Magnetic Field Amplification in SNR by Richtmyer-Meshkov Instability K. Nishihara, T. Sano Institute of Laser Engineering, Osaka University C. Matsuoka Department of Physics, Ehime University amplification B-field line amplification B-field line parallel perpendicular shock shock NDAMS, Kyoto, 2011/10/31-11/3
Out utline of of my tal alk 1. Introduction and background of the research ≥ ・ Recent observations indicate strong magnetic field amplification ( 100 times) in SNR (Supernova Remnant). ・ Richtmyer-Meshkov instability: nonuniform velocity shear left by rippled shocks (Wouchuk & Nishihara PoP (97), Nishihara et al Phi. Trans. R. Soc. A (10)) ≥ 2. 2D MHD simulation results of B-field amplification ( 100 times) ・ Three cases: a shock perpendicular, parallel and oblique to B-field 3. Physical mechanism of the magnetic field amplification ・ Stretching of the interface and spike due to RMI along the B-field
Rapi apid v d var ariat ation on of of sync nchr hrotron X n X-ray ay i int ntens ensity ( ~ 1 1 yr. yr.) Introduction 3 B-amplification indi ndicates es s strong ong magnet agnetic fiel eld am d ampl plification ( n (~100 100) in n young oung SNR X-ray map of SNR: RXJ1713, Uchiyama (07) Synchrot otron on X-ray ay var ariab ability: ~ 1 yr. yr. (U (Uch chiyama (0 (07)) )) Sync nchr hrotron cool ooling ng rat ate: e: − 1.5 − 0.5 ε B t synch yr ≈ 1.5 mG keV ≈ − B 0 . 1 1 mG （ B ISM ~ 5 µ G ） Nonuni nifor form Inter Inter Stel tellar M Matter atter X-ray image (color scale) B-fiel eld d amplificat ation: n: ~100 100 <-> Synchrotron emission CO (j=1-0) line emission (iso-contour) <-> molecular cloud (n~100 cm -3 )
ISM (Int nter Stel ellar Mat atter er) cons onsists of of Introduction 4 ISM CNM CNM (Col old d Neut eutral M Medi edium um) and and WNM NM (War arm N Neut eutral M Medi edium um) ISM: an open system radiation heating / cooling Heating: equilibrium states (Field(69); Wolfir(95)) (balance between heating and cooling) radiation and cosmic rays from stars ∝ n Heating rate cooling Cooling: line emission from excited atoms and molecular T<10 3 K: atomic fine structure (ε∼ 0.01eV) CO rotational transition T>10 3 K: electron transition (ε∼ 1eV) heating (Ly- α , C, O, Fe etc) Cooling rate − ε ∝ 2 kT n e WNM (low density n~1cm -3 ): stable CNM (high density n>10cm -3 ): stable unstable domain for iso-pressure perturbations Inoue, Yamazaki, : cooling rate per unit mass Inutsuka (09)
After er an an inc ncide dent shoc hock hi hits a a cor orrug ugated ed int nter erface, Introduction 6 RMI rippl pples es on on ref eflected and d and trans ansmitted s d shoc hocks ar are e induc nduced ed and and RM i ins nstabi ability i is dr driven by en by v vel eloc ocity s shear hear l lef eft by by t the r he rippl ppled ed sh shocks. cks. shocked interface I S I δ v 0 a δ v 0 b vortex sheet Matsuoka, Nishihara from linearized relation of the shock Rankin-Hugoniot Fukuda (PRE(03)) − − u u ( ) δ = ξ a δ b = ξ − st v k 1 v , v k 1 sr v v A=0.376, ξ 0 /λ=0.02 o o i o o i 1 u u si si ξ 0 k , ; where amplitude of the initial interface corrugation and its wave number, u , u , u ; incident, transmitted and reflected shock speeds, and si st sr v i , v ; interface speed after the interaction and fluid velocity behind the incident shock. 1
Introduction 11 Ful ully nonl nonlinea near ev evol olut ution n with h vor ortex sheet heet model odel: Doubl ouble s e spi piral al Nonlinear RMI struc uctur ure e is obs obser erved d as as Jac acobs obs & Sheel heeley ex exper perimen ent. asymptotic linear growth rate Col olor or sho hows the he vortic icity (Matsuok oka a (06)) v lin (weak shock limit) ρ δ − ρ δ 0 0 v v = bf yb af ya v lin ρ + ρ bf af Wouchuk huk (97) 97) Paramet eter ers A = = 0. 0.155 155 k ξ 0 = 0 = 0.2 .2 kv kv lin in t = 0 = 0, 1 , 1, , 2,,, ,,,,12 Jac acob obs
Out utline of of my tal alk 1. Introduction and background of the research ≥ ・ Recent observations indicate strong magnetic field amplification ( 100 times) in SNR (Supernova Remnant). ・ Richtmyer-Meshkov instability: nonuniform velocity shear left by rippled shocks (Wouchuk (97), Nishihara (10)) 2. 2D MHD simulation results of B-field amplification ・ Three cases: a shock perpendicular, parallel, and oblique to B-field ・ A shock wave propagates through a sinusoidal corrugated interface. ≥ ・ Amplification factor of magnetic field ( 100 times) ・ parameter dependence of amplification factor 3. Physical mechanism of the magnetic field amplification ・ Stretching of the interface and spike due to RMI along the B-field
