Accepted by The Astrophysical Journal, November 1998
Dynamics of the Solar Chromosphere.
II. Ca II H.... V and K.... V Grains versus Internetwork Fields
B.W.Lites
High ltitude Observatory,National Center for tmospheric Research,P.O.Box 3000,Boulder CO 80307-3000
R.J.Rutten
Sterrekundig Instituut,Postbus 80 000,NL –3508 T Utrecht,The Netherlands
T.E.Berger
Lockheed-Martin Solar and strophysics Lab,Dept.H1-12,Bldg.252,3251 Hanover St.,
Palo lto,C 94304
Abstract
We use the Advanced Stokes Polarimeter at the NSO/Sacramento Peak Vacuum Tower Telescope to search for spatio-
temporal correlations between enhanced magnetic .elds in the quiet solar internetwork photosphere and the occurrence
of Ca II H 2.... grains in the overlying chromosphere.We address the question of whether the shocks that produce
the latter are caused by magnetism-related processes,or whether they are of purely hydrodynamic nature.The
observations presented here are the .rst in which sensitive Stokes polarimetry is combined synchronously with high-
resolution Ca II H spectrometry.We pay particular attention to the nature and signi .cance of weak polarization
signals from the internetwork domain,obtaining a robust estimate of our magnetographic noise level at an apparent
.ux density of only 3 Mxcm -2 .For the quiet Sun internetwork area analyzed here,we .nd no direct correlation
between the presence of magnetic features with apparent .ux density above this limit and the occurrence of H 2....
brightenings.This result contradicts the one-to-one correspondence claimed by Sivaraman &Livingston (1982).We
also .nd no correspondence between H 2.... grains and the horizontal-.eld internetwork features discovered by Lites
et al.(1996).
1 Introduction
This paper continues studies of dynamical phenomena
in the solar chromosphere as displayed by the Ca II H&K
resonance lines at . =396 .849 nm and 393.368 nm.n
earlier study (Lites,Rutten &Kalkofen 1993;henceforth
Paper I)concentrated on the dynamics of chromospheric
network elements.We now turn to the internetwork do-
main,i.e.,the areas of quiet-Sun chromosphere that over-
lie photospheric supergranulation cell interiors and that
are bordered by the irregularly patterned chromospheric
network.In particular,we address the long-standing
issue whether the so-called Ca II H 2.... and K 2.... grains,
which intermittently appear within internetwork areas,
mark sites of enhanced magnetic .eld.In order to clarify
this issue,we begin by reviewing its context.
1.1 H2.... and K2.... Grains
The major dynamical phenomenon displayed by the
Ca II H&K lines in internetwork regions consists of the
"chromospheric three-minute "oscillation.This is nei-
ther a purely chromospheric nor a purely three-minute
wave mode (e.g.,Kulaczewski 1992);the term describes
the wide-band (f ˜3 -8 mHz)modulation peak that
gradually replaces the .ve-minute p -mode peak in tem-
poral power spectra describing Doppler shift or inten-
sity variations measured at increasing height of forma-
1.tion (Fig.1 of Noyes 1967,reprinted as Fig.1 of Rutten
1995).This modulation occurs in a "mesoscale "pattern
in which the characteristic patches of coherent oscillation
measure a few arcseconds,somewhat smaller than the co-
herent patches resulting from p -mode interference in the
photosphere (Fig.3 of Paper I).In movies constructed
from high-resolution (i.e.,of order 1 arcsec)Ca II K .lter-
grams the oscillation pattern is seen as wispy,thread-like
texture displaying rapid morphology changes which often
give the impression of highly supersonic proper motion
over the surface.The H 2.... and K 2.... grains are intermit-
tent,localized enhancements of this dynamical brightness
pattern.They last less then a minute,often re-appear a
few times at 2 –4 min intervals at about the same place,
and frequently occur in pairs.They are spectrally lim-
ited to a narrow wavelength band (.. ˜8 pm)about
16 pm to the violet of the H&K line centers (e.g.,Cram
&Dam ´e 1983;Figs.1 –2 of Paper I;Fig.3 of Hofmann
et al.1996).This property is the de .ning one that gave
K 2.... grains their name,but their spatio-temporal pattern
is part of the wider band line-center modulation (Fig.2
of Rutten 1994,Fig.1 of Rutten et al.1999).
Figures 1 –3 illustrate the K 2.... grain pattern using im-
ages from high-quality Ca II K and G band (CH lines
around . =430 .5 nm).ltergram sequences taken by
R.A.Shine with the Swedish Vacuum Solar Telescope
at La Palma on October 5,1995.They are part of a
data set described and analyzed in more detail by Loef-
dahl et al.(1998)and Berger et al.(1998);the reduction
included restoration of the G-band images with phase-
diverse speckle techniques.The Ca II K .lter had a
.. =0 .3 nm passband containing the core of the Ca II K
line at . =393 .3 nm.The 70-min temporal average in the
lower panel of Fig.1 demonstrates the rapid variation of
the internetwork brightness patterning by showing con-
siderable suppression of its time-averaged contrast rela-
tive to the network,when compared with the individual
snapshot in the upper panel.
Figure 2 illustrates that the network bright points
("patches ")seen in Ca II K overlie clusters of smaller
scale G-band bright points.The latter are unresolved
even at 0.2 arcsec resolution,lie within intergranular
lanes,and mark locations of strong-.eld .ux elements
(Berger 1997).The three isolated Ca II K features that
are marked in the upper panel behave similarly to the
"persistent .asher "of Brandt et al.(1992,1994).The
full image sequence shows that the identi .ed features
brighten at irregular intervals while migrating at subsonic
speed.Each of the three Ca II K features is accompanied
by intermittent G-band bright points in the underlying
photosphere,as seen in the lower panel for this image
pair.The G-band bright points travel along intergran-
ular lanes at local .ow speeds.They become distorted
or fragment or combine in very dynamical fashion set
Figure 1:A high-resolution (sub-arcsec)Ca II K .ltergram
(upper panel)of the solar surface taken with the Swedish
Vacuum S lar Telescope sh ws both active netw rk (or small
plage)which appears bright in Ca II K,andquiet internet-
w rk which is considerably darker.The area utlined by the
upper rectangle is c mpared to the underlying photosphere in
Fig.2.The l wer rectangle utlines a quiet internetw rk area
sh wn als at subsequent moments in Fig.3.The Ca II K
emission pattern consists of elongatedridges with l calized
enhancements.The lower panel is a temp ral average ver
the 70-min .ltergram sequence.The network patches remain
stably present and retain high c ntrast in the average.The in-
ternetw rk pattern changes rapidly and therefore has greatly
reduced contrast in the time average.
by the evolution of the surrounding granules,but nev-
ertheless maintain a long-term identity that signi .es the
2.Figure 2:A comparison f a partial Ca II K .ltergram,cor-
responding t the upper rectangle in Fig.1,with a simulta-
neous G-bandimage demonstrates the magnetic origin of the
bright Ca II K emissi n patches.The G bandimage maps
the underlying photospheric granulati n at 0.2 arcsec res lu-
tion (the telescope di .raction limit reached by phase-diverse
speckle rest ration)andsh ws tiny bright points that mark
strong-.eld .ux elements.The three isolatedfeatures that
are markedin the upper panel might be taken t represent
internetw rk K 2V grains fr m this single Ca II K snapshot,
but when the image sequences are displayed as movies they
are seen to represent "persistent .ashers "that correspond
to intermittently present G-band bright p ints in the photo-
sphere.
presence of magnetic .eld.
Finally,Fig.3 shows examples of the wispy,rapidly
changing texture which may be seen continuously nearly
everywhere in the internetwork.The .rst two panels il-
lustrate a case of supersonic apparent motion (cf.Stef-
fens et al.1996,Wellstein et al.1998),while the other
panels show repetitive appearance of a pair of adjacent
K 2.... grains.These .ltergrams contain no information
on the spectral signature of the emission features across
the K-line core,so they do not reveal whether they are
"regular "K 2.... grains;i.e.,whether their emission is lim-
Figure 3:The wispy pattern of the internetwork domain and
its rapidvariation are illustratedby selectedframes from the
La Palma Ca II K sequence.The area c rresp nds t the
lower rectangle in Fig.1.The markers in the .rst tw frames,
taken nly 43 sec apart,identify the apparent supers nic mo-
ti n (70 km s - 1 )f a brightening which travels along a pat-
tern ridge.The tw markers in the ther panels (at .xed l -
cations)identify tw concurrent recurrent K 2V grains which
brightened,in phase,a few times at 2 –3 min intervals.
ited to the K 2.... peak alone.However,they are likely to
be K 2.... grains because the texture in these .ltergrams
is set largely by the inner-wing whiskers which precede
the grains (cf.the spectral displays in Figs.4 –5 of Cram
&Dam ´e 1983 and Fig.3 of Hofmann et al.1996)but
display the same spatio-temporal pattern (Rutten 1994,
Rutten et al.1999).
It is also not known whether the migrating "persistent
.asher "of Brandt et al.(1992,1994)and the three fea-
tures marked in Fig.2 emit primarily at K 2.... or whether
they represent a core-wide enhancement similar to that
of network elements.There are no such .ashers obvi-
ously present in the spectral data presented in this pa-
per so that this question remains open.In any case,at
locations well away from the network the .asher phe-
nomenon is rare compared to the ubiquitous K 2.... inter-
network grain/whisker activity.
