Centre for Fusion, Space & Astrophysics

Valery M NakariakovUniversity of Warwick, UK

My vision of Chapter 2: "Kink oscillations and waves in the corona”

ISSI-Bj, China, 14/10/2019, 9:15-9:30

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

^*J8@GJ*B+'G@S,D*B+J'BF'\]^'ABK@J'BF'"'W"A/$1+5'2#:X'1:L$3

! ! ! ! ! !"" " "

"

#$ % #$ %$ % $ % "$ % $ %

! ! "" # $" # $ "

! ! "

% ! & ' ! &( ) ! ( ) !% ! & ' ! &

! " ! "# # # =

\,U+@DB)RKGBKR+,A*E'N\]^P'@XC,D*B+J'!

QXC*S*TG*CA'!

;*+@,G*J,D*B+!

$BC+K,GR'EB+K*D*B+J

G='Y>1"/9"%9'1;$,%&V'"/9'1$%W+/,#,A&K *+D@G,ED*B+'BF'\]^'H,M@J'H*D)'A,U+@D*E'JDGCEDCG@J'N`,*DJ@M'l'"D@8,+BM&'-2

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

Y*+I'NAn-P'ABK@J3

?)*J'ABK@'*J'@JJ@+D*,SSR'EBA8G@JJ*M@&',+K'ACJD'+BD'T@'EB+FCJ@K'H*D)'D)@'7SFMo+'H,M@

NH)*S@&'JBA@D*A@J'*D'*J'E,SS@K'b7SFMo+*EcP

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

^,A8*+U3'@FF@ED'BF'G@JB+,+D',TJBG8D*B+'BF'I*+I'H,M@J

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

!F'D)@'7SFM@+'J8@@K'*J'+B+C+*FBGA *+'D)@'G,K*,S'K*G@ED*B+&'HJK$L&

!+'D)@'SBB8'D)@G@',G@'G@U*B+J'H)@G@'D)@'I*+I'ABD*B+J',G@'*+'G@JB+,+E@'H*D)'D)@'SBE,S'DBGJ*B+,S'N7SFM@+P'8@GDCGT,D*B+J:'

T*ZT

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

\,D)@A,D*E,SSR&'*D'EBGG@J8B+KJ'DB'D)@',88@,G,+E@'BF'D)@'J*+UCS,G*DR'*+'D)@'UBM@G+*+U'@XC,D*B+J3

[)R'*J'*D'#6+#7, ,TBCD'5#4ZZ

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

7'J@A*+,S'8,8@G'BF'V,+'^BBGJJ@S,@G@'@D',S:'100.7l7:::.1.:-064V'''

! ?)@'@FF@ED'BF'ECGM,DCG@'*J'+BD'JDGB+U3'D)@'JDG,*U)D'ERS*+K@G'ABK@S'*J'UBBK'@+BCU):'

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

=,JEB@'@D',S:'10--789:::

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

?HB'G@U*A@J'BF'I*+I'H,M@'K,A8*+U3

10-57l7:::44-7::52]

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

7EEBC+D*+U'FBG'D)@'M,G*,D*B+'BF'K@+J*DR',+K'A,U+@D*E'F*@SK',SB+U'D)@'ERS*+K@G3'

V@GD) @D',S:'100f7l7:::.f6:-0-4V'''

1004"B=)::112:::

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

7SD@G+,D*M@'D)@BGR3'Y*+I'BJE*SS,D*B+J'*+'5,%,/"#'"%5"9$0N]*+KA,+'l'9,*+'10-4789:::f-.::-04]',+K'FBSSBH'C8'8,8@GJP''

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

1:'hTJ@GM,D*B+J'BF'I*+I'BJE*SS,D*B+J'T@FBG@'?e7(Q

OGBA'-2f57l7:::-10::-f4Y

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

500#J&'f0#J&'.5#J'8@G*BK],BB#$%'-$#,5+1&',05+##"1+,/0BF'D)@'UG@@+'EBGB+,S'S*+@'4505'7'O@'L*M:NE:F:';*&'^:@D ,S:''10-f7l7:::6-

