Spectro-polarimetric simulations of the solar limb: absorption-emission FeI $6301.5\mathrm{\AA}$ and $6302.5\mathrm{\AA}$ line profiles and torsional flows in the intergranular magnetic flux concentrations

2.8 MB·English

by  S. Shelyag

Draftversion January6,2015
PreprinttypesetusingLATEXstyleemulateapjv.04/20/08
SPECTRO-POLARIMETRIC SIMULATIONS OF THE SOLAR LIMB: ABSORPTION-EMISSION FEI 6301.5˚A
AND 6302.5˚A LINE PROFILES AND TORSIONAL FLOWS IN THE INTERGRANULAR MAGNETIC FLUX
CONCENTRATIONS
S. Shelyag
School ofMathematical Sciences,MonashUniversity,Victoria3800,Australia
(Dated: 01.01.01/01.01.01)
Draft version January 6, 2015
5 ABSTRACT
1
Using radiative magneto-hydrodynamic simulations of the magnetised solar photosphere and de-
0
tailed spectro-polarimetric diagnostics with the Fei 6301.5˚A and 6302.5˚A photospheric lines in the
2
local thermodynamic equilibrium approximation, we model active solar granulation as if it was ob-

n served at the solar limb. We analyse general properties of the radiation across the solar limb, such
a as the continuum and the line core limb darkening and the granulation contrast. We demonstrate
J
the presence of profiles with both emission and absorption features at the simulated solar limb, and

5 pure emission profiles above the limb. These profiles are associated with the regions of strong linear
polarisation of the emergent radiation, indicating the influence of the intergranular magnetic fields
] on the line formation. We analyse physical origins of the emission wings in the Stokes profiles at the
R
limb, and demonstrate that these features are producedby localisedheating and torsionalmotions in
S
the intergranular magnetic flux concentrations.
.
h Subject headings: Sun: Photosphere—Sun: Surfacemagnetism—Plasmas—Magnetohydrodynam-
p ics (MHD)
-
o
tr 1. INTRODUCTION standing the physics of the solar photosphere can be
s demonstratedbyanexcellentagreementbetweenthevar-
a The solar photosphere at the limb remains one of the
ious numerical codes used to simulate the solar surface
[ largelyunexploredsolarregionsdueto the lackofbright
and extended emissive features, such as spicules in the layers (Beeck et al. 2012).
1 In this paper, we use numerical simulation of the so-
chromosphere,andsharplimbdarkening,associatedwith
v lar photosphere with the MURaM code (Vo¨gler et al.
low light conditions and high instrumental noise levels
0 2005)andone-dimensionallineprofilesynthesiswiththe
in the observations of this region. On the other hand,
7 NICOLE code (Socas-Navarro et al. 2014) to perform
the solar limb has potential for the diagnostics of paral-
8 the modelling of the spectro-polarimetric properties of
lel to the solar surface photospheric flows and magnetic
0 fields. Together with solar disk observations, it can pro- the radiation at the solar limb with the 6301.5˚A and
0 videnewandmoredetailedinformationonthegeometry 6302.5˚A Fei lines in the LTE approximation. We show
.
1 oftheflowandmagneticfieldstructuresinthesolarpho- the average properties of simulated radiation, such as
0 tosphere,on the details of transitionbetween the photo- centre-to-limb variation of the continuum intensity and
5 sphere and the chromosphere, as well as on the origins the intensity in the line core. We also show the connec-
1 of chromospheric features. tion between the line core intensity and the linear po-
v: Groundbreaking spectro-polarimetric observation of larisation above the limb. At the limb, we demonstrate
i thesolarlimbwithHinodeSOT(Tsuneta et al.2008)by thepresenceofthetransitionlayerbetweenpureabsorp-
X Lites et al. (2010) revealed a thin, sub-arcsecond layer tionandpureemission,spectropolarimetricallysimilarto
r of photospheric emission in the 6301.5˚A and 6302.5˚A the observations by Lites et al. (2010). In the transition
a layer, the profiles with emission wings are found. Using
lines ofneutraliron. These lines, normallyin absorption
response functions to the temperature for the 6301.5˚A
withinthesolardisk,undergoatransitionintopureemis-
line,weanalysethe line formationprocessandprovidea
sion above the limb. The transition between absorption
simple model for emission-absorption line profile forma-
andemissionis characterisedby the appearanceofemis-
tion at the solar limb. In our simulations, the emission
sive wings in the line profiles, their significant Doppler
wings in the profiles are produced by positive tempera-
shifts, and linear (radially directed) light polarisation.
