Table Of ContentDraft version January 8, 2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
HOMOLOGOUS HELICAL JETS: OBSERVATIONS BY IRIS, SDO AND HINODE
AND MAGNETIC MODELING WITH DATA-DRIVEN SIMULATIONS
Mark C. M. Cheung1, B. De Pontieu1,2, T. D. Tarbell1, Y. Fu1,3, H. Tian4, P. Testa4, K. K. Reeves4,
J. Mart´ınez-Sykora1,5, P. Boerner1, J. P. Wu¨lser1, J. Lemen1, A. M. Title1, N. Hurlburt1, L. Kleint6 ,
C. Kankelborg7, S. Jaeggli7, L. Golub4, S. McKillop4, S. Saar4, M. Carlsson2 and V. Hansteen2.
1. LockheedMartinSolarandAstrophysicsLaboratory,3251HanoverStreetBldg. 252,PaloAlto,CA94304,USA
2. InstituteofTheoreticalAstrophysics,UniversityofOslo,P.O.Box1029,Blindern,NO-0315Oslo,Norway
3. SpaceSciencesLaboratory,UniversityofCalifornia,Berkeley,7GaussWay,Berkeley,CA94720,USA
4. Harvard-SmithsonianCenterforAstrophysics,60GardenStreet,Cambridge,MA02138,USA
5. BayAreaEnvironmentalResearchInstitute,6252ndSt. Ste209,Petaluma,CA94952
6. UniversityofAppliedSciencesandArtsNorthwesternSwitzerland,Bahnhofstr. 6,5210Windisch,Switzerlandand
5
7. DepartmentofPhysics,MontanaStateUniversity,Bozeman,P.O.Box173840,Bozeman,MT59717,USA
1
Draft version January 8, 2015
0
2 ABSTRACT
n We report on observations of recurrent jets by instruments onboard the Interface Region Imaging
a Spectrograph (IRIS), Solar Dynamics Observatory (SDO) and Hinode spacecrafts. Over a 4-hour
J periodonJuly21st2013, recurrentcoronaljetswereobservedtoemanatefromNOAAActiveRegion
7 11793. FUV spectra probing plasma at transition region temperatures show evidence of oppositely
directed flows with components reaching Doppler velocities of ±100 km s−1. Raster Doppler maps
] using a Si IV transition region line show all four jets to have helical motion of the same sense.
R
SimultaneousobservationsoftheregionbySDOandHinodeshowthatthejetsemanatefromasource
S region comprising a pore embedded in the interior of a supergranule. The parasitic pore has opposite
. polarity flux compared to the surrounding network field. This leads to a spine-fan magnetic topology
h
p in the coronal field that is amenable to jet formation. Time-dependent data-driven simulations are
- used to investigate the underlying drivers for the jets. These numerical experiments show that the
o emergence of current-carrying magnetic field in the vicinity of the pore supplies the magnetic twist
r needed for recurrent helical jet formation.
t
s Subject headings: Sun: photosphere – Sun: chromosphere – Sun: transition region – Sun: corona –
a
Sun: atmosphere – magnetic fields
[
1
v 1. INTRODUCTION larDynamicsObservatory(SDO,Pesnelletal.2012)and
3 Since the discovery of coronal jets in X-ray (e.g. Shi- bytheInterfaceRegionImagingSpectrograph(IRIS,De
9 Pontieuetal.2014). Section3presentsphotosphericob-
bata et al. 1992) and EUV (e.g. Chae et al. 1999) imag-
5 servations in and around the source region of the jets by
ing observations, there has been a growing body of ob-
1 the Solar Optical Telescope (SOT, Tsuneta et al. 2008)
servational and theoretical work investigating the phys-
0 onboard the Hinode spacecraft (Kosugi et al. 2007).
ical mechanisms behind this phenomena. While the de-
. Section4.1describestheevolutionofthephotospheric
1 tailed physical processes responsible for the acceleration
0 of jet material depends on the local conditions (e.g. see field in the region of interest as revealed by vector
5 Takasaoetal. 2013),thereisoverwhelmingevidencethat magnetograms from the Helioseismic and Magnetic Im-
1 magneticreconnectioniskeyfortheimpulsiveenergyre- ager (HMI, Scherrer et al. 2012; Schou et al. 2012) on-
v: lease associated with jets. As for the driving mechanism boardSDO.Section4.2presentsresultsfromsimulations
of coronal and chromospheric field evolution driven by
i thatallowsforenergybuild-up,ithasbeenreportedthat
X many jets are associated with emerging flux and/or flux HMIvectormagnetograms. Thephysicalimplicationsof
this study are discussed in section 5.
r cancellationeventsinthephotosphere. Inthecaseofre-
a currentjets(e.g.Chaeetal.1999;Chiforetal.2008;Guo
2. OBSERVATIONALEVIDENCEFORHOMOLOGOUS,
et al. 2013; Schmieder et al. 2013; Chandra et al. 2015)
HELICALJETS
emanating from the same source region on the Sun, an
The recurrent jets and the source region of these jets
additional question is how the underlying driver leads to
were simultaneously observed by IRIS, SDO and Hin-
magneticconfigurationsthatrepeatedlyerupttoproduce
ode. Instruments onboard these satellites provide com-
jets of a homologous nature.
plementarycoverageinwavelength,temperatureandthe
We address the question posed above by performing a
spatiotemporal domains. Together they present an inte-
study of recurrent jets observed by multiple spaceborne
gratedpictureofthemagneticandatmosphericenviron-
observatories and by using data-driven simulations. The
ment responsible for driving and initiating the set of re-
rest of the article is structured as follows. Section 2
current jets. The following sections discuss observations
presents observations of the jets in the transition region
of the region of interest as seen by the various instru-
andcoronabytheAtmosphericImagingAssembly(AIA,
ments.
