The solar chromosphere at high resolution with IBIS. II. Acoustic shocks in the quiet internetwork and the role of magnetic fields
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ESO 2018September 16, 2018
The solar chromosphere at high resolution with IBIS
II. Acoustic shocks in the quiet internetwork and the role of magnetic fields
A. Vecchio , , G. Cauzzi , , and K. P. Reardon , INAF - Osservatorio Astrofisico di Arcetri, 50125 Firenze, Italy Dipartimento di Fisica, Universit`a della Calabria, 87036 Rende (CS), Italy National Solar Observatory, P.O. Box 62, Sunspot NM, USASeptember 16, 2018
ABSTRACT
Context.
The exact nature of the quiet solar chromosphere, and especially its temporal variations, are still subject of intense debate.One of the contentious issues is the possible role of magnetic field in structuring the quieter solar regions.
Aims.
We characterize the dynamics of the quiet inter-network chromosphere by studying the occurrence of acoustic shocks and theirrelation with the concomitant photospheric structure and dynamics, including small scale magnetic structures.
Methods.
We analyze a comprehensive data set that includes high resolution chromospheric (Ca II 854.2 nm) and photospheric(Fe I 709.0 nm) spectra obtained with the IBIS imaging spectrometer in two quiet-Sun regions. This is complemented by high-resolution sequences of MDI magnetograms of the same targets. From the chromospheric spectra we identify the spatio- temporaloccurrence of the acoustic shocks. We compare it with the photospheric dynamics by means of both Fourier and wavelet analysis, andstudy the influence of magnetic structures on the phenomenon.
Results.
Mid-chromospheric shocks occur within the general chromospheric dynamics pattern of acoustic waves propagating fromthe photosphere. In particular, they appear as a response to underlying powerful photospheric motions at periodicities nearing theacoustic cut-o ff , consistent with 1-D hydrodynamical modeling. However, their spatial distribution within the supergranular cells ishighly dependent on the local magnetic topology, both at the network and internetwork scale. We find that large portions of the inter-network regions undergo very few shocks, as “shadowed” by the horizontal component of the magnetic field. The latter is betrayed bythe presence of chromospheric fibrils, observed in the core of the Ca II line as slanted structures with distinct dynamical properties.The shadow mechanism appears to operate also on the very small scales of inter-network magnetic elements, and provides for a verypervasive influence of the magnetic field even in the quietest region analyzed. Conclusions.
The magnetic field might play a larger role in structuring the quiet solar chromosphere than normally assumed. Thepresence of fibrils highlights a clear disconnection between the photospheric dynamics and the response of the geometrically overlay-ing chromosphere. As these results hold for a mid-chromospheric indicator such as the Ca II 854.2 line, it is expected that diagnosticsformed in higher layers, such as UV lines and continua, will be a ff ected to a larger extent by the presence of magnetic fields, even inquiet regions. This is of relevance for the chromospheric models that make use of such diagnostics. Key words.
Sun: chromosphere — Sun: magnetic fields — Sun: oscillations
1. Introduction
Observations have long shown that the outer solar atmosphereis not in radiative equilibrium, with the net radiative loss ofthe quiet chromosphere estimated at between ≈ − (Vernazza et al. 1981) and 14 kWm − (Anderson & Athay1989). The identification of the source and exact mechanism ofdeposition of the energy necessary to maintain a stationary situa-tion is often referred to as the problem of chromospheric heating.It has been a vexing problem in solar physics for decades.In stellar atmospheres, strong density stratification makesit relatively easy for propagating acoustic waves, excited bythe turbulent convection, to develop into shocks. Indeed thismechanism was proposed early on as a plausible means toprovide the necessary energy input to the solar chromosphere(Biermann 1948; Schwarzschild 1948). Much theoretical andnumerical work has since been conducted to assess the vi-ability of the acoustic heating as the basic heating mecha-nism for nonmagnetic chromospheres of slowly rotating stars(e.g. Narain & Ulmschneider 1996; Ulmschneider & Musielak2003). A landmark work on this topic was the 1-D radiative-hydrodynamical modeling of Carlsson & Stein (1995, 1997,2002), who derived the chromospheric response to acousticwaves in the absence of magnetic fields. Using an observed pho-tospheric piston, they could reproduce the temporal evolution ofthe chromospheric Ca II H spectral line over long intervals withremarkable accuracy. In particular, they reproduced the occur-rence of the H V (K V ) grains observed in the spectral profile ofthe resonance H and K lines of of Ca