Solar surface and atmospheric dynamics: The Photosphere

0.51 MB·English

by  V. Martinez Pillet

Noname manuscript No.
(will be inserted by the editor)
Solar surface and atmospheric dynamics
The Photosphere
Mart´ınez Pillet, V.
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0 Received: date/Accepted: date
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Abstract Various aspects of the magnetism of the quiet sun are reviewed. The
a
J suggestion that a small scale dynamo acting at granular scales generates what
9 we call the quiet sun fields is studied in some detail. Although dynamo action
2 has been proved numerically, it is argued that current simulations are still far
from achieving the complexity that might be present on the Sun. We based this

] statement not so much on the low magnetic Reynolds numbers used in the simu-
R
lationsbut, aboveall,in the smallnessof the kineticReynolds numbers employed
S
by them. It is argued that the low magnetic Prandtl number at the solar surface
.
h mayposeunexpected problemsfortheidentificationof theobserved internetwork
p fields with dynamo action at granular scales. Some form of turbulent dynamo at
- bigger (and deeper) scales is favored. The comparison between the internetwork
o
r fields observed by Hinode and the magnetism inferred from Hanle measurements
t areconvergingtowardsasimilardescription.Theyarebothdescribedasrandomly
s
a oriented,largelytransversefields in theseveral hecto-Gaussrange.These similar-
[
ities are ever making more natural to assume that they are the same. However,

1 andbecauseofthelargevoidsofmagneticfluxobservedinthespatialdistribution
v of the internetwork fields, it is argued that they are not likely to be generated
3 by dynamo action in the intergranular lanes. It is concluded that if a dynamo
3 is acting at granular scales, the end product might have not been observed yet
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at current spatial resolutions and sensitivities with the Zeeman effect. Thus an
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effort to increase these resolutions and polarimetric sensitivities must be made.
.
1 New ground- and space-based telescopes are needed. The opportunity offered by
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the Solar Orbiter mission to observe the Quiet Sun dynamics at the poles is seen
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as oneof the mostimportanttestsfor confirmingtheexistence,or otherwise,of a
1
granularlydriven surface dynamo.
:
v
i Keywords Quiet Sun magnetism · turbulent dynamo
X
r
a InstitutodeAstrof´ısicadeCanarias
38200, LaLaguna, Tenerife,Spain
Tel.:[phone]
Fax:[phone]
E-mail:[email protected]
2 Mart´ınezPillet,V.
1 Introduction
1
A consensus about the existence of a small-scale dynamo (SSD ) operating at
the solar photosphere is being consolidated in today’s solar physics (see, e.g.,
Vo¨gler and Schu¨ssler2007;Abbett2007;PietarilaGraham et al.2010;Stein2012,
for a review). High resolution magnetograms from ground and (mostly) space-
based telescopesobservedin theinternetworkareoftenused toindicatethatsuch
a surface dynamo exist (e.g. Danilovicet al. 2010a; Lites 2011). On theoretical
grounds, simulations of various kinds have been used to suggest how universal
the various ingredientsof such a dynamo seems to be (Moll et al. 2011). They all
indicatethat turbulentshear stresses actingon the inertialrange act as the main
mechanismabletoefficientlyconvertkineticintomagneticenergy.Theconclusions
from the various simulationsof turbulence in a conducting fluid seems to be that
it would have been a lot harder to explain the absence of a surface SSD than its
presence. With an emphasis on the observationalside, we review in this work the
currentstatusofthisconsensusandtrytopinpointwhichaspectsaremoresolidly
established and which are less settled.