Centre for Fusion, Space & Astrophysics

Forward modelling and effects of LoS integration

• De Moortel & Pascoe, 2012ApJ...746...31D “The effects of line-of-sight integration on multistrand coronal loop oscillations”

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

P='^.!'+W"A+/A',L0$%-"1+,/0',2'9$5"&+/A'*+/*',05+##"1+,/0',2'5,%,/"#'#,,B0KO*GJD'BTJ@GM,D*B+3'-./0f/-22f'

NQiV&'?e7(QP

=@G),8J&'SB+U@JD'Q\'H,M@J'G@JBSM@K'*+'D*A@',+K'J8,E@p

7JE)H,+K@+@D',S:'-222789:::410::ff07

W,I,G*,IBM'@D',S:'-222"E*:::1f4::f61W'

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

Y*+I'BJE*SS,D*B+J'H*D)'"^h/7!73

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

! hJE*SS,D*B+'''''''8@G*BK&

> ^@E,R'D*A@

]BH'H@',+,SRJ@ *D3

Centre for Fusion, Space & Astrophysics

5. Seismological estimation of the magnetic field:

• One of the specific aims of SDO/AIA

Nakariakov & Ofman, 2001A&A...372L..53N

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

"^h/7!7'-

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

7'8BJJ*TS@'A@E),+*JA3'A@E),+*E,S'K*J8S,E@A@+D'BF'D)@'SBB8'TR';(Q'FGBA'D)@'@XC*S*TG*CA'N*+'24q'BF'BTJ@GM@K'@M@+DJP

Centre for Fusion, Space & Astrophysics

Alternative mechanisms:

• Blast wave, e.g. McLaughlin & Ofman2008ApJ...682.1338M

• Upflows at footpoints, Zaitsev & Stepanov1989SvAL...15...66Z

• Collision of unsteady counter-streaming upflows along the loop

Antolin et al. 2018ApJ...861L..15A

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

QLE@8D*B+3'b],GAB+*E,c'@M@+D

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

Q='>1"1+01+5"#'B%,B$%1+$0'"/9'05"#+/A0

hFA,+l'7JE)H,+K@+

1001789:::4

Centre for Fusion, Space & Astrophysicsx, arcsec

-1000 -500 0 500 1000

y, ar

csec

-1000

-500

0

500

1000new datapointsold datapoints

Loca

tions

of a

llde

tect

ed k

ink

osci

llatio

ns

Zim

ovet

s&

Nak

aria

kov

2015

A&A.

..577

A...4

ZN

echa

eva

et a

l. 20

19Ap

JS..2

41...

31N

Comprehensive catalogues:

Centre for Fusion, Space & Astrophysics

Amplitude, Mm0 15 25

Num

ber o

f cas

es

0

5

15

25

35

45combined datanew data

5

Period, min0 15 25

Num

ber o

f cas

es

0

5

15

25

35combined datanew data

5

Looplength, Mm0 100 300 500 700

Num

ber o

f cas

es

0

5

15

25combined datanew data

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+gBKK,GK'@D',S:&'7l7'4f4&'7-5

Centre for Fusion, Space & Astrophysics

Ck, km/sec0 500 1500 2500 3500

Num

ber o

f cas

es

0

5

15

combined datanew data

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

! ! P # (B+J*JD@+D'H*D)'G@JB+,+D',TJBG8D*B+

Centre for Fusion, Space & AstrophysicsAmplitude, Mm

0 5 15 25

Dam

ping

time/

perio

d

01

3

5

7

9 old datapointsnew datapoints

Amplitude, Mm100 101

Dam

ping

time/

perio

d

100

101

Is the damping a nonlinear process?