The extensive older literature on this subject is of
both observational and interpretive nature and dates
back to Hale &Ellerman (1904).It has been reviewed at
length by Rutten &Uitenbroek (1991a)who concluded
that most grains are of acoustic origin and mark sites of
constructive interference between multiple wave modes.
Rutten &Uitenbroek ended their review by predicting
that the question why the grains appear should soon be
3.answered.By now that is indeed the case,but the ques-
tions of where the grains appear and whether their loca-
tions possess diagnostic value are yet open.We address
these here.
The more recent literature on this topic has been re-
viewed by Rutten (1994,1995,1996).The most im-
portant development consists of the successful repro-
duction of repetitive K 2.... and H 2.... grain formation by
Carlsson &Stein (1992,1994,1995,1997)whose work
crowns a sequence of earlier wave modeling e .orts (e.g.,
Leibacher et al.1982;Rammacher &Ulmschneider 1992;
Fleck &Schmitz 1991b,1993;Kalkofen et al.1994;Sut-
mann &Ulmschneider 1995a,1995b).Carlsson &Stein 's
one-dimensional radiation-hydrodynamics simulations of
some of our data presented in Paper I have de .nitely
con .rmed that the repetitive grains mark acoustic shock
interactions in which fast (order of 10 km s -1 )post-shock
down .ows interact with fresh shocks that result from the
steepening of upward propagating acoustic waves.Carls-
son &Stein have thus con .rmed the earlier suggestions
of thay (1970),Cram (1972),and Liu &Skumanich
(1974),the forward data inversion of Mein et al.(1987),
and the grain-formation scenario of Rutten &Uitenbroek
(1991a,1991b).t two of the four solar locations sim-
ulated by Carlsson &Stein (1997)the correspondence
between computed and observed Ca II H spectral behav-
ior is excellent even in detail;for the two other locations
the observations and computations are su .ciently similar
to accept the latter as a qualitatively valid reproduction
of the solar phenomenon.In addition,Carlsson &Stein
(1997)show diagnostic diagrams and results from exper-
iments which clarify to large extent how H 2.... and K 2....
grains form spectrally.The shocks themselves remain
weak;they do not lift or heat the time-averaged chromo-
sphere substantially.However,they nevertheless make
the internetwork chromosphere a medium that is far too
dynamic to be described by traditional hydrostatic mod-
eling (Carlsson &Stein 1995).
The Carlsson-Stein simulations are one-dimensional
and do not answer the question why grains occur where
they do.The success of the simulations indicates that
the internetwork chromosphere portrayed by Ca II H&K
is largely controlled by the directly underlying photo-
sphere,a fact that was earlier established observationally
by measuring large coherence and well-de .ned phase rela-
tionships co-spatially between photospheric and chromo-
spheric internetwork oscillations (e.g.,Deubner &Fleck
1990;Paper I).However,it should be noted that the
Carlsson-Stein simulation piston,located slightly below
the surface in their model,was derived directly from
our data by constraining it to reproduce the observed
Doppler excursions of the photospheric Fe I 396.682 nm
line shown in Fig.3 of Paper I.The simulations there-
fore contained implicitly all non-local in .uences that af-
fected the actual formation of Fe I 396.682 nm,such
as the p -mode interference patterns,the granular dy-
namics and the mesoscale and supergranular .ows.In
particular,there was no magnetic .eld in the Carlsson-
Stein simulations,but if solar magnetism in .uenced the
Fe I 396.682 nm Doppler signal in some way,some of that
in .uence might be accounted for through the inferred
subsurface piston modulation.
direct relation between K 2.... grain occurrence and
internetwork magnetism was claimed by Sivaraman &
Livingston (1982;cf.Sivaraman 1991;Kariyappa et al.
1994)who blinked a one-hour sequence of Ca II K spec-
troheliograms against two Fe I 868.8 mm magnetograms
taken just before and after,and found that all K 2.... grains
correspond one-to-one to magnetic internetwork features,
with a qualitative correlation between grain brightness
and magnetic .eld strength.Magnetic anchoring of the
grains was also suggested by Dam ´e and coworkers (Dam ´e
et al.1984;Dam ´e 1985;Dam ´e &Marti ´c 1987,1988)on
the basis of the apparent "location memory "implied by
repetitive grain appearances in Ca II K .ltergram movies.
The existence of one-to-one correspondence between
K 2.... grains and .eld enhancements has often been
doubted.Rutten &Uitenbroek (1991a)suggested that
it concerns only exceptional patches such as the .asher
above but that the prevalent K 2.... grain phenomenon is
set primarily by non-magnetic wave interference.This
suggestion has since been supported observationally by
Kneer &Von Uexkull (1993),Von Uexkuell &Kneer
(1995),Ste .ens et al.(1996),Hofmann et al.(1996),
Remling et al.(1996),and Nindos &Zirin (1998).ppro-
priate non-magnetic pistons,if identi .able at all,might
then consist of the peak amplitudes in the p -mode in-
terference pattern (Ste .ens et al.1996;Hofmann et al.
1996),convective downdrafts in intergranular lanes (Rut-
ten 1995),or even faster subsurface down .ow plumes
(Hoekzema &Rutten 1998).
Theoretical work on the piston issue has so far been
restricted to discussions of the amount of 3-min power
present in the Carlsson-Stein piston by Cheng &Yi
(1996)and Theurer et al.(1997).The latter authors
suggest that atmospheric .ltering produces the excess of
3 –min power observed for the Fe I 396.682 nm line in Pa-
per I as compared to the subsurface prediction from the
Lighthill-Stein theory for turbulent convection (Lighthill
1952;Stein 1967;Musielak et al.1994).They so im-
ply that the subsurface pistons driving the K 2.... grains
result from convection in straightforward fashion.How-
ever,Kalkofen (1989,1990,1991,1996)has also furnished
speculations in which internetwork .elds play a key role
in various disguises,ranging from kiloGauss .ux tubes
down to weak .elds.His latest suggestion invokes colli-
sions between medium-strong (500 G or more)internet-
work .ux tubes and granules (Kalkofen 1996).
4.In summary,the issue of correspondence between in-
ternetwork K 2.... grains and internetwork .eld elements is
not conclusively resolved.major source of the uncer-
tainty arises from limitations of observational technique,
which we confront directly with the observations reported
herein.Internetwork .elds present a similarly open issue,
towhichweturnnow.
1.2 Internetwork Magnetism
Solar internetwork .elds remain elusive entities (e.g.,
Zwaan 1987,and the excellent introductory review to
Keller et al.1994).The initial report by Livingston &
Harvey (1971)described their appearance as ubiquitous
bipolar patterns of random nature in which the single-
polarity patches extend over 2 –10 arcsec.Harvey (1977)
speci .ed a mixed-polarity pattern with element diame-
ters of about 2 arcsec and net .uxes (area-integrated ap-
parent .eld strength)of about 5 ×10 16 Mx per element.
More recently,Keller et al.(1994)derived a sub-
kiloGauss upper limit to the intrinsic .eld strength |B |of
a few isolated high-signal internetwork .eld patches with
size about 3 arcsec and total .ux about 1 ×10 17 Mx.
n average value |B |˜500 Gauss was reported by
Lin (1995)for those internetwork features observed at
1.56 µm that were strong enough to exceed his sensitiv-
ity cuto .at .ux density 1 .5 ×10 16 Mx per 0.48 arcsec 2
spatial sample,or B BBSO
app >6Mxcm -2 where B BBSO
app
stands for the apparent .ux density measured in this
particular data set at the Big Bear Solar Observatory
(BBSO)1 .Internetwork features with such .eld strength
make up a relatively rare class,as evident from the BBSO
quiet Sun magnetogram that is shown (rather confus-
ingly at three di .erent orientations)in Fig.1 of Wang
et al.(1995),Fig.1 of Zirin (1995)and Fig.1 of Lee
et al.(1997),and which belongs to a sequence called the
"best ever BBSO quiet-sun one "by Zhang et al.(1998)
who also show parts of other frames (at yet another ori-
entation).The internetwork .elds in this map are not
ubiquitously .lling the cell interiors but stand out as
isolated patches,"distinguished against .eld-free back-
ground "(Lee et al.1997).Lin (1995)attributed them to
ensembles of thin magnetostatic .ux tubes.Solanki et al.
(1996)supported this view and suggested that they are
due to weak convective collapse.t a professed resolution
of 2 arcsec the distributions of .ux per observed patch
1 Measured Stokes V/I circular polarization signals translate into
apparent flux density estimates which only rarely equal actual solar
field strengths |B |, and which are strongly instrument- and seeing-dependent,
a point to be emphasized at the outset and elaborated
in Sect. 3 below. Following Sect. 2.1 of Keller et al. (1994), we
distinguish the two quantities throughout this paper by expressing
apparent flux density B app in Mxcm- 2 and intrinsic solar field
strengths |B |and B long (the longitudinal component of the field)
in Gauss.
are distinct from that of the strong-.eld network features
(Wang et al.1995),indicating intrinsically di .erent na-
ture (cf.Lee et al.1997;Meunier et al.1998).These inter-
network patches tend to appear initially with mixed po-
larity,to migrate towards the supergranulation cell bor-
ders and to disappear quickly,often through merging or
cancellation;they may be the most important source of
magnetic .ux to sustaining the quiet Sun network (Wang
et al.1996;Schrijver et al.1997;Zhang et al.1998).