Section 2 will be the only one that concentrates on simulations and the theo-
retical aspects related to the problem of the existence of SSDs on the Sun. It will
addressthemostcontroversialargumentquestioningtheexistenceofsuchamech-
anism,namelythefactthatthesolarconvectivezonehasamagneticPrandtlnum-
ber thatisordersof magnitudesmallerthanone,whilesimulationsworknearthe
∼1regimemostofthetime.LowmagneticPrandtlnumbersareknowntoseverely
discourage dynamo action since the early simulations of convectively driven tur-
bulentdynamos(Nordlund et al.1992;Schekochihin et al.2004a,2005).Recently,
progresshasbeenachieved,however,thatindicatesthatanSSDisindeedpossible
inthelowmagneticPrandtlregime(Iskakov et al.2007;Schekochihin et al.2007;
Brandenburg2011).But thesituationis notconclusiveand thepapersaddressing
this issue often resort to the fact that a mixed polarity field is observed at the
solar surfaceas the firmest indicationthat such a mechanism should exists. How-
ever, and in the absence of a clear proof that this observed (internetwork) fields
originatefromanSSD–andsuchaproofisnotavailableyet–theonlyprogressto
settle this issue will come from further work in the simulationfront.
The observational arguments that have been put forward to favor the pres-
ence of a solar surface dynamo are discussed later in Section 3. There are ba-
sically two such arguments. First, the evidence from the observed Hanle effect
in lines such as the SrI 4607 ˚A line and the careful modeling of these signals
indicate the existence of a tangled field with a mean strength of < B >∼ 130
G (TrujilloBueno et al. 2004) some few hundred kilometers above the solar sur-
face (see also TrujilloBueno et al. 2006, and references therein). This number
was originally derived under some model assumptions that made it uncertain
to within a factor two. However, a recent study (Shchukina and Trujillo Bueno
2011) of the predicted Hanle signals from the MHD simulations described in
PietarilaGraham et al. (2009b) has eliminated some of this model dependency
and confirmed such large mean field strengths. As a mixed polarity tangled field
at unresolved scales leaves basically no trace in the Zeeman profiles, these fields
1 Small scale here refers to generation of magnetic fields at scales smaller than the energy
injectionone,thegranulation.
Solarsurfaceandatmosphericdynamics 3
havealwaysbeen a primecandidateto be considered as originatedfrom a surface
SSD.Ifthetanglingoccursatscalesnearorabovepresentresolutions,somesigna-
turescanbedetected,though.Itisunclearifthesefieldshavebeenobservedusing
theZeemaneffect(butseeLites et al.2009;Bellot Rubio and Orozco Su´arez2012,
andSection3).ThesecondobservationalargumentinfavorofanSSDcomesfrom
theHinodespectropolarimeter(SP)instrument(Tsuneta et al.2008;Kosugi et al.
2007) and its unprecedented characterization of the internetwork fields using the
Zeemaneffect(Lites et al.2008;Ishikawa and Tsuneta2011;Orozco Su´arez and Bellot Rubio
2012). While transverse fields were known to exist in the quiet sun, as originally
foundbytheAdvanced StokesPolarimeter(ASP;Lites et al.1996),itwastotally
unexpected thatthesefieldshavea predominanttransversecharacter.Thistrans-
verse nature seems to fit in a natural way with an origin related to a turbulent
dynamo as shown by recent simulations(see Schu¨ssler and V¨ogler 2008).
Apossibleoutcomegiventhisstateofaffairscouldbeasfollows.Theexistence
ofanSSDactingatgranularscalesatthesolarsurfacecaneventuallybeconfirmed
from a set of improved SSDs simulations(along the lines described in Section 2).
In them, a continuous distributionof fields is obtained that is able to explain the
Hanledepolarizationlevels from those fields created at the smaller scales and the
largely horizontal internetwork fields from those at larger scales. The separation
between these two sets of fields does not have to be sharp and a range of spatial
scales can contribute to both the Zeeman and Hanle results (or, perhaps, that
the two observed processes are due to fields exactly at the same scales as it can
beinferredfromtherecentresultsofBellot Rubio and Orozco Su´arez2012).Note
that, such a field distribution would solely depend on the existence of the always
present turbulent convective motions near the surface and, thus, should be inde-
pendentoflatitudeandofactivitycyclephase.Whilethisconclusionseemsrather
plausible given the current evidence, the aim of this work is to address some of
the known problems that might prevent such an outcome. In particular, Section
4 describes some observations recently obtained with the IMaX/SUNRISE mag-
netograph(Mart´ınez Pillet et al.2011;Solanki et al.2010)thatshowregionsthat
display very little magnetic activity, either measured as residual signals in time-
averageddeepmagnetogramsorasevidencedbyalackoffluxemergenceepisodes
in the form of small-scaleloops (as discovered by Mart´ınez Gonza´lez et al. 2012).
