1. Periodic Acceleration of Electrons in Solar Flares
1S. Kamio, 2M. Shimojo, 2A. Asai, 1H.Isobe, and 2K. Shibasaki
1Kwasan and Hida Observatories, Kyoto University
2Nobeyama Solar Radio Observatory, NAOJ

2. Introduction
Hard X-ray, microwave, and gamma-ray are produced by high-energy particles during the impulsive phase of flares.  Behavior of these emissions can provide clues for understanding the particle acceleration process in the flare
Some papers have reported quasi-periodic pulsation (10-100s) in hard X-ray and microwave Kane et al.(1983), Nakajima et al.(1983), Kiplinger et al.(1983) and so on.

3. Loop oscillation
Oscillation of EUV loops TRACE observation found coronal loop oscillations induced by flares. e.g. Nakarikov et al.(1999)
Miyagoshi et al.(2004) They performed three-dimensional MHD simulation of coronal loop oscillation. The period of oscillation is equal to the Alfven transit time along the loop.

4. Quasi-periodic pulsations
Asai et al.(2001) Pulsation in spatially resolved microwave and hard X-ray data.
Oscillation period 6.6s
remote microwave
17GHz flux

5. Pulsation periods
Asai et al.(2001) The period of pulsation is similar to the Alfven transit time along the flare loop.
Kundu et al.(2001) Variation of the oscillation period is due to density increase. They assumed a disturbance propagating along the loop in Alfven speed.
Our goal:
To examine if the relationship is a common feature
Estimate the relationship between macroscopic magnetic environment and particle acceleration

6. Data selection Surveyed data from Jun 1992 to Dec 2000
Selection criterion - Observed with Yohkoh/HXT and NoRH - HXT M1 maximum count > 4 (cts/sec/sc) - 4 or more peaks are clearly seen
Selected 3 flares (from 368) - 1 Dec 1997 in NOAA 8113 (M1.2) - 10 Nov 1998 in NOAA 8375 (C7.9, studied by Asai et al.) - 24 Apr 2001 in NOAA 9433 (M2.1)

7. Flare 1: 1-Dec-1997 Pulsation period: 6.4s (Wavelet analysis)
Microwave peaks delayed about 1s from HXT peaks.
movie

8. Estimating physical quantities
EM and Temperature inferred from Yohkoh/SXT filter ratio analysis.
Potential field calculation from MDI using MAGPACK2
Estimated configuration (cartoon) HXR sources: Foot points Radio source: Loop top
Loop Length: 1x109cm Loop width: 4x108cm
Density: 2x1010cm-3
Temperature: 13MK
Field strength: 240G

9. Flare 2: 10 Nov 1998 Flare in the west limb (Studied by Asai et al.)
Pulstation in HXR and remote microwave source
microwave
HXR
Pulsation Period: 6.6s

10. Configuration Flare loop: 1 1.5x104 km (estimated) Bright in SXR
Faint loop: 2 5.0x104 km HXR in the south foot point Microwave in the north foot point Pulsation delay between microwave and HXR is about 1 sec
Microwave 2 1
HXR
Yohkoh/SXT image

11. Flare 3: 24 April 2001 Pulsating remote source in microwave
Pulsation Period: 5.2s
movie

12. Possible configuration
Magnetic field eruption followed by the magnetic reconnection.
Microwave pulsation at the foot point of faint loop.
Non-thermal electron produced by the flare emitted HXR and microwave.

13. What determines the period?
Periodic pulsations may be related to the loop oscillation.
The periods of several oscillation modes are calculated using observed quantities.
Ls: Loop Length (in 108cm)
rs: Loop radius (in 108cm)
B: Field strength
n10: Density (in 1010cm-3)
T: Temperature
(j=1)
(m=1)
oscillation modes in a uniform magnetic loop

14. Pulsation periods
1 Dec 1997
10 Nov 1998
24 Apr 2001
Observed
6.4
6.6
5.2
Fast sausage
7.7
6.8
5.7
Fast kink
5.8
8.3
17.4
Slow MHD 36 67 75
Propagating MHD
4.7
4.1
3.5
Torsional
Periods of fast sausage mode is the closest to the observed periods.
Pulsation may be related to the fast sausage mode oscillation.

15. Flux
Spectral index
HXR index becomes gradually softer, while radio index become harder. same as nominal flares
Index variation at flux peaks: opposite trend in HXR and microwave Each peak shows the similar behavior of a single flare.
HXR index
hard
soft
Flux
Peak
Valley
HXR index
hard
soft
Radio index
Radio index
hard
soft

16. Interpretation
Spectral index α<0 Microwave pulsation is caused by non-thermal electrons (gyrosynchrotron)
HXR sources are located near foot point of flare loops Emission by thick target model
Each peak of pulsation indicate the same index variation as nominal flares. Modulation of non-thermal particle acceleration
The pulsations of remote microwave source are delayed from HXR The delay is flight time of non-thermal electrons from HXR source to microwave source

17. Model of pulsation
Our results suggest that the pulsation period is related to the fast sausage mode oscillation of coronal loops. The pulsation may be caused by the modulation of particle acceleration.
flare-loop
Tsuneta and Naito 1998
Loop oscillation
The oscillation of loops affect the length of fast shock region and hence change the efficiency of particle acceleration or injection. (proposed by Asai et al. (2001))

18. Summary We studied 3 flares indicating pulsation in HXR and microwave.
Observed pulsation periods are close to the estimated periods of fast sausage mode oscillation of flare loop.
The evolution of spectral index in each flux peak indicated the same characteristics of nominal flares.
Pulsation may be caused by the modulation the efficiency of particle acceleration.
RHESSI will provide more detailed spectral data in HXR and γ-ray

19. Template
Item

20. Flux
Spectral index (cont.)
HXR index becomes gradually softer, while radio index gradually harder.
Index variation at flux peaks
HXR index
hard
soft
Flux
Peak
Valley
HXR index
hard
soft
Radio index
Radio index
hard
soft