Apparent

God

dard

& N

akar

iako

v, A

&A 9

0, L

5, 2

016

Q∝A-2/3

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

?@GG,K,J @D',S:'789'6f

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

H=')$4'%$A+W$K'9$5"$00

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+[,+U'@D',S:'789

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

7+'BJE*SS,DBGR'8,DD@G+'BEECGJ'T@FBG@'D)@'B+J@D'BF'D)@'A,*+'BJE*SS,D*B+3W*JD*EB@D',S:'10-57l7:::4417::4

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

7+F*+BU@+DBM @D',S:&'J,1$/24%J,1$/*"7,4 COP&'7-56&'10-4

^@E,RS@JJ G@U*A@'BF'I*+I'BJE*SS,D*B+J3

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

Centre for Fusion, Space & Astrophysics

Seismology of a “quiet” active region by decaylessoscillations

Anfin

ogen

tov

& N

akar

iako

v A&

A in

pre

ss

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

]BH'E,+'H@'),M@','K@E,RS@JJ AB+BE)GBA,D*E'BJE*SS,D*B+'BF','K,A8@K'BJE*SS,DBGZ

(,+ ;K1L%T@'8@G*BK*EZ'NQ:U:&'S@,I,U@'BF'8#ABK@J&'E)GBABJ8)@G*E'5#A*+'BJE*SS,D*B+JP

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

),'0+A/"1:%$0',2'%$0,/"/5$

]$W,/01%"1+,/'1;"1'1;$'9$5"$00 *+/*',05+##"1+,/0'"%$'/,1'$X5+1$9'L&'1;$'#$"*"A$',2'BJW,9$0'"/9'PJW+/',05+##"1+,/0='W,I,G*,IBM'@D',:&'7l7'42-&'

;4&'10-6'

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

),'0+A/"1:%$0',2'%$0,/"/5$

Centre for Fusion, Space & Astrophysics

Thus, f(t) cannot be periodic: no signature of resonance.

BTW, how is it consistent with the claimed detection of kink waves propagating from the chromosphere to the corona??

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

]BH'E,+'H@'),M@','K@E,RS@JJ AB+BE)GBA,D*E'BJE*SS,D*B+'BF','K,A8@K'BJE*SS,DBGZ

(BCSK'D)@'KG*M@G';K1L T@'G,+KBA&';K1LM=K1LZNQ:U:'UG,+CS,D*B+'ABD*B+JP

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

e@J8B+J@'BF',+'BJE*SS,DBG'DB'G,+KBA'KG*M*+U

?)@'8),J@'*J'+BD'JD,TS@&'KB@J'+BD'A,DE)'BTJ@GM,D*B+J

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

i+K,A8@K I*+I'BJE*SS,D*B+J'E,+'T@'0$#2J,05+##"1+,/0K

!+'EB+DG,JD'H*D)'KG*M@+'BJE*SS,D*B+J&','J@SF#BJE*SS,DBG'*DJ@SF'J@DJ'D)@'2%$a:$/5&',+K'B;"0$ H*D)'H)*E)'*D'*J'KG*M@+&'*$$B+/A'1;$'2%$a:$/5&'"/9'B;"0$ FBG','+CAT@G'BF'8@G*BKJ:

Centre for Fusion, Space & Astrophysics

In a self-sustained oscillator (self-oscillator), the driving force is controlled by the oscillation itself so that it acts in phase with the velocity, causing a negative damping that feeds energy into the vibration:

no external rate needs to be adjusted to the resonant frequency.

Examples:• Heart,• Clocks,• Bowed and wind musical instruments,• Devices that convert DC in AC.

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

e,RS@*U)'QX:3

!"#$%"&'(%&)*+,(#-&./01"&2&3+$%(/45+,1+

Centre for Fusion, Space & Astrophysics

Sketch of our model of undamped kink oscillations of loops:

Loops

Quasi-steady flows (supergranulation?)

Centre for Fusion, Space & Astrophysics

Conclusions• Appearance of large-amplitude rapidly-damped

kink oscillations is associated with low coronal eruptions (LCE).

• Possible excitation mechanism is the mechanical displacement of the loop from the equilibrium by the LCE (observed in 86% cases).

• Some cases are clearly inconsistent with this mechanism.

• Evidence of nonlinear damping: the quality-factor depends on the oscillation amplitude.

V.Nakariakov@warwick.ac.uk

Centre for Fusion, Space & Astrophysics

Conclusions - 2• There is another, decayless and low-amplitude

regime of the oscillations.• The period also depends on the loop length.• Seismology during quiet periods.• The amplitude does not depend on period.• Are decayless oscillations self-oscillations?

V.Nakariakov@warwick.ac.uk