Observation of coronal loop torsional oscillation

4 Pages·0.1 MB·English

by  T. V. Zaqarashvili

Astronomy & Astrophysics manuscript no. zaqarashvili February 2, 2008
(DOI: will be inserted by hand later)
Observation of coronal loop torsional oscillation
T.V. Zaqarashvili
Abastumani Astrophysical Observatory,Al. Kazbegi ave. 2a, 380060 Tbilisi, Georgia
e-mail: [email protected]
3 Received November22, 2002/ Accepted January 14, 2003
0
0
Abstract. Wesuggestthattheglobaltorsionaloscillation ofsolarcoronalloopmaybeobservedbytheperiodical
2
variation of aspectral linewidth.Theamplitudeof thevariation must bemaximal at thevelocity antinodesand

n minimal at thenodes of thetorsional oscillation. Then thespectroscopic observation as a time series at different
a heights above the active region at the solar limb may allow to determine the period and wavelength of global
J
torsional oscillation and consequently the Alfv´en speed in corona. From the analysis of early observation (Egan

6 & Schneeberger 1979) we suggest thevalueof coronal Alfv´en speed as ∼500km·s−1.
1

Key words.Sun:corona – Sun:oscillations
1
v
6
1 1. Introduction ofenergyfromthe kinkmode toAlfv´en(azimuthal)oscil-
3 lationswithinthe inhomogeneouslayer.Consequentlythe
1 Magnetohydrodynamic (MHD) waves and oscillations resonantabsorptionof globalkink modes may leadto the
0 play an important role in the dynamics of the solar
global torsional oscillation of coronalloops.
3 corona (Roberts 2000). They can heat and accelerate the
0 Unfortunately, contrary to the sausage and kink
coronal plasma (Goossens et al. 1995) and also offer an
/ modes, the global torsional oscillations do not cause nei-
h unique tool for developing a coronal seismology (Edwin
therintensityvariationnorthespatialdisplacementofthe
p & Roberts 1983, Nakariakov & Ofman 2001). The so-
- loopposition.Therefore they hardly subjectto the obser-
o lar corona is highly structured into narrow coronal mag-
vation in usual coronalspectral lines.
r neticloopswhichareanchoredintothedensephotosphere.
t The influence of torsional waves propagating along a
s The loops permit the propagationof three kinds of MHD
a waves: sausage, kink and torsional Alfv´en waves. The thin, vertical,photospheric flux tube on Zeeman-splitpo-
: larized line profiles (Stokes profiles) was studied recently
v closed boundary conditions at the loop footpoints lead to
i the discrete spectrum of harmonics and consequently to by Ploner & Solanki (1999). In the presence of such a
X
wave spatially resolved Stokes profiles are found to oscil-
the formation of global oscillations.
r latestronglyinwavelength,amplitudeandblue-redasym-
a The global MHD oscillation in the sausage mode
metry. Also observation on the Solar and Heliospheric
(Roberts et al. 1984) modulate loop cross section and
Observatory (SOHO) showed an increase of spectral line
causes the variation of the density and emission measure
widthwithheight(Doyleetal.1998,Banerjeeetal.1998)
of radiating plasma. Using coronal loop images obtained
which can be interpreted as vertically propagating un-
withtheYohkohsoftX-raytelescope(SXT),McKenzie&
damped Alfv´en waves (Moran 2001). However no wave
Mullan (1997) found the periodical modulation of the X-
parameters (wavelength, frequency) were identified, be-
ray brightness, which was interpreted as the signature of
cause of the propagating pattern of waves. On the other
globalmodeoscillation.Theglobalkinkoscillationscanbe
hand,thestationarycharacterofstandingAlfv´enwavesin
detected as transverse displacement of spatial loop posi-
magnetic tubes (or torsional oscillations) allows to iden-
tionsbetweenfixednodes.Thetypicalpropertyofrecently
tify the velocity nodes and antinodes and thus may be
observedkink oscillations by TRACE (Aschwanden et al.
used for determining the wave parameters.
1999, Nakariakovet al.1999) is very shortdamping time.