II. The grains consist ofquasi-periodic brightenings in the violet wings of the lines, witha ∼ ff value of ∼ average chromospheric temperature (Carlsson & Stein A. Vecchio et al.: The solar chromosphere at high resolution with IBIS ff erent diagnostics, over extended fields of view (FOV).Most of the debate to this point has been based on (older) spec-trographic observations obtained in the Ca II H and K lines, andon UV spectral data obtained by Skylab or, more recently, bySUMER on board SOHO (Wilhelm et al. 1995). Spectrographicdata su ff er however from a limited FOV in fixed slit observa-tions, or from a low cadence when scanning an extended region.In the UV, the limited flux and instrumental response furtherlower the achievable spatial and temporal resolution, an impor-tant limitation if the dynamic picture just described for the chro-mosphere is the correct one (Wedemeyer-B¨ohm & W¨oger 2008).Historically, imaging with broad-band filters has been widelyused, both in the UV and visible range. Such data, however, of-ten mix signals arising from vastly di ff erent regions of the so-lar atmosphere, as well as miss signatures of strong velocitiesthat might shift the lines outside the filter band. For a generalreview on the issues of chromospheric observations we refer toRutten (2007), only adding here that recently the POLIS spectro-graph (Beck et al. 2005) has become operational, producing newhigh quality Ca II H spectra that have been employed in studiesof the quiet chromosphere (Rezaei et al. 2007; Beck et al. 2008;Rezaei et al. 2008).In this paper we use an entirely di ff erent type of instrument,the Interferometric BIdimensional Spectrometer (IBIS, Cavallini2006), to derive novel results about the dynamics of the quietsolar chromosphere and in particular the presence (or absence)of acoustic shocks. IBIS is an imaging spectrometer installedat the Dunn Solar Telescope (DST) of the US National SolarObservatory, and provides observations that combine high spa-tial and temporal resolution over an extended two-dimensionalFOV, with the full spectral information in both photosphericand chromospheric lines. In this sense, it is an ideal instrumentto overcome many of the observational shortcomings outlined Fig. 2.
Full disk EIT images acquired in Fe XII 19.5 nm on 2004May 31 (left) and 2004 June 02 (right). The cross-hairs indicatethe center of the IBIS FOV for each day. The IBIS FOV coversroughly the small coronal bright point intersected by the cross-hair on the right panel.above. We analyze the behavior of the chromospheric Ca II 854.2nm line which, as shown in Cauzzi et al. (2008) (hereafter PaperI), is one of the most promising diagnostics for high resolu-tion chromospheric studies. Equally important, the availabilityof spectral information over a 2-D FOV is crucial to understand-ing the very dynamic and non-local chromosphere. We furthercombine the Ca II 854.2 observations with simultaneous andcospatial photospheric data also obtained with IBIS and mag-netic data from MDI (Scherrer et al. 1995). This allows us toaddress the relationships between the chromospheric and photo-spheric dynamics, and the influence of magnetic field. We an-alyze two completely analogous data sets obtained on separatedays, both times in quiet regions near disk center, and in so do-ing uncover the fundamental role played by the local magnetictopology.The paper is organized as follows. In Section 2 we de-scribe the observations. Sections 3 and 4 provide evidence thatmid-chromospheric acoustic shocks are clearly observed in theCa II 854.2 nm line, and outline the methods we use to identifythem. In Sect. 5 we report on the derived shock properties, bothin relation to earlier findings obtained primarily with Ca II Kobservations, and shock15.gc.as new results regarding their spa-tial distribution. Sections 6 and 7 address the occurrence of theshocks in relation to the magnetic field structure and evolution,and the photospheric dynamics. Finally, in Sections 8 and 9 wediscuss our findings and provide conclusions.
2. Observations
The IBIS design and general issues on data reduction have beendescribed in earlier papers (Cavallini 2006; Reardon & Cavallini2008; Janssen & Cauzzi 2006), so we mention here only thecharacteristics most relevant to the present work.IBIS is based on two air spaced Fabry Perot Interferometersin a classical mount, and acquires quasi-monochromatic imagesin the range 560-860 nm (FWHM = ff erent wavelengths allows the spectral sampling of anumber of selected lines, providing spectral information over acircular, 80” diameter FOV. Typically, a spectral line is sampledin 10–30 spectral points, within a total acquisition time of 3–10s. Data can be obtained at the full resolution of 0.083” / pixel, orbinned to increase the photon flux and reduce the CCD readouttime. Coupled with the high-order adaptive optics system of on . Vecchio et al.: The solar chromosphere at high resolution with IBIS 3 Fig. 1.