The "salt-and-pepper "general background pattern re-
ported by Livingston &Harvey (1971)and Harvey (1977)
has not been discussed recently,but it is present in Fig.4
of Lites et al.(1996)as rather grey,relatively noisy areas
away from the "bloom "of network patches.
In addition to the ubiquitous background pattern and
the stronger B long
˜500 Gauss vertical-.eld features
studied at BBSO,Lites et al.(1996)found horizontal in-
ternetwork .elds (HIFs),apparent only in Stokes Q and
U ,that are characterized by predominantly horizontal
.ux orientation.They are short-lived (5 min),compact
(sub-arcsecond),and intrinsically weak ( |B |well below
1 kiloGauss).
Finally,truly weak background .elds may exist as
well.The Hanle depolarization estimates of Faurobert-
Scholl (1993)and Bianda et al.(1998)indicate an upper
limit well below |B |=100 Gauss.However,their exis-
tence in the low chromosphere has recently been brought
into question by the application of detailed atomic and
radiative transfer computations including the e .ects of
lower-level polarization to observed polarization pro .les
of the Na I D-lines (Landi Degl 'Innocenti 1998).
1.3 Internetwork Grains versus Internetwork
Fields
Since Sivaraman &Livingston (1982)claimed a one-
to-one relationship,only two papers,both recent,have
addressed the issue of grain –.eld correspondence obser-
vationally.The .rst is by Remling et al.(1996)who
adopted spectral brightening in the CN band head at
. =388 .3 nm as a proxy for the presence of strong-.eld
.ux tubes and compared CN spectrograms to simultane-
ous Ca II K spectrograms covering a 6 ×340 arcsec 2 area.
They found that K 2.... grain locations brighten simultane-
ously in CN,with 4-5 min modulation over 10 to 15 min
duration,but without the longer-lasting CN enhance-
ment expected for long-lived internetwork .eld elements
as the ones recorded by Sivaraman &Livingston (1982).
Remling et al.(1996)conclude that the CN enhance-
ments portray the same upper-photospheric modulation
that is evident in the inner-wing Ca II H&K "whiskers "
(Beckers &rtzner 1974),and that the absence of longer-
duration enhancement excludes one-to-one alignment be-
tween K 2.... grains and strong-.eld .ux tubes.
5.The other recent paper on grain-.eld correspondence
is by Nindos &Zirin (1998)and is not limited to strong-
.eld elements.It combines BBSO magnetograms with
co-temporal Ca II K .lter images and represents a much
more direct repeat of the observations of Sivaraman &
Livingston (1982).The images were not taken strictly si-
multaneously,but K .ltergrams were selected that were
taken within a few minutes of a magnetogram construc-
tion.Bright K features were then compared with magne-
togram features.The .rst conclusion is that the K-line
intensity increases linearly with the apparent .ux density
B BBSO
app for network elements with B BBSO
app >10 Mx cm -2 .
In the internetwork domain which they de .ned to be
B BBSO
app <10 Mx cm -2 ,Nindos &Zirin (1998).nd a di-
chotomy between two types of K-line brightenings:fairly
scarce long-lived "magnetic brightenings "with apparent
.eld strength above the average noise level,and more
widespread weaker "non-magnetic brightenings "with ap-
parent .eld strength below the noise level.The latter was
estimated at a few Mx cm -2 as determined by subtract-
ing successive magnetograms.The "magnetic "K bright-
enings were found to migrate at about 1 km s -1 ,charac-
teristic of the mesoscale convection .ow speeds,whereas
the "non-magnetic "K brightenings were found to live
shorter and to move at much larger apparent speeds,of
order 40 km s -1 .lthough Nindos &Zirin (1998)did not
use temporal modulation of the latter features as a diag-
nostic,it seems likely that these correspond to K 2.... grain
behavior as illustrated in Fig.2,whereas their "magnetic
brightenings "correspond to features as the ones that are
marked in Fig.2 and are akin to the internetwork .asher
of Brandt et al.(1992,1994).We think it likely that
the "magnetic brightenings "correspond to the relatively
strong internetwork .eld elements studied by Lin (1995),
Wang et al.(1995),Wang et al.(1996),Lee et al.(1997),
and Zhang et al.(1998).
In this paper we take a more quantitative approach
to test the Sivaraman &Livingston (1982)conjecture by
utilizing spectrographic techniques to enhance the mea-
surement accuracy at the expense of .eld-of-view.First,
we use high-resolution Ca II H spectrograms to de .ne a
H 2.... grain wavelength band that is considerably narrower
than the 0.11 nm spectroheliograph bandpass used by
Sivaraman &Livingston (1982)which sampled the full
Ca II K 232 line core.Second,we observed an area which
is truly quiet 2 ,in contrast to the partial Ca II K heli-
ogram that is reproduced (at unspeci .ed scale)in Sivara-
man &Livingston (1982)and is very crowded with what
seems active rather than quiet network in addition to
plage.Third,we did not take magnetograms only be-
fore and after the spectral sequence,but have obtained
2 Just north and west of the disk-center region studied in this
paper, slightly enhanced network is found on co-temporal full-disk
Ca II K images taken at NSO/Sacramento Peak.
Ca II H spectra and Fe I 630.3 nm Stokes diagnostics syn-
chronously and continuously.Fourth,we used the NSO
Vacuum Tower Telescope at Sacramento Peak at fairly
good seeing,achieving angular resolution (1 –2 arcsec)
undoubtedly better than that of Sivaraman &Livingston
(1982).Finally,we used the H O/NSO dvanced Stokes
Polarimeter (ASP)of which the reliability and sensitiv-
ity in full-vector magnetic .eld measurements has been
established beyond doubt (e.g.,Lites et al.1994;Lites
1996;Skumanich et al.1997).In general,SP observa-
tions of the Zeeman-sensitive Fe I 630 nm lines together
with the elaborate ASP calibration and analysis proce-
dures provide exceptionally sensitive measures of active
region,network and internetwork magnetic .eld charac-
teristics.For example,the time series records by Lites
et al.(1998)of sunspot umbrae in which the temporal
variations in the inferred intrinsic .eld strengths |B |re-
main within only a few Gauss,the precision measure-
ments of the vector .elds of solar plage by Mart ´inez Pil-
let et al.(1997),and the discovery of HIFs by Lites et al.
(1996).have demonstrated the sensitivity of the SP
to both weak and strong .elds in the solar photosphere.
We show below that the ASP discerns internetwork .elds
down to B ASP
app
˜3Mxcm -2 in the data analyzed here.
The organization of this paper is as follows.We
present our observing technique,data,and initial reduc-
tion in the next section,the analysis in Sect.3,and the
results in Sect.4.Our main conclusion,discussed in
Sect.5,is that we .nd no evidence for spatial coincidence
between internetwork K 2.... grains and internetwork .elds
down to the limit set by the ASP sensitivity.There is also
no obvious response of the Ca II chromosphere to hori-
zontal internetwork .eld (HIF)events in the underlying
photosphere.Taken together,these two results indicate
that magnetic .elds are not an essential ingredient for
the production of K 2.... grains.
2 Observations
The observations used in this paper were obtained on
September 5 1996 with the dvanced Stokes Polarimeter
(hereafter SP;Elmore et al.1992)at the Vacuum Tower
Telescope of the National Solar Observatory/Sacramento
Peak at Sunspot,New Mexico.The observations were
part of a wider campaign to investigate chromospheric
and coronal manifestations of disturbances in the photo-
spheric magnetic .eld (SOHO Joint Observing Program
46)and focused on a very quiet area near solar disk cen-
ter.It is shown in Fig.4.In this paper we concentrate on
the small internetwork area contained within the upper
part of the narrow strip that is indicated at the center of
the images of Fig.4.
The SP cameras were con .gured to observe the
Zeeman-sensitive Fe I line pair at . =630 .15 630 .25 nm
6.Figure 4:The spatial context f the time series data is revealed by this ASP map of a wider area during 13:55 -14:12 UT on
1996 Sept.5.The vertical lines near the center indicate the extent of spatial maps f the time series.The h rizontal lines within
delimit the very quiet internetw rk area analyzed in detail.The rectangle at right de .nes a sub-area sh wn in Fig.10.The I c
panel,fr m the c ntinuum near . =630 nm,shows the photospheric granulati n.The horiz ntal black bar is fr m a .ducial
hair on the slit andthe darkenedcolumn near x =95 was probably causedby a miller moth (Euxoa Auxiliaris [Grote]) in the
light path.The grey scale f the upper right panel displays the intrinsic .eld strength |B |(bright =strong .eld)from the ASP
inversion.N inversion was attemptedfor the uniform grey areas having P tot <0 .003 (Eq.3).The selectedinternetw rk area
is .eld-free at this threshold.Bright areas mark netw rk patches dominated by unres lved |B |˜1400 Gauss .ux tubes,having
B app
~
>700 Mxcm - 2 (Eq.4)andspatial .ll fraction f
~
>0 .5 (cf.Fig.8).The dark edges f netw rk patches are probably
spuri us (see Sect.3.3 f text).The b ttom panels show the apparent .ux density B ASP
app (Eq.1)using the calibration relation
sh wn in Fig.8.The grey scale is clippedat |B
ASP
app
|=174 Mxcm - 2
and |B
ASP
app
|=14Mxcm - 2
in the l wer-left andlower-right
panels,respectively,revealing "bl m "of network patches t large apparent size (cf.Fig.7).Small areas f mixed-polarity
weak magnetic .ux,close t the noise limit of |B ASP
app
|3Mxcm - 2 (see Fig.9),are clearly visible in internetw rk regions such
as that within the rectangle at upper right,which is displayed in m re detail in Fig.10.