ture gradients and torsional line-of-sight motions within
Realistic numerical simulations of solar surface
theintergranularmagneticflux tubes. Incontrastto the
magneto-convection have long been successful in re-
proposedroleofnon-LTEscattering(Lites et al.2010)in
producing, explaining and even predicting various so-
formationofphotosphericlineprofilesabovethelimb,we
lar photospheric (see e.g. Stein 2012, and refer-
are able to reproduce the wing emission in the profiles
ences therein), and, recently, chromospheric phenom-
in pure one-dimensional LTE approximation. We sug-
ena (Leenaarts et al. 2012; Pereira et al. 2013). Centre-
gest that both non-LTE scattering and Doppler-shifted
to-limb variation of solar radiation has been exten-
emissioninthefluxtubesareresponsibleforthecomplex
sively studied using simulations (Keller et al. 2004;
Stokes-I profile shapes at the solar limb.
Koesterke et al. 2008; Kitiashvili et al. 2014). Ulti-
The paper is organised as follows. In Section 2 we
mately, the success of numerical modelling in under-
describethe simulationsetupweusedtomodelthesolar
2 S. Shelyag
limbradiationandpolarizationinformation. Section3is granularmagneticfluxconcentrationsinsimulationsand
divided into subsections 3.1 and 3.2, where we describe analysed by Shelyag et al. (2013); Shelyag & Przybylski
thegeneralpropertiesofthesimulatedlimb,andanalyse (2014).
thephysicaloriginsofemissioninthelineprofilewingsat In order to calculate Stokes profiles for 6301.51˚A
the limb, respectively. Section 4 concludes our findings. and 6302.49˚A Fei absorption lines, the horizontal one-
dimensionalcolumnsfromthesolarlimbmodelwereused
2. SIMULATIONSETUP
asaninputforspectro-polarimetricline profilesynthesis
We use a single extended photospheric MHD model codeNICOLE(Socas-Navarroet al.2000;Socas-Navarro
snapshot from a unipolar magnetic field simulation 2011; Socas-Navarro et al. 2014). No multi-dimensional
of a plage region produced by the MURaM code scattering or non-LTE effects were included in the com-
(Vo¨gler et al. 2005). The code solves radiative MHD putation. The excitation potentials V = 3.65 eV and
equations on a Cartesian grid. The magneto-convection loggf = 0.59, and V = 3.686 eV and loggf = 1.13
simulation is set through injecting a uniform magnetic were used−for 6301.51˚A and 6302.49˚A Fei lines−syn-
field of 200 G into a previously calculated non-magnetic
thesis, respectively. The full Stokes vectors for the
convection model. The resolution is 25 km in the hori- lines were calculated within 6301.2˚A 6301.8˚A, and
zontaldirectionsand10kmintheverticaldirection. The 6302.2˚A 6302.8˚A wavelength ranges−with 3 m˚A res-
simulationbox hasa size of12 12Mm2 and3.2 Mmin −
× olution.
the horizontal and vertical directions, respectively. The
average continuum formation layer is located at about 3. RESULTS
2 Mm above the bottom boundary. The bottom bound- 3.1. General properties
ary of the domain is open for in- and outflows, and the
The average radiation intensity structure across the
top boundary is open for outflows, while the inflows are
simulated limb is shown in Fig. 2. The solid curve rep-
keptatconstanttemperature 6000K inorderto mimick
resents the normalised continuum intensity variation. A
the chromospheric layers of the Sun. The side bound-
region with sharp intensity decrease from 0.5 to nearly
aries are periodic. We use FreeEOS equation of state
zero at 696.6 Mm has thickness of about 200 km. At
(Irwin2012)toaccountforchangesinthegaslawdueto
the rest wavelength of the Fei line core, λ = 6302.49˚A,
partial ionization. No Hall term or ambipolar diffusion
the average intensity (dashed curve) is about 0.5 of the
is included in the simulation.
continuum intensity at the solar disk. However, due to
A solar limb region is constructed by adding together
theincreasedopacityinthelinecore,thesimulatedsolar
16 copies of the chosen snapshot and locally changing
limb is higher in the solar atmosphere by about 300 km
the geometry of the snapshots to cylindrical geometry
andspreadsoverasomewhatlargerheightrangeofabout
with radius R =695 Mm in order to mimic the curva-
⊙ 300 km. Similar behaviour is demonstrated by the min-
ture of the solar surface in one dimension. The finalsize
imum intensity in the line profile (shown as dash-dotted
of the domain is about 192 10 Mm in the horizontal
× curve). It should be also noted that the averaging has
and vertical directions, respectively, which corresponds
to 8◦ inclination between the surface and the line-of- been done over a single computational snapshot, which
± does not account for the oscillations and time depen-
sight (LOS), or µ = 0 0.14. The LOS components of
− dencepresentinthesimulations. Thereforesignaturesof
the magnetic field and the plasma velocity are recalcu-
intensity variability due to granulation are also present.