Wesuggestthattheglobaltorsionaloscillationofcoro-
It was suggested that the oscillations may be damped ei-
nalloopcanbedetectedbyperiodicalbroadeningofspec-
ther due to the phase mixing with anomalously high vis-
tral lines due to the periodic azimuthal velocity. The am-
cosity(Ofman&Aschwanden2002)orduetotheresonant
plitude of the azimuthal velocity in the torsional oscilla-
absorption (Ruderman & Roberts 2002) acting in the in-
tion is maximal at the antinodes and tends to zero at the
homogeneousregionsofthetube,whichleadstoatransfer
nodes. Therefore the torsional oscillation causes the peri-
Send offprint requests to: T. Zaqarashvili odical variation of spectral line broadening with different
2 T.V. Zaqarashvili: Observation of coronal loop torsional oscillation
amplitudes atdifferent heights fromthe solar surface:the where v is the rotation velocity at x=R (R is the radius
place of stronger variation corresponds to the antinode of the tube). So the Doppler shifts at different x from the
and the place of constant broadening corresponds to the tube axis cause the spectral line broadening by 2 ∆λ. It
| |
node. Then the time series of spectroscopic observations must be mentioned that the broadening of spectral lines
at different heights above the active region at the solar can be caused by thermal motion of ions and turbulent
limb may allow to determine the period and wavelength motionofgas,howeverhereweconsideronlythenonther-
ofglobaltorsionaloscillationandconsequentlytheAlfv´en mal broadening of spectral lines caused by the azimuthal
speed in the coronalloops. velocity of the tube.
Recently, strongly damped Doppler shift oscillations Now suppose that the tube undergoes the torsional
of hot (T>6 MK) coronal loops were observed with oscillationduetotheclosedboundaryconditionsimposed
SUMER on SOHO (Kliem et al. 2002, Wang et al. 2002). at the tube ends. For simplicity the density ρ and the
These oscillations were interpreted as signatures of slow- magnetic field B=(0,0,B0), directed along the axis z of
modemagnetosonicwavesexcitedimpulsivelyintheloops acylindricalcoordinatesystemr,φ,z,areconsideredtobe
(Ofman&Wang2002).Itispossiblethattheslowmagne- homogeneousthroughoutthe tube.Thenthe velocityand
tosonic waves (as well as the kink waves) may also cause the magnetic field components of the torsional oscillation
the oscillation of Doppler broadening in given direction can be expressed as
of propagation. However the velocity field of waves is in-
homogeneous(which is necessary for the line broadening) Bφ =−B0αcos(ωnt)cos(knz), (2)
only at wave nodes and thus may lead only to negligible
V =V αsin(ω t)sin(k z), (3)
effect.Ontheotherhand,thevelocityfieldatwaveantin- φ A n n
odes will cause the Doppler shift oscillation as was inter-
where VA =B0/√4πρ is the Alfv´en speed, kn =nπ/L (L
pretedbyOfman&Wang(2002).Howeveritisalsopossi-
is the length of the tube and n=1,2,3...) is eigenvalue of
blethattheDopplerbroadeningofthelineisduetosuper-
wavenumber,ω isthecorrespondingeigenfrequencyand
n
imposeofseveralloopsintheline ofsightcontainingslow
αistherelativeamplitudeofoscillations.Eigenvaluesand
wavesatdifferent phases.But in this case the broadening
eigenfrequencies satisfy the dispersion relation of Alfv´en
must be nearlyconstantor it will showrather chaotic be-
waves
haviourintime thanthe periodicalone.Recently Sakurai
ω
n
etal.(2002)presentedatimesequenceover80minofcoro- =V . (4)
A
k
nalgreen-linespectraobtainedwitha ground-basedcoro- n
nagraph at the Norikura Solar Observatory. They found Thevelocityfieldofeachnthmodehasdifferentamplitude
the oscillations of the spectral line Doppler shifts and in- of oscillation, but the same frequency ω along the tube:
n
terpretedthemaspropagatingslowMHDwaves.Noclear the amplitude is maximal at the antinodes (sin(k z) =
n
evidence of the Doppler width oscillations was found. It 1) and tends to zero at the nodes (sin(k z)=0).
