, Ulsan National Institute of Science and Technology, Korea) with Hyesung Kang (Pusan Nat. U, Korea), Jungyeon Cho (Chungnam Nat. U.), Sungwook E. Hong (KIAS, Korea), Kiwan Park (UNIST, Korea) T. W. Jones, David H.Porter (U of Minnesota, USA), and etc - Turbulence in clusters in simulations - Magnetohydrodynamic turbulence - Nature of magnetic fields in clusters
Physical quantities in clusters of galaxies size of clusters density of baryonic matter flow velocity gas temperature magnetic fields Energetics gas thermal energy gas kinetic energy cosmic-ray energy magnetic energy L ~ a n T ~ 10 8 ~ 10 2 cm 3 υ ~ several 10 K B ~ a few µ G E E E E thermal kinetic cosmic-ray magnetic few Mpc ~ 10 ~ 10 10 11 ~ 10 ~ 10 2 km/s erg/cm erg/cm 12 12 3 3 erg/cm erg/cm plasma beta β 100 dynamically not important! 3 3 β P P gas magnetic
Magnetic fields in galaxy clusters appears in observations CIZA J2242.8+5301 Sausage relic Hydra North (van Weeren et al 2010) (Shea Brown) Faraday rotation measure Vogt & Ensslin (2005) Coma cluster Relic halo
Origin of magnetic fields in galaxy clusters - turbulence generated at shocks in the LSS of the universe + turbulence dynamo with weak seed fields (Ryu et al 2008) probably energetically most important - AGN outflows operating all over clusters mostly in cluster core regions - microscopic instabilities such as mirror instab, fire-hose instab, macroscpic instabilities such cosmic-ray induced instab, cosmic-ray flux, and etc not yet clear!
Overview of a model for the origin of magnetic fields in galaxy clusters large-scale structure formation gravitational collapse & flow motions shocks in clusters & LSS shock shock dissipation the main channel to flow the gravitational energy to the intergalactic medium (gravity is the ultimate source of energy in astrophysics!) generation of heat fresh acc. & re-acc. of CRs genera. of magnetic fields generation of vorticity amp by stretching and comp turbulent amp. of mag. fields turbulent acceleration of CRs
Shocks around a simulated cluster in 3D Mach number distribution accretion shocks surrounding the cluster M s > ~10 internal shocks inside the cluster M s < ~ several Ryu et al (2003)
(6h -1 Mpc) 2 Shocks around a simulated cluster in 2D (in the plane through the center) Hong, Ryu et al (2014) gas density temperature shock Mach no. R200 accretion shock merger shock infall shock (accretion from Structures of shocks in galaxy clusters WHIM to hot IGM) are complex! 7
- Vorticity generated at cosmological shocks - directly at interacting and curved shocks at curved shocks at interacting shocks ϖ cs ~ Porter, Jones, Ryu (2015) 2 1 ( ρ2 ρ1) ρ ρ 2 U n R div(v) ω ρ 1 ρ 2 U n R preshock density postshock density preshock flow speed unit normal to shock surf. curvature radius of surf. - by the baroclinic term 1 ϖ bc = 2 ρ ρ p baroclinity constant ρ constant p due to entropy variation induced at shocks - Magnitude of vorticity enhance by compression and stretching during the development of turbulence
Turbulence in high resolution simulations of galaxy clusters vorticity in the plane through a cluster center Miniati (2013)
Turbulence energy estimated from simulation Ryu et al (2008) clusters E turb /E therm ~ 1 M turb ~ 1 (transonic turbulence) in filaments E turb /E therm ~ 0.1 0.2 M turb < 1 (subsonic turbulence) inside and outskirts of clusters
Turbulence + magnetic field Magnetohydrodynamic turbulence Magnetic fields can be amplified by turbulence from weak seed fields Turbulence dynamo or small-scale dynamo
Seed magnetic fields in the large-scale structure (LSS) of the universe Suggestions include: - generation in the early universe(e.g., see Widrow, Ryu et al 2012 for review) e.g.) during the electroweak phase transition (t~10-12 sec) during the quark-hadron transition (t~10-5 sec) uncertain but maybe challenging (?) - generation before the formation of the LSS of the universe through plasma physical processes (e.g., see Ryu et al 2012 for review) e.g.) Biermann battery at shocks instabilities, thermal fluctuations, photo-ionization and etc weak (~ 10-20 G) and some at small scales, yet most promising(?) - astrophysical processes e.g.) magnetic fields from the first stars maybe not the first magnetic field Origin of seeds for comic magnetic fields is uncertain!
