Oscillations on width and intensity of slender Ca II H fibrils from Sunrise/SuFI

7.6 MB·

by  R. Gafeira

DRAFTVERSIONJANUARY12,2017
PreprinttypesetusingLATEXstyleemulateapjv.05/12/14
OSCILLATIONSONWIDTHANDINTENSITYOFSLENDERCaIIHFIBRILSFROMSUNRISE/SUFI
R.GAFEIRA1,S.JAFARZADEH2,S.K.SOLANKI1,3,A.LAGG1,M.VANNOORT1,P.BARTHOL1,J.BLANCORODRÍGUEZ4,
J.C.DELTOROINIESTA5,A.GANDORFER1,L.GIZON1,6,J.HIRZBERGER1,M.KNÖLKER7,D.OROZCOSUÁREZ5,
T.L.RIETHMÜLLER1,ANDW.SCHMIDT8
1MaxPlanckInstituteforSolarSystemResearch,Justus-von-Liebig-Weg3,37077Göttingen,Germany;[email protected]
2InstituteofTheoreticalAstrophysics,UniversityofOslo,P.O.Box1029Blindern,N-0315Oslo,Norway
3SchoolofSpaceResearch,KyungHeeUniversity,Yongin,Gyeonggi446-701,RepublicofKorea
4ImageProcessingLaboratory,UniversityofValencia,P.O.Box22085,E-46980Paterna,Valencia,Spain
5InstitutodeAstrofísicadeAndalucía(CSIC),ApartadodeCorreos3004,E-18080Granada,Spain
7 6InstitutfürAstrophysik,Georg-August-UniversitätGöttingen,Friedrich-Hund-Platz1,37077Göttingen,Germany
1 7HighAltitudeObservatory,NationalCenterforAtmosphericResearch, P.O.Box3000,Boulder,CO80307-3000,USA
0 8Kiepenheuer-InstitutfürSonnenphysik,Schöneckstr.6,D-79104Freiburg,Germany
2 DraftversionJanuary12,2017

n ABSTRACT
a
J WereportthedetectionofoscillationsinslenderCaIIHfibrils(SCFs)fromhigh-resolutionobservationsac-
quiredwiththeSUNRISEballoon-bornesolarobservatory. TheSCFsshowobviousoscillationsintheirinten-
0
sity, butalsotheirwidth. Theoscillatorybehaviorsareinvestigatedatseveralpositionsalongtheaxesofthe
1
SCFs. A large majority of fibrils show signs of oscillations in intensity. Their periods and phase speeds are

analyzedusingawaveletanalysis. Thewidthandintensityperturbationshaveoverlappingdistributionsofthe
]
R waveperiod.
The obtained distributions have median values of the period of 32±17s and 36±25s, respectively. We
S
h. findthatthefluctuationsofbothparameterspropagateintheSCFswithspeedsof11+−4191km/sand15+−3145km/s,
respectively.Furthermore,thewidthandintensityoscillationshaveastrongtendencytobeeitherinanti-phase,
p
or,toasmallerextent,inphase. Thissuggeststhattheoscillationsofbothparametersarecausedbythesame
-
o wavemodeandthatthewavesarelikelypropagating. Takingalltheevidencetogether, themostlikelywave
r modetoexplainallmeasurementsandcriteriaisthefastsausagemode.
t
s Keywords:Sun: chromosphere–Sun: oscillations–Sun: magneticfields–techniques: imaging
a
[

1. INTRODUCTION andspicules(DePontieuetal.2007;Linetal.2007;Pietarila
1
v Magnetohydrodynamic(MHD) waveshave beenobserved et al. 2011; Okamoto & De Pontieu 2011; Tsiropoula et al.
1 in various plasma structures in the solar atmosphere, partic- 2012).