lated accordingly. After the domainis projectedback to
Averagecontinuumintensites acrossthe full solardisk
the Cartesian grid, it is resampled to a somewhat lower
werealsocomputed. Fig.3showstheaverage6300˚Anor-
(25 km) vertical resolution to reduce the computational
malised intensities calculated for the same model snap-
cost,andsmoothedalongthelines-of-sightwithaboxcar
functionwiththewidthof100kmtoavoidnumericalin- shot at different observational angles at the solar disk
stabilities due to sharp gradients between granular and µ=1, √3/2, 0.5, 0.2, 0.1, 0.05 using the domain incli-
intergranular solar magneto-convection features during nationmethod(seee.g.Shelyag & Przybylski2014,black
radiative transport computations. With the optical ray solid line), the average intensities from the limb simula-
lengthofabout5 Mmthe effectofthe smoothingis neg- tion (µ = 0.14 0; green solid line), the granulation
−
ligible. Usingthesamemodelsnapshottocoverthesolar contrast(blackdashedline)andthegranulationcontrast
limb allows us to study the same features under the dif- fromthelimbsimulation(greendashedline). Astheplot
ferent inclination angles as well as at the solar limb. A shows,thelimbdarkeningdependencesonµfitexactlyin
vertical cut through half of the constructed solar limb the overlapping region between µ=0.05 0.1. The rms
−
domain is shown in Fig. 1. As is evident from the fig- contrast dependence on µ for the limb simulation shows
ure, in the constructed domain both the regions of the largescatter due to significantly smallerstatistics. How-
solar disk (with optically thick, hot and dense plasma) ever, the scatter is found to be close around the average
andthe solarlimb(opticallythin)arepresent. The LOS contrast values for the solar disk computation.
components of the magnetic field and the velocity are A continuum intensity image (Fig. 4, top-left panel)
predominantly horizontal in this simulation. Therefore, shows low-contrast solar limb granulation and a corru-
granular upflows and magnetised downflows do not in- gatedsolarlimbsurface. The limbheightvariabilitydue
fluence the radiation. However,the photospheric part of to granulation is small, of the order of 100 200 km, as
−
the domain is coveredwith horizontallyexpanding mag- the(deeper)intergranularlanesarecompletelyhiddenby
netic fields and with the radially elongated line-of-sight the granulation. Brightgranularwalls (faculae) are visi-
velocity structures of alternating sign corresponding to ble (Keller et al. 2004). There are no noticeable contin-
Alfv´enic horizontal torsional motions. These motions uumintensityfeaturesabovethesolarlimb. The6301.5˚A
have been recently demonstrated to exist in the inter- line core intensity image (top-right panel in Fig. 4) and,
Spectro-polarimetric simulations of solar limb 3
Fig.1.— Vertical cut through a half of the simulation domain representing the solar limb. The temperature, LOS velocity and LOS
magnetic fieldstrength areshowninthe upper,middleand bottom panels,respectively. Thevertical axis intheplots corresponds tothe
distancefromthesolarcentre. Thedashedlineinthepanelsindicatesapproximatelevelofthesolarsurface.
Fig.2.—Limbdarkeningacrossthesolarlimb. 6300˚Acontinuum Fig.3.—6300˚Acontinuumlimbdarkeningacrossthesolardisk.
intensityisshownwiththe solidline,the dashedlinecorresponds Solidcurve-simulatedaveragenormalizedintensity,dashedcurve
to the intensity at the wavelength of the line core 6302.49˚A, and -rmscontrastofgranulation. Thesolarlimbmodel(µ=0.15 0)
the dash-dotted linecorresponds to the minimum intensity of the isshowningreen. Trianglesshowtheinclinationanglesusedto−cal-
Fei6302.49˚Alineprofile. Thehorizontalaxisisthedistancefrom culatetheradiationparameters,µ=1, √3/2, 0.5, 0.2, 0.1, 0.05.
thesolarcentre.
flux tubes, this leads to generation of strong and asym-
morepronounced,the 6301.5 0.15˚Aline wing intensity metric, multi-lobed profiles in all polarization compo-
− nents, as it is demonstrated in the next subsection.