It is unclear how these voids are compatible with a granularly driven SSD. That
the situation is far from clear has been corroborated recently by the study of
(Stenflo 2012, based on SDO/HMI magnetograms)who proposes the existence of
a basal flux of order 3 G that is suggested to be an upper limit to the efficiency
of an SSD at the solar surface. Accordingto this result all the internetworkfields
observed with Hinode/SP will not be generated through such a mechanism and
only the Hanledepolarizing fields could be originatedthrough it (if at all).
In spite of this somewhat confusing situation, it is important to stress that
our understandingabout the natureand the propertiesof the quiet sun fields has
improved enormously in recent years. But it is clear that a number of important
questionsremainsonthetheoretical/modellingsideandontheobservationalfront.
Section 5 finishes this work proposing a way forward to further advance in this
understandingofthequietsun magnetism.Notsurprisingly,wepromotean effort
toincreasethepolarimetricsensitivityandthespatialandtemporalresolutionsof
both,theHanleand theZeemanobservations.Studyingthestatisticsofthequiet
sun fields at various latitudes will also provecrucial.
4 Mart´ınezPillet,V.
2 Small scale dynamo action at low Pm. Implications for the solar case
Theseminalreferencethattriggeredthepresentdebateon theexistenceof acon-
vectively driven turbulent dynamo at the solar surface was the work of Cattaneo
(1999), although the debate is older (see, e.g., Petrovay and Szakaly 1993; Lin
1995). It is important to point out that this work mentioned, both, the granular
andsupergranularscalesaspossiblecontributorstosuchnon-helicaldynamo.The
simulations used closed upper and lower boundaries with vertical fields in both
of them. The Reynolds and magnetic Reynolds numbers could be clearly defined
for this simulationthanksto the fixed computationalgridused to solvethe MHD
equations. They were Re=ul/ν =200 and Rem =ul/η =1000, with l the char-
acteristic length of the energy injecting convective cells, u the velocity of these
cells and ν and η the molecular viscosity and the magnetic diffusivity, respec-
tively. These numbers are large enough to ensure the development of turbulence.
But it is important to note that Re was five times smaller than Rem (magnetic
Prandtl number of Pm = Rem/Re = ν/η = 5 > 1). Under these circumstances,
themagneticfield sees a smoothmean flow efficientlyactingon it.Thenumerical
simulationresultedindynamoactionsaturatingat20%ofthekineticenergyflow.
Thecrucialingredientwasthechaoticnatureofthedrivingflows.Figure2ofthis
paper already showed that, at the surface, the strong fields were localized in the
downflow lanes, while the cell interiors showed no (vertical) field signature. The
situation was different in deeper layers where fluctuating fields were filling basi-
cally the whole volume. At the time of the publication, the dominant transverse
nature of the internetwork was not known (see Section 3) and this aspect was
not analyzed. For this reason, the profiles synthesized by S´anchez Almeida et al.
(2003) using these simulations concentrated on the study of the asymmetries in-
ducedintheStokesVprofiles(circularpolarization)anditscomparisonwiththose
observed in the internetwork. A shortage of asymmetries indicated that the sim-
ulations still did not achieveas much complexityas present in the Sun. However,
usingthissynthesis,andafterincludingeffectssuchastelescopediffraction,itwas
predictedthatwhenimprovingthespatialresolutionfrom1 arcsecto0.15arcsec,
one should detect four times more Stokes V polarizationsignals.
