SPATIALLY RESOLVED MINUTE SPATIALLY RESOLVED MINUTE PERIODICITIES OF MICROWAVE PERIODICITIES OF MICROWAVE

EMISSION DURING A STRONG SOLAR EMISSION DURING A STRONG SOLAR FLAREFLARE

Kupriyanova E.1,Melnikov V.1, Shibata K.2,3, Shibasaki K.4

1 Pulkovo Observatory, Russia2 Kyoto University, Japan

3 Kwasan and Hida Observatory, Japan4 Nobeyama Solar Radio Observatory,Japan

2

Until recent time, quasi-periodic pulsations (QPPs) with periods from 1 to 15 minutes have been observed in solar microwave emission above the sunspots only (Gelfreikh et al., Solar Phys., V.185, P.177, 1999).Last time, QPPs with that periods became to appear during the flares also. In the microwaves. They was discribed in the papers:Zaitsev et al., Cosmic Research, V.46, P.301, 2008; Meszarosova et al., Astron. Astrophys., V.697, P. L108, 2009; Sych et al., Astron. Astrophys., V.505, P.791, 2009; Reznikova, Shibasaki, Astron. Astrophys., V.525, P.A112, 2011; Kim et al., The Astrophysical Journal Letters, V. 756, P. L36, 2012

In X-rays, minute QPPs were studied by Jakimiec and Tomczak (Solar Phys., V.261, P.233, 2010) Studies of these oscillations became especially topical in view of their possible relationship to flare energy release and heating of the solar corona: Nakariakov and Zimovets, Astrophys. J.L., V.730. P.L27, 2011; Zaitsev and Kislyakova, Radiophys. Quant. El., V.55. P.429. 2012.

Introduction

Study of the spatial structure of QPPs with periods of several minutes in the microwave emission of the solar flare on May 14, 2013.

The aim

1.

2.

3

)(

)()()(

tF

tFtFt

sm

sm

Methodology.Analysis of QPPs in Time Profiles

3.

• 4. NoRH radio maps at 17 and 34 GHz are built (time cadence is 1 s); • 5. small boxes are selected in a different parts of flaring area;• 6. time profiles of the integrated fluxes are calculated for each box;• 7. the time profiles are studied using the method discribed in items 1-3.

Analysis of spatial structure of QPPs

)()()( tFtFt sm

• 1. Time profiles of high-frequency component are calculated for each box using formula

(1)

Here F (t) is original flux (Stokes I or Stokes V) from a whole box, F sm (t) is its low-frequency background obtained using method of running average with time intervals = 30500 s .

• 2. The time profiles () are studied using methods of correlation, Fourier and wavelet analysis.3. For each: auto-correletion functions R() and their Fourier periodograms; wavelet spectra of .

4

Integrated (spatially unresolved) time profiles

Fig. 1

4.

5

4. Cross-correlations of NoRH and NoRP signals

• The time profiles of the NoRH correlation amplitudes are well correlated with NoRP integrated flux Fig. 1. Their cross-correlation function at 17 GHz are shown in Fig. 2 (upper panel), and that for 34 GHz(35 GHz) (downer panel).

• The total time profiles (without detrending) of the NoRH correlation amplitudes are well correlated at frequences 17 GHz and 34 GHz (Fig. 3) with correlation coefficient r ≈ 1.0.

• The total time profiles (without detrending) of the NoRP fluxes are well correlated at frequences 17 GHz and 34 GHz (Fig. 3) with correlation coefficient r ≈ 0.8.

Fig. 2 Fig. 3

6

Phase of flare maximum 01:06:30 – 01:08:00 UT.

QPPs with period 50 s are well pronounced at both frequincies.

The time profile at 34 GHz delays relatively to time profile at 17 GHz by 12 s

Spectral properties of the integrated signal (correlation amplitudes)

5.

7

Dynamic of the source of microwave emission

6.

Time profiles of emission fluxes intergrated over the whole area

Dynamic of the source of microwave emission

6.

N = 1800from

01:00:00 to 01:29:59 UT

Variance map

Data cube is stable

9

Analysis of spatial structure of QPPs7.Flare maximum phase

QPPs with P ≈1 min reveal obvious delays between time profiles from large loop relatively to time profile of the small loop

10

Spectral analysis of QPPs8.

Period, s

Spe

ctra

l pow

er

From violet to orange lines

= 15, 30, 60, 90, 120, 150,180 s

Periods detected:

50 s, 60 s, 100 s, 150 s

11

Cross-correlation analysis of QPPs9.

Spe

ctra

l pow

erThe fluxes from box 1, box 2, and box 3 in the big loop delay with respect to the flux from box 0 in the small loop by t ≈ 36–40 s

Standing MHD modes trapped in magnetic tube.