image(middle-leftpanel),however,showalargenumber
The line parameters, namely the linear
of small-scale vertically extending features with some-
whatenhancedlinecoreandstronglyenhancedlinewing (R pQ2+U2dλ) and circular (R V dλ) polarisa-
| |
intensities above the average solar limb radius at this tion, are shown in the bottom-left and bottom-right
wavelength, R > 697 Mm. The 6302.5˚A line core in- panels of Fig. 4, respectively. The images show the
presence of strong Stokes signals both at the solar limb
tensity (middle-right panel) shows similar, although less
and in the simulated solar disk region. As expected
prominent features. Reversed granulation is also visible
due to the weakness of the LOS magnetic field and
(Cheung et al. 2007).
strong magnetic field component perpendicular to the
As can be seen from the bottom panel of Fig. 1, the
line-of-sight above the limb, the signal in Stokes-V
LOSmagneticfieldmainlycorrespondstothehorizontal
magnetic field of the intergranular magnetic field con- becomes weaker, and the signal in pQ2+U2 becomes
centrations, expanding in the solar atmosphere. There- stronger above the solar limb region.
fore, along the line of sight, both polarities of the mag- Scatter plots of the intensity in the line core versus
neticfield,aswellasastrongcomponentofthemagnetic total Stokes-V and pQ2+U2 areas are shown in the
field perpendicular to the line of sight, are present. To- left and right panels of Fig. 5, respectively. Both figures
gether with torsional oscillatory flows in the magnetic clearly show two separate populations of points: above
4 S. Shelyag
Fig.4.— Continuum (top left), 6301.5˚A line core (top right), 6301.5 0.15˚A line wing (middle left), 6302.5˚A (middle right) line core
−
normalisedintensityimagesfromthesimulations,andRpQ2+U2dλ(bottom left)andR V dλ(bottom right)simulatedimages. Small-
| |
scalelocalbrighteningsarevisiblein6301.5˚Alinewing,and,tosomeextent,inthelinecores. IntegratedStokesparametersshowpresence
ofbothcircularandlinearpolarisation. Thelinearpolarisationissignificantlymorepronouncedabovethesimulatedlimbcomparedtothe
circularlypolarizedlightinthesameregion.
Fig.5.— Scatter plots of intensity in the line core vs the total Stokes-V area (left panel) and of intensity in the line core vs the total
Stokes-pQ2+U2 area(rightpanel)forFei6302.5˚Aline. Thegreendots correspondtother>696.8MminFig.4.
the solar limb (marked by green dots) and at the so- 695.875, 696.6, 696.675, 696.775, 697.2 Mm. The pure
lar disk (black dots). While the solar disk population absorption profiles are obtained for the position within
doesnotshowadependence ofthe Fei6302.5˚Alinecore the simulated solar disk at R = 695.875 Mm. Stokes-
intensity on the magnetic field, the solar limb popula- Q and V show the presence of strong linear (verti-
tion demonstrates such dependence: the larger the lin- cal) and line-of-slight polarisation signals. At the limb,
ear and/or circular polarisation, the higher the line core R = 696.6 Mm, Stokes-I profiles show an absorption
intensity is. core, while the profile wings show emission.
The horizontally averaged Stokes-I, Q/I, U/I, and Stokes-V profiles have lower amplitude compared to
V/I profiles for 6301.5˚A and 6302.5˚A lines across the the disk due to the inclination of magnetic field with
respect to the LOS, and the multi-lobed structure of
solar limb are shown in Fig. 6 for the radii R =
Spectro-polarimetric simulations of solar limb 5
formation of these profiles in our simulations.
3.2. Absorption-emission profiles at the solar limb
Figure 7 shows simulated I, Q/I, U/I and V/I slit
images for the horizontally-averaged simulated profiles
(top row), for a slit positioned vertically across the so-
lar limb at the position marked by the vertical dotted
line in Fig. 4 (middle row), and for the slit positioned
horizontally at the solar limb, as marked in the top-left
(Stokes-I) panel of the figure (bottom row).
The horizontally-averaged Stokes-I profiles show ab-
sorption within the simulated solar disk, the emission
profiles far above the solar limb, and the transition
from pure absorption to pure emission, which is charac-
terisedbythepresenceoftheprofileswiththeabsorption
Fig.6.—HorizontallyaveragedStokes-I,Q/I,U/I,V/I profiles core and the raised, emissive wings. Stokes-Q/I profiles
for the radii R = 695.875, 696.6, 696.675, 696.775, 697.2 Mm
within the disk are positive predominantly because the
(fromthetoptothebottom)inthemodel. Thedottedlinesshow
zerolevelsforQ/I,U/I andV/I profiles,whicharenormalisedso magneto-convectionmodel used in this simulation has a
onetickintervalinthecorrspondingplotsisequalto0.03. unipolarverticalmagneticfield. Abovethelimb,Stokes-
Q/I change their signs. Horizontally-averaged Stokes-
the profiles becomes more pronounced due to presence
U/I profilesgenerallyhavemulti-lobedshapesandlower
of both positive and negative polarities of the magnetic
amplitudes, as has already been shown, due to the ab-
field and velocity variations along the LOS and within
senceofapreferreddirectionforthe magneticfieldspar-
the horizontal averagingelement.
