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. 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