Top row: data set 1; bottom row: data set 2. The images refer to data acquired around the middle of the observing sequences.Axes are given in arcsec. Panels a, e : Broadband continuum at 710 nm. The image in data set 2 has been speckle reconstructed withthe technique of W¨oger (2007). Panels b, f : co-temporal HR MDI maps, saturated at ±
500 G. Data set 2 attains to an enhanced,bi-polar network region. Panels c, g : Intensity in the red wing of the CaII 854.2 nm at about 0.1 nm from line core. Bright pointsclearly correspond to small scale magnetic features. Panels d, h : Line core intensity of CaII 854.2 nm. Note the large extension offibrils originating in the magnetic elements.
Fig. 3.
Representative field lines from the MDI-extrapolated potential magnetic field.
Left panels : data set 1.
Right panels : data set2. The green thick lines trace the open field lines, the red thin line draw field lines closing within the considered area. The whitedashed circles delineate the IBIS FOV for each data set. The vertical scale in the bottom panels is the height given in Mm.
A. Vecchio et al.: The solar chromosphere at high resolution with IBIS the DST (Rimmele 2004), IBIS images often attain spatial reso-lution close to the di ff raction limit of the 76-cm telescope. The data utilized in this work were acquired in two quiet ar-eas in close proximity to disk center, on 2004 May 31 (in thefollowing data set 1) and 2004 June 02 (data set 2). In both daysthe same acquisition scheme was adopted, sampling sequentiallythe photospheric Fe I line at 709.0 nm and the chromosphericCa II 854.2 nm line. The time necessary to scan the lines was,respectively, 4 s and 7 s, while the overall cadence for the fullsequence was 19 s (the Fe II 722.4 nm line was also includedin the sequence, but not used in this paper). The spatial scalewas set to 0.166” / pixel ( ≈
120 km at the solar surface). The pho-tospheric data for set 2 has been utilized in Janssen & Cauzzi(2006), while both photospheric and chromospheric data, againfor set 2, have been analyzed in Vecchio et al. (2007), hereafterV07. The Ca II data for both days has been further described inPaper I.We analyzed two stretches of 55 minutes of continuous ob-servations (175 time steps) obtained in good to excellent seeingconditions on each day. Data set 2 had a better seeing than dataset 1. We examined the full spectral profiles, as well as studyingparameters extracted from them. In particular, for each spatialposition in the FOV we extract by means of spline interpolationboth the intensity and the position of the minima of the spectralline profiles. The latter are interpreted in terms of Doppler-shift,with the zero position for the velocity scale defined as the spatio-temporal average of the whole dataset over a quiet portion of theFOV (see also discussion in Janssen & Cauzzi 2006, and PaperI). Fig. 1 gives a synopsis of the data around the middle ofthe observational sequence for both days. The observed FOVis shown at di ff erent wavelengths together with the simultane-ous high resolution (HR) MDI magnetograms. The leftmost col-umn shows the broadband continuum at 710 nm, indicating onboth days a mostly quiet scene, with slightly lower contrast inthe magnetic regions that delineate the supergranular network.At higher magnification these can be resolved as tiny brightpoints embedded within the intergranular lanes (especially inthe speckle-reconstructed image of data set 2). The second col-umn displays the high resolution MDI data obtained simultane-ously to the IBIS data sets: the network elements are well dis-cernible in the two FOVs, but highlight a very di ff erent mag-netic environment, with a weaker, unipolar network in data set1, and an enhanced bipolar network for data set 2. The third col-umn shows IBIS images acquired at about 0.1 nm from the coreof the Ca II 854.2 nm line. Together with the reversed granu-lation pattern, these monochromatic images display bright el-ements with a one-to-one correspondence to magnetic elements(Leenaarts et al. 2006, Paper I). Finally, the fourth column showsthe images in the core of the Ca II line, that outline a “segre-gated” picture, with part of the FOV occupied by fibrils orig-inating from even the smallest magnetic elements, and part ofit, farthest from the magnetic network, showing an abundance ofsmall bright points surrounded by much darker regions (comparethe temporal evolution of this region from Movie 2 in Paper I). High resolution MDI magnetograms are available for almost thewhole