Quasi-Periodic Pulsations as a Feature of the Microwave Emission Generated by Solar Single-Loop...

Quasi-Periodic Pulsations as a Feature of the Microwave Emission Generated by Solar

Single-Loop Flares

Seismology of Stellar Coronal Flares, 21-24 May 2013, Leiden

Introduction

''Long'‘ QPPs, with periods from several to tens of minutes : active region dynamics and global oscillations of the Sun Gelfreikh et al., 1999, Solar Phys. 185, 177. Shibasaki, 2001, Astrophys. J. 550, 1113. O’Shea et al., 2001, Astron. Astrophys. 368, 1095. McAteer et al. 2004, Astrophys. J. 602, 436

Quasi-periodic pulsations (QPPs) during solar flares can be caused by the modulation of the intensity of radio emission or by the modulation of the acceleration of electrons. The periods of QPPs can be split into several bands, from sub-seconds up to tens of minutes.''Short'‘ (sub-second) QPPs in the m-dm-cm radio emission : kinetic processes caused by the dynamic interaction of electromagnetic, plasma or whistler waves with energetic particles trapped in closed magnetic fields during solar radio bursts. Aschwanden, 1987, Solar Phys. 111, 113. Fleishman et al., 2002, Astron. Astrophys., 385, 671.

1.

''Medium period'‘ (seconds to several minutes) QPPs detected in microwave, white light, EUV and X-ray emission : magnetohydrodynamic (MHD) processes in solar flaring loops. “Medium” QPPs are interesting due to their possible association with the fundamental physical processes operating in flares: spontaneous and triggered energy releases, magnetic reconnection, thermodynamics, MHD oscillations, particle acceleration and other kinetic effects

Observations with high spatial resolution give the possibility -- to define size of a flaring area, - to study a spatial structure of QPPs, and - to identify MHD mode of pulsations.

1. Introduction

2009 г. 4

Радиогелиограф в НобеямеNobeyama Radioheliograph

Analysis of imagesTemporal resolution: 0.1 s Spatial resolution: 10’’ at 17 GHz

5’’ at 34 GHz

Nobeyama Radiopolarimeters

Analysis of full Sun fluxes with high temporal resolution (0.1 s).

Frequencies: 1, 2, 3.75, 9.4, 17, 35, 80 GHz

Integrated, or spatially unresolved, signal1.

Spatial resolved signal – analysis of images2.

We have used NoRP : the total flux density at f = 17 GHz and f = 35 GHzNoRH : the mean correlation amplitude at f = 17 GHz and f = 34 GHz

NoRH: Analysis of images with high temporal (100 ms) and angular (5’’ and 10’’ at 34 GHz and 17 GHz) resolution.

Purpose of our studyAll of the events in previous studies were selected based on the visible presence of well-indicated QPP patterns in the time profiles.

The purpose is to carry out a statistically broader study based upon the analysis of twelve well-resolved “single flaring loops”, seeking answers to the following questions:

1. Is the presence of QPPs in a single flaring loops a common phenomenon?

2. How often may more than one spectral component occur in a single flaring loop, and is multi-periodicity a common feature of QPPs?

3. What is the characteristic evolution of the QPPs spectrum during the flare?

2.

Flares under study 3.

14-Mar-2002

The microwave source should: 1. be well resolved by NoRH,

that is, its length should be larger than the beam size at 17 GHz;

2. have a single loop shape;3. be located near the solar disk

centre, or have relatively small intensity if located near the limb, reducing the influence of positional ambiguity in the image synthesis.The visible presence or

absence of QPPs in time profiles are not accounted for in the selection.

Method of analysis of time profiles4.

Fourier periodogram of R

Wavelet spectrum of

Auto-correlation function R( )

modulation depth)(

)()()(

tF

tFtFt sm

sm


This was done for a broad range of smoothing intervals τ form 5 s to 60 s, allowing us to understand whether the spectral peak found is real or produced by the smoothing (filtering) procedure.

Set of spectral components:P and W

Method of analysis of time profiles4.

For the final analysis and classification, we have chosen only those oscillatory patterns which satisfy the following criteria.

1. The oscillations should be well pronounced in the data from both instruments (NoRH and NoRP) and have similar frequency-time behaviour of the wavelet spectra.