Lemen et al. 2012; Boerner et al. 2012) onboard the So-
2.1. Photospheric and coronal observations by SDO
[email protected]
2
Continuous full disk observations from SDO provide threedifferentpositionsindicatedbytheblue,greenand
context about the environment in which the recurrent red cursors straddling the jet in the slit-jaw image. We
jets are generated. Fig. 1 shows the large-scale structure first inspect the profiles of the Si iv lines at 1393.8 and
of active region (AR) 11793 in the time period during 1402.8 ˚A. Both are transition region lines that form at
whichIRISobservedtherecurrentjets. Duringthistime logT/K ∼ 4.9 (from CHIANTI 7.0, Landi et al. 2012).
range the AR is roughly centered at a Stonyhurst longi- For this reason, the shapes of the line profiles are very
tude and latitude of W11 deg and N23 deg, respectively. similar. By visual inspection, it can be discerned that
We refer to each of the four observed jets as J1, J2, J3 the Si iv line profiles at the three positions have very
and J4 in chronological order. The four jets are shown different bulk Doppler shifts. While the centroids of the
in separate panels of Fig. 1. Each panel consists of blue and green profiles have blueshifts of ≈ 80 and 30
a HMI line-of-sight magnetogram (from the hmi.M 45s km s−1, respectively, the centroid of the red profile is
data series) overlaid with an EUV image from the AIA clearly redshifted. The spectral profiles at all three loca-
94 ˚A channel. The aia prep.pro routine in SolarSoft tions have wide wings with contributions beyond ±100
was used to align the full disk images from the two in- km s−1 relative to the centroid positions. The spectral
struments and to remap them to a common plate-scale readout window of Si iv 1403 spectra includes the O iv
of 0.6 arcsec per pixel. Inspection of the overlaid im- 1401 line, which forms at logT ∼ 5.2. The signal from
ages (and accompanying animation, available online) re- this line appears in the plotted Si iv 1403 spectra at
veal that the jets emanate from a strong plage region in Doppler shifts beyond −300 km s−1.
the northeastern edge of the leading (negative) polarity The bottom panel of the right column in Fig 2 shows
patch of the AR. spectra for the Cii lines, which are expected to form at
Though the jets are not identical, they possess strik- logT/K ∼4.4(fromCHIANTI7.0,Landietal.2012). In
ingly similar features. First of all, the ejecta in the jets the plots the rest wavelength of the red line (1335.71 ˚A)
are channeled into closed loops connecting the leading was used to calculate the effective Doppler shift. The
and trailing polarities of the AR. This is unlike some shapes of the C ii lines are much more complex than
jets found in coronal hole regions, in which jet material thoseoftheSiivlines. Theprofilesatthegreenandred
is channeled into open magnetic field lines (e.g. Cirtain cursor positions are bimodal. However the green profile
et al. 2007; Savcheva et al. 2007; Moreno-Insertis et al. has a higher amplitude peak on the blue side of the line
2008; Patsourakos et al. 2008). Secondly, each of the jet while the red line has a higher amplitude peak on the
eventscanbeconsideredtopossessatwo-partstructure, red side. Even more complex is the blue profile, which
namelytheinclinedjetitselfaccompaniedbythebright- has a trimodal shape. One may initially be tempted to
eningofacompactclosedloop(ormultipleclosedloops) interpret the bimodal profiles in terms of oppositely di-
adjacent to the jet (Shibata et al. 1994; Shimojo et al. rected Doppler flows. However, we caution that the Cii
1996). Itisworthnotingthatthejetscanalsobeidenti- linesareusuallyopticallythick,sothedipinbimodal(or
fied in the other EUV channels. This likely implies that trimodal) line profiles likely results from opacity effects.
they have multithermal structure. Fig. 3 is similar to Fig. 2 but for J3. There are many
In all four cases, the footpoints of the bright compact qualitative similarities between the profiles in these jets.
loopsclosesttothejetsarefoundinthenegativepolarity For instance the red and blue colored profiles here show
network whereas the conjugate footpoints are located at bulk red- and blueshifts, respectively. In the case of J3,
a parasitic polarity patch within an adjacent supergran- thelinesareevenbroader(withcontributionsupto±200
ule. We will discuss the magnetic configuration of the km s−1 relative to the centroid position) and the pair of
environment around the jets in sections 3 and 4. Ciilinesarenowcompletelyblended. Thegreenprofiles
for the Si IV lines in Fig. 3 show a bimodal structure.