0 ularlyinelongatedfeaturesinthesolarchromosphereandin Images recorded in the CaIIK passband (with a filter
8 thecorona(forrecentreviewssee,e.g.,Banerjeeetal.2007; widthof1.5Å)withthe1-mSwedishSolarTelescope(SST;
2 Zaqarashvili & Erdélyi 2009; Mathioudakis et al. 2013; Jess Scharmer et al. 2003) in an active region close to the solar
0 et al. 2015). According to the theory of MHD oscillations, disk center revealed the presence of slender, bright fibrils,
1. thewavesmayappearasasinglemode, orasacombination extendingseeminglyhorizontallyinthelowerchromosphere
0 of several modes (i.e., kink, sausage, torsional, or longitudi- (Pietarila et al. 2009). Only recently, the second flight of
7 nal)withdistinctpropertiesanddifferentobservationalsigna- the 1-m balloon-borne solar observatory SUNRISE (Solanki
1 tures(Edwin&Roberts1983). Thesewavesareoftenexcited etal.2010;Bartholetal.2011;Berkefeldetal.2011;Solanki
: atphotosphericheights(e.g. bygranularbuffeting, Evans& etal.2016)provideduswithahighquality,seeing-freetime-
v
i Roberts 1990, or vortex motion, Kitiashvili et al. 2011), and series of CaIIH images (with a filter width of 1.1Å). The
X either propagate away from their source, or form a standing relatively long duration of the observations (one hour) in an
r oscillation. activeregion(closetodiskcenter)enabledathoroughstudy
a While transverse waves, such as kink or global Alfvénic ofpropertiesoftheslenderfibrils(Gafeiraetal.2016). Inad-
modes cause swaying of a flux tube or of an elongated fea- dition,Jafarzadehetal.(2016b)havefoundubiquitoustrans-
ture, sausage-mode oscillations result in a periodic axisym- versewavesintheslenderCaIIHfibrils(SCFs)in SUNRISE
metricexpansionandcontractionofthestructureatoneposi- data. TheSCFshavebeenshowntomapthemagneticfields
tion. Torsional or twisting motions are associated with tor- inthelowsolarchromosphere(Jafarzadehetal.2016a). Ear-
sional Alfvén waves propagating along the axis of fibrillar lier, (Pietarila et al. 2009) had shown that the fibrils, or the
structures(e.g.,Spruit1982;Solanki1993). magneticcanopyoutlinedbythem,eithersuppressedoscilla-
Thedifferentwavemodesinelongatedstructureshavebeen tions or channeled low frequency oscillations into the chro-
mostly observed at coronal heights in, e.g., coronal loops mosphere,dependingontheirlocation.
(e.g.,Aschwandenetal.1999;DeMoorteletal.2002;Wang Inthispaperweinvestigatewidthandintensityoscillations
etal.2002;Wang&Solanki2004;Tomczyketal.2007;Sri- intheSCFsobservedwith SUNRISE. Periodsofthefluctua-
vastava et al. 2008; Nakariakov et al. 2012, see Nakariakov tionsinindividualSCFsaredeterminedandthephasespeed
&Verwichte2005forareview),aswellasattheupperchro- ofthewavespropagatingalongthethinstructuresarequanti-
mosphericlevelsinfeaturessuchasfilaments,fibrils,mottles fied(Sect.3). WediscussourresultsinSect.4,wherewealso
2 GAFEIRAETAL.
conclude that the observed oscillations are likely manifesta-
tionsofsausagewavestravelingalongthefibrils.
2. OBSERVATIONS
For the present study we use the data set described in QR
Gafeira et al. (2016), Jafarzadeh et al. (2016b), and Solanki
et al. (2016). The data set includes high spatial and tempo-
ralresolutionobservationsofanactiveregionobtainedinthe
CaIIHpassband(withafullwidthathalfmaximum,FWHM,
of ≈ 1.1Å) of the SUNRISE Filter Imager (SUFI, Gandor-
feret al.2011) onthe 1-meter SUNRISE balloon-bornesolar
observatory (Solanki et al. 2010; Barthol et al. 2011; Berke-
feldetal.2011)duringitssecondscienceflight(Solankietal.