2. They should be seen in periodograms of auto-correlation and cross-correlation functions at 17 and 34 GHz.

3. The value of their period should not depend upon the selected low frequency filter (the specific value of τ ), at least inside the corresponding error bar.

4. The number of observed periods of QPPs should be at least three.

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

~sA2.0

~sA

8~ P s

16~ P24

~ P1.0nA2.0nA

Amount of tests is 500

s

s

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

:

biib Pttf 2sin)(

m

j jisjis PtAtf0

~2sin

~)(

nnin Aftf ;0:)(


= 15 s

s16~ P

1ns AA100N

= 20 s

Testing the method5.s16

~ P1ns AA

100N

= 25 s


~ P1ns AA

100N

= 30 s


~ P1ns AA

100N

= 40 s


~ P1ns AA

100N

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


~ P1ns AA

100N

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


1. In ten out of the twelve events under study, at least one significant oscillation with a period in the range from 5–60 s has been found. This means that QPPs is quite a common phenomenon in solar flares.

2. The quality of the oscillations is rather low; it mostly varies in the range 12 to 40, with an average of 25, in only one case the quality reaches 85.

3. Two oscillations were detected in two events, and one event was found to have three pronounced oscillations.

4. In only two events significant periodicities, which would satisfy the imposed selection rules, were not found.

Results of analysis of QPPs in single flaring loops6.

Kupriyanova, Melnikov, Nakariakov, Shibasaki, 2010, Sol. Physics, 267, 329


2.5–5 min Reznikova, Shibasaki A&A 525, A112 (2011)

According to the time evolution, we divide the QPPs into four types:

1. those with stable mean periods in the range 5 – 20 s (eight events);

2. those with spectral drift to shorter periods in the rise phase of the burst (two events);

3. those with drift to longer periods in the decay phase (two events);

4. those with an X-shaped drift between periods of 20 – 40 s (one event).


28 June 2002

mins3dtdP35s100

s5.8

Qt

P

QPP

Results of analysis of QPPs in single flaring loops.

Type 1 – QPPs with stable period

6.

18 Jule 2002

12s,5.16

12s,5.9

22

11

QP

QP


Type 1 – QPPs with stable period

6.

31 May 2002

15

mins14

5

min1

s917

Q

dtdP

n

t

P

QPP


Type 2 – QPPs with spectral drift to shorter periods

6.

3 July 2002

16

mins11

5

s3022,

12

s15

2

22

1

1

Q

dtdP

n

P

Q

P

Results of analysis of QPPs in single flaring

loops.

Type 3 – QPPs with spectral drift to longer periods

6.

21 May 2004

mins10

s30

mins10

s22

s38

2

1

dtdP

P

dtdP

P

P


Type 4 – QPPs with X-shaped drift

6.

Discussion7.Physical mechanisms of QPPs are

1. Periodic regimes of spontaneous magnetic reconnections

2. Magnetic reconnections, which induces periodically by external oscillations

3. Varying electric current in the equivalent RLC-contour

4. MHD-oscillations in an emitting plasma structures

Discussion7.

L is loop lengthn is a harmonic numbervph is the phase velocity

Period of the standing MHD wave or of alfven wave:

4. MHD-oscillations in an emitting plasma structures.

2 L nvph

P =

z

Dispersion equation of the MHD modes in the simplest magnetic tube:

Preliminary restriction on the MHD mode (or modes) produces the QPPs observed.

That is spatial distribution of amplitudes and phases of QPPs in a flaring loop?

Integrated, or spatially unresolved, signal1.

Spatial resolved signal – analysis of images2.


NoRH: Analysis of images with high temporal (100 ms) and angular (5’’ and 10’’ at 34 GHz and 17 GHz) resolution.

Analysis of the integrated (spatially unresolved) signal.

Kupriyanova, Melnikov, Nakariakov, Shibasaki, 2010, Sol. Physics, 267, 329

The flare on 3 July 2002

1.

Kupriyanova, Melnikov, Shibasaki, 2013, Sol. Physics, 284, 2, 559

Inglis and Nakariakov, 2009, Astron. Astrophys., 493, 259

The methodology of analysis of images2.

Modulation depth)(

)()()(

tF

tFtFt sm

sm

Stabilization of images; study of the behaviour of the source;

data reduction;

data handling using the methods of autocorrelation, Fourier and wavelet analysis; analysis of spatial features of QPPs; identifying the oscillation modes which are able to produce observed QPPs.