7.Figure 5:These Ca II H&K data sh w a slit-jaw .ltergram (left)with a passband .. =0 .3 nm centeredon Ca II K and the
simultaneous,spatially alignedCa II H spectrogram (right).The vertical dark line in the .ltergram is the spectrograph slit and
the tw horiz ntal lines are .ducial hairs n the re .ecting slit jaws.The grainy bright structure in the center f the slit-jaw .eld
marks a cluster f strong-.eldchromospheric netw rk elements which produce bright streaks throughout the bservedsegment
of the spectrum.The dark region just ab ve the netw rk patch is the quiet internetwork area studied in detail.
8.Figure 6:Sh wn in the four panels at left are ASP St kes
spectra f the Fe I 630.2 nm doublet at time t =37minand
map position x =6 arcsec in the time series.The grey scale
of the Q and panels is clippedat 0.2%of the continuum
intensity I c and V is clippedat 0 .4%I c in order to emphasize
weak p larization features.The Stokes Q panel shows slight
crosstalk from the strong internetw rk features in the Stokes
V panel but no signi .cant linear p larizati n elsewhere.The
panel at upper right is a p rti n f the simultane us Ca II K
slit-jaw image sh wn in Fig.5.The highlightedpixel column
t the right of the dark slit indicates the slit p sition as seen
by the ASP at 630 nm,displaced from the Ca II K slit p -
sition by the wavelength dependent refraction f the Earth 's
atmosphere.The panel at l wer right shows a small spec-
tral sample of Ca II H spectrogram corresponding t the o .set
slit p siti n.The netw rk elements around y =23arcsecand
y =40 arcsec produce bright emissi n throughout the Ca II H
line core.The bright Ca II H 2V grain near y =57arcsecis
accompanied by the typical dark redshifted H 3 darkH 2R
and bright wing "whiskers ".It does n t produce any bvi-
ous polarization signatures in the ASP panels.Interpolation
of the Ca II H spectrograms t compensate for di .erential re-
fraction results in images that are co-spatial but n t exactly
simultaneous with the ASP data.
in all four Stokes parameters (cf.Lites et al.1993a;Lites
et al.1995).In addition,a camera from the NSO Multi-
Diode rray (MDA)was placed in the focal plane of
the spectrograph to register the intensity pro .le of the
Ca II H resonance line at . =396 .8 nm (cf.Balasubra-
maniam et al.1997).The spectrograph was con .gured
to project a relatively wide (.. =0 .9nm)wavelength
region on this camera,containing a large segment of the
violet Ca II H wing in order to obtain spectral windows
that range in formation height from the photosphere to
the chromosphere.Sampling the photospheric "contin-
uum "window in the far H-line wing permits accurate
alignment of the H-line spectra with the simultaneous
. =630 nm SP data,including compensation for dif-
ferential atmospheric refraction between the two wave-
lengths.This con .guration resulted in spectral sam-
pling of 2.014 pm/pixel (8th order)at . =630 nm and
4.035 pm/pixel (12th order)at . =397 nm.The 630 nm
spectrograms have coarser sampling than the customary
SP 9th-order observations with 1.259 pm/pixel disper-
sion.The di .raction angle is also farther from the grat-
ing blaze.The SP sensitivity was therefore slightly less
than usual.The angular pixel size along the projected
slit was 0.37 arcsec.
second NSO-MD camera registered the image
re .ected from the spectrograph slit through a .. =
0 .25 nm wide Lyot .lter centered on the Ca II K line
at . =393 .3 nm.These slit-jaw images were taken syn-
chronously with the spectrograms.They display the loca-
tion of the spectrograph slit in the .eld and the evolution
of the chromospheric morphology during the observing
sequence.
n example of a Ca II K slit-jaw image and the cor-
responding Ca II H spectrogram is shown in Fig.5,and
an example set of SP data is shown in Fig.6.The
latter .gure shows representative Stokes I ,Q ,U and V
spectrograms in the four panels at left.The grey scale of
the Q ,U ,and V panels is set to saturate at low values
("clipped ")in order to bring out the weakest polarization
features.The two panels at right show the simultaneous
Ca II K slit-jaw image (top)and a segment near line-
center of the corresponding Ca II H spectrogram (bot-
tom).There is a prominent H 2.... grain near y =57arc-
sec.
The time series data set analyzed below consists
of co-spatial and co-temporal series of spectral SP
and Ca II H maps that were generated by stepping the
0 .6 ×84 .4 arcsec spectrograph slit repeatedly across an
10 .5 ×84 .4 arcsec area in 11 steps of 1.05 arcsec.The
cameras took about one frame every six seconds during
the period 14:16 –15:25 UT;the average time interval be-
tween successive 11-step maps is 63.25 sec.The NSO
correlation tracker (Rimmele et al.1991)was used to
stabilize the telescope image.It performed best during
9.the .rst 40 minutes,when the residual image excursions
were small and when there was only a slow image drift.
Later on,the drift accelerated and there were occasional
interruptions when the tracker lost its lock on the solar
granulation.We therefore analyze only the .rst 40 min-
utes of the time series data set here:a series of 38 ASP
data cubes and 38 Ca II H data cubes,each consisting of
maps per spectral resolution element,with accompanying
Ca II K slit-jaw images.
During the twenty minutes prior to the time series
data acquisition,the SP executed a single-pass map
over a ten times wider area around the 11 arcsec wide
time series strip.This was done by stepping the slit 200
times incrementally over 0.525 arcsec.The results are
shown in Fig.4.The domain of the time series is indi-
cated by vertical lines near the center of all panels.It
contained a small patch of network at the center.The
upper part included a very quiet internetwork area that
is also indicated in each panel.We focus on this small in-
ternetwork area using the time sequence of ASP and Ca II
data cubes to derive the space-time parameter charts that
are shown in Figs.11,12,and 14 –16.The network patch
provided a convenient positional reference for compensa-
tion of the pointing drifts.Its relatively strong polariza-
tion signals and large intrinsic magnetic .eld strengths
also provide a robust calibration of very weak observed
Stokes V signals in terms of apparent .ux density per
pixel (Sect.3.3 and Fig.8).
3 Analysis
3.1 ASP – Ca II Alignment
The telescope guiding drifts were determined and cor-
rected through cross-correlation of the successive net-
polarization maps as constructed from the ASP data
cubes.The network patches in the time series .eld pro-
vide su .ciently stable anchors for such pattern tracking.
The slit-jaw Ca II K images and the Ca II H spectro-
grams (including those in Fig.6)have been spatially
scaled,shifted,and interpolated to obtain spatial align-
ment with the corresponding SP Stokes spectrograms.
Di .erential refraction in the Earth 's atmosphere causes
a spatial o .set between . =396 nm and . =630 nm.
In the present data it has components of about 2 arc-
sec both along and perpendicular to the slit.These
shifts were determined by cross-correlation of the quasi-
continuum maps registered in the Ca II H wing window
at . =396 .25 nm with the SP continuum maps mea-
sured near . =630 nm.The far-wing Ca II H window
is formed su .ciently deep in the photosphere to enable
such correlation.Exact alignment would have been more
problematic had we recorded only the Ca II H core.The
Ca II spectrograms have been shifted along the slit to
compensate for the parallel component of the refractive
o .set.The displacement perpendicular to the slit was
corrected through spectrogram interpolation among the
11 slit positions in each map of the sequence.The result-
ing alignment is signi .cantly better than 1 arcsec.
The interpolated Ca II H spectrograms represent the
same spatial location as the Stokes panels,but they are
not strictly simultaneous with the latter,di .ering by a
delay of about 6 -12 s.This is su .ciently brief compared
to the one-minute lifetime of H 2.... grains.The MD CCD
recorded a smaller area than the ASP cameras as is ev-
ident in the lower part of the H 2.... panel of Fig.6.The
Ca II K slit-jaw image at the upper right was taken simul-
taneously with the Stokes panels.The dark slit shows its
actual position seen by the Ca II H spectrum,while the
bright pixel column immediately to the right indicates
the approximate slit position seen by the SP at the
time of this measurement.
3.2 Spectral Measurements
We have evaluated various parameters for each
0.37 arcsec spatial sample along the projected spectro-
graph slit for each set of simultaneous Ca II H and SP
spectrograms.From the Ca II H spectrograms (shifted
and interpolated as described above)we measured some
of the H-line intensity indices that are de .ned in Ta-
ble 1 of Paper I:the H-index (0.1 nm wide band around
line center),the H 2...and H 2.... indices (0.008 nm around
displacements from line center .. = ±0 .016 nm,respec-
tively),and the Doppler shift ratio (H 2....
