Coronal Loop Oscillations observed by TRACE

（ Newton, 2002年 10月号）

(Today’s reference is Ofman, ApJ, 568, L135)

Coronal Loop Oscillations observed by TRACE

Nakariakov et al. 1999, Science, 285, 862

Aschwanden et al. 1999, ApJ, 520, 880Aschwanden et al.2002, Sol.Phys, 206,99

•Nakariakov et al. 1999, Science, 285, 862•Aschwanden et al. 1999, ApJ, 520, 880

coronal loop oscillations associated with flares- loop length : 130000 km- period : about 4 min - decay time : about 870 s

•What is the mechanism of enhanced dissipation?- enhanced large Viscosity or Reynolds number (Nakariokov, Ofman, Aschwanden) R=10^(5-6) ! classical value : 10^(14)- phase mixing large R number (Ofman and Aschwanden, 2002)- leakage under chromosphere (De Pontieu et al. 2001)- fast mode propagation (Miyagoshi & Yokoyama, in prep.)

•The analysis of loop oscillations and its damping mechanism is ...

- coronal plasma characteristics- an important impact on coronal heating theories- wave heating - reconnection theories

Ofman 2002, ApJ, 568, L135

•1.5 dimensional MHD•Three components of V & B are included

(the thermal pressure is neglected compared with the magnetic pressure)

X : along the loopY : transverse to the loopZ : vertical

Normalize Unit : L = 10000 kmn = 10^14V = 10km/s

Oscillation amplitude 20km <<Coronal Va 1000km :the oscillations are nearly linear

Initial Condition

(Loop length : 130000km)

0' /2 Lkk

0.5'

5.0'

k

k

5.0' k

(Typical case)(high freq.)

Previous Work (Linear Theory)

•The linear theory predicts that the leakage time of the Alfvén waves is given by (e.g., Berghmans & De Bruyne 1995)

When the Alfvén speed jumps discontinuously from the photospheric value to the coronal value, the reflection coefficient can be approximated by (e.g., Davila 1991)

here, Va0=10km/s, Va=1000km/s,L = 130000km so R=0.980 and Td = 6500 s (observation : 870s)

R : wave reflection coefficient

•De Pontieu et al. (2001) use the following expression for the timescale of the leakage through the ends of the loop (with Chromosphere model):

De Pontieu et al. (2001) made a mistake. The correct value is, Td=3179s(Re,spot = 0.90, Re, plage = 0.94)

•The energy reflection coefficient of Alfvén waves was obtained by Leer et al. (1982) for Alfvén waves in the solar wind (their eqs. [44] and [46]) and used by Hollweg (1984) and De Pontieu et al. (2001) in coronal loops.

Previous Work (Linear Theory)

Td = 4127 s (typical case)Td = 342 s (short wavelength)

Numerical ResultsThe linear analytical calculation of the leakage time is sensitiveto the estimated theoretical value of the reflection coefficient. In the numerical model, the leakage time is calculated from the decrease of the wave amplitude in the loop as a function of time, without the need to estimate the reflection coefficient.

•Without Choromosphere: Td = 6453 s excellent agreement with the theoretical value

•With Choromosphere: Td = 4406 s good agreement (7% longer)

Numerical Results(t = 939s)

Vx component of the velocity is produced by the nonlinear coupling of the Alfvén wave to the fast wave.

However, since the amplitude of the wave is small (2%) compared with the coronal Alfvén speed, the nonlinearity does not affect the dynamics or the leakage time significantly.

Vy

VxVa

Short wavelength case (k=5):Td = 397 s good agreement (16% longer)

Discussions and Conclusions

They find that the leakage time in this loop is 4406 s, which is 5 times longer than the observed damping time. Based on this model, they conclude that the chromospheric footpoint leakage cannot explain the observed rapid oscillation damping, in agreement with the conclusion of Nakariakov et al. (1999). I find that short-wavelength Alfvén waves will leak on a much shorter timescale.

Discussions and Conclusions•The leakage time depends on several observed and assumed parameters.

-An increased or decreased chromospheric scale height will leaded to a faster or slower wave leakage,

-the values of photospheric and coronal Alfvén speeds, the loop length, and the wavelength can vary from one location to another in an active region and may be different in various active regions and in various loops

•The dynamic variations and shocks in the chromosphere were not included in the model.

•In the present 1.5-dimensional MHD coronal loop model, the geometric divergence of the magnetic field near the footpoints is not included. To account for the magnetic divergence requires multidimensional modeling of the coronal loop.

Miyagoshi & Yokoyama (2003, in prep)

•Three – dimensional MHD numerical simulations•Vy of typical case is 80 % of the local sound speed (strong nonlinear effect)

Numerical Simulation Results

AVLP /2

1damp RVA

12

,2

,)(

,)(2

1

2fast

2fastdamp

2fast

2

2

R

VC

w

VC

Ew

VCSVV

dt

dE

SwVE

AA

Af

It can be explained… Energy loss by fast mode propagation around

Numerical Simulation Results

•For this mechanisim, three dimensional effect is essential.

•Comparison between TRACE observation and our model…

Observation (Nakariakov et al. 1999)Period : about 240 s (4 min)Decay time : about 870 sFor loop length 130000km

Our Model (Miyagoshi and Yokoyama)Period : 260 sDecay time : 750 sFor loop length 130000km,Coronal sound speed 100km/s