2.2. Transition region observations by IRIS This is probably different than the two-component spec-
tral profiles studied by Tian et al. (2012) in their study
Between11:34and16:34UTCon2013-07-21,IRISran
of EUV jets. In their case, they performed a double
amediumcoarse20-steprasterobservationprogramwith
GaussianfittospectralprofilestakenbytheEUVImag-
150 repeats on the region of interest. The field-of-view
ing Spectrograph (EIS) instrument onboard Hinode and
ofslit-jawimages(SJI)is60(cid:48)(cid:48)×60(cid:48)(cid:48) andtheapproximate
found that one component corresponds to steady back-
pointing is indicated by the yellow box in the top right
ground emission, while a blue-shifted second component
panelofFig.1. Therasterstepsizeis2(cid:48)(cid:48) soeachspectral
is attributed to outflows from the jet. In our case (green
rasterspansaFOVof38(cid:48)(cid:48)×60(cid:48)(cid:48). Eachrepeatofaspectral SiIV 1394 profile in Fig. 3), one component has a bulk
raster is accompanied by five slit-jaw images in each of
redshift while the other component has a bulk blueshift.
the C ii 1330, Si iv 1400 and Mg II k 2796 channels
Inspection of corresponding profiles at positions north
and one continuum image in 2832. Level 2 data was
and south of this location (i.e., as indicated by the blue
used for all of the following analysis. Slit-jaw images in
and red cursors on the slit-jaw image) shows the pro-
the level 2 data product are dark-subtracted, flatfielded
file to the north has a blueshifted component, while the
andgeometricallycorrectedsothatimagesfromdifferent
profile to the south has a redshifted component. Since
channels are on a common grid. The same corrections
the profile sampled at the position of the green cursor
are applied to NUV and FUV spectra. Furthermore, the
is mid-way between the two, it is not surprising that
spectra are stacked as 3D raster cubes for convenient
the green spectral profile has both red- and blueshifted
analysis.
components. In contrast, the FUV line profiles in the
Figure 2 shows a Si iv 1400 slit-jaw image of J1.
post-impulsive phase (four minutes later, see Fig. 4) are
The spectrograph samples along the vertical dark slit at
dimmer by almost two orders of magnitude, are much
x=154arcsec. FUVspectrallineprofilesareplottedfor
Homologous Helical Jets 3
Figure 1. HMIline-of-sightmagnetograms(greyscale)overlaidwithAIA94˚Achannelimagesofthefourrecurrentjets. Theejectafrom
the jets are channeled into closed loops connected the leading and trailing polarities of AR 11793. The yellow box in the top right panel
showsthefieldofviewofIRISslit-jawimages.
Figure 2. Left: Siiv1400slit-jawimageofthefirstrecurrentjet. Right: Spectrallineprofilessampledattheblue,greenandredcursor
positions (all lying on the vertical slit) for Siiv 1403, Siiv 1394 and the pair of Cii lines at 1334 and 1336 (the rest wavelength of the
latterisusedasareference). ThespectraareplottedasfunctionsofDopplershiftfromtheirrespectiverestwavelengths.
4
Figure 3. SameasFig.2butforthethirdjet. TheFUVprofilesinthiscaseareevenbroader,withlineshavingcontributionsfromup
to±200kms−1 Dopplershiftsrelativetothecentroids.
Figure 4. Same as Fig. 3 but 4 min later. The jet has already subsided and the FUV profiles are also much narrower than during the
impulsivephaseofthejet.
Homologous Helical Jets 5
narrower and have zero mean Doppler shift. electron densities of logn / cm−5 =10.8−11.2.
e
The FUV line profiles for different locations spanning
3. PHYSICALDRIVERSOFRECURRENTHELICALJETS
the widths of J1 and J3 both indicate a bulk blueshift
near the northern edge of the jet and a bulk redshift ObservationsbySDO/AIAandIRISestablishthecase
nearitssouthernedge. Usingrasterscans,weinvestigate that the jets are homologous and helical in nature. The
whetherthisisapatternthatpertainstoallfourjets. As four jets are homologous in the sense that they share
per the above discussion, the Si iv 1394 line is simplest substantial similarity in their observed spatial structure
to analyze. Using this line, we calculate the zeroth and and evolution. This begs the question of the underlying
first moments drivingmechanismsthatleadtotheinitiationofthejets.
(cid:90) There is a large body of work using numerical MHD
I = dI (1) simulations to study how emergence of magnetic flux
line
into pre-existing coronal field initiates jets (Yokoyama
(cid:90)
& Shibata 1995; Miyagoshi & Yokoyama 2004; Archon-
(cid:104)v (cid:105)=I−1 Idv , (2)
line line los tis et al. 2005; Galsgaard et al. 2005; Isobe et al. 2007;
Moreno-Insertis et al. 2008; Nishizuka et al. 2008; Hegg-
where I is the spectrograph intensity (in DN sec−1
landetal.2009;Archontisetal.2010;Archontis&Hood
pixel−1) and vlos is the line-of-sight Doppler veloc- 2013; Moreno-Insertis & Galsgaard 2013; Takasao et al.