-H 2...)/(H 2.... +
H 2...).The latter two quantities are not used in the
present analysis.
From the SP spectrograms we measured the total
(signed)fractional (relative to I c )Stokes V signal
V tot =

. 0
0 V (. )d . -sgn(V blue 
 8. 0 V (. )d .
I c 
 d . (1)
where sgn(V blue denotes the sign of the blue peak of the
Stokes V pro .le of one of the two Fe I lines,the integra-
tion is over two passbands containing the two 630 nm
lines,and . 0 denotes the line center wavelength of the
line being integrated.I c is the continuum intensity near
. =630 nm.In the limit of small |B |the amplitude of
Stokes V scales linearly as the line-of-sight component of
the .eld,B long (see Chapt.11 of Sten .o 1994),weighted
by the .ll factor f (Rabin 1992,see also Eq.(4)below.)
The integral de .ning V tot serves to increase the sensi-
tivity to weak signals by averaging over many spectral
samples.
Likewise,we determined the fractional net linear po-
larization
L tot =
 [Q 2 (. )+U 2 (. )]1 2 d .
I c 
 d . (2)
10.and the fractional net polarization
P tot =
 [Q 2 (. )+U 2 (. )+V 2 (. )]1 2 d .
I c 
 d . .(3)
The normalization implies that these total polarization
measures are pro .le-averaged quantities.The integrals
for L tot and P tot were carried out over the 630.25 nm
line only.
In addition to these measurements,we applied the
elaborate SP inversion procedures described by Sku-
manich et al.(1997)at those space-time samples for
which the polarization signals were su .ciently large to
warrant detailed modeling of the Stokes pro .les.The in-
version algorithm delivers estimates of:the intrinsic .eld
strength |B |,the inclination of the .eld . with respect to
the local vertical ("zenith angle "),the spatial .ll fraction
f ,other measures characterizing the line formation,and
error estimates of each parameter of the .t to the Stokes
pro .les (Lites et al.1994.)The meaning of f is discussed
below.
3.3 ASP Polarization Analysis
Most of the network elements in this quiet region pos-
sess only small Stokes Q or U amplitude (cf.Fig.6),
indicating that the corresponding magnetic .elds were
aligned closely along the line of sight (vertical).Ex-
cept for the occurrence of transient small-scale horizontal
.elds (HIFs)discussed below,the observed polarization
in the internetwork part of the .eld is also dominated
by Stokes V rather than Q or U .This is illustrated by
the Stokes panels in Fig.6,which show very little lin-
ear polarization (Q and U )even at enhanced sensitivity.
Crosstalk of about 3 -4%from V Q is evident as weak
antisymmetric signal in the Q panel at the location of the
network elements,indicating incomplete correction for
telescope polarization.Because there were no sunspots
available near disk center during our observing period,we
have not been able to re .ne the telescope polarization
model by the technique described by Skumanich et al.
(1997)and we have therefore used an older model.The
turret mirrors of the Vacuum Tower Telescope have been
re-.gured and re-aluminized since that earlier determi-
nation of the telescope Muller matrix.Because the tur-
ret mirrors cause most of the telescopic modi .cation of
the input polarization state,it is not surprising that the
polarization model employed here is not optimal.How-
ever,residual instrument polarization in Stokes Q at the
low level evident in Fig.6 does not change any result
below since 1)the network .elds are primarily longitu-
dinal,2)a spurious antisymmetric signature in Stokes Q
has no e .ect on the SP inversion which assumes a sym-
metric pro .le,and 3)the transient HIFs discussed below
are characterized by very weak Stokes V ,such that any
V Q crosstalk is inconsequential.
The parameter f delivered by the SP inversion al-
gorithm is set largely by the fractional polarization P tot
whereas the vector .eld parameters |B |and . are set
largely by the relative amplitudes and pro .le shapes of
Q (. ),U (. ),and V (. ).It is important to appreciate
that the .ll fraction f is the dominant factor in setting
the apparent .ux density.It depends sensitively on the
instrument and the (time-dependent)atmospheric see-
ing.Apparent .ux densities are frequently quoted in
the literature with the implicit suggestion that they are
solar properties,or may be taken as such by unwary
readers.In fact,apparent .ux densities are instrument-
dependent,and even observation-dependent.Figure 7
illustrates this for the case in which the observed solar
area contains magnetic .elds exclusively in the form of
identical strong-.eld .ux tubes —a case that is appropri-
ate for unipolar network.Since the .ux tube diameters
are well below the e .ective angular resolution,their in-
trinsic polarization signatures consist of clusters of point
sources.The observed apparent .ux density then cor-
responds to a summed local sampling of multiple point
spread functions,each centered at a .ux tube location.
The apparent .ux density at a sample location may then
be written as
B app =f |B |cos .,(4)
where |B |=1400 Gauss and |cos . |=1 in this ide-
alized case.The dimension of B app equals that of the
intrinsic solar .eld strength (magnetic induction) |B |,
but following Keller et al.(1994)we use Mx cm -2 rather
than Gauss for B app in order to express its observation-
dependent character.More speci .cally,we use B app to
designate .ux density estimates that are based on de-
tailed inversion modeling of Stokes I ,Q ,U ,and V mea-
surements,and we add appropriate labels such as SP
and BBSO to B app for .ux density estimates that are
obtained magnetograph-wise from Stokes V alone.The
.ll fraction f quanti .es the e .ect of the object convolu-
tion with the point spread function.The latter is gener-
ally dominated by atmospheric seeing and tends to pos-
sess extensive wings,far beyond the 1 arcsec halfwidth
that corresponds to "good "seeing at most magnetograph
sites.Thus,mapping the apparent .ux density B app at
very high sensitivity,as is done below in order to display
weak .elds,causes the "bloom "extending outward from
the strong polarization signals of network elements.The
bloom results from seeing-diluted sampling of relatively
distant kiloGauss .elds.
If the intrinsic .elds are unipolar and single-valued
in |B |and . within the entire area that contributes,via
the point spread function,to the polarization signal at
a given pixel (as in the hypothetical case of Fig.7),the
ASP inversion procedure yields estimates of |B |and cos .
that correspond closely to the intrinsic solar values.The
11.1 arcsec
Figure 7:This cart n illustrates ASP p larimetry f verti-
cal,unip lar,B =1400 Gauss .ux tubes representedby dots
of diameter 0.25 arcsec.The grid represents the 0.37 arcsec
spatial sampling along the projectedASP slit.The large cir-
cles surrounding each dot represent smearing f the strong
p larization signal from each .ux tube due t scattering in
the ptics andatmospheric seeing,such that the blurredsig-
nal reaches the noise level f the observations at this radius
(sh wn here as 5 spatial samples).Netw rk elements "bloom "
to apparent sizes f this rder when p larizati n maps are dis-
playedso as t reveal weak p larization (cf.Fig.4).
inferred .ll fraction f then re .ects the e .ective dilution
of the polarization.Such analysis is limited ultimately
by random noise,so that at very low signal,in the outer
reaches of the point-spread disks,the inversion breaks
down and yields large scatter in |B |,. ,and f .
Figure 8 displays SP inversion results for all 0 .37 ×0 .52 arcsec 2 spatial samples in Fig.4 that have total
net polarization P tot >0 .003;i.e.points for which
the polarization exceeds the line-integrated noise level by
about an order of magnitude.This threshold has been
determined as necessary to achieve reliable .ts to the
Stokes pro .les.The .rst three panels of Fig.8 show
a bimodal split into two categories.The samples with
1200 < |B |<1600 Gauss (.rst panel)are plotted with
larger symbols.With only a few exceptions,they fall
within two tightly constrained linear branches obeying
B app
˜fB 0 with B 0 = ±1400 Gauss in the upper-right
panel,and they cluster at cos . = ±1 in the lower-left
panel.Clearly,these samples describe network .elds
with intrinsic .eld strength |B |˜1400 Gauss,inclination
|cos . |˜1 and .ll fraction f that varies from small val-
ues up to about f =0 .7 according to resolution-smeared
sampling as in Fig.7.The second category of samples
is characterized by small apparent .ux density B app and
large spread in the model-.tted values of |B |,cos . ,and
f .These points include both a few small patches of
internetwork .elds that have polarization greater than
the threshold for inversion,and the outer edges of net-
Figure 8:This .gure illustrates the calibration of |V tot
|(Eq.1)
in terms f apparent .ux density B app......The parameters
|B |,f ,andcs . plottedalong the abscissae result from
the ASP inversi n f those l cati ns in the map shown in
Fig.4 with total net polarization P tot >0 .003.The product
B app =f |B |cos . pl ttedon the rdinates represents the
apparent .ux density measured in Mx cm - 2 .Thesamples
with 1200 < |B |<1600 Gauss,markedwith slightly larger
symbols,are dominated by cos . ˜±1 andp pulate the tw
slantedlinear relations in the upper right panel.These prop-
erties mark them as network .elds,sampled at various levels
of p int-spreaddilution as illustratedin Fig.7.The remain-
ing samples have small apparent .ux density B app andlarge
scatter in the inferredvalues of |B |,cs . and f .Theymark
internetw rk .elds and the uter limits f diluted network
p larizati n.The b ttom right panel shows a fairly tight c r-
relation between B app andpro .le-averaged V tot comprising
b th network anddilutednetwork.The slope of the linear
.t is usedas a calibrati n c nstant to enable inference f ap-
parent .ux densities B
ASP
app from V tot at locations where the
p larization is t weak for detailed Stokes pro .le inversion.
work point-spread disks where the inversion modeling
breaks down.The former may be identi .ed in the up-
per right panel of Fig.4 as the few isolated,very small
dark patches,whereas the latter are the dark borders
surrounding the larger,lighter shade network patches.