2016). The observations were obtained between 23:39 UT
on 2013 June 12 and 00:38 UT on 2013 June 13 with a ca-
denceof7s. TheseobservationscoveredapartofNOAAAR
11768, mainly its following polarity that was dominated by
aseriesofpores,someofwhichlieatleastpartlywithinthe
SUFI field-of-view (FOV). The FOV also contained a num-
ber of plage elements and two granulation-scale flux emer-
gences(e.g.,Centenoetal.2016). TheFOVwascenteredat
µ=cosθ=0.93,whereθistheheliocentricangle.
Fig. 1 illustrates a CaIIH image (right panel) along with
its co-spatial and co-temporal photospheric filtergram (left
panel) recorded at 300nm with the SUNRISE/SUFI instru-
ment. ThearrowontheCaIIHimagemarksanexampleSCF
studiedhere. Alltheintensityvalueswherenormalizedtothe
meanintensityoftherelativelyquietregion,indicatedbythe
whiteboxinthetopleftcorneroftheFig.1.
TheCaIIHimagehasboth,aphotosphericandalowchro-
mospheric component. The latter is strongly enhanced in an
activeregion(Danilovicetal.2014;Jafarzadehetal.2016a). Figure1. : Right: Example of a CaIIH image recorded by
ThefibrilsdominatingmuchoftheCaIIHimageareexpected SUNRISE/SUFI.Left: Animagerecordedat300nm,aligned
tobelocatedinthelowerchromosphere,asnoneofthephoto- withtheCaIIHfiltergram. Thewhitearrowintherightpanel
sphericchannelsonSUNRISEevenremotelyshowsanysigns indicatesasampleslenderCaIIHfibril(SCF).Thewhitebox
ofsuchfibrils(seeJafarzadehetal.2016a). marksthequietregion(QR)usedtonormalizetheintensities
intheCaIIHand300nmimages.
3. ANALYSISANDRESULTS
To analyze both, the intensity and width variations of the calculatedfromequallyspacedlinesperpendiculartothisref-
SCFs with time, we first have to extract the fibrils from the erencebackbone. Thismeshisbasedonthefibrilbackbone,
CaIIH filtergrams. We follow the identification and track- i.e. the temporal average of all fibrils, and is therefore time-
ing method described in detail in Gafeira et al. (2016). In a independent,allowingthestudyofthetemporalvariationsof
firststep,thismethoddefinesabinarymaskofallthefibrils. its brightness and width. We use a mesh with a fixed total
Thismaskisobtainedbyapplyinganunsharpmaskingandan width of 1.2(cid:48)(cid:48) for all the fibrils, while the length is the same
adaptive histogram equalization method to the intensity im- as the reference backbone of each individual SCF. This pro-
agestoincreasetheircontrast. Intheseimages,athresholdof cedureresultsinatotalnumberof598detectedSCFoverthe
50% of the maximum intensity defines the binary mask iso- fulldatasetwithlifetimesof35sorlonger.
lating the fibrils from the background. All features smaller Using this approach, we straightened each identified SCF
than the diffraction limit of the telescope are discarded. For in each image (observed at different times) by interpolating
the temporal evolution of a fibril we require at least 10 pix- its intensity onto every point of the mesh. After these steps
elsofthefibriltobevisibleatthesamepositioninatleast5 we can represent the SCF along a straight line, as shown in
outof6subsequentframes,correspondingtoaminimumlife- Fig. 3 for an example fibril pictured at 40 time steps. Every
timeof35s. Inalltheseframes, afibrilbackboneisdefined black-framed box in Fig. 3 includes the straightened SCF at
as the line equidistant to the fibril’s border. A second order a given time. This way of stacking the temporal snapshots
polynomialisfittedtoallbackbonesoftheindividualfibrils. of a fibril allows us to easily follow fluctuations of its inten-
Fibrilsofcomplexshape, thatarepoorlyfitted, areexcluded sity(andwithsomeadditionaleffortalsoofitswidth)atany
fromtheanalysis. Weextendthisfittedcurveby0.3(cid:48)(cid:48) inboth location along the reference backbone of the SCF during its
end points, the approximate width of a fibril, to compensate entire lifetime. Thus we can identify different types of os-
forthereductionofthefibriltoasingle-pixelstructure. The cillations/pulsations in these structures. The example shown
resultinglineiswhatwecallthereferencebackbone(seered in Fig. 3 illustrates a clear fluctuation of the intensity with a
line in Fig. 2). For more details, we refer to Gafeira et al. period of approximately 147s (21 frames), indicated by the
(2016). This reference backbone is the central line for the double-headedverticalarrow.