Pobs ≈ 50–180 sObserved periods

Kink mode

PKI = 12–17 s

PKII = 6–9 s

PKIII = 4–9 s

T0 = 5·106―2107 Kn0 = 5·1010–1011 cm-3

B0 = 300 G

L = 22 Mm

PSMAI ≈ 61–120 s

PSMAII ≈ 32–60 s

PSMAIII = 20–40 s

Slow magneto-acoustic mode

Sausage mode

PSI does not exist

PSII does not exist

PSIII = 3–4 s

Discussion. MHD-oscillations

Balloning mode

PBI = 11–16 s

PBII = 6–8 s

PBIII = 4–6 s

10.

a/L ≈ 0.2

Standing MHD modes trapped in magnetic tube.

Pobs ≈ 50–180 sObserved periods

Kink mode

PKI = 65–92 s

PKII = 34–48 s

PKIII = 24–33 s

T0 = 5·106―2107 Kn0 = 5·1010–1011 cm-3

B0 = 100 G

L = 40 Mm

PSMAI ≈ 173–245 s

PSMAII ≈ 87–122 s

PSMAIII = 58–82 s

Slow magneto-acoustic mode

Sausage mode

PSI does not exist

PSII does not exist

PSIII = 15–21 s

Discussion. MHD-oscillations

Balloning mode

PBI = 63–89 s

PBII = 32–45 s

PBIII = 22–31 s

10.

a/L ≈ 0.2

14

L — loop lengthn — harmonic numbervph — phase velocity

The period of the standing MHD wave is:

2 L nvph

P =

Dispersion equation for MHD mode in a simplest magnetic loop: L,

N0,B0,T0

Ne, Be, Te

a

The periods can be caused by SMA mode of MHD oscillations in a loopPobs ≈ 1 min

Periods observed

Discussion. MHD oscillations. Standing waves?

But...

L2 = 22 Mm

L 1= 40 Mm

Period is the samein the both loops

10.

Induced oscillations11. The small loop:

T0 = 5·106 Kn0 = 5·1010 cm-3

B0 = 300 G

The fundamental PSMAI ≈ 61

sSecond harmonic PSMA

II ≈ 60 s

T0 = 2·107 Kn0 = 5·1010 cm-3

B0 = 300 G

T0 = 5·106–107 Kn0 = 5·1010–1011 cm-3

B0 = 100–300 G

vph ≈ 330–510 km/s

Pobs ≈ 1 min

Observed periods

15 t ≈ 40 sDelays

The big loop:

L = vph · t

L ≈ 16000 km

SMA waves

L = 22 Mm

L = 40 Mm

L

16

Conclusions

Spatially resolved quasi-periodic pulsations (QPPs) periods P = 50, 60, 100, 155, 180 s are found in microwave emission during solar flare on May 14, 2013. Data of Nobeyama Radioheliograph (NoRH) and Radio Polarimeters (NoRP) at 17 GHz and 34 GHz are used.

The QPPs with the same period of P ≈ 1 min originate from two flaring loops having different lengths L during the impulsive phase of the flare.

These QPPs in the big loop delays over the QPPs from the small loop by t ≈ 40 s.

The periods QPPs in the small loop correspond to the standing SMA mode. QPPs in the large loop are induced by oscillation of the small loop.

Thank you

for your attention !

18

But...

Slow magnetoacoustic waves in two-ribbon flares?

11.

The loop in the middle appears after the border loops

22

Testing the method5.

it is time: i = 0..N–1, N is number of points in time series

NPb 3NPb 2

05.0~

sA1.0

~sA

2.0~

sA

8~ P s

16~ P

24~ P

1.0nA2.0nA

Amount of tests is 500

s

s

)()(1)()(1 inisibi tftftftf Model function

:

biib Pttf 2sin)(

m

j jisjis PtAtf0

~2sin

~)(

nnin Aftf ;0:)(

23

Testing the method5.

= 15 s

s16~ P

1ns AA100N

24

= 20 s

Testing the method5.s16

~ P1ns AA

100N

25

= 25 s

Testing the method5.s16

~ P1ns AA

100N

26

= 30 s

Testing the method5.s16

~ P1ns AA

100N

27

= 40 s

Testing the method5.s16

~ P1ns AA

100N

28

PP ,:s40,30,25,20,15,13,10,7,5

Testing the method5.s16

~ P1ns AA

100N

29

Results for period s16~ P

> 90 %

> 96 %

> 99 %

> 99 %

s1~

s2~

5.0;100

PP

PP

A

AN

n

s

s1~

s1~

0.1

PP

PP

A

A

n

s

s5.0~

s8.0~

5.0;300

PP

PP

A

AN

n

s

s2.0~

s8.0~

0.1

PP

PP

A

A

n

s

Testing the method5.