INITIATION AND EVOLUTIONOF

CORONAL SHOCK WAVES

B. Vršnak, T. Žic, S. Lulić(Hvar Obs.)

N. Muhr, A. Veronig, M. Temmer, I. Kienreich(Uni.-Graz)

This work has been supported in part by Croatian Scientific Foundation

under the project 6212 „Solar and Stellar Variability“ (SOLSTEL).

Observational signatures

� Type II radio bursts(Wild & McCready 1950, Aust.J.Phys. 3, 387)

� Moreton waves(Moreton & Ramsey 1960, PASP 72, 357)

KSO

EUV, SXR, He I, coronograph, radio,...

EIT/SoHO

Yohkoh

NRH

270

290

310

330

350

45 50 55 60 65 70 75 80

151 MHz

164 MHz

237 MHz

327 MHz

Ha/EIT

t (min after 09:00 UT)

F

CME

b)

EIT/SoHOMLSO

Domain / Signature

Corona- radio type II- WL fronts, streamers

IP(radio, WL)

in situ

Low Corona(EUV)

Upper Chromosphere & TR(Hα, HeI, …)Moreton, disturbed filaments, …

timing, kinematics, intensity, spectral, morphology, …

Terminology

bowshock

pistonshock

blas

t-sho

ck

shoc

k

bow

-sho

ck

piston piston

< <> >Vp V0 Vp V

0

Vp > V0

Vsh >Vp

Vsh =Vp

Vsh >Vp

projectile

Large-amplitude wave (shock)

� impulsive plasma motion perpendicular to the magnetic field ("strong" acceleration)

� large amplitude wavefront is created� shock forms after certain time/distance due to the

nonlinear evolution of the perturbation (signal velocity

0

0.1

0.2

0.3

0.4

0 1 2 3 4X-X0

U

nonlinear evolution of the perturbation (signal velocity depends on the amplitude!)

w(t) = w0 + k u(t)

k=4/3, w0=cs0 at β >> 1k=3/2, w0=vA0 at β << 1

u wu

w

vA0

xxf

0)( 23

0 =∂∂++

∂∂

x

uuv

t

u

Piston Mechanism (simulations)

0.0

0.5

1.0

1.5

2.0

0 0.1 0.2 0.3

v

t- amplitude growth + steepening � shock formation

- after t~0.15 ~const. amplitude/velocity

1D - planar

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3

x

t

wave

piston

2D - cylindrical

- amplitude growth + steepening � shock formation

- lower amplitude, formation of rarefaction region

- after t~0.08 decreasing amplitude/velocity

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3

x

t

dip

-0.2

0.2

0.6

1

1.4

0 0.1 0.2 0.3

v

t

Wave evolution (2D)

2.5-D MHD simulation

BφBz By

+

β = 00.1

1

10

100

1000

10000

100000

1000000

10000000

0 0.2 0.4

rho(

y)

y

Ch

TR

Co

0.00.20.40.60.81.0

0 0.1 0.2 0.3

Bφφφφ

Bz

MHD simulation: Corona (horizonatal)

- steepening + ampl. increase � shock

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4

x

t

0.2

0.1 0.080.1

0.2

0.3

0 0.05 0.1

x

t

piston

wave

- steepening + ampl. increase � shock

- deceleration; ampl. decrease

- corona/Moreton offset

- corona/Moreton delay

t

0.00.51.01.52.02.53.03.54.04.5

0 0.1 0.2 0.3 0.4

w

t

0.2 0.10.08

piston

y = 0.012x - 0.098

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60

Vm

ax/V

A

B/B0

MHD simulation: Corona (above)

streamer (current sheet)

(reconnection outflow jet)

contactsurface

“standing” shock

fast-mode

standing shock

MHD simulation: Moreton wave

1000

1200

1400

1600

1800

2000

H (

km)

H analyt (X0=1.9)H num(B0=10)H analyt (X0=3.5)H num(B0=20)

-35

-30

-25

-20

-15

-10

-5

v(k

m/s

)

V analyt (X0=1.9)V num(B0=10)V analyt (X0=3.5)V num(B0=20)

comparison with

analytical:

ρv2 w = const.;

cs = 10 km/s = const.

-35

-30

-25

-20

-15

-10

-5

00 20 40 60 80 100 120

v(k

m/s

)

t (s)

V analyt (X0=1.9)V num(B0=10)V analyt (X0=3.5)V num(B0=20)

600

800

0 20 40 60 80 100 120t (s)

-5

0100012001400160018002000

H (km)

1.0

1.5

2.0

2.5

3.0

3.5

4.0

100012001400160018002000

X =

rho

/rho

0

H (km)

X (X0=1.9)X (X0=3.5)

Conclusion

� upward (type II burst) = driven bow/piston shock

� lateral (EUV, HeI, Hα) = temporary piston (“CME

overexpansion”)

� the time/distance of the shock formation and its

amplitude/speed depend strongly on the impulsiveness

of the pistonof the piston

� Moreton wave appears only if shock is sufficiently strong

(fast); only the upper chromosphere is affected

� downward propagating chromospheric disturbance is

quasi-longitudinal fast-mode shock that can be well

approximated by a sound shock

� Moreton wave lags behind the coronal wave due to

chromospheric inertia

Thank you

for for

your attention