mesh, displayed in Fig. 2. All other points of the mesh are Toinspectthefluctuationsinboth, theintensityrelativeto
OSCILLATIONSONWIDTHANDINTENSITYOFSLENDERCAIIHFIBRILS 3
Figure2.: Illustration of backbones of a sample SCF (at dif-
ferent times and averaged) and the grid associated with the
SCF.Theindividualbackbonesofthisfibrildeterminedinthe
imagesrecordedatdifferenttimesarerepresentedbytheindi-
vidualblacklines. Thereferencebackboneisrepresentedby
theredlineandthemeshisshownbytheblackgrid.
themeanintensityofthequietSun,andthewidthoftheSCFs
in detail, we evaluate the intensity at 17 positions along the
backboneofthefibril(lyingbetween20and80percentofthe
full length of the reference backbone measured from one of
itsends),perpendiculartowhichwecreateartificialslits(that
correspond to a given set of x positions in the mesh frame).
We then compute the position of the maximum intensity of
the fibril, the intensity at this position, as well as the width Position
of the fibril along each of these slits following the method
outlinedfurtherbelow.
Insomecasesasecondfibrilmaybepresentinsidethemesh
Figure3. : Temporal variation of a SCF. The images of a
determined for one fibril, usually near the edge of the mesh.
straightenedfibrilatdifferenttimesareverticallystacked. In-
Asaresult,morethanonelocalmaximumispresentalongthe
dividualimages,recordedevery7s,areseparatedbyhorizon-
artificial slit used for the determination of the fibril’s width.
talblacklines. Theverticalarrowindicatestheperiodofthe
Insuchcases,wechoosethelocalmaximumwhichiscloser
fibril’s intensity fluctuation. The colour represents intensity,
to the center of the mesh, i.e., the reference backbone of the
normalized to the mean value of the quiet region marked in
fibril.
Fig.1.
ThewidthofafibriliscomputedbyfittingaGaussianfunc-
tion plus a linear background to the intensity profile perpen-
3.1. Waveletanalysis
diculartothebackbone. Tominimizetheinfluenceofneigh-
boringfibrils,thesixpointsclosesttothemaximumintensity We apply a wavelet analysis to characterize the temporal
positionaregiven30%higherweights.TheFWHMofthefit- variation of the power spectrum of the width and intensity
tedGaussiandefinesthefibrilwidth. InFig.4wepresentan oscillations. We use the wavelet algorithm described by Ja-
exampleofthesemeasurements,wherepositionsofthemaxi- farzadeh et al. (2016c). For the cases with a clear intensity
mumintensity(redcircles)andthewidthofthefibril(vertical and width oscillation, we also calculate cross power spectra,
black lines) are marked at various positions along the SCF i.e., the multiplication of the wavelet power spectrum of the
(within each image) and at different times (from one image oscillationinagivenquantityatonepositionalongthefibril
in the stack to the next). For better visibility, we have cho- by the complex conjugate of the same wavelet power spec-
sen a relatively short-lived SCF for clarity (i.e., we need to trum at a different location along the same fibril. This pro-
showfewertime-steps). Theplotclearlyshowsthatthewidth vides us with the phase differences between the consecutive
isbiggerinthebrighterpartofthefibril. Thewaythewidth positionsinwidthandintensityoscillations, andhence, with
isdetermined(seeabove),isindependentofthefibril’sinten- thephasespeedofthewavesalongthefibrils.Finally,wealso
sity,aslongastheprofileshapeoftheintensityperpendicular determinethewaveletcrosspowerspectrumbetweenbright-
tothefibril’saxisdoesnotchangeandthefibril’sintensityis nessandwidthoscillationsthatprovidesthephasedifference
higherthanthebackground. Wenotethatthelocationsalong betweenthem.
