Magnetic Field Amplification in SNR by Richtmyer-Meshkov Instability - - PowerPoint PPT Presentation

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 amplification B-field line B-field line parallel shock perpendicular shock NDAMS, Kyoto, 2011/10/31-11/3

Out utline of

• f 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

≥ ≥

X-ray map of SNR: RXJ1713, Uchiyama (07)

Introduction 3 B-amplification

Rapi apid v d var ariat ation

• n of
• f sync

nchr hrotron X n X-ray ay i int ntens ensity ( ~ 1 1 yr. yr.) indi ndicates es s strong

• ng magnet

agnetic fiel eld am d ampl plification ( n (~100 100) in n young

• ung SNR

Synchrot

• tron
• n X-ray

ay var ariab ability: ~ 1 yr. yr. (U (Uch chiyama (0 (07)) )) Sync nchr hrotron cool

• oling

ng rat ate: e:

≈1.5 B mG      

−1.5

ε keV      

−0.5

tsynch yr

mG B 1 1 . − ≈

（BISM ~ 5µG） B-fiel eld d amplificat ation: n: ~100 100

Nonuni nifor form Inter Inter Stel tellar M Matter atter X-ray image (color scale) <-> Synchrotron emission CO (j=1-0) line emission (iso-contour) <-> molecular cloud (n~100 cm-3)

Introduction 4 ISM

ISM (Int nter Stel ellar Mat atter er) cons

• nsists of
• f

CNM CNM (Col

• ld

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: radiation and cosmic rays from stars Heating rate

n ∝

Cooling: line emission from excited atoms and molecular T<103K: atomic fine structure (ε∼0.01eV)

CO rotational transition T>103K: electron transition (ε∼1eV) (Ly-α, C, O, Fe etc)

kT

e n

ε −

∝

2

Cooling rate

equilibrium states (Field(69); Wolfir(95)) (balance between heating and cooling)

WNM (low density n~1cm-3): stable CNM (high density n>10cm-3): stable : cooling rate per unit mass unstable domain for iso-pressure perturbations

cooling heating

Inoue, Yamazaki, Inutsuka (09)

After er an an inc ncide dent shoc hock hi hits a a cor

• rrug

ugated ed int nter erface, rippl pples es on

• n 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

• city s

shear hear l lef eft by by t the r he rippl ppled ed sh shocks. cks.

I S I shocked interface vortex sheet

; , ,

sr st si

u u u

δv0

a

δv0

b

, 1

i si st

• a
• v

u u k v         − = ξ δ

( )

1

1 v v u u k v

i si sr

• b
• −

        − = ξ δ

from linearized relation of the shock Rankin-Hugoniot

; ,

0 k

ξ ; ,

1

v vi

incident, transmitted and reflected shock speeds, and amplitude of the initial interface corrugation and its wave number, where interface speed after the interaction and fluid velocity behind the incident shock. Matsuoka, Nishihara Fukuda (PRE(03)) A=0.376, ξ0/λ=0.02

Introduction 6 RMI

Ful ully nonl nonlinea near ev evol

• lut

ution n with h vor

• rtex sheet

heet model

• del: Doubl
• uble s

e spi piral al struc uctur ure e is obs

• bser

erved d as as Jac acobs

• bs & Sheel

heeley ex exper perimen ent.

Col

• lor
• r sho

hows the he vortic icity (Matsuok

• ka

a (06))

Paramet eter ers A = = 0. 0.155 155 kξ0 = 0 = 0.2 .2 kv kvlin

int = 0

= 0, 1 , 1, , 2,,, ,,,,12 Jac acob

• bs

Introduction 11 Nonlinear RMI

af bf ya af yb bf lin

v v v ρ ρ δ ρ δ ρ + − =

asymptotic linear growth rate vlin (weak shock limit)

Wouchuk huk (97) 97)

Out utline of

• f 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

≥ ≥

parallel shock ( to B-field ) ( B-field lines interface ) 0blique shock ( to B-field ) ( B-field lines interface )

Initial al Condi ndition

• n of 2-d MHD Simulat

ations

• ns
• Density Jump:
• Mach Number of the Shock:
• Initial Corrugation Amplitude:
• Field Strength:

shoc hock front

• nt

corrugat gated ed int nter erfac ace

10

2 =

= ρ ρ δ 10 = =

s s

c V M 1 . = = λ α ξ

8 2

10 8 = = B P π β

three cases perpendicular shock ( to B-field ) ( B-field lines // interface )

⊥

∠

2d MHD 1

parallel shock ( B-field lines interface )

⊥

mass density

2-d d MHD simul ulat ation

• n of a shoc
• ck perpend

pendicul ular ar to B-field ld

2d MHD 2 B // interface

B-field lines vorticity

RMI gr grow

• wth in

n 2-d MHD simul ulat ation

• n of a shoc
• ck

perpend endicul ular ar to B-field ld

2d MHD 3 B // interface

time evolution of RMI growth rate and spike height

growth rate normalized by Vlin length normalized by wavelength

normalized length between spike top and bubble top Growth rate reaches its maximum around kvlint = 1.5 and decreases with time