Standard picture of MHD turbulence with weak initial field (small-scale dynamo) growth of magnetic energy E kin at saturation E mag /E kin ~ 2/3 exponential growth linear growth E mag saturation
Evolution of magnetic field power spectrum at early stages 1 inverse cascade linear growth exponential growth
Power spectrum at saturation E kin E mag
Effects of compressibility (Porter, Jones, Ryu, 2015) - simulations of compressible turbulence of M s ~ 0.45 at saturation - purely solenoidal forcing or driving purely compressive forcing or driving V 0, V = V = 0, V 0 0 E kin E kin,comp E mag E kin,sol E mag solenoidal forcing compressive forcing Magnetic field amplification is very inefficient in the case of compressive forcing.
Power spectrum at saturation P kin (k) for sol. mode P kin (k) for comp. mode P mag (k) P kin (k) for sol. mode P mag (k) P kin (k) for comp. mode purely solenoidal forcing purely compressible forcing Power spectrum is different in the two cases.
Turbulence in high resolution simulations of galaxy clusters total sol. mode comp. mode Miniati (2014) fraction of compressional mode ~ 20 30% turbulence with solenoidal forcing may be more relevant
Viscosity and resistivity in the ICM mean free-path for electron-electron & proton-proton collisions l p p Braginskii viscosity 5 2 10 T (K) ~ le e ~ cm ~ a few kpc 3 ln Λ n (cm ) e ν ~ υ l therm p p p p ~ l t 2 p p p p T ~ n 5/2 e resistivity η ~ ( c / t ω p e p ) 2 ~ T 3/2 high temperature, low density high viscosity, low resistivity very high magnetic Prandtle number P m = ν η
Turbulence with large P m assuming that the plasma is described by a fluid with high viscosity and low resistivity (?) (Park, Ryu, et al 2015) E kin Growth of kinetic and magnetic energies E mag at saturation magnetic energy > kinetic energy
Power spectrum at saturation P(k) mag P(k) kin with E mag >> E kin, excitation of V by B B 2 B ~ ν V transfer of magnetic energy to smaller scale ε ~ B τ 2 decay ~ constant of k k P( k ) P( k ) kin mag ~ k 3 ~ k 1
A model for magnetic fields in galaxy clusters filaments - vorticity generated at shocks and also due to baroclinity - turbulence developed - standard picture of MHD turbulence applied - magnetic field produced by turbulence dynamo φ and E turb from simulation clusters E B 2 B = = φ( ω t) 8π (Ryu et al 2008) Ε turb conversion factor from separate MHD turbulence simulations no fine tuning to normalize B! ρ, v B
Magnetic fields in the large-scale structure averaged strength and integral scale of magnetic fields at z = 0 predicted from turbulence dynamo - in clusters <B> ~ a few µg, L int ~ a few x 10 kpc - in filaments (10 5 K < T < 10 7 K, or WHIM) <B> ~ 10 ng, L int ~ a few x 100 kpc the integral scale is a length scale of magnetic field, which would be relevant to Faraday rotation measure L int = 2π ( E / k) dk / B (Cho & Ryu 2009) E B dk
Schematic diagram for magnetic field power spectrum P mag (k) K +1 K -5/3 K -1 injection scale/2 ~100 kpc viscous scale ~ a few kpc k
Summary - Magnetic fields in galaxy clusters: ~ µg - Turbulence of E turb /E therm ~ 0.1 in galaxy clusters can amplify weak seed fields to magnetic field of ~ µg ( E mag /E therm ~ 0.01 or β ~ 100) L int ~ a few x 10 kpc through turbulence dynamo - Coulomb mean free path, l coul ~ a few kpc. - The nature of magnetic fields below l coul is not clear.
Thank you!