ity. Iline is simply the integrated intensity across the 2013;Fangetal.2014). Mostofthesimulationsfocuson
line. Over the field-of-view of the IRIS rasters, the single jets following reconnection between the emerging
ratio I1394/I1403 is generally close to the theoretical magnetic system with the ambient field. Recent work
value of 1.95 as predicted using CHIANTI (Landi et al. started to investigate how multiple jets can be emitted
2012), which suggests the Si IV lines are optically thin. from the same source region. From a 3D MHD simula-
Adopting this assumption, we interpret (cid:104)vline(cid:105) to be an tion of flux emergence, Archontis et al. (2010) reported
intensity-weighted mean Doppler velocity. that a series of reconnection events between the emerg-
Figure 5 shows raster maps of Iline and (cid:104)vline(cid:105) for the ingfluxsystemandambientcoronalfieldledtorecurrent
Si iv 1394 line for all four jets. While the amplitude of jets. Moreno-Insertis & Galsgaard (2013) performed a
(cid:104)vline(cid:105)islargerinsomejetsthanothers,allfourjetstend similar numerical experiment and found a succession of
tohaveblue-andredshiftsattheirupper(northern)and eruptions, some of which have physical properties that
loweredges(southern),respectively. Thistypeofspatial resembled the ‘standard’ type of jet while others were
pattern in Doppler maps have previously been detected miniaturefluxropeejectionsthatthatmaybeassociated
inindividualjets(Pike&Mason1998)andsurges(Curdt with so-called blowout jets (Moore et al. 2010). While
& Tian 2011). While Pike & Mason (1998) used data the Moreno-Insertis & Galsgaard (2013) paper mentions
from the Coronal Diagnostic Spectrometer (CDS, Har- that the erupting flux ropes in the simulation seem to
rison et al. 1995) and Curdt & Tian (2011) used data rotate as if they were converting twist into writhe, the
fromtheSolarUltravioletMeasurementsofEmittedRa- possible helical motion of the jets themselves were not
diation (SUMER, Wilhelm et al. 1995) instrument, both studied.
studies used the same O v transition region line, which Fang et al. (2014) modeled solar jets by performing
formsatlogT/K ∼5.4. Inbothstudies,thespatialpat- 3DMHDsimulationsoftwistedfluxtubesemerginginto
tern of Doppler shifts was taken as evidence for helical a coronal layer with an ambient inclined field. They
motion. We adopt the same interpretation and take our included magnetic field-aligned thermal conduction in
IRIS Doppler maps as evidence for helical motion in all their model, which provides the dominant mechanism
four of the recurrent jets. In a local Cartesian reference for energy loss by plasma that has been heated to tran-
frame where ˆl points along the jet (increasing height), sition region and coronal temperatures. They reported
the spatial pattern of (cid:104)v (cid:105) corresponds to rotational the existence of columnar jets consisting of plasma at
line
motion with vorticity ω = (∇×(cid:126)v) < 0. This implies a broad range of temperatures (chromospheric to coro-
l l
thekinetichelicityofplasmamotionassociatedwiththe nal). Due to acceleration by the Lorentz force acting on
jet is u ω <0 (by definition, u is positive since it is the reconnected field lines, the jet columns exhibit spinning
l l l
component of plasma flow along the jet direction). motion. Synthetic intensity-weighted Dopplergrams (us-
O iv lines observed in IRIS FUV spectra allow us ing coronal lines) of a simulated jet column from a side
to perform density diagnostics on the jet material. We perspective gives net Doppler shifts of ± 20 km s−1 on
used two different line ratios to measure the densities. opposite sides of the columnar jet axis.
The first is the ratio of the Oiv 1401.1 and 1404.8 lines. Recently, Lee et al. (2015) performed a 3D MHD sim-
The 1404.8 line is blended with a S IV line, so we used ulation of the emergence of a strongly twisted flux tube
the S IV 1406.02 line and the assumption of optically fromtheconvectionzoneintotheatmosphere. Theyim-
thin emission to extract the intensity of O iv 1404.8. parted a density deficit distribution to the tube so that
TheOiv1404.8lineisnotalwayspresentinthespectral twosegmentsofthetubewouldemergeandinteractwith
readout window of IRIS. However, in a number of slit each other as well as with the ambient inclined coronal
positions where there is sufficient blueshift, we find the field. The simulation yielded four episodes of twisted
ratio O iv 1401.1/1404.8 to be in the range 4.0−4.5. flux rope ejections carrying signicant mass loads away
For a temperature range of logT/K =4.5−5.5 (derived from the emerging flux region. These flux tubes untwist
fromtheratioofSIV1404.8toSIV1406.02),thisratio as they are ejected, resulting in signatures of torsional
gives densities ranging from logn / cm−5 =10.8−11.0. Alfv´en wave propagation.
e
Similarly, a ratio computed for the 1399 and 1401 lines Apart from magnetic flux emergence, there is another
of Oiv has values in the range 0.29−0.35, which yields means by which photospheric magnetic evolution can
6
(a) Jet1 (b) Jet2
(c) Jet3 (d) Jet4
Figure 5. Total intensity and mean Doppler velocity of the four jets as computed from IRIS observations of the Siiv 1394 line. In all
four jets, there is a tendency for northern edge to be blueshifted while the southern edge is redshifted. This spatial pattern suggests all
fourjetsarehelicalwiththesame(negative)signofkinetichelicity.