2d MHD 1 Initial al Condi ndition on of 2-d MHD Simulat ations ons parallel shock ρ 2 = δ = ρ Density Jump: 10 • 0 V Mach Number of the Shock: = = M s 10 • c s 0 α Initial Corrugation Amplitude: ξ = λ = • 0 . 1 π 8 P shoc hock front ont Field Strength: β = B = 8 0 10 • 0 2 three cases perpendicular shock ( to B-field ) corrugat gated ed ( B-field lines // interface ) int nter erfac ace parallel shock ( to B-field ) ⊥ ( B-field lines interface ) 0blique shock ( to B-field ) ∠ ( B-field lines interface ) ⊥ ( B-field lines interface )
2d MHD 2 2-d d MHD simul ulat ation on of a shoc ock perpend pendicul ular ar to B-field ld B // interface B-field lines mass density vorticity
RMI gr grow owth in n 2-d MHD simul ulat ation on of a shoc ock 2d MHD 3 B // interface perpend endicul ular ar to B-field ld time evolution of normalized length RMI growth rate and spike height between spike top and bubble top growth rate normalized by V lin length normalized by wavelength Growth rate reaches its maximum around kv lin t = 1.5 and decreases with time
B-field am ampl plification on for or a a shoc hock per perpen pendi dicular to o B-field, d, 2d MHD 5 B // interface Strong ong a amplificat ation on ( (~300 300) appear appears at at mus ushr hroo oom um umbr brel ella kv lin t = 10 B-field (|B| / B 0 ) B-field lines
2d MHD 6 2-d d MHD Simulat ation on for a shoc ock paral allel el to B-field ld ⊥ B interface B-field lines mass density vorticity
B-fiel eld d amplificat ation n for for or a a shoc hock par paral allel t to o B-fiel eld, d, 2d MHD 7 ⊥ B interface Lar Large ge am ampl plification (~80 80) appear appears at at the he mus ushr hroom stem em kv lin t = 10 B-field (|B| / B 0 ) B-field lines
B-field am ampl plification on for or the he cas ase e of of a a shoc hock obl oblique que to o B-fie ield ld 2d MHD 8 ∠ B interface Strong ong a amplificat ation on (~120 20) appear appears at at int nter erface al aligned gned to o B-fiel eld kv lin t = 10 B-field (|B| / B 0 ) B-field lines
B-field am ampl plification on fac actor ors for or thr hree ee di differ erent cas ases es 2d MHD 9 becom bec ome about about 100 100 to o 1000 1000 B // interface ∠ B interface ⊥ B interface Largest amplification factor is obtained for B-field // to the interface ( perpendicular shock ).
Magne agnetic pr pres essure does does not not ex exceed eed to o pl plas asma a pr pres essure e 2d MHD 11 ev even en for or par paral allel shoc hock square root of the ratio of magnetic pressure to plasma pressure for different its initial values Amplification factor of B-field becomes > 100 for initial plasma β > 10 3
Out utline of of my tal alk 1. Introduction and background of the research ≥ ・ Recent observations indicate strong magnetic field amplification ( 100 times) in SNR (Supernova Remnant). ・ Richtmyer-Meshkov instability: nonuniform velocity shear left by rippled shocks (Wouchuk (97), Nishihara (10)) ≥ 2. 2D MHD simulation results of B-field amplification ( 100 times) ・ Three cases: a shock perpendicular, parallel, and oblique to B-field 3. Physical mechanism of the magnetic field amplification ・ Stretching of the interface and spike due to RMI mainly results in the amplification along the B-field
B-field am ampl plification on in n ideal deal MHD B-amplify 1 - adv advec ection, stretchi hing g and and com ompr pression on al along ong B fiel eld d line ne - Magnetic field amplification ∂ B ∂ 1 ( ) B = −∇ × advection E 2 = − ⋅ ⋅ ∇ B B v ∂ ∂ t 2 t ( ) v stretching ( ) + ⋅ ⋅ ∇ B B = ∇ × × v B compression − ∇ ⋅ 2 B v = − ⋅ ∇ + ⋅ ∇ − ∇ ⋅ v B B v B v advection stretching compression stretching compression advection Advection does not increase B-field along the plasma Stretching of the interface along a magnetic field mainly leads to the magnetic amplification
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