duration of the IBIS observations on both days. They have a spatial scale of 0.6” / pixel, and a cadence of 1 minute. The MDImaps outline a very di ff erent magnetic configuration of the tworegions (Fig. 1 panels b , f ). Coronal images confirm this di ff er-ence: while at photospheric level both regions could be classifiedas quiet, EIT Fe XII 19.5 nm images acquired around the time ofthe IBIS observations clarify that the May 31 region is localizedat the edge of an equatorial coronal hole, while the June 2 regioncorresponds to a decaying coronal bright point (Fig. 2). In nei-ther case did we observe significant variations of the magneticconfiguration over the duration of the IBIS observations.The di ff erences in magnetic topology are already reflectedat the chromospheric level, in the morphology shown by theCa II line core intensities. In set 2 we observe a large numberof elongated fibrilar structures, with a complex spatio-temporalevolution and connecting, in many cases, regions of opposite po-larity. On the contrary, the number and length of fibrils in dataset 1 are much lower, suggesting either short loops that closenearby the network elements, or more vertical structures thatfollow magnetic field lines extending into interplanetary space.To assess qualitatively the 3-D magnetic field configuration, wecompute a potential field extrapolation starting from the MDIlongitudinal field, assumed as the vertical component of the vec-tor field at a height of about 200 km. The area utilized for theextrapolation is about six times larger than the IBIS FOV. InFigure 3 we show the resulting magnetic fields, extrapolated upto a height of 2.5 Mm. Representative closed lines within thisextended region are drawn in red (thin lines), while field linesthat open to more distant regions or the interplanetary space aredrawn in green (thick lines). The closed field lines closely re-semble the chromospheric morphology: in data set 2 the volumeis dominated by field lines connecting opposite polarity networkpoints, spanning large fraction of the FOV, and reaching heightsup to about 2 Mm. The quieter data set 1, instead, is character-ized by short, and low-lying, closed field lines fanning out fromthe network points and reaching to nearby internetwork weakmagnetic concentrations. The fibrillar structures so prominent inthe Ca II core images appear a reliable proxy for the presence ofa magnetic canopy (Paper I, V07).
3. Evidence for acoustic shocks in the internetwork
As for the Ca II H and K lines, the formation of Ca II 854.2 nmspans a wide range of atmospheric heights (Paper I). From the farwings in toward the core, the line gradually samples from the lowto the high photosphere, while the line core itself is formed inthe lower chromosphere. However, as shown by Skartlien et al.(1994) and more recently by Pietarila et al. (2006), the presenceof hydrodynamic shocks in the non-magnetic chromosphere de-termines a large range of heights for the formation of the linecore, spanning from as low as 700 km up to 1300 km. The shocksinduce rapid variations in the thermodynamics of the a ff ected at-mosphere, resulting in asymmetric Ca II 854.2 spectral profiles(cf. Figs. 3 and 7 of Pietarila et al. 2006).Fig. 4 displays the observed temporal evolution of the IBISCa II 854.2 nm spectral profiles for four representative pixels,two for each data set. The pixels have been chosen as typical ofthe internetwork regions of the FOV. As described in Paper I,the sequence of line core images shows a rapidly evolving scenewith areas that are seething with small bright features immersedin an otherwise dark background (compare Movie 2 in PaperI). The spectral profiles of Fig. 4 clearly show how this appear-ance is the result of the line being repeatedly shifted, stronglytowards the blue followed by a slower, smaller amplitude driftback toward the red. The pattern is repeated at the dominant . Vecchio et al.: The solar chromosphere at high resolution with IBIS 5 Fig. 4.
Ca II 854.2 nm spectral profiles vs. time (given in s), for four positions within the internetwork. Panels a, b refer to data set1; panels c, d to data set 2. The time axis spans the whole duration of the observations. Note the distinctive saw-tooth appearance.The thin white line in panel a indicates the evolution with time of the line core Doppler shift. Maximum velocities reach 6–7 kms − from average position.chromospheric periodicity of ≈ ff period of ≈
180 s is prescribed by the strong de-crease in density and the approximate conservation