leadtojets,especiallythosewithrotationalmotion. One sisting of purely open magnetic field lines. About the
possibility of generating homologous helical jets was in- axis of symmetry of this parasitic pole, they applied ro-
vestigated by Pariat et al. (2009, 2010). In their numer- tationalmotionatafractionofthelocalAlfv´enspeedto
icalMHDstudies,theauthorsconsideredthescenarioin mimictwistingofthefieldduetohorizontalphotospheric
which a circularly shaped patch of magnetic flux is em- flows. Thenumericalsimulationsshowedthat,givensuf-
bedded in an environment with predominantly vertical ficient cumulative rotation (greater than one turn), the
field of the opposite sign. For convenience let us call the magnetic system is driven to a state where reconnection
circularly shaped patch of magnetic flux the ‘parasitic’ of the magnetic field allows it to impulsively release the
pole. The initial potential field configuration has a coro- storedmagneticenergy. Aconsequenceoftherelaxation
nal null with a fan that forms a quasi-separatrix (QSL). istheformationofahelicaljet. Subsequently, continued
The QSL separates two magnetic volumes, one consist- applicationofrotationaldrivingatthebottomboundary
ingofthesetofclosedfieldlinesconnectingtheparasitic led to the formation of similar helical jets.
pole with its surroundings, and an exterior volume con- The driving mechanism considered by Pariat et al.
Homologous Helical Jets 7
(2009, 2010) is in principle different to that of emerging thevicinityoftheparasiticpore. Thesebrightgrainpairs
flux in that only horizontal motions at the photosphere are separated by a dark lane with a length of 1−2 Mm.
is applied. However, the emergence of magnetic flux can This type of phenomena is a robust proxy for emerging
also drive systematic horizontal flows that shear already flux (e.g. Strous & Zwaan 1999; Cheung et al. 2008;
emergedfield(ManchesterIV2001;Magara&Longcope Guglielminoetal.2010)andtheirpresenceinthevicinity
2003; Manchester IV et al. 2004; Magara 2006; Cheung of the parasitic pore suggests flux emergence may play a
etal.2010;Fangetal.2010,2012;Cheung&Isobe2014, role in driving the recurrent jets.
, section 3.6.3). Emergence-driven shear flows can lead
toinjectionofmagneticenergyandmagnetichelicityfor 4. MAGNETICFIELDEVOLUTION
driving eruptive phenomena, including jets and CMEs. Inthissectionweinvestigatehowthemagneticfieldin
So the physical mechanism driving the recurrent jets re- thesourceregionofthejetsevolve,andhowthisleadsto
ported here may not be exclusively due to one scenario recurrent jet production. For this purpose we use HMI
or the other (i.e. flux emergence vs. shearing/rotational vectormagnetogramstodrivesimplifiednumericalmod-
motion). els of chromospheric and coronal field evolution.
To investigate the underlying physical driver(s) that
cause the observed helical jets, we examine observations 4.1. HMI Vector Magnetograms
oftheloweratmospherebyHinode/SOTandSDO/HMI.
The Hinode/SP vector magnetogram shown in Fig. 6
3.1. Lower atmospheric observations by Hinode/SOT suggests the presence of electric currents in the photo-
spheric field around the parasitic pore. Due to Hinode
Figure 6 shows SOT observations of the jet emitting
telemetry limitations, only one SP map is available in
regionofAR11793. Theleftpanelshowsthecontinuum
the interval containing the four jets. So for the purpose
intensity image from a Hinode/SP raster scan. The cen-
of inspecting the evolution of the photospheric magnetic
tral panel shows the vector magnetogram from a Milne-
field, we used vector magnetograms from HMI instead.
EddingtonStokesinversion(Lites&Ichimoto2013;Lites
Each HMI vector magnetogram is produced by a
et al. 2013). The right panel shows a broadband filter
image from the Caii H channel during ocurrence of the Milne-EddingtoninversionofIQUVStokesmapstempo-
rally interpolated over an apodization window spanning
thirdjet. Thelattershowsasetofclosedloopsandaset
1350 s (Hoeksema et al. 2014). This is done to increase
of inclined loops pointed toward the northeast direction.
the signal-to-noise ratio of the Stokes parameters and to
The morphology of the loops is somewhat reminiscent of
filter out p-mode oscillations. While HMI vector mag-
the jet studied by Liu et al. (2009, see figure 1 of their
netograms are not instantaneous representations of the
article). In their paper, they studied SOT observations
ofajetusingCaiiHimagesalone. Fromthemorpholog- photospheric field at any given time, the pixels in the
same magnetogram are co-temporal. HMI provides vec-
ical evolution, they concluded that the apparent motion
tor magnetograms of the full AR at a regular cadence of
of the jet material was consistent with a helical jet with
oneframeper12min. Weusevectormagnetogramsfrom
untwistingmagneticfieldlines. Inthecasetheystudied,
the HMI data series hmi.sharp cea 720s (Sun 2013).
the jet was observed off the solar limb so the two-part
ThisseriesprovidesvectormagnetogramsinARpatches,
structure comprised of the closed loops and the inclined
such that the magnetic field vectors have been disam-
open loops were not contaminated by background emis-
sion. In our case, contribution to the SOT Caii H chan- biguated, transformed and remapped onto a cylindrical
equal area grid. The magnetic vector is expressed as
nelbyemissionintheupperphotospheremakesitharder
(B ,B ,B ), corresponding to the radial, longitudinal
to delineate the specific features. Still, the morphologi- r θ φ
andlatitudinalcomponents,respectively. Sinceourmain
cal similarities with the case studied by Liu et al. (2009)
region of interest is relatively small (L ∼ 30 Mm) , we
support their conclusion that their jet exhibited helical
ignoretheeffectsofcurvatureandusethefollowingmap-
motion.