A numberofassumptionsmadein thissimulation(suchas theBoussinesqap-
proximation)havebeen relaxed in morerecent works.The morerealisticones (in
terms of their proximity to the physical conditions on the Sun) are those made
with the MURaM code (Vo¨glerand Schu¨ssler 2007; Schu¨ssler and Vo¨gler 2008;
PietarilaGraham et al. 2010). In particular, they have addressed the important
questionoftheroleplayedbytheclosedboundaryconditionsassumedinCattaneo
(1999).Stein et al.(2003)pointedoutthat,inthesolarconvectivezone,fieldsare
submerged efficientlyto the bottomof the convectivezone by strong and concen-
trated downflows showing little recirculation near the surface. This recirculation
wasartificiallyenhancedinthesimulationsofCattaneo(1999)bytheuseofclosed
boundary conditions. Stein et al. (2003) concluded that diverging upflows sweep
thefluidintodownflows,oftenvortical,wherestretchingandtwistingbecomesef-
fective(andbalancedbydiffusion)butallthesefieldsareratherrapidlysubmerged
down into the bulk of the convectivezone. The energy added to the flux that vis-
its the surface was a very small fraction of the global budget of magnetic energy
and the effect cannot be considered a local dynamo. This criticism has, however,
been superseded by the MUraM simulations which used an open boundary and
Solarsurfaceandatmosphericdynamics 5
allowfora non-zeropointingflux atthebottomboundary.Thewayin whichthis
boundary condition was implemented in the simulations of V¨ogler and Schu¨ssler
(2007) was by imposing an artificially increased magnetic diffusivity there. This
diffusivityensuredthathorizontalfieldsmovingdownwardinthesimulationleave
the box unimpeded while, at the same time, prevented horizontal flux from en-
teringthedomain.Allflux leavingthebottomboundaryin thesesimulationswas
created by dynamo action inside the box. Vo¨gler and Schu¨ssler (2007) concluded
thatwhilethedownwardpumpingoffluxoutsideofthedomaindoesindeedreduce
thegrowthrateofthedynamo,itdoesnotshutitdown.Theypredictthataslong
as a sufficiently high Rem is used (above the critical magnetic Reynolds number,
ReC), dynamo action will be observed in the simulations. Specifically, they see
m
exponential growth of the magnetic energy for Rem of 2600, while they find a
decrease for Rem below 1300. Now, here we should caution that the exact values
of Rem and Re (and thus of Pm) are not as easily defined as in Cattaneo (1999)
simulations. The need to resolve shocks with artificial viscosity schemes or the
implementationof the bottom boundary diffusivity necessarily implies that these
numbersaremoredifficulttoascertain.AnestimateoftheeffectiveReynoldsand
PrandtlnumbersfortheMURaMsimulationswasgivenbyPietarilaGraham et al.
(2010)usingvariousmomentsofthevelocityandmagneticspectra(orTaylormi-
croscales). The various dynamo runs available from this code turn out to have
Rem ∈ [2100,8300] (with the latter value using a grid resolution of 4 km) and
Pm ∈ [0.8,2]. This set of simulations all displayed an SSD generating magnetic
fields inside their volume. The conclusion was that current MURaM simulations
(withPm ∼1) willshow dynamoaction as long as Rem >ReCm ∼2000.Themain
mechanism identified for this generation was the stretching and twisting of field
linesbyfluidmotionsintheinertialrangeofthespectrumofvelocityfluctuations.
Inparticular,itwasconcludedthatdynamoactionisconcentratedintheturbulent
downflows as field line stretching against magnetic tension is very efficient there
(e.g. Stein 2012, for a review). In order to clarify the nature of the observed dy-
namoaction,Moll et al.(2011)haveanalyzedtheunderlyingphysicalmechanism
under various physical conditions and assumptions. They concluded that for the
casesstudied(incompressibleMHD,Boussinesqconvectionandcompressiblesolar
convection), the field is amplified by similar inertial range shear stresses that are
independent of the conditions at the injection scale. The inclusion of compress-
ibilityeffects or the asymmetry between upflows and downflowsgenerated by the
strong stratification did not influence the result. They, thus, termed the dynamo
mechanism as universal.
OneconcernremainsabouttheexistenceofapossibleSSDontheSun,though.