allel to the limb in the simulation. Stokes-V/I profiles,
Abovethelimb,Stokes-I becomegraduallymoreemis-
while also being complex and multi-lobed, show some
sive in the optically thin part of the simulated atmo-
preferencetowardspositive blue lobes atthe disk, which
sphere. In agreement with the observations (Lites et al.
isconsistentwiththegeometryofmagneticfieldinopen-
2010), the 6302.5˚Aline profile becomes entirely emissive
ing magnetic flux tubes of positive polarity.
closer to the limb than the 6301.5˚A profile. At about For the vertically-aligned slit, the Stokes-I slit image
300 km above the simulated limb both lines are in the showsstrongcontinuumvariabilityonthediskandemis-
emission regime. In the topmost layers of the simula- sion cores above the limb for both the lines. However,
tion domain, both lines become fully emissive with no themostpronouncedfeatureintheimageisthepresence
core absorption. The line intensity ratio of 3.4, which is of bright features in the blue wings1 of both 6301.5 and
close to the ratio of the values ofthe oscillatorstrengths 6302.5˚AFeilineswiththeintensitieshigherandspatially
used for the lines 3.47 (see Section 1) indicates opti- unrelated to the continuum intensity enhancements. At
∼
cally thin emission regime of the lines. Stokes-Q profiles the same locations as the bright features in the Stokes-I
demonstrate strong linear polarisation above the limb, wings,Stokes-Q/I andU/I showstrongpolarisationsig-
whileStokes-V becomessomewhatsmaller,complexand nals and rapidly change sign within the same intensity
multi-lobed, indicating that the LOS velocity and mag- feature. Notably, Stokes-Q/I and U/I are, in general,
netic field experience significantchanges in the regionof ofsimilarlylargeamplitudes ( 0.4),indicating the pres-
the line formation. Stokes-U does not show any signifi- enceofstrongperpendicular to±the LOSmagnetic fields.
cant horizontal polarisation due to the geometry of the Above the limb, Stokes-Q/I show a multi-lobed struc-
magnetic field in the simulation. ture,whichdoesnotvarywithheightsignificantly,while
Lites et al.(2010)suggestedthat the Fei6301.5˚Aand Stokes-U/I vanishes. Stokes-V/I signals within the disk
6302.5˚A line profile reversals to the emission regime in showmultiplelobesofbothpolaritiestoo,indicatingthe
the wings in proximity to the solar limb are caused by presence of the gradients of LOS velocity and magnetic
non-LTEexcitationofironatomsbyscatteredlightcom- fields (see e.g. Shelyag et al. 2007). It should be noted
ing from the photosphere. Our simulation, however, thatnoaveragingorimagedegradationhasbeenapplied
shows the presence of such horizontally average profiles, for the shown vertically-aligned slit, therefore the only
computed using the pure one-dimensional LTE approx- sourceofstronglyasymmetricmulti-lobedStokes-V pro-
imation. To determine the physical mechanism of the filesisthe variationofthe physicalparametersalongthe
wingemission,wefirstperformedthecomputationofthe LOS.
Fei line profiles in the horizontally averagedmodel with Abovethelimb,Stokes-V/Ivanishesinagreementwith
zero LOS velocity. This simple numerical experiment the bottom-right panel of Fig. 4.
showed the absence of emission wings in the computed The Stokes-I, Q/I, U/I and V/I images for the
line profiles and LTE-type transition of the lines from horizontally-positioned slit at the solar limb are shown
the absorption to emission regime across the simulated in the bottom row of Fig. 7. The Stokes-I image shows
solarlimb. Therefore,in the simulation we present here, the presence of profiles with emission wings almost ev-
the wingemissioninthe horizontally-averagedprofilesis erywherealongtheslitforbothlines. Itshouldbenoted
createdby the superpositionof the local,possibly asym-
metric emission-absorption profiles produced by strong 1 Note that the presence of onlythe bluewingemissionhereis
LOS (tangential to the solar surface) velocity and tem- purely a selection effect introduced by choosing a position with a
bright feature in the blue wing of the profile. Similarly frequent
perature gradients at the corrugatedsurface of the solar
features inthe redwingare alsofoundinthe simulations, as well
limb. In the next subsection, we analyse the details of asthefeatureswithtwoemissivelobesofloweramplitude.