n
±
mayindicatethateither they couldnotcatchthe velocity Thenthe velocityfield(3)leadsto the periodicalvari-
antinodes of the global torsionaloscillation or the oscilla- ationofDopplerwidthateachpointz alongthetubeaxis.
tions are not common in corona and they are related to It means that the torsional oscillation causes the period-
the flareormassejection. Future spaceandground-based ical variation of spectral line broadening (expressed by a
spectroscopicobservationsarenecessaryto makethecon- halfoflinewidth,∆λ ,hereafterHW)withthesamefre-
B
clusion. quency,butwithdifferentamplitudesalongthetube.The
In the next section we briefly describe the method of amplitude of HW variation will be maximal at the veloc-
observation and interpret the early observation of Eagen ity antinodes and minimal atthe nodes.According to the
& Schneeberger (1979) as the global torsional oscillation equations (1) and (3) HW can be expressed by
of coronal loop.
αV λ
A
∆λ = sin(ω t)sin(k z). (5)
B n n
c | |
2. Observation of the torsional oscillation
The distance between the points of maximal variation
Consider a coronal loop as straight magnetic tube, the i.e. between the velocity antinodes will be the half wave-
axis of which is perpendicular to the line of sight. If the lengthoftorsionaloscillation.Thentheobservedperiodof
tube rotates about its axis with an angular velocity Ω, HW variation allows to determine the Alfv´en speed from
then the Doppler shift of the observed spectral line with thedispersionrelation(4).AlsotheamplitudeofHWvari-
wavelength λ is ∆λ = (λΩ/c)x, where x is the distance ation at the velocity antinodes (maximal value of ∆λ
B
from the tube axis in the plane perpendicular to the line along the tube axis) gives the value of α i.e. the ampli-
ofsightandcisthespeedoflight(theexpressionmustbe tude of torsional oscillations.
multipliedbysiniifthetube isinclinedwiththeanglei). However we have to be sure that the periodical varia-
The largest shift occurs at the edges of the tube and has tionofspectralline broadeningcanbe causedonlyby the
a value torsionaloscillations.The velocityfieldofotherwavemo-
tionsmaycausetheDopplershiftvariations.Forexample,
λ
∆λ= v, (1) theslowmagnetosonicwavespropagatingalonganapplied
c
T.V. Zaqarashvili: Observation of coronal loop torsional oscillation 3
magnetic field may lead to this effect recently observed
by SUMER in given arbitrary loop orientation (Kliem
B
et al. 2002, Wang et al. 2002, Ofman & Wang 2002). *
A
Howeverneitherslowmagnetosonicwaves,norkinkwaves * 66 000 km
can cause the significant periodical variation of Doppler
88 000 km
broadening at given height from the solar surface. The
velocity field of waves must be highly inhomogeneous to
produce the line broadening. The velocity field of slow
magnetosonicwaves(aswellasthekinkwaves)isinhomo-
geneous at velocity nodes, where they can produce only
negligible Doppler broadening. On the other hand, they
can produce the Doppler shift oscillations at antinodes
where the velocity is maximal and almost homogeneous.
HoweveritisalsopossiblethattheDopplerbroadeningof
the line is due to superimpose of several loops in the line
of sight containing slow waves at different phases. But in
thiscasethebroadeningmustbenearlyconstantoritwill
showratherchaoticbehaviourintime thanthe periodical Fig.1. Schematic picture of a coronal loop at the solar
one. Therefore from our point of view the torsionalwaves limb is presented. The points A and B correspond to the
are best candidates for producing the periodicalvariation velocity antinodes of second mode of global torsional os-
of spectral line broadening. cillation. Both points are located at 88 000 km from
∼
Thus the observation as a time series at different the surface.Howeveronly 66 000km partis visible in the
heightsabovetheactiveregionatthesolarlimbmayallow caseofpointB,becausethefootpointisanchoredintothe
to determine the wavelength and the period of torsional reverse side of the solar surface.
oscillation.Asanexampleofproposedmethodletanalyse
the observation made almost two decades ago by Egan &
The period of torsional oscillations will be 12.2 min i.e.