The problem has been known since the early studies of dynamo action in con-
ducting fluids. It was originallyformulated by Batchelor (1950) who studied how
turbulent motions stretch the field lines and amplify the magnetic energy as long
asthisprocessremainsunimpededbyohmicdiffusion.Fieldlinestretchingispro-
duced by fluid motions in the inertial range whose dissipation scale is set by the
viscosityofthefluid.Highviscosityν couplesthefieldlinestotheflowandallows
ittobendthemefficiently.Largemagneticdiffusivityη decouplestheplasma(and
theflows)fromthefield linesand preventsthebending.Thus,itwasalwaysclear
thatthe efficiency of theSSD was goingto be controlledby theinterplayof these
twoeffects as measured by theratioPm =ν/η. Clearly,both conditionsRem ≫1
(tofavorfieldlinestretching)andPm ≫1(tocouplefluidmotionsandfieldlines)
6 Mart´ınezPillet,V.
Fig. 1 The Reynolds number, magnetic Reynolds number and (inverse) Prandtl number in
the solarconvective zone according tothe mixing-lengthmodel of Spruit(1974). TheX near
thesurfacemarksthetipicalvaluesachievedofbothReandRem inthesimulations.
boost local dynamo action. Based on an analogy between vorticity and magnetic
fields Batchelor(1950)even concludedthatforPm <1 noSSD waspossible.This
conclusion was later criticized by a number of authors as the analogy cannot in-
clude the different initial and boundary conditions seen by these two fields (see,
e.g.Boldyrev and Cattaneo2004).However,simulationsintheearly90’s(see,e.g.,
Nordlund et al. 1992), including compressibilityand strong stratification,already
resulted in dynamo action only for Pm ≥ 1 with efficient shutting down of the
dynamo for Pm < 1. Other simulations encountering the same problem are dis-
cussed in Boldyrev and Cattaneo (2004) and in Schekochihin et al. (2005). Thus,
thequestionoftheexistenceofanSSDatlowPrandtlnumbershasreceivedsome
attentionin recent years.
Before we briefly describe the results from the numerical studies about the
existence of an SSD at low Prandtl numbers, it is important to remember what
are the actualnumbers that occur in the solar convectivezone and get an idea of
howfarorhowclosearewefromsimulatingtheseconditions.Tothisend,Figure1
−1
shows Re, Rem and Pm as computed in themixing-lengthbased model of Spruit
(1974). The velocities at the injection scale u are obtained as part of the model
and the characteristic length is assumed here to be l = z/2, with z the depth
5
inside the convective zone. The magnetic Reynolds number changes from 10 at
9
thephotosphereto10 atthebottomoftheconvectivezone,whereastheReynolds
12 −7 −3
number stays constant at a level of 10 . This makes Pm ∈[10 ,10 ], with the
smallest value reached at the photosphere. Thus, everywhere in the Sun, we have
Solarsurfaceandatmosphericdynamics 7
Re ≫ Rem ≫ 1 and Pm ≪ 1 which is exactly the regime where the existence of
an SSD becomes problematic. It is generally believed that for a sufficiently high
Rem there will always be an SSD at work. But the above mentioned simulations
prompted a deeper study about the existence and nature of an SSD under solar
conditions.Asalreadymentioned,thesimulationsbyCattaneo(1999)hadPm =5
and those from the MURaM code alwaysmove close to the Pm ∼1 case (there is
onewithPm =0.8thatis discussed below).NotethattheregimewhereRem and
Re are similar is actually very favorable for the numerical codes as similar grid
sizes resolvethe dissipativescales of both, magnetic and velocityfields.
WhatisthephysicalargumentbehindthisdifficultytogenerateanSSDwhen
Pm ≪ 1?. Under such conditions the viscous (lν) and resistive (lη) scales follow
lη/lν ∼Pm−3/4 ≫1(Schekochihin et al.2004a, 2005)and theresistivescalelη falls
in the middle of the inertial range. Turbulent eddies of scales l > lη do the nec-
essary field line bending and twisting for dynamo action at a rate of u /l (with
l
ul the typical flow velocity at this scale). If Pm > 1 only these eddies occur and
the field lines always see a spatially smooth flow. However, if Pm < 1 one has
now eddies below the resistive scale l < lη. These eddies act on the field as a
turbulent diffusion with diffusivityu l and destroy magneticenergy. It is the pre-
l
dominanceofthislastprocesswhatcanmakedynamoactionimpossibleasitwas
seen in the previously mentioned simulations. Using an incompressible spectral
2
MHD code and the PENCIL code , Schekochihin et al. (2005) studied what are
the possible asymptotic limits when Re ≫ Rem and the corresponding values of
the ReC for the existence of a dynamo. The above described effect always trans-
m
lates into a sharp increase in ReCm as Pm → 0 (see also PietarilaGraham et al.