The eastern (left) ends of the closed loops in the Caii ping to a local Cartesian coordinate system Bθ → Bx,
B →B andB →B . Thisenablesustocomputethe
H image appear to be anchored at a compact patch of φ y r z
vertical current density
positive polarity field located at (x,y) = (165(cid:48)(cid:48),287(cid:48)(cid:48)).
Inspection of the accompanying continuum image shows ∂B ∂B
this positive patch to be a pore. This positive polarity jz = ∂xy − ∂yx. (3)
pore is embedded in the interior of a supergranule. In
contrast, the network field surrounding this supergran- Inspection of maps of j during the jet-emitting period
z
ule is predominantly negative (the same polarity as the reveals a persistent patch of positive j near the para-
z
nearbyleadingspot). Inthissensetheporeisaparasitic sitic (positive polarity) pore. Fig. 7 shows HMI vector
pole. Inspection of the transverse field (i.e. the ampli- magnetograms in the neighborhood of the pore at 09:00,
tudeoftheplane-of-skycomponent|B |)showsthepres- 10:46, and 12:34 UT. The left column shows the verti-
t
enceofstronghorizontalfield(B >700G)onthewest- cal component B . The positive polarity pore is roughly
t z
ern(right)sideofthepore. Furthermorethereisamod- centered at (x,y) = (−2,0) Mm in all three snaphots.
erate transverse field (|B | ∼ 300 G) pervading a large Thehorizontalmagneticfieldcanbedecomposedintothe
t
fraction of the sugergranular cell. The left-right asym- sum of a potential component (calculated from B ) and
z
metryoftheB distributionabouttheporeissuggestive a current-carrying component. These are respectively
t
of electric currents associated with a non-potential mag- showninpanelsinthemiddleandrightcolumns. Aper-
netic field configuration (more on this in section 4.1). sistentpatchofcurrent-carryingfieldcanbefoundonthe
Inspection of the temporal sequence of Caii H images west side of the pore at (x,y) = (−1,0). This feature is
indicates the presence of bright grain pairs that form in also found in the middle panel of Fig. 6, which shows
8
Figure 6. HinodeSOTobservationsofthejetemittingregionofAR11793.Left: ContinuumimagefromaHinode/SPrasterscan.Center:
Vector magnetogram of the same field of view. The line-of-sight component (B) of the magnetic field is denoted such that blue and red
l
denotepositiveandnegativepolarities,respectively. Greencolorcodingshowsthestrengthofthetransversecomponent(Bt). Overplotted
lines show the orientation of the transverse field. Right: Broadband Filter (BFI) image in the Ca II H channel during the occurrence of
thethirdjet.
the Hinode/SP vector magnetogram of the same region. where B(cid:126) =∇×A(cid:126),(cid:126)j =∇×B(cid:126) and
TheHinode/SPmapprovidesamoreaccuratefieldmea-
1
surementduetohigherspectralcoverageandresolution. (cid:126)v = (cid:126)j×B(cid:126). (5)
The strength of the current-carrying horizontal field in ν
this patch reaches 1 kG and exceeds the field strength The magnetofrictional coefficient ν is given by
of the current-free counterpart. This indicates that the
magnetic field on the west side of the pore is strongly ν =ν B2(1−e−z/L), (6)
0
twisted. Inspection of the B time sequence from HMI
z
shows that magnetic flux is emerging in this area. The where ν0 = 10 s Mm−2 and L = 1.7 Mm. As described
orientationoftheemergingfluxissuchthatnegativeand in Cheung & DeRosa (2012), the code uses a staggered
positive polarity field are migrating in roughly the north grid (Yee mesh) such that A(cid:126) and (cid:126)j are defined at cell
and south directions, respectively. So both Hinode/SP edges, B(cid:126) is defined on cell faces and (cid:126)v is defined at cell
and SDO/HMI vector magnetograms give evidence for
centers. The code has been updated to use a van Leer
theemergenceoftwistedfieldinthevicinityofthepore.
slope limiter (van Leer 1977) to interpolate (cid:126)v onto cell
Inthefollowingsection,wepresentnumericalsimulations
edges when computing the −(cid:126)v × B(cid:126) electric field. We
to investigate howthis photospheric driving is relatedto
find that this scheme provides better numerical stabil-
the phenomena of recurrent helical jets.
ity while being less diffusive than explicitly imposing an
4.2. Numerical Experiments using a Data-Driven anomalous resistivity.
Magnetofrictional Model
4.2.1. Initial and boundary conditions
We use a time-dependent magnetofrictional (Yang
et al. 1986; Craig & Sneyd 1986; van Ballegooijen et al. Theobservedrecurrentjetsoccurintheneighborhood
2000) model to carry out data-driven numerical experi- ofambientinclinedfieldaspartofasetofARloopsthat
ments of coronal field evolution. Under this model, the connecttheleadingandfollowingpolaritiesofAR11793.
fluidvelocityv appearingintheinductionequationisas- To capture the large-scale magnetic connectivity, we use
sumedtobeproportionaltothelocalLorentzforce(cid:126)j×B(cid:126). a computational domain sufficiently large to encompass
theentireAR.Thedomainspans248and131Mminthe
Thisleadstoanevolutionofanyarbitrarymagneticcon-
x (longitudinal) and y (latitudinal) directions, respec-
figurationtorelaxtowardaforce-freefield. Magnetofric-
tively. Thebottomboundaryislocatedatz =0andthe
tionhasbeenusedtomodeltheformationandevolution
top boundary is located at 105 Mm. The horizontal and
of filaments (Mackay et al. 2000; van Ballegooijen 2004;
vertical grid spacings are 364 and 547 km, respectively.