B-field am ampl plification

• n for
• r a

a shoc hock per perpen pendi dicular to

• B-field,

d, Strong

• ng a

amplificat ation

• n (

(~300 300) appear appears at at mus ushr hroo

• om um

umbr brel ella B-field (|B| / B0) B-field lines

2d MHD 5 B // interface

kvlint = 10

2-d d MHD Simulat ation

• n for a shoc
• ck paral

allel el to B-field ld

mass density B-field lines vorticity

2d MHD 6 B interface

⊥

B-fiel eld d amplificat ation n for for

• r a

a shoc hock par paral allel t to

• B-fiel

eld, d, Lar Large ge am ampl plification (~80 80) appear appears at at the he mus ushr hroom stem em B-field lines

2d MHD 7 B interface

⊥

B-field (|B| / B0)

kvlint = 10

B-field am ampl plification

• n for
• r the

he cas ase e of

• f a

a shoc hock obl

• blique

que to

• B-fie

ield ld Strong

• ng a

amplificat ation

• n

(~120 20) appear appears at at int nter erface al aligned gned to

• B-fiel

eld B-field lines

2d MHD 8 B interface

∠

B-field (|B| / B0)

kvlint = 10

B-field am ampl plification

• n fac

actor

• rs for
• r thr

hree ee di differ erent cas ases es bec becom

• me about

about 100 100 to

• 1000

1000

2d MHD 9 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

• pl

plas asma a pr pres essure e ev even en for

• r par

paral allel shoc hock

2d MHD 11

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 > 103

Out utline of

• f 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

• n in

n ideal deal MHD

• adv

advec ection, stretchi hing g and and com

• mpr

pression

• n al

along

• ng B fiel

eld d line ne -

( )

v B v B B v B v E t B ⋅ ∇ − ∇ ⋅ + ∇ ⋅ − = × × ∇ = × −∇ = ∂ ∂

advection stretching compression

Magnetic field amplification

B-amplify 1

( )B

v B B t ∇ ⋅ ⋅ − = ∂ ∂

2

2 1

( )v

B B ∇ ⋅ ⋅ + v B ⋅ ∇ −

2

advection stretching compression

stretching compression advection Stretching of the interface along a magnetic field mainly leads to the magnetic amplification

Advection does not increase B-field along the plasma

current density spatial profile (initial B // interface: at kvlint=2.0) density B field lines vorticity B-field amplification rate by stretching

B-amplify 2 B // interface

Stretching ng of

• f t

the i he int nter erface at at the t he top of

• p of t

the s he spi pike e caus auses es B-field am ampl plification

• n at

at ear early stage age in n the he cas ase e of

• f B // int

nter erface

Int nterface stret etching ng rat ate e obt

• btai

ained d from

• m nonl

nonline near ar vor

• rtex

ex sheet heet model

• del

show hows lar arge ge stretchi hing r g rat ate e at at the he top

• p of
• f the

he spi pike i e in n ear early s stage. age.

stretching rate of the interface in RMI (nonlinear vortex sheet model)

B-amplify 3 B // interface

interface stretching rate from kvlin t=0 to 6

interface length vs time

• bserved in 2d MHD simulation

Stretching rate at t=2.0,the peak value is about 1/kvlin, which is comparable to the growth rate of B-field. Grow

• wth rat

ate e of

• f B-field (

d (// int nter erface) obs

• bser

erved agr d agrees ees f fai airly wel ell with t h the he stret etching rat ate e of

• f int

nter erface f e from

• m nonl

nonline near ar v vor

• rtex

ex s sheet heet model

• del

The B-field in the shock propagation direction ( By ) grows later, which corresponds to the nonlinear stretching of the spike. B-field growth local stretching rate of the interface

B-amplify 4 B // interface

B-field ar arrai aigned ed the he int nter erface e appear appears at at ear early stage age due due to

• vel

eloc

• city shear

hear at at the he int nter erface, ev even en for

• r par

paral allel shoc hock.

B-amplify 5 B interface

⊥

( at kvlint=0.5) density B field lines B-field amplification rate by stretching vorticity Bx component grows linearly

( at kvlint=6.0 )

B interface

⊥

B-field am ampl plification

• n at

at root

• ot of
• f stem

em appear appears lat ater er in n par paral allel el shoc hock whi hich cor

• rres

espond nds to i

• its s

stret etching ng due t due to

• int

nter eraction n with bul h bulk vortic ictiy iy.

B-amplify 6 B interface

⊥

density B field lines B-field amplification rate by stretching

⊥

( at kvlint=10)

Due to the interaction between the vortex sheet and bulk vorticity left behind a rippled strong shock, the stretching of the root of the stems appears later for a case of parallel shock ( B-field lines interface)

⊥

Conc nclus usion

• n and Ackno

nowled edgem gement ent

• 1. We showed strong amplification of magnetic field by the Richtmyer-Meshkov

instability for three different shock propagation directions to magnetic field.

• 2. The amplification factor obtained from 2-d MHD simulations were greater than

100 for every cases, which agrees with the observations in SNR. We also discussed various parameter dependences of the amplification factors.

• 3. It is shown that the stretching of the interface and spike due to RMI mainly

causes the magnetic field amplification. I thank to Dr. Takeshi Inoue at Aoyama Gakuin Univ. for introduction of B-field amplification in SNR and valuable discussions.