the fibrils are determined only as long as the intensity along In some cases, the determination of the maximum inten-
the SCF is larger than the average intensity of the image at sityandwidthofafibrilatsomepositionsalongthefibrilat
eachtime-step. Therefore, thepositionsclosetotheleftend a given time is difficult, leading to gaps in some of the 17
of the example SCF shown in Fig. 4 are not detected at all positions along the fibril backbone. These gaps are filled by
times. linearly interpolating in time to provide the wavelet analysis
4 GAFEIRAETAL.
(within a given fibril). The most likely phase speed of the
waveisdeterminedinthesamewayfromthewavelet-cross-
power spectrum between different spatial locations along a
fibril. Only the highest peaks that are above the 95% confi-
dence leveland inside thecone of influence(i.e., frequency-
time areas that are not influenced by the ends of the time-
70 series)areconsidered.
3.2. Statistics
Thetwo-dimensionalhistogramofintensityandwidthpe-
riodspresentedinFig.5demonstratesthatmostofthefibrils
56 oscillatewithperiodsbetween20sand40sinbothquantities,
with median values of 32±17s and 36±25s for the peri-
odsofthewidthandintensityoscillations,respectively. Fora
largefractionofthefibrils(≈75%)theperiodsinbothquanti-
tiesaresimilar.Forthephasespeedsweobtainmedianvalues
42 of 11+49km/s and 15+34km/s for width and intensity oscil-
−11 −15
lations, respectively, without any correlation between them.
These median periods are rather short, well below the cut-
off frequency of the atmosphere, while the phase speeds are
above the sound speed in the temperature minimum region
28 andlowerchromosphere.
120 1.0
0.9
14
100 0.8
y
[s] 0.7 bilit
d a
o 80 0.6 b
eri pro
Position nsity p 60 00..45 alized
te 0.3 m
n r
I 40 o
Figure4.: An example of intensity maxima and width detec- 0.2 N
tions along cuts perpendicular to the axis of a SCF. Plotted
0.1
are vertically stacked images of a fibril recorded in CaIIH 20
observed at different times. Individual images, recorded ev- 0.0
20 40 60 80 100 120
ery7s, areseparatedbyhorizontalblacklines. Thereddots
within a given image represent the locations of the fibril’s Width period [s]
maximumintensityalongaseriesofcutsroughlyperpendicu-
Figure5. : Two-dimensional histogram showing the relation
lartothebackboneofthefibril,whiletheverticalblacklines
betweentheperiodsofthewidthandtheintensityoscillations
indicate the width of the fibril at the same locations. The
in SCFs. The bin size follows the period resolution that is
colour represents intensity, normalized to the mean value of
limited by the life time of the fibrils. The black curved line
the quiet region in the SUFI frame (marked in Fig. 1). The
indicatesthe95%confidencelevel.
whitearrowinthelowerpartofthebottomimagemarksthe
location at which the oscillations plotted in Fig. 7 occurred.
NotethatthisfibrilisnotthesameaspresentedinFig.3. We computed the wavelet cross-power spectra between
width and intensity oscillations within a given cut across a
SCFanddeterminedthephaselagbetweentheoscillationsin
with equidistant data points. Such interpolations can result
these quantities. A wide range of phase lags was obtained.
in overestimation of, e.g., periods of the oscillations. Gaps
Fig. 6 illustrates the distribution of values of this quantity.
are sufficiently rare, however, that their influence turned out
The distribution has two clear peaks, a weaker one at 0◦ (in
to be relatively insignificant. We find that 74% of the fibrils
phase), and strong peak at 180◦ (anti phase). As an exam-
display above 95% confidence level (inside the cone of in-
pleforsuchananti-phaseoscillationwepresentinFig.7the
fluence)oscillationsinintensity,withonaverage42%ofthe
temporalevolutionoffibrilwidthandintensityofthesample
cuts along each oscillating fibril displaying such an oscilla-
SCFatthepositionindicatedbyawhitearrowinFig.4.
tion. Similarly, 82% of the fibrils exhibit oscillations of the
width,whereby38%ofthecutsthroughthebackboneofos-
4. DISCUSSIONANDCONCLUSIONS
cillating fibrils show the oscillations (on average). For the
fibrils displaying an oscillation with a sufficiently high con- We have provided observational evidence for oscillations
fidence, the frequency at which the wavelet power spectrum of the width of fibrils and of intensity along slender CaIIH
hasitsstrongestpeakistakenastheperiodoftheoscillation fibrils(SCFs)inthelowerchromosphere.