6 S. Shelyag
Fig.7.—SimulatedI,Q/I,U/I,V/I slitimagesforthehorizontallyaveragedprofiles(toprow),forapositionacrossthesimulatedsolar
limbmarked by the dotted lineinFig. 4(middle row), and for aslitpositioned horizontally at the limb(bottom row, markedinthe top
rowStokes-I imagewiththedashedline). Thepositionoftheverticalslitshowninthemiddlerowismarkedbythehorizontaldashedline
inthebottom row.
that most of the profiles are strongly asymmetric, with both emission and absorption is analysed below. An
emission either in the blue or in the red lobe. The pres- arbitrary position within the simulated solar disk, but
ence of the emission lobes shows some correlation with close to the limb was selected, where the 6301˚A line
the continuum intensity variation. The emission lobes profile shows both absorption in the line core and emis-
are strongly shifted with the corresponding LOS veloci- sion in the blue wing. Response functions (RFs) of all
ties of 4 8 km s−1. There is a weak visual correlation Stokes parameters to a small temperature perturbation
−
between Stokes-Q/I, U/I amplitudes and the emission (∆T =100 K) in the corresponding one-dimensional at-
lobes, while Stokes-Q/I has expectedly largeramplitude mosphere were computed. Fig. 8 shows the calculated
than Stokes-U/I. Nevertheless,the Stokes-Q/I andU/I RFs (grayscale images) together with the correspond-
signal patterns coincide with the emission lobes of the ing line profiles (plots in the top row), and the photo-
profiles, while there are no strong signals in the line ab- spheric parameters (vertical plots). A clear correspon-
sorption cores. A similar dependence is found for the dence is seen between the emission part of the profile
Stokes-V/I signal. at ∆λ = 0.1˚A, and a sharp temperature rise at about
The process of formation of the profiles which show 1.5 Mm d−istance along the LOS. At the same location,
Spectro-polarimetric simulations of solar limb 7
Fig.8.—SimulatedI,Q/I,U/I,V/I profiles(toprow),theirresponsefunctionstothetemperatureperturbation(grayscaleimages)and
thestructureofthecorresponding1DatmospherealongtheLOS.Dashedverticallinesmarkzerovaluesforvlos,Blos,B| andB⊥.
a strong plasma flow of about 4 5 km s−1 towards the
−
observer is found, which shifts the emission wavelength A B C
towards the blue side of the spectrum. The LOS com-
T T >T T <T
ponent of the magnetic field Blos changes the direction 1 2 1 3 2
and amplitude from 200 G to 250 G, leading to the B~
−
formation of a strong and asymmetric Stokes-V/I sig-
nalatthesamewavelength(seee.g.Shelyag et al.2007).
Line-of-sight
Thevertical,perpendiculartotheLOScomponentofthe
magneticfieldB isalmostalwayspositivewiththemin-
| V
t
imum magnetic field of a few Gauss. In the emission Granule
region it increases up to about 600 G, indicating that
the line-of-sight crosses an intergranular magnetic field Surface
concentration there. The Stokes-U/I RF has a maxi- Granule
mum in this region, and the Stokes-U/I profile shows
two lobes of large amplitude in the blue. The horizon-
tal, perpendicular to the LOS magnetic field component
B has expectedly smaller amplitude and also shows an
⊥
increase in the emission region up to 250 G.
A summary of the process of photospheric emission-
Fig. 9.— Emission-absorptionlineprofileformationinthenon-
absorptionFeilineprofileformationisprovidedinFig.9.
uniformsolarphotosphereatthelimb. Theline-of-sightclosetothe
The line-of-sight crosses three distinct regions. The first solarlimbcrossesthreedifferentregions: (A)anon-magneticgran-
region (A) is above the granule, where both the LOS ularregion,wherethecontinuumradiationisformed,(B)theinter-
components of the velocity and the magnetic field are granular magnetic field concentration, where the emission part of
theprofileisformed,andwhichischaracterisedbyradiativeheat-
small (from 0 to about 1.0 Mm along the LOS in Fig. 8.
ing,positivetemperaturegradient(T2>T1),andtorsionalplasma
Inthis region,the continuumradiationis formed. Then, motions(Vt),and(C)anon-magneticregionoverthegranulewith
the line-of-sight crosses the intergranular magnetic field a negative temperature gradient (T3 <T2), where the absorption
partoftheprofileisformed.