Mackay&vanBallegooijen2006,2009;Yeatesetal.2007,
The initial condition is a potential field of the AR com-
2008;Yeates&Mackay2009),thecoronalfieldabovethe
puted for the magnetogram at 2013-07-21T06:12 UT (5
quiet Sun magnetic carpet (Meyer et al. 2012) and the
h 22 m before the start of the IRIS observation) and the
evolution of ARs (Cheung & DeRosa 2012; Gibb et al.
simulations are evolved forward in time from that state.
2014).
As discussed in Cheung & DeRosa (2012), the bottom
Following Cheung & DeRosa (2012), we use a Carte-
boundary condition for the magnetofrictional model is
sian magnetofriction code that solves for the vector po-
given by the transverse components of the photospheric
tential A(cid:126), namely
electric field, namely −∂ A = E and −∂ A = E .
t x x t y y
∂A(cid:126) The retrieval of the horizontal electric field from vector
=(cid:126)v×B(cid:126), (4) magnetogramsisadifficultinverseproblem(Fisheretal.
∂t
Homologous Helical Jets 9
Figure 7. SDO/HMIvectormagnetogramsoftheparasiticporeanditssurroundings. Left: VerticalcomponentofB(cid:126) (greyscalesaturated
at ±200 Mx cm−2). Middle: Horizontal components of current-free (i.e. potential) part of B(cid:126). Right: Horizontal components of the
current-carryingpartofB(cid:126). Astrong,persistentpatchofcurrent-carryfieldisfoundonthewestsideofthepore. ComparisonwiththeBz
distributionshowsthiscurrent-carryingpatchiscoincidentwithanemergingfluxregion(justnorthwestoftheparasiticpore). Contours
forBz =500and1000Mxcm−2 areshownonallpanelstoindicatethepositionofthepore.
2010, 2012). As recently demonstrated by Kazachenko fied. Specifying the horizontal divergence of the electric
et al. (2014), the incorporation of Doppler flows as a field:
constraint leads to inversion results that accurately re- D(x,y)=∇ ·E(cid:126) . (8)
h h
produceelectricfields(andtheassociatedPoyntingflux)
fully constrains the problem. In our numerical experi-
in an anelastic MHD simulation. The validation of this
ments, we assume
method for use with vector magnetograms at the reso-
lution and sensitivity of HMI on photospheric magnetic
structures is work in progress. D(x,y)=jz(x,y)U0, (9)
Instead of attempting to perform a faithful retrieval
where j =(∇×B(cid:126)) is the vertical current density com-
of the photospheric electric field for this problem, we z z
puted at the photosphere. This choice of the functional
use a different method to compute electric fields with a
form for D is motivated by the following scenario. Con-
given assumption. Given the sequence of input vertical
sideranaxisymmetrictwistedmagneticfluxtubethatis
magnetograms B , its relation to E(cid:126) =(E ,E ) is given
z h x y invariant along its axis and let the tube axis be parallel
by the vertical component of the induction equation
to the vertical direction zˆ. Let the tube rise vertically
∂Bz∂(tx,y) =−zˆ·(∇×E(cid:126)h). (7) wthieth−(cid:126)v(cid:126)v=×UB(cid:126)0zˆe.lecIttriccanfieblde cshororwesnptohnadtintghetoditvheirsgemnocteioonf
is given by Eq. (9). By adopting Eq. (9), we have cho-
In order to solve for E(cid:126) , another relation must be speci- sen to inject twist via the bodily emergence of twisted
h
10
field (c.f. Leka et al. 1996). For driving the numerical To visualize the magnetic field lines, we calculate a
experiments described here, j is computed from HMI scalar proxy emissivity ε(x,y,z) using the following pro-
z
vector magnetograms and U is a free parameter (with cedure. For each field line traced from a position at the
0
dimensions of velocity). Varying U changes the effec- photospheric (z = 0) boundary, we compute the follow-
0
tive injection speed of magnetic twist (as described by ing field-line averaged quantity:
j ) into the computational domain.