2009a), but does not prevent the existence of a dynamo in this regime. The two
asymptotic limits are, first, as Re → ∞, ReC → const, so that dynamo action is
m
possible for higher Rem and, second, ReCm → ∞ with ReCm/Re → PCm =const, in
which case no dynamo is possible (turbulent diffusion efficiently dissipates mag-
netic energy at small scales). Which exactly of the two asymptoticlimitsprevails
has been under much debate in recent years. While Schekochihin et al. (2004a)
andSchekochihin et al.(2005)(seetheirFigure2)favortheexistenceofaPC (no
m
dynamo)fromsimulationsofincompressiblemagnetoconvectionreachingvaluesof
Pm assmallas0.15,Boldyrev and Cattaneo(2004)providedanalyticalarguments
favoringthe existence of a ReC.
m
Whilethedebatein themidlastdecadedidnotlookpromisingforconfirming
the existence of an SSD at the solar surface, the situation has changed recently
(even ifnot completelysettled).Schekochihin et al.(2007) (seealsoIskakov et al.
2007)performedsimulationsofincompressibleMHDturbulencereachingvaluesof
Pm =0.1 and with a sufficiently high Rem that indicated a plateau region where
a ReC is observed (see their Figure 1b). Admittedly, the number of such simula-
m
tions proving the existence of this plateau is very small but the authors consider
it enough numerical certainty. The results from Brandenburg (2011) using the
PENCIL code (that includes compressible effects) and low values of Pm resulted
indynamoactionbeingactivatedaswell.Pietarila Graham et al.(2010)alsofind
growth of magnetic energy in the one case they analyzed with Pm = 0.8. Thus,
themostadvancedexistingnumericalsimulationsofsmall-scaledynamoactionin
2 Seehttp://www.nordita.dk/software/pencil-code.
8 Mart´ınezPillet,V.
turbulent MHD currently favor the occurrence of such a process in the low Pm
regime. However,a number of caveats remain:
– First, and most importantly, ReCm increases with decreasing Pm. The exact
factor depends on the specificities of the simulations. Boldyrev and Cattaneo
(2004) suggest a factor 7 increase in ReCm when shifting from the Pm ≫ 1
to the Pm ≪ 1 case. They use an analytical model of isotropic and homoge-
neous turbulence that includes the extra roughness of the velocity field for
Pm < 1. Schekochihin et al. (2007) find from incompressible forced turbu-
lence a factor 3 increase. As in the MURaM simulations one has ReC ∼2000
m
(PietarilaGraham et al. 2010), this means that as soon as we move into the
low-Pm regime, we need magnetic Reynolds numbers above at least 6000
to be able to trigger dynamo action. These magnetic Reynolds numbers are
not currently achieved by this code. In particular, none of the runs used by
Danilovicet al. (2010a) would be able to actually sustain dynamo action. On
top of that, the saturated field strength is known to decrease with decreasing
Pm, thus the expected field strengths willbe smallerthan thosecomputed for
Pm ∼ 1. The exact amount of this reduction is still a very controversial issue
(seeSchekochihin et al.2004a,2007;Brandenburg2011)anditsmagnitudefor
the solar case unknown. But the net effect will be a reduction in the fields as
compared to those computed for Pm >1.
– Tocompletethedemonstrationoftheexistenceofadynamodrivenbyfluidmo-
tionsintheinertialrangeatlowPmvalues,agrowthrateofthedynamoscaling
withRe1/2 mustbeobtainedfromthesimulations.NeitherSchekochihin et al.
m
(2007) nor PietarilaGraham et al. (2010) have reached that (see Figure 3 of
thelatterwork).Simulationswithanincreasedresolutionareneededtofinally
settle this issue. Schekochihin et al. (2007) concludes that, as long as this is
not achieved, the mechanism that sustains the growth of the magnetic field
fluctuationsin the low-Pm regime will remain basically unknown.