Assuming that solar network .ux tubes all have in-
12.trinsic .eld strength |B |˜1400 Gauss,the network
distributions in Fig.8 may be compared to other ob-
servations.Figure 9 of Lin (1995)is directly compara-
ble to the upper-left panel of Fig.8.The scale along
its y -axis is labeled ".ux in Mx ",but it actually mea-
sures apparent .ux density B BBSO
app per 0.48 arcsec 2 spa-
tial sample.The .gure shows a similar peaked cluster
centered at |B |=1400 Gauss,but it reaches only up to
|B BBSO
app
|˜100 Mx cm -2 while the samples in our Fig.8
reach |B app
|˜800 Mx cm -2 .We attribute this factor-
of-eight di .erence to the apparent .ll fraction f ,i.e.,to
di .erence in spatial resolution.Expressed in terms of see-
ing quality,it indicates that our angular resolution was
nearly three times better.t lower values of |B |,Lin 's di-
agram shows a low-strength tail rather like the one in the
upper-left panel of Fig.8.The distribution seems similar,
including slight clustering around |B |=500 Gauss.
similar comparison is feasible with the two network
.eld distributions plotted in Figs.6 –7 of Nindos &Zirin
(1998).They reach up to only B BBSO
app
˜30 Mx cm -2
and B BBSO
app
˜40 Mx cm -2 ,respectively,indicating yet
lower angular resolution.Note that not only the seeing
(integrated over as long as four minutes in the BBSO
magnetogram acquisition)may contribute to this di .er-
ence,but that also the sophistication of the modeling
and other factors are important (cf.Lites et al.1994;
Zirin 1995;Lites 1996;Skumanich et al.1997).
The .nal panel at the lower right in Fig.8 is es-
sential to the analysis of weak polarization in this pa-
per.It shows that the apparent .ux density B app in-
ferred by the inversion algorithm correlates closely with
the pro .le-averaged circular polarization signal V tot de-
.ned by Eq.(1).Since V tot is measured with relatively
high signal-to-noise resulting from the wavelength aver-
aging over both line pro .les,the good quality of this
correspondence permits us to derive apparent .ux den-
sities B ASP
app from the measured V tot at locations and
times where the polarization falls considerably below
the threshold needed for inversion of the Stokes pro-
.les.The calibration relation indicated by the linear .t
is B ASP
app =(15572 ±56)V tot with B ASP
app in Mxcm -2 .
Itsusepermitsustoconstructcomplete B ASP
app maps and
space-time charts,including also the areas with very weak
polarization.
4 Results
4.1 Properties of Internetwork Fields
Nindos &Zirin (1998)separate network features from
internetwork features in their observations at a ".eld
strength "of about 10 Gauss.In view of the discussion
above,this implies network/internetwork separation at
an apparent .ux density measured at BBSO on speci .c
Figure 9:Histograms f the t tal St kes V signal, |V tot
|as
de .ned by Eq.(1),indicate the minimum useful p larizati n
signals as limitedby rand m noise in ASP measurements.The
solidcurve sh ws the frequency of ccurrence f |V tot
|for all
pixels of Fig.4.The dashed curve is a similar histogram for
Stokes V spectra integrated ver an identical bandwidth,but
shiftedin wavelength t span only continuum having negligi-
ble polarization.This curve represents the n ise distribution.
It has been n rmalized to force coincidence of the downward
slopes for |V tot
|<2 ×10 - 4
,which are attributed to noise
for both distributions (random n ise reduces the likelih d
of very small excursions).The n ise level of the V tot is es-
timatedfrom the l cation (.rst m ment)f the peak of the
dashed curve: |V tot
|=2 ×10 - 4 .
days of about |B BBSO
app
|=10Mxcm -2 .Can we set a sim-
ilar dividing value?The locations with maximum |B app
|in our data undoubtedly describe network .elds,but even
these do not portray individual magnetic elements but
rather unresolved element clusters as evident in the G-
band panel of Fig.2 3 .Our samples with smaller apparent
.ux density |B app
|either correspond to true internetwork
.elds,or represent the blurring of nearby .ux tubes in the
neighborhood of network patches.Even where we mea-
sure |B app
|<10 Mx cm -2 the signal may yet be caused
by distant strong-.eld network.This is demonstrated
below (Fig.13).Thus,network/internetwork discrimi-
nation is not feasible by setting a single |B app
|dividing
value.The internetwork area studied here,as outlined in
Fig.4,was selected by inspection of the slit-jaw Ca II K
movie.On such movies the network patches stand out as
being relatively stable amidst the rapid pattern changes
caused by the apparently supersonic motions that the
internetwork brightenings display.The H 2.... space-time
charts in Fig.12 indeed con .rm that the selected region
contains no network since there are no bright streaks that
3 Or for a much larger field on the high-resolution La
Palma poster available at URL http://diapason.lmsal.com/ ~ber-ger/
images/gallery.html.
13.Figure 10:Spectropolarimetry of a very quiet internetw rk region at the upper right f Fig.4 emphasizes properties f weak
.ux.The upper panels are individual Stokes V spectrograms corresponding t the four slit p sitions highlighted in the spatial
maps bel w,as identi .ed by alphabetic labels and arrows.The grey scale displays Stokes V in the range |V |=0 .003 I c......The
l wer panels show maps f the apparent .ux density B
ASP
app at very high sensitivity andvarious values f l wer threshold:0,3,
4.5,and6 Mx cm - 2
for panels e ,f ,g ,and h ,respectively.B
ASP
app =6Mxcm - 2
corresponds t |V tot
|=0 .0004.The horizontal
arrows in spectrogram c andall B ASP
app images indicate a very weak Stokes V feature near the noise limit f the bservati ns.
14.persist during 40 min.The apparent .ux densities in this
area (in the scale of our particular data set!)remain be-
low |B ASP
app
|˜40 Mx cm -2 (Fig.13).
Next we consider the lower cuto .for B app When
the line polarization falls below the noise level,the esti-
mation of B ASP
app from V tot via the calibration relation of
Fig.8 breaks down.Because we have spectral measure-
ments containing continuum that is e .ectively devoid of
solar polarization,we are able to use this continuum to
establish a de .nitive measure of the noise in V tot The
lower threshold of validity is revealed in the histogram
indicated by the solid curve in Fig.9,which shows the
occurrence distribution of V tot over the full map in Fig.4.
The histogram shows a peak around log 10
|V tot
|= -3 .7.
We attribute the rapid decline at smaller values of |V tot
|to random noise which inhibits the occurrence of small
V tot t these ASP signal levels,Stokes V is limited
by the statistics of photon detection.We quantify the
threshold by adding a second histogram (dashed curve
in Fig.9)that is determined in the same fashion as the
solid curve,but measured for the continuum rather than
a line.The bandwidth of the spectral average of Stokes
V represented by the dashed curve is identical to that of
the V tot integration in Eq.(1).This histogram represents
the noise distribution since the continuum has negligible
circular polarization.Its peak location provides an es-
timate of the noise threshold in our polarization data:
the .rst moment suggests that values |V tot
|>2 ×10 -4 ,
or correspondingly |B ASP
app
|>3Mxcm -2 ,aresigni .-
cant.This noise limit is slightly worse than the cus-
tomary sensitivity of the ASP in its standard mode of
operation and at excellent seeing.The present data have
lower signal-to-noise due to the larger spectral dispersion
(2.014 pm/pixel instead of 1.259 pm/pixel),the larger de-
parture from the grating blaze,and the somewhat coarser
angular resolution (about 1.5 arcsec seeing,instead of
1 arcsec or even better).
We now consider to what extent "salt-and-pepper "
internetwork .elds as described by Livingston &Har-
vey (1971)and Harvey (1977)are detectable in our data.
This issue is addressed by Fig.10.The upper panels show
sample Stokes V spectrograms for the quiet sub .eld out-
lined by the rectangle at the upper right of Fig.4.The
lower panels show the corresponding B ASP
app map of this
area produced through the calibration relation of Fig.8.
The map is displayed four times for progressively higher
thresholds:Panel e ,without threshold,is simply an en-
largement of the rectangle in the fourth panel of Fig.4;
panels f ,g ,and h have thresholds set to |B ASP
app
|=3,
4.5,and 6 Mx cm -2 ,respectively.The feature crowd-
ing diminishes from left to right because the weaker fea-
tures vanish into the grey threshold.Our noise estimate
derived from Fig.9 indicates that all non-grey features
in the two maps at right should be signi .cant,whereas
the two panels at left should contain appreciable random
noise in addition to solar features.Furthermore,noise
varies spatially from pixel-to-pixel,whereas solar polar-
ization is limited to areas of at least several pixels due to
seeing and actual solar clustering of weak .ux.