z (cid:90) L
Another possible way to inject twist is by means (cid:104)WD(cid:105)=L−1 F(cid:126) ·(cid:126)vdl, (10)
of shearing and rotational motions in the photospheric Lorentz
0
plane. In MHD models of the emergence of twisted flux
tubes, such flows are accelerated by magnetic torques where L is the length of a field line and F(cid:126) ·(cid:126)v rep-
Lorentz
exerted by the Lorentz force (Longcope & Welsch 2000; resents the rate of work done by the Lorentz force. In
Manchester IV et al. 2004; Magara 2006; Fan 2009; a full MHD model, F(cid:126) ·(cid:126)v appears as a source term
Lorentz
Cheung et al. 2010; Fang et al. 2012; Cheung & Isobe in the kinetic energy equation and as a sink term (with
2014). Twist injection by both bodily emergence of negative sign) in the magnetic energy equation. In a
current-carrying field and rotational motions in the pho- magnetofrictional model,
tosphere are likely present in our region of interest (see
section 3.1). For simplicity, however, we assume in our F(cid:126) ·(cid:126)v = 1 [(∇×B(cid:126))×B(cid:126)]2 ≥0. (11)
numericalsetupthattwistinjectionisduetotheformer.1 Lorentz 4πν
so that (cid:104)WD(cid:105) ≥ 0. If a field line crosses one of the side
4.2.2. Results of Numerical Experiments or top boundaries of the computational domain, we set
We carried out three numerical experiments, one each (cid:104)WD(cid:105) = 0 so that the field line is not emissive. A mag-
for U = 0, U = 1.1 and U = 2.2 km s−1. For the neticfieldlinewillcrossanumberofcellelementsinthe
0 0 0
run with U =0, E(cid:126) is decoupled from the photospheric computational domain. For each of these cell elements,
0 h we increment the local value of the emissivity by
distribution of j . In this case there is no systematic
z
current injection and we do not find any magnetic field
dε=G(cid:104)WD(cid:105)∆x∆y, (12)
evolution resembling the helical motion of the observed
jets. For U = 1.1 km s−1, we find repeated episodes of where G is some arbitrary scale-factor (here we use
0
twisting followed by untwisting in the model magnetic G = 1). Row (c) shows integrals of the resulting proxy
field that shares qualitative similarities with the recur- emissivity along vertical lines-of-sight. This method al-
rentjets. Fig.8showssnapshotsoftwosuchhomologous lows us to inspect a large number of fields lines (here we
episodesofevolutionfromthemodel. Row(a)showsB traced 4 field lines per pixel), each lit up according to
z
at the bottom boundary of the domain, which is con- the field-line averaged rate of magnetic energy loss due
strained to match the B observed by HMI. Row (b) to work done by the Lorentz force. The images shown
z
showssyntheticchromospheric“magnetograms”(i.e. B in row (c) are log-scaled so they do not depend on the
z
sampled at z = 4.5 Mm). We chose to sample the mag- specific value of the constant G.
netic field at a height that is above the nominal height Fig. 9 shows a 3D visualization of the magnetic struc-
range associated with 1D models of the solar chromo- ture from the same data-driven simulation (U = 1.1
0
sphere (∼ 1 to 2 Mm, e.g. see Withbroe & Noyes 1977; km s−1) at 11:02 UT. The topological structure in this
Vernazza et al. 1981) since 3D radiative MHD simula- case is similar to those in scenarios examined by Pariat
tions show that magnetic flux emerging into the atmo- et al. (2009, 2010). In their numerical experiments, a
sphere can lift the chromosphere and transition region parasitic polarity is embedded in an ambient field that
layers by a few Mm (Mart´ınez-Sykora et al. 2008). In is either vertical (Pariat et al. 2009) or inclined (Pariat
bothcases,theearliestchromosphericmagnetogram(i.e. et al. 2010). In both cases, the model coronal field has
panels (b1) and (b4) ) shows a positive polarity feature a null point. Associated with the null point is a spine
pressedagainstanegativepolarityfeatureinaying-yang field line connecting the parasitic polarity with the null
pattern. Inspectionofthehorizontalvectorsandthedis- and a set of magnetic field lines forming a fan locus (i.e.
tribution of j at that height shows that the field near a so-call fan-spine topology, see e.g. Parnell et al. 1996).
z
the polarity inversion line is sheared and carries current. As shown in Fig. 9, the same type of magnetic skeleton
When we inspect subsequent vector magnetograms, we is found in the data-driven model. In this case, the am-
find the horizontal vectors have, on average, rotated in bient field (with polarity opposite to that of the pore)
a clockwise direction. This is a result of the untwisting is concentrated at the supergranular boundary, so the
of the magnetic field by a clockwise rotational flow. The fan field lines emanating from the coronal null are con-
vertical component of vorticity for such a flow is nega- nected to network flux. This type of topology is similar
tive, consistent with the sign of vorticity of the observed to the one inferred for the (un)twisting jet event studied
recurrent jets. by Guo et al. (2013) and Schmieder et al. (2013). That
event also occurred above a parasitic patch embedded in
1 For the specific case of an axisymmetric flux tube with az- a supergranule at the edge of an AR.
imuthal field Bθ(r) = qrBl(r), where q is the twist parameter As demonstrated by the numerical MHD experiments
andBl(r)isthelongitudinalcomponentofthemagneticfield,one by Pariat et al. (2009, 2010), persistent rotation of the
canpickparametersforthetwoscenarios(i.e.bodilytransportof
parasitic polarity leads to a series of homologous helical
twistedfieldandrotationalmotion)thatresultinidenticalbound-
ary conditions. For such a tube rotating about its axis with an jets. The simplistic MF model used in our data-driven
angular velocity ω0, it can be shown that ∇·E(cid:126)h = −q−1ω0jz, simulations do not solve for the continuity, momentum
whichisequivalenttoEq. (9)withU0=−qω0. norenergyequationssothemodeldoesnotyieldplasma