OSCILLATIONSONWIDTHANDINTENSITYOFSLENDERCAIIHFIBRILS 5
0.006 tively. Again, uncertainty intervals reflect standard devia-
e
c tions. Given that these waves display brightness and width
n
urre0.005 signatures, they have to be compressible, ruling out Alfvén
c waves. Simultaneous periodic fluctuations of intensity and
c
of o0.004 width in elongated structures are manifested by either slow-
y mode waves or fast sausage-mode waves (Van Doorsselaere
c
en0.003 etal.2011;Suetal.2012). Inadditiontoobservationsofthe
qu latter wave mode in the upper solar atmosphere (i.e., in the
e
ed fr0.002 useprpvearticohnrsomofossapuhseargeeanodsciinlltahtieocnosrohnavae,Ianlgsloisbeeteanl.r2e0p0o9rt)e,doba-t
s
ali0.001 loweratmosphericheights,instructuressuchaspores(Doro-
m tovicˇ etal.2008;Mortonetal.2011).
or
N To distinguish which wave modes are present in the SCFs
0.000
150 100 50 0 50 100 150 weneedtocomparethephasespeedsoftheoscillationswith
Phase difference the expected plasma Alfvén and sound speeds. The values
Figure6.:Distributionofphasedifferencesbetweenwidthand for the Alfvén and sound speeds were computed using the
intensity oscillations in the SCFs at a given cut across each NC5flux-tubefrom(Bruls&Solanki1993)embeddedinthe
fibril. VAL-Aatmosphere(Vernazzaetal.1981). Foramajorityof
the detected waves these velocities are larger than the sound
speedatthelowchromosphericheightssampledbytheSUFI
1.1Å CaIIH filter, which lies around 7km/s. The measured
phasespeedsarecomparabletothelocalAlfvénspeedforthis
heightregion,withtypicalvaluesintherangeof7–25km/s.
Interestingly,20%oftheSCFsshowphasedifferencesbe-
tween −30◦ and +30◦, indicative of in-phase oscillations. A
strong peak was found at 180◦, with about 50% of all os-
cillations having a phase difference within 30◦ of 180◦ (anti
phaseoscillations). Phasedifferencesofaround±90◦arerel-
ativelyuncommon.
A phase difference in the range of |150◦−180◦|, as dis-
played by the example shown in Fig. 7, is consistent with
the signature of sausage-mode oscillations in the SCFs un-
der the assumption of an optically thin plasma. The validity
ofthisassumptionisconfirmedbythefactthattheobserved
intensityincreasesattheintersectionpointsofcrossingSCFs,
suggesting that we can partly see through individual fibrils.
Thecontractionofthefibrilcausedbythesausage-modeos-
cillation leads to a narrow fibril with a higher density. In an
Figure7.: Anexampleofaclearanti-correlationbetweenos- optically thin regime, a higher density implies an increased
cillations in maximum intensity (blue line) and width (red intensity. The subsequent expansion phase of the oscillation
line) of the sample SCF in Fig. 4, at the location marked by leads to an increase of the fibril’s width at lower intensity.
the white arrow in the lowest panel of that figure. The error Forsuchaplasma,theintensityfollowstheelectrondensity.
bars represent the standard deviations of the photon counts However, a detailed model of the brightening of these struc-
fortheintensity,andtheuncertaintiesoftheGaussianfitting turesisrequiredtodeterminethebehaviouroftheplasmaun-
tothecross-sectionofthefibrilforthewidth. derconditionstypicalofthelowerchromosphere.