– Schekochihin et al.(2007)andIskakov et al.(2007)concludedthatinthePm ≪
1 regime, the magnetic energy spectra is fundamentally different from that
foundinthePm ≫1.Thespatialdistributionofthegrowingmagneticfieldsis
qualitativelydifferenttoo(seeFigure2inSchekochihin et al.2007).Thisindi-
cates that the use of simulationsin the Pm ∼1 range to compute the ensuing
Stokes profiles and its comparisonwith those observed may not be justified.
– TheoftensimulatedcasewithPm ∼1hasthesamespectralenergyproperties
and field distribution as the Pm ≫ 1 case (Schekochihin et al. 2004b). This
is probably why the case with Pm =0.8 simulated by PietarilaGraham et al.
(2010) was so similarto the those in the range of Pm ∈[1,2].
Letusfinalizethissectionbystressingthatifthesituationlooksconfusing,itis
becausethishasindeedbeenthecaseinthistopicforsometime(seeIskakov et al.
2007; Schekochihin et al. 2007, who speak about a frustrating outcome). One ar-
gument commonly given to promote the existence of an SSD is the observation
of a mixed polarityfield in the internetworkregions of the Sun (and many of the
abovementionedworksusethisargumentonewayoranother).Figure2 of,both,
Cattaneo (1999) and Vo¨gler and Schu¨ssler (2007) clearly indicate that this is a
reasonable argument. The point we want to stress here is that the same applies
to Figure 10 from Stein and Nordlund (2006), which does not include an SSD.
PietarilaGraham et al. (2009a) estimate for this simulation a Rem ∼ 600, which
Solarsurfaceandatmosphericdynamics 9
isknowntobetoosmalltodevelopdynamoaction.However,theirmixedpolarity
distributionlocated in the interganularlines looks as ‘solar’as in the other cases.
In the work of Stein and Nordlund (2006) emphasis is made on divergingupflows
bringing flux to the surface, expulsion to the intergranular lanes and sweeping
of field lines into strong downflows that carry the flux into deeper layers. These
simulations extent typically further down than those that concentrate in SSD
generation and also include larger scales such as those associated with the meso-
granulation.AsshowninFig.1, thedeeper wemoveintotheSun,thelargerRem
andPm (althoughstillsmallerthanone).Thus,avalidquestionisifitisnotmore
natural to ask if a solar SSD exists at meso- and supergranular scales and, if so,
whether they dominate over that that might exists at granular ones. This point
will be further discussed in Section 4.
3 Observed signatures of small scale dynamo action at the solar surface
We now turn to the observational aspect of the discussion and ask the question:
HaveweseenthefieldsproducedbyapossibleSSDoperatingatthesolarsurface?
As it will become evident, there has been, as before, solid observational progress
and areas with much confusion. Basically, two candidates exist that are often
considered as by-products of an SSD, the internetwork fields and the, so-called,
hidden fields that generate the Hanle depolarizationsignatures.
3.1 Zeeman signals
There is no question that Hinode/SP data has produced a major quantitative
andqualitativejumpforwardinourunderstandingoftheinternetworkfields.The
publication by Lites et al. (2008) of a gigantic slit scanned map with consistent
−3
10 polarimetric sensitivity and homogeneous spatial resolution of 0.3 arcsec
changed our view of the quiet sun magnetism. In this map, a myriad of patches
withpredominantlinearpolarizationsignatureswasdiscovered.TheASPalready
found the existence of episodic burst of largely transverse fields (the Horizontal
InternetworkFeatures,HIF, Lites et al.1996) but they werethoughttobe rather
sporadic.Theonlypreviousindicationoftheirexistenceandglobalcharactercame
from the SOLIS instrument as found by Harvey et al. (2007). But no prediction
fromthesimulationsorestimateoftheirmagnitudewasavailable.Theexistenceof
this ubiquitous horizontalfield has now received full confirmationfrom the SUN-
RISE/IMaX data(Danilovicet al.2010b) who could makethefirststudy of their
evolution(seetheanimationin Solanki et al.2010)andestablishasolidstatistics
of their lifetimes.Both instruments,Hinode/SP and SUNRISE/IMaX coincidein
locatingthese HIF at the borders of the upflowinggranules for a largefraction of
their evolution. Lites et al. (2008) emphasized that the linear polarization signa-
tures were not co-spatialwith line-of-sightfields that were more frequentlyfound
in the intergranularlanes.