Comparison with the sample Stokes V spectrograms in
the upper panels enables veri .cation of the signi .cance of
the features in the lower panels of Fig.10.Slit positions
for each spectrogram are indicated by bright columns in
the maps,each labeled with the corresponding spectrum
panel designation.Stokes V spectral features may be
identi .ed with their B ASP
app signature.For example,the
strong Stokes V signal around y =43 in spectrogram a is
due to a weak,negative polarity network patch appear-
ing as an isolated feature in |B |and B ASP
app of Fig.4.In
spite of its weakness,it is saturated in the lower panels
of Fig.10,exceeding the |B ASP
app
|=47Mxcm -2 upper
limit (corresponding to a clipping value |V tot
|=0 .003).
The four di .use,weaker patches of positive Stokes V sig-
nal in spectrogram b produce corresponding weak,but
brighter-than-grey features at slit location b ,thecores
of which survive the threshold |B ASP
app
|>6Mxcm -2 for
panel h .The double arrow in spectrogram c at y =51 .5
and in all lower panels identi .es a di .use and very weak
feature with barely detectable yet signi .cant Stokes V
spectral signature.The B ASP
app measurement is a pixel-
by-pixel process which does not utilize any information
from adjacent pixels,but visual inspection picks up the
presence of this feature in panels e and f because of its
larger spatial signature.Inspection of panel c clearly re-
veals its presence thanks to the visual pattern recognition
of the distinctive antisymmetric Stokes V spectral signa-
ture that is present over several pixels and in both lines.
Are there locations in this internetwork area that are
truly .eld-free?Inspection of the upper panels of Fig.10
indicates that there are locations without discernible
Stokes V signature,for example below the double arrow
in panel c .Given our noise limit,we can only conclude
that |B ASP
app
|<3Mxcm -2 at these places.However,there
is an increase in the spatial occurrence of single-polarity
patches with 2 –5 arcsec sizes from right to left in the bot-
tom panels.Similar patches are also seen in other parts
of the lower right panel of Fig.4.Since their sizes seem
to exceed the coincidences of a very few pixels expected
for random noise,we suspect that smaller .ux concen-
trations than |B ASP
app
|˜3Mxcm -2 do exist.
4.2 H2.... Grains versus Internetwork Fields
We now turn to the issue of internetwork grain –
magnetic .eld correlation.Figure 11 shows examples
of the H 2.... index (upper panels)and the apparent .ux
density B ASP
app (lower panels)derived from the time se-
quence of maps.The narrow panels at the left are in-
15.Figure 11:A comparison is sh wn between Ca II H 2V brightness modulati n and apparent magnetic .ux density B
ASP
app for the
sequentially mappedregion outlinedin Fig.4.One map obtainedat t =37 min is sh wn in the panels at left.The upper left
map shows the H 2V index (Sect.3.2.)The l wer left map sh ws the c rresp nding apparent .ux density B
ASP
app on a grey scale
clippedat ±50 Mxcm - 2
.The middle c lumn displays the ev luti n f the H 2V index and B
ASP
app for the slit p sition highlighted
in the left panels,at the same scale as the images n the right.The bright Ca II H 2V grain at y =57 arcsec at left is seen at
t =37 min in the H 2V space-time chart andis also sh wn in Fig.6.The internetw rk sub-area outlinedin Fig.4,as highlighted
in the middle columns,is enlarged in the right column.The upper right sh ws three-minute H 2V m dulation.The brightest of
these events are bracketedin the enlargedspace-time charts,andthe same brackets verlie the enlarged B
ASP
app chart at lower
right.The grey scale of that image ranges from -16 .7t +22 .2Mxcm - 2
.It reveals no bvi us spatial alignment f the bright
H 2V locations with magnetic .eldenhancements.
16.Figure 12:Space-time chart pairs for the internetwork region are sh wn for each of the eleven spatial p sitions f the spectrograph
slit in the time series f maps.In each panel,h rizontal is time andvertical is the spatial distance along the slit.The spatial
step between slit p sitions is 1.05 arcsec.The left column f each pair sh ws the H 2V index (see Sect.3.2),identi .ed by slit
p sition at upper left.The panel pair for slit p sition x =6 is enlargedin Fig.11.The right columns sh w apparent .ux density
B
ASP
app .The grey scale is clippedat |B
ASP
app
|=40 Mxcm - 2
.TheH 2V charts f r slit p siti ns x =10 and11 are inc mplete due
to the di .erential refracti n between the tw wavelengths.
17.Figure 13:Histograms f |B ASP
app
|,comprisedof the internet-
w rk space-time charts of Fig.12 sh w n distinction of the
distributi n f r grains.The s lid curve is the distributi n f r
every pixel of charts 1 –9,andthe dashedcurve represents
the distribution for only the H 2V excess locations such as
those identi .ed by the brackets in in Fig.11.The dotted and
l ng-dashedcurves are the same as in Fig.9 anddescribe the
full-.eld |B
ASP
app
|distributi n and the Stokes |V |c ntinuum
.uctuati ns,respectively.
dividual maps of these two quantities,constructed from
the eleven-position slit map taken about 37 minutes af-
ter the beginning of the map sequence.The H 2.... map is
truncated at the bottom due to the limited .eld-of-view
of the MD detector and at the right due to di .eren-
tial refraction.The bright pixel columns indicate the slit
position for which the space-time charts of the middle
and right panels were derived.These cover the entire
time sequence for this slit position,which was selected
for this display because it contains the bright H 2.... grain
at y =57arcsecand t =37 min.This grain is also visible
in the Ca II H spectrogram of Fig.6.The lower cuto .
of the H 2.... chart is curved due to the correction for slow
drift of the .eld along the slit (Sect.3.1).
The internetwork region outlined in Fig.4 is indicated
by a highlighted box in the space-time charts of the mid-
dle panels,which in turn are enlarged in the panels at
right.The H 2.... panel displays modulation that is char-
acteristic of the chromospheric three-minute oscillation
(cf.Fig.4 of Rutten 1994;Fig.6 of Rutten 1995).The
brackets were de .ned by application of a median .lter
to this space-time chart in order to locate local max-
ima of the H 2.... index.These brackets also overlie the
corresponding expanded B ASP
app space-time chart.There
is no obvious association of H 2.... brightenings with ei-
ther localized .eld excesses or with .eld de .cits.Note
that the grey scale for the enlarged display ranges over
-16 .7 =B ASP
app
=22 .2Mxcm -2 (the extrema of variation
of this internetwork region)so that this comparison is a
highly sensitive one,emphasizing the very weakest .elds
down to the |B ASP
app
|˜3Mxcm -2 noise limit.
Figure 12 displays the H 2.... —B ASP
app internetwork
space-time comparisons for all eleven spectrograph slit
positions comprising the time series of maps.There are
a few coincidences,most noticeably at slit position x =8
where the slowly drifting negative polarity feature in the
B ASP
app panel seems to be accompanied by slowly increas-
ing H 2.... brightness,and possibly by enhanced H 2.... grain
activity in the .rst half of the adjacent x =9 panel.
This magnetic feature peaks at B ASP
app = -55 Mx cm -2 ;
its distribution along the slit has a FWHM of 1 arcsec.
It appears to be con .ned to the x =8 slit position,so
that its total magnetic .ux is less than 3 ×10 17 Mx.Its
possible association with H 2.... grain activity peaking at
x =9 may make it an "internetwork .asher "similar to
that of Brandt et al.(1992,1994)and the three features
marked in Fig.2.However,considering the entire ASP
data set,there is certainly no one-to-one spatio-temporal
correlation between H 2.... brightenings and .ux density
enhancements as was claimed by Sivaraman &Livingston
(1982).In particular,the brightest H 2.... grains such as
the ones in panels x =2 -3and5 -7 do not show obvious
magnetic connections at the SP sensitivity.
Further evidence for lack of correlation between H 2....
brightness excess and enhanced vertical .eld strength in
the internetwork domain is provided by the solid and
dashed histograms in Fig.13.These histograms dif-
fer from those of Fig.9 in that |V tot
|is converted to
|B ASP
app
|,and that only the internetwork region of the se-
quentially mapped area is considered.The solid curve
speci .es the distribution over all internetwork space-time
samples,whereas the short-dashed curve represents the
partial distribution over only the "H 2.... grain "locations
having chromospheric H 2.... brightness excess as brack-
eted in Fig.11.Signi .cant departure between the two
curves would be expected for any association between
H 2.... brightness excess and magnetic .ux.However,the
two distributions are virtually identical.
The other two curves in Fig.13 measure the distri-
bution of |B ASP
app
|and the Stokes |V |continuum .uctu-
ations over the full .eld of Fig.4.They are the same
as in Fig.9 but are presented on the linear |B ASP
app
|scale
and are normalized to the same peak height as the in-
ternetwork histograms.The lower (long-dashed)curve,
representing random noise,falls well below the internet-
work distribution.The upper (dotted)curve includes
the network patches in the full .eld and falls well above
the internetwork distribution at these small values of
|B ASP
app
|.This departure is a result of seeing and instru-
mental scatter from strong but distant .ux tubes,show-
18.ing once again that one cannot de .ne a speci .c value
of |B ASP
app
|as a network/internetwork discriminator.For
|B ASP
app
|<2Mxcm -2 the histograms from the sequen-
tially mapped region (solid,dashed curves)present a
much larger occurrence of very small polarizations due
both to the larger bin size of these histograms and,more
importantly,to the e .ect of spatio-temporal interpola-
tion between adjacent V tot samples of opposite sign.