Schneeberger(1979).Theypresentedthe time seriesofFe ∼
double of observed period. Then we easily calculate the
XIV coronal emission line spectra above both active and
Alfv´enspeed incorona(here the constantAlfv´enspeedis
quiet regions at the solar limb. They found the Doppler
assumedalongtheloop,howeverinrealconditionsitmay
widthtemporalvariationswiththeperiodof6.1 0.6min
± be inhomogeneous which complicates the problem)
above the active region. The width fluctuations were am-
plified in two 5500 km long segments at heights of 66 000 V 500kms−1. (7)
A
∼ ·
kmand88000kmabovethe limb.The amplitudeofvari-
ation was 0.125 ˚A at 88 000 km, while at lowest heights If the regions of amplified Doppler width oscillations
itreduces to 0.04˚A. They alsofound amarginalevidence belong to two different loops, then the similar calculation
for 6 min intensity oscillations at these two positions.For for the loop with velocity antinodes at 66 000 km gives
quite region they found neither Doppler width nor inten-
−1
V 360kms , (8)
sity variations. A ∼ ·
We suggestthatthisobservationcanbeinterpretedas which is below the expected value of the Alfv´en speed in
the global torsional oscillation of coronal loop. The two corona. Also it seems unreal that the two different loops
regions of amplified Doppler width variation may corre- havethesameperiodsofglobalmode.Ontheotherhand,
spond to the velocity antinodes of torsional oscillation. the global oscillation of coronal loop in other wave mode
They likely belong to the second mode of oscillation, be- may not cause the periodic oscillations of Doppler width.
cause it has two velocity antinodes at the middle of both Only the temperature changing due to the nonadiabatic
footpoints, while first mode has only one at the top (the slow MHD wavesmay leadto this variation.But it seems
velocityantinodeatthelooptophardlyundergototheob- again unreal that the nonadiabaticity leads to the varia-
servationinthisspectrallinebecauseofrapidlydecreasing tion of line broadeningwith 25%.Therefore we suggest
∼
intensity in the corona). thatthetorsionaloscillationofoneloopcanbethereason
Astheobservationswereperformedoffthesolarlimbit for the observed phenomenon.
isreasonabletosupposethattheantinodeswerelocatedat We also easily calculate the amplitude of torsional os-
88000kmheightfromthephotosphere,butthesecond cillation for Fe XIV (λ5303) spectral line from the equa-
∼
footpoint was anchoredat the reverseinvisible side ofthe tion (5)
Sun, so that only 66 000 km part of footpoint was visible
−1
7kms . (9)
(Fig.1).Thenthewavelengthofglobaltorsionaloscillation
∼ ·
can be
This result is calculated when the loop axis is perpendic-
ular to the line of sight. The amplitude of oscillation will
λ=4 88000km 352000km. (6) be even greater in the case of loop inclination.
· ≈
4 T.V. Zaqarashvili: Observation of coronal loop torsional oscillation
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Wesuggestthattheglobaltorsionaloscillationofthecoro-
nal loop, axis of which is not parallel to the line of sight,
canbeobservedbytheperiodicalvariationofspectralline
width. The amplitude of the variation must be maximal
at certain regions which correspondto the velocity antin-
odesoftorsionaloscillations.Thenthe periodofvariation
will be the half of oscillation period and the distance be-
tweentheregionswithmaximalvariationswillbethehalf
ofwavelength.Thespectroscopicobservationasatimese-
riesatdifferentheightabovetheactiveregionatthesolar
limb may allow to determine the wavelength and the pe-
riodofthetorsionaloscillation.ThentheAlfv´enspeedcan
becalculatedwhichisveryimportantfordeterminationof
magnetic field strength in corona. The observation of the
spectrallineswithlargerwavelengthswillbemoresuccess-
ful,becauseoftheirsensitivitytotheDopplershift.Both,
ground based coronagraphs and space based instruments
can be used. The analysis of early observation (Egan &
Schneeberger 1979) give the values of Alfv´en speed and
the amplitude of torsional oscillations as 500kms−1
and >7kms−1 respectively. ∼ ·
·
We hope that the observation of torsional oscillations
after the damping of coronal loop kink oscillations will
provide the clue for the damping mechanism and con-
sequently for the coronal heating (Ruderman & Roberts
2002).
Acknowledgements. Theauthorthankstheanonymousreferee
for helpful suggestions.