Analysis of the spatial structure. Loop geometry

3.

1 pix = 2.5’’

Single flaring loop

Dynamics of the radio source4.

d

The analysis of the spatial structure of QPPs. 5.

Set of 211 images, t = 1 s

5.

For each box:

The analysis of the spatial structure of QPPs.

Set of 211 images, t = 1 s

)(

)()()(

tF

tFtFt sm

sm

Search of an area with significant signal5.

For each box:

remoteNS

)(

)()()(

tF

tFtFt sm

sm

Spectral analysis of time profiles5.

For each box:

remoteNS

Periodogram of R

Wavelet spectrum of

Auto-correlation function R( )

Set of spectral components:P and W

Where are an areas with similar periods ?

Where are an areas with maximal spectral powers ?

and

)(

)()()(

tF

tFtFt sm

sm

Positions of the sources of different spectral components.

6.

6.

Modulation depth


6.

Modulation depth Auto-correlation function


6.

Wavelet Power Spectrum Global WPS Periodogram of auto-correlation function


6. Positions of the sources of different spectral components.

Dynamics of the radio source4.

Wavelet Power Spectrum Global WPS

sausage (|B|, )kink

torsional (incompressible)acoustic (, V)flute (|B|, )

Five principal modes in a simplest coronal loop7.

• kink horizontal

• sausage

• kink vertical

• acoustic (the second harmonic)

Five principal modes in a simplest coronal loop7.

L is loop lengthn is a harmonic numbervph is the phase velocity

2 L nvph

P =

Period of the standing wave:

Discussion of the oscillating modes8.

a / L 1 / 5

1. Acoustic mode T0 = 7106 K

PAI ≈ 165 s

PAII ≈ 82 s

PAIII = 55 s

2. Sausage mode

n0 = 1011 cm-3

B0 = 70 G

PSI does not exist

PSII = 26 s

PSIII = 23 s

3. Kink mode

n0 = 5 1010 cm-3

B0 = 180 G

PKI = 31.7 s

PKII = 16.8 s

PKIII = 11.7 s

4. Ballooning moden0 = 5 1010 cm-3

B0 = 180 G

PBI = 30.6 s

PBII = 15.7 s

PBIII = 10.8 s

PobsI ≈ 31.2 ± 2.5 s

PobsII ≈ 18.7 ± 1.0 s

PobsIII ≈ 11.5 ± 0.4 s

Observable periods

Horizontal kink oscillations9.Dulk and Marsh, 1982:

S19W48

θ > 48° in the northern footpoint

θ < 48° in the southern footpoint

θ ≈ 70° in the loop top

ΔI /I ≈ 2–5 % in the loop top and footpoints

Δ θ ≈ 1.5–3°

δ = 4.7

B ≈ const

Vertical kink oscillations10.

Dulk and Marsh, 1982:

Aschwanden and Schrijver, 2011: Fundamental

mode

Δθ<<1δ = 4.7

is maximal at the loop top

Observations

d

B Ia

10.

Vertical kink oscillations

B I

a

10.


d

Dulk and Marsh, 1982:

Aschwanden and Schrijver, 2011: Fundamental

mode

Δθ<<1δ = 4.7

is maximal at the loop top

10.


1. Quasi-periodic pulsations (QPPs) with at least three simultaneously existing spectral components with periods about 30 s, 20 s and 10 s were detected during the decay phase of solar flare on 03 July 2002, observed with NoRH.

2. It is shown that the source of the QPPs with period 30 s has its maximum amplitude in the inner region of the loop, between the footpoints. QPPs with period 20 s are localized at the periphery of the loop, mainly in the outer parts of the footpoints. The spatial distribution of oscillations with period about 10 s contains three regions of high QPP amplitudes: two near the footpoints and one in the middle of the flaring region.

3. It is shown that the observed properties of the spectral components are most accurately described by the fundamental, second and third harmonics of the kink mode standing waves. This is the first identification of the kink mode in flare loops which is based on strict limitations derived from data on the spatial structure of a pulsating flare region.

11.

Conclusions

Kupriyanova, Melnikov, Shibasaki, 2013, Sol. Physics, 284, 2, 559

Kupriyanova, Melnikov, Shibasaki, 2013, PASJ, in press

Thank you for your

attention!

Quasi-Periodic Pulsations as a Feature of the Microwave Emission Generated by Solar Single-Loop...

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