4.3 Properties of Horizontal Internetwork
Fields
We now turn to the horizontal internetwork .elds
(HIFs)discovered by Lites et al.(1996).These are very
small,transient appearances of predominantly horizon-
tally oriented magnetic .ux that tend to be accompa-
nied by blueward Doppler shifts.Because small dynamic
events in the photosphere may produce much more dra-
matic phenomena higher up,we thought it worthwhile to
search for an association between HIFs and H 2.... grains.
This is done in Figs.14 –16.We .rst compare the HIFs
with the longitudinal .elds in the internetwork.
Figure 14 displays space-time charts of L tot and B ASP
app
in the format of Fig.12 for all slit positions covering the
sequentially mapped internetwork region.Locations of
enhanced linear polarization with L tot
=0 .00073 (i.e.,
HIFs)are highlighted in the adjacent B ASP
app panels.Some
are labeled alphabetically.HIF event d in the 9th panel
pair of Fig.14 is also shown in Fig.15.
The scarcity and the transient nature of the HIF
events is striking when compared with the persistence of
the stronger Stokes V features.The latter produce long-
duration dark and bright streaks in the B ASP
app panels that
oftenextendover2 -3 arcsec into the neighboring pan-
els for adjacent slit positions,while most HIFs measure
only 1 arcsec or less.few HIF events might coincide
with the appearance or disappearance of bipolar features
in the B ASP
app space-time charts.In particular,the HIFs
identi .ed in Fig.14 by b and c at slit positions x =4
and x =6 seem to occur at the initial spreading of two
very weak opposite-polarity Stokes V features,suggestive
of the emergence of new .ux,whereas HIF d in panel 9
seems to lie at the coalescence and cancellation of a very
weak bipolar V feature pair.Lites et al.(1996)specu-
lated that HIFs may mark .ux emergence sites.These
data do not con .rm this suggestion conclusively but hint
that it may be partially the case.
4.4 H2.... Grains versus Horizontal Internetwork
Fields
Finally,we test the possibility that H 2.... grains coin-
cide (possibly at some time delay)with locations where
HIFs occur in the underlying photosphere.Figure 15
shows SP Stokes spectrograms in which HIF event d in
Fig.14 is prominent,especially in Stokes U .The pan-
els at the right of the .gure show corresponding spatial
maps and space-time charts for H 2.... brightness,linear po-
larization L tot and the apparent .ux density B ASP
app .The
arrow in each panel indicates the HIF space-time loca-
tion.The brightness peaks in the H 2.... space-time chart
(upper right)are again indicated by bracket pairs that
are also overlaid on the L tot and B ASP
app charts.Figure 16
displays similar comparisons for all slit positions.There
is no obvious correlation between the occurrence of H 2....
grains and HIFs,even considering time delays.In addi-
tion,the HIFs are smaller than the H 2.... brightenings and
occur much less frequently.
5 Discussion
We have found no clear correlation between the occur-
rence of internetwork grains as evidenced by Ca II H 2....
brightenings and the presence of internetwork Stokes V
features with apparent .ux density above our |B ASP
app
|˜3Mxcm -2 noise threshold.We have also not found
direct correspondence between internetwork grains and
HIFs.
The .rst result contradicts the claim of Sivaraman &
Livingston (1982)that Ca II K 2.... grains are co-located
one-to-one with internetwork .eld enhancements,and
further that they obey a qualitative correlation between
brightness and apparent .ux density (that they denote as
".eld strength ").We believe that our higher angular res-
olution,the narrower Ca II passband used here,the syn-
chronicity of our polarimetry and Ca II H spectrometry,
and the overall quality of the ASP as well as its reduction
procedures combine to make this conclusion quite robust.
Indeed,the .ux density histogram in Fig.2 of Sivaraman
&Livingston (1982)peaks near |B KPNO
app
|=15Mxcm -2 ,
indicating a noise level of this order although they claim
a "background "of about 5 Mxcm -2 .Its tail extends to
|B KPNO
app
|>70 Mx cm -2 ,while the internetwork tail in
our Fig.13 does not reach |B ASP
app
|=40Mxcm -2 .Since
we are con .dent that our angular resolution is much bet-
ter,we suspect that their extended tail betrays the in-
clusion of network .elds and that these have contributed
to the apparent one-to-one correspondence.
The second result,absence of H 2.... –HIF correspon-
dence,does not exclude that HIFs possess a chromo-
spheric signature,nor does it establish their nature.s
noted by Lites et al.(1996),these small transient features
tax the limits of SP capability.Signi .cant advances in
polarization sensitivity,angular resolution,temporal and
spatial coverage are needed to improve on these.Because
the polarization is small in the visible,infrared spectropo-
larimetry may present a more sensitive diagnostic of these
features.
19.Figure 14:L cations f HIF (horizontal internetwork .eld)events in the internetw rk region are compared in the format f
Fig.12 to the ev luti n f the apparent .ux density.Space-time chart pairs f r the internetw rk regi n are sh wn f r all eleven
spatial slit p sitions.The left image of each pair sh ws the pro .le-averagedlinear polarization L tot......The grey scale is clipped
at 0 .0004 =L tot
=0 .0008 andthe sign is reversedso that large linear polarization appears dark.The right panel f each pair
sh ws the apparent .ux density B
ASP
app with the grey scale clippedat |B
ASP
app
|=40 Mxcm - 2
(same as |B
ASP
app
|in Fig.12 but with
HIF events highlighted.)Various HIF events are markedalphabetically in the left panels andall HIF events are highlightedin
the right panels.
20.Figure 15:A HIF event is comparedt the bservedCa II H brightness.The arrow in each panel indicates the space-time l cation
f the HIF.The f ur panels at left sh w ASP Stokes spectra f r slit p siti n x =9 arcsec andtime step t =21min.Thethree
panels in the middle present spatial maps at t =21 min.Panels n the right are space-time charts of the internetwork region
for the H 2V index (t p),the pro .le-averaged net linear polarization L tot (middle),and the apparent .ux density B
ASP
app (b ttom)
corresponding t the highlighted slit p sition in the maps,and also t the St kes spectra.The brackets in the space-time
charts specify the locations f H 2V brightenings derivedf r the top chart.The highlighted pixel c lumns (bright r dark)in
the panels at right indicate times f r which the maps in the middle panels are displayed.The displays f r L tot have been
sign-reversedso that large polarization appears dark.The grey scales are clippedat ±0 .002 for the Q ,,and V Stokes spectra,
at 0 .0004 =L tot
=0 .0008 for the L tot panels,andat |B ASP
app
|=20 Mxcm - 2 for the B ASP
app panels.
21.Figure 16:H 2V intensity m dulation is compared t HIF events for all slit p sitions.The left columns sh w H 2V space-time
charts as in Fig.12,andthe right columns sh w L tot space-time charts as in Fig.14.There is n bvious correlation between
H 2V brightenings andHIF events.
22.Finding that the occurrence of internetwork grains,
apart from the rare persistent .ashers,does not depend
on magnetism raises the question whether there are other
phenomena that act as speci .c pistons for grain excita-
tion.On the basis of other work we suspect that sudden
convective down .ows at or just below the surface that
seem to produce "acoustic events "and "intergranular
holes "may also enhance grain production in the over-
lying chromosphere (cf.Restaino et al.1993;Rimmele
et al.1995;Rast 1995;Roudier et al.1997;Hoekzema &
Rutten 1998;Hoekzema et al.1998;Goode et al.1998).
6 Conclusions
We have supplied yet more evidence that the occur-
rence of most Ca II K 2.... and H 2.... grains in solar internet-
work regions does not depend on the presence of magnetic
.elds.Whether their occurrence marks speci .c piston
locations with future diagnostic value remains an open
question.nswering this question may become both eas-
ier and more important now that the ultraviolet images
from the TRACE mission mission 4 display internetwork
grains similar to those in K 2.... and H 2.... .Inthefuture,
the planned Solar-B mission may enable measurements
as presented here without the handicap imposed by the
Earth 's atmosphere.
We thank Fritz Stau .er at NSO/Sacrament Peak for
s ftware to synchronize the MDA and ASP exp sures and
the bservers at the NSO/SP T wer Telescope,S.Hegwer,
D.Gilliam,andB.Armstrong for their expert assistance
in setting up and running the ASP.Furthermore,we thank
D.Elm re andK.Streander of HAO for assistance at NSO
during this bserving run.We thank H.Peter f r suggesting
many improvements to the manuscript.RJR is indebted to
HAO and LMSAL f r hospitality.BWL was supp rtedin part
by NASA SOHO Guest Investigator AwardW-19,328.TEB
was supportedby NASA contract NAS8-39747 (SOHO/MDI)
and Lockheed-Martin Independent Research Funds.RJR 's
travel to LMSAL was partially supp rtedby NASA SR&T
Grant NASW –98008.
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