concentrationregion(B).Strongtorsionaloscillatorymo-
tions with speeds of a few km s−1 within the magnetic
concentration(Shelyag et al.2013;Shelyag & Przybylski 1.0 to 2.0 Mm in Fig. 8). At the same time, radia-
2014) Doppler-shift the line formation wavelengthin ac- tive heat exchange with the hot granular wall (see e.g.
cordance to the direction of motion in this region (from Spruit 1976; Vo¨gler et al. 2004) and resistive heating
8 S. Shelyag
(Moll et al. 2012; Shelyag & Przybylski 2014) cause the better understood (see e.g. Wedemeyer & Steiner 2014),
localised temperature increase within the magnetic flux there is little doubt of their presence in the mag-
tube and emission. Finally, the line-of-sight leaves the netic field concentrations. Furthermore, non-magnetic
magnetic field concentration and enters the rarified re- or weakly magnetised photospheric models also show
gion above the next granule (C), where the LOS veloci- torsional motions in intergranular lanes (Shelyag et al.
ties are generallysmallerand temperature decreases(up 2011a; Moll et al. 2011; Kitiashvili et al. 2012, 2013).
to the chromospheric layers, to which the photospheric Whileinthiscaseofzeroorweakphotosphericmagnetic
lines under consideration are not sensitive), leading to field the magnetic tension is small and does not prevent
the formation of an absorption line core. tornado-likeappearanceof the vortex,the purely hydro-
dynamic vortex flows in the intergranular lanes would
4. DISCUSSION lead to the presence of torsional motions consequently
In this paper, we presented a novel spectro- leading to the similar mechanism of emission-absorption
polarimetric simulation of photospheric radiation at the line profile formation at the solar limb.
solar limb. We used a single snapshot from magneto- A natural point of concern is the use of LTE approxi-
convection simulations of a plage region to construct a mation in the presented study. While there is no doubt
cylindrical solar limb-like region and performed detailed thenon-LTEeffectsareimportantespeciallyatthelimb,
radiative diagnostics computation on this domain with theprimaryaimofthestudywastodemonstratetheLTE
the 6301.5˚A and 6302.5˚A pair of photospheric lines of effectsofthelimbradiationformation. Furthermore,the
neutral iron in the LTE approximation. We computed neutral iron lines used for spectropolarimetric diagnos-
the average radiation parameters at the transition be- tics in this paper are formed low in the photosphere ir-
tween the solar disk and limb, such as limb darkening, respectively of the position at the solar disk, where the
rms granulation contrast and average Stokes profiles. LTEassumptionisstillreasonable,atleastforthe inter-
TheaverageStokesprofilesshowedthe emissionabove granular lanes (Shchukina & Trujillo Bueno 2001). The
the limb, the presence of emissive line wings, absorption basic process of emission-absorption line profiles forma-
core and significant polarisation signal at the limb, sim- tion at the limb, which is described in the paper, relies
ilar to the observations (Lites et al. 2010), where it was on the presence of torsional motions and heating within
suggested that the emissive wings are the result of ra- the intergranularmagnetic flux tubes.
diation scattering and non-LTE excitation in the solar Thestructuresdescribedinthepaperarerathersmall-
atmosphere. Our results, however, suggest that the ra- scale, with linear dimensions of about 100 km. Taking
diationscattering at the limb is not the only mechanism into account low light and high noise levels, inevitably
causingtheemissioninthelinewings. Itisdemonstrated associated with limb observations, it would be difficult
that, in the LTE approximation, the emission lobes in toprovidedetailedanddirectobservationalconfirmation
Stokes-I profiles at the limb can be formed due to the of the effect of torsional flows in magnetic field concen-
presence of the torsional bidirectional flows along the trations on the photospheric line formation at the solar
line-of-sight and the local heating in the intergranular limb. Nevertheless, future, large-scale instruments, such
magnetic field concentrations. When the line-of-sight, as DKIST, will be able to observe these small features.
along which the radiation is formed, crosses the inter- Finally, further study is needed and planned to analyse
granularmagnetic concentrationregion, it experiences a their lifetimes and links to chromospheric fine structure,
temperaturerise,leadingtoemission,andaDopplershift bidirectional flows and oscillations (Sekse et al. 2013).
tothe blue (orred)sideofthespectrum. After that, the
line-of-sight crosses an absorption region with a smaller
LOS velocity and a temperature decrease, which leads
to the formation of the absorption core. As there is no 5. ACKNOWLEDGEMENT
preferred direction for the torsional flows in magnetic Theauthorthanksthe anonymousrefereeforhisvalu-
field concentrations, both blue- and red-wing emission able comments. This research was undertaken with
is observed in the simulations. The profiles with two the assistance of resources provided at the NCI Na-
emissive lobes are also found in the regions where the tional Facility systems at the Australian National Uni-
line-of-sightcrossesthe layersofopposite rotationinthe versity through the National Computational Merit Al-
magnetic flux tubes (Shelyag et al. 2011b). When aver- location Scheme supported by the Australian Gov-
agedspatially,theseprofilesleadtotheappearanceofthe ernment, and at the Multi-modal Australian ScienceS
Stokes-I profileswithemissivelobesandabsorptioncore. Imaging and Visualisation Environment (MASSIVE)
Thepolarisationsignalsatthelimbshowthepresenceof (www.massive.org.au). The author also thanks Centre
vertically(radially)orientedmagneticfields,whichisex- for Astrophysics & Supercomputing of Swinburne Uni-
pected since aplage modelwith 200G verticalmagnetic versity of Technology (Australia) for the computational
field was used for the computation. resources provided. Dr Shelyag is the recipient of an
Despite the detailed characteristics of torsional mo- AustralianResearchCouncil’sFutureFellowship(project
tions in magnetic field concentrations still need to be number FT120100057).
REFERENCES
Beeck,B.,Collet,R.,Steffen, M.,etal.2012,A&A,539,A121 Keller,C.U.,Schu¨ssler,M.,V¨ogler,A.,&Zakharov, V.2004,
Cheung,M.C.M.,Schu¨ssler,M.,&Moreno-Insertis,F.2007, ApJ,607,L59
A&A,461,1163 Kitiashvili,I.N.,Kosovichev,A.G.,Mansour,N.N.,Lele,S.K.,
Irwin,A.W.2012,AstrophysicsSourceCodeLibrary,11002 &Wray,A.A.2012, Phys.Scr,86,018403
Spectro-polarimetric simulations of solar limb 9
Kitiashvili,I.N.,Kosovichev,A.G.,Lele,S.K.,Mansour,N.N., Shelyag,S.,Cally,P.S.,Reid,A.,&Mathioudakis,M.2013,ApJ,
&Wray,A.A.2013,ApJ,770,37 776,L4
Kitiashvili,I.N.,Couvidat,S.,&Lagg,A.2014,arXiv:1407.2663 Shelyag,S.,&Przybylski,D.2014, arXiv:1405.5954
Koesterke,L.,AllendePrieto,C.,&Lambert,D.L.2008,ApJ, Socas-Navarro,H.,TrujilloBueno,J.,&RuizCobo,B.2000,
680,764 ApJ,544,1141
Leenaarts,J.,Carlsson,M.,&RouppevanderVoort,L.2012, Socas-Navarro,H.2011, A&A,529,A37
ApJ,749,136 Socas-Navarro,H.,delaCruzRodriguez,J.,AsensioRamos,A.,
Lites,B.W.,Casini,R.,MansoSainz,R.,etal.2010, ApJ,713, TrujilloBueno,J.,&RuizCobo,B.2014,arXiv:1408.6101
450 Spruit,H.C.1976,Sol.Phys.,50,269
Moll,R.,Cameron,R.H.,&Schu¨ssler,M.2011, A&A,533,A126 Stein,R.F.2012,LivingReviewsinSolarPhysics,9,4
Moll,R.,Cameron,R.H.,&Schu¨ssler,M.2012, A&A,541,A68 Tsuneta,S.,Ichimoto, K.,Katsukawa, Y.,etal.2008,Sol.Phys.,
Sekse,D.H.,RouppevanderVoort,L.,DePontieu, B.,& 249,167
Scullion,E.2013,ApJ,769,44 V¨ogler,A.,Bruls,J.H.M.J.,&Schu¨ssler,M.2004,A&A,421,
Pereira,T.M.D.,Asplund,M.,Collet,R.,etal.2013,A&A,554, 741
A118 V¨ogler,A.,Shelyag, S.,Schu¨ssler,M.,Cattaneo, F.,Emonet, T.,
Shchukina, N.,&TrujilloBueno,J.2001,ApJ,550,970 &Linde,T.2005, A&A,429,335
Shelyag,S.,Schu¨ssler,M.,Solanki,S.K.,V¨ogler,A.2007,A&A, Wedemeyer, S.,&Steiner,O.2014,arXiv:1406.7270
469,731
Shelyag,S.,Keys,P.,Mathioudakis,M.,&Keenan,F.P.2011,
A&A,526,A5
Shelyag,S.,Fedun,V.,Keenan,F.P.,Erd´elyi,R.,&
Mathioudakis,M.2011,AnnalesGeophysicae, 29,883