In about 25% of our SCFs we did not find a clear correla-
tion between the fluctuations in the two parameters. The in-
The high-resolution, seeing-free images under study were
tensityoscillationscouldalsobecausedbyslowmodewaves,
recordedwithSUNRISE/SUFIandrevealedthatsuchoscilla-
whichareexpectedtobepresentinsidestrong-fieldmagnetic
tions are almost ubiquitous all over the field of view, which
features,suchasfluxtubes(althoughitisuncleartowhatex-
covered part of NOAA AR 11768. Fluctuations in length of
tent the SCFs can be described as flux tubes). However, the
someoftheSCFswerealsoobserved,althoughitisnotclear
median phase speeds obtained in our analysis are too high
howindependentthisparameterisfromtheintensity.
for slow mode waves. Only for a few SCFs do we obtain
The oscillatory behavior of both parameters (i.e., fibril
lowphasespeedsthatmaywellbecompatiblewiththeslow
width and intensity) was identified in wavelet power spectra
mode.
determinedataseriesoflocationsalongthebackboneofeach
Toourknowledge,ourobservationsofsausagemodeoscil-
detected SCF. The wavelet transform was employed to ana-
lations in the SCFs are the first direct evidence of this wave
lyzethefluctuations,fromwhichmedianperiodsof32±17s
modeinthelowersolarchromosphere. Mortonetal.(2012)
and 36±25s were obtained for the width and intensity os-
inspectedoscillationsofwidthandintensityinHαelongated
cillations, respectively, with the uncertainty intervals repre-
fibrils and short mottles (in the upper chromosphere). They
senting the standard deviations of each distribution. Cross
found a phase speed of 67±15km/s for their MHD fast
powerspectrabetweentheperturbationsatdifferentlocations
sausage waves, which is much larger than those we found
along a given fibril revealed phase speeds of 11+49km/s and
−11 in the SCFs. Like us, they also found a phase difference of
15+34km/s for the width and intensity fluctuations, respec-
−15
6 GAFEIRAETAL.
180◦betweentheirdetectedintensityandwidthperturbations. DePontieu,B.,McIntosh,S.W.,Carlsson,M.,etal.2007,Science,318,
Dorotovicˇ etal.(2008)andMortonetal.(2012)showedthat 1574
theenergythesesausagewavescarryissufficienttocontribute Dorotovicˇ,I.,Erdélyi,R.,&Karlovský,V.2008,inIAUSymposium,Vol.
247,WavesOscillationsintheSolarAtmosphere:Heatingand
(around 10%) to the heating of the chromosphere and/or the
Magneto-Seismology,ed.R.Erdélyi&C.A.Mendoza-Briceno,351
corona. Jess et al. (2012) claim to see a fluctuation of the
Edwin,P.M.&Roberts,B.1983,Sol.Phys.,88,179
widthofwhattheycallachromosphericspicule(observedon Evans,D.J.&Roberts,B.1990,ApJ,348,346
thediskasanHαdarkfibril).Theyinterpretthesefluctuations Gafeira,R.,Solanki,S.K.,Lagg,A.,etal.2016,ApJS,inpress(thisissue),
assausagemodesinthechromosphere. arXiv:1612.00319
Gandorfer,A.,Grauf,B.,Barthol,P.,etal.2011,Sol.Phys.,268,35
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toadvanceourknowledgeandunderstandingofthedetected A&A,503,569
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velocities, wouldhelptodistinguishbetterbetweendifferent issue),arXiv:1610.03104
possible wave modes. Another important step is to compute Jafarzadeh,S.,Solanki,S.K.,Gafeira,R.,etal.2016b,ApJS,inpress(this
issue),arXiv:1610.07449
MHD wave modes in simple models of fibrils, possibly de-
Jafarzadeh,S.,Solanki,S.K.,Stangalini,M.,etal.2016c,ApJS,inpress
scribedasflux tubesembeddedina magnetizedgas. Sucha (thisissue),arXiv:1611.09302
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anceforfutureobservationsandtheirinterpretation. Finally, ApJ,727,L50
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