BeforethepublicationofLites et al.(2008)mostofthediscussionontheinter-
network flux concentrated on obtainingits mean unsigned flux (see Solanki 2009,
for a review on this topic previous to the impact of the Hinode measurements).
The idea was that an intricately complex field with mixed polarities observed
10 Mart´ınezPillet,V.
in the best available Stokes V magnetograms was the outstanding description of
the internetwork fields. Increased resolution (or sensitivity) will result into ever
increasing amounts of longitudinal signals observed as there was less and less
cancellation due to instrumental effects. Either because of lack of reliable mea-
surements of the field inclination or because of a habit to focus studies of solar
magnetism exclusively in longitudinal magnetograms, no mention to its possible
transversecharacterwas traditionallymade. As the field strengths were expected
to be near or below equipartitionvalues (less than 500 G, see Keller et al. 1994),
these fields were not thought to be necessarily vertical either. Before the Hinode
results, measurements of < |B | > (the spatially averaged unsigned longitudinal
L
flux in the internetwork) were routinely being made and its variation with the
spatial resolution closely followed (S´anchez Almeida et al. 2003). In a way, Hin-
ode/SP results have made this emphasis obsolete. We now know that these fields
arelargelytransverseandoneshouldmainlycareabout<|B |>orsimplyabout
T
thespatiallyaveraged<|B|>.We shouldcautionherethatthesemagnitudesare
obtained by observations of different Stokes parameters that have different sensi-
tivitiestotherealmagneticfieldcomponentsontheSunandtothefractionofthe
observed pixel that they occupy (the filling factor). Thus, the steps to compute
< |B| > from the observed < |B | > and < |B | > are more problematic than
L T
what one might anticipate. Lites et al. (2008) estimated that the quiet sun map
obtainedbyHinode/SPhad a<|Bapp|>of11G (orMx cm−2) anda <|Bapp|>
L T
of 55 G. These estimates were based on using integrals of the Stokes parameters
thatwerecalibratedagainstmagneticfluxesbutwithnoaccountforthefractionof
thepixeloccupiedby thefields.Thisiswhythey arenamed‘apparent’fluxes.An
analysisperformedbyOrozco Su´arez et al.(2007)ofthesamedata,but thistime
using a Milne-Eddington (M-E) inversion code including a filling factor as a free
parameter,resultedalsoinapredominantlytransversenatureoftheinternetwork,
albeit with a smaller ratioof transverseto longitudinalapparent fluxes.
It is no exaggeration to say that the ratio measured by Lites et al. (2008)
<|Bapp|>/<|Bapp|>∼5 cameas a surpriseand was, thus, subjected to a deep
T L
scrutiny by the community.
Several factors can create a systematic bias in this ratio. Spatially averaging
noise affects a positively defined quantity such as B in a way different than
T
what it does to a signed quantity (B ). As the Zeeman effect has a sensitivity
L
different for each of these two components, the visibility of a given field strength
is different depending on whether it is a field aligned with the LOS or perpen-
dicular to it. In particular, fields close to the noise levels translate into different
visibilitythresholds. Last but not least, there is the already mentioned difference
in how the filling factor couples to the real field strengths and inclinations for
eachoneofthetwocomponentsand dependingon thespecific methodofanalysis
used. These effects and their impact into the factor 5 obtained by the first Hin-
ode/SPmeasurementshavebeenstudiedbyvariousauthors(Asensio Ramos2009;
Borrero and Kobel 2011; Stenflo 2011; S´anchez Almeida and Mart´ınez Gonza´lez
2011; Steiner and Rezaei 2012, see the latter for a review). It all translates into
understanding how exactly noise influences the final result given the method of
analysis one follows and the various thresholds for inclusion of a given pixel or
not. Depending on the specific case, different values for < |Bapp| >, < |Bapp| >,
T L
or inverted parameters B, inclination, azimuth and filling factor are obtained.
Figure 2 shows the central portion of the same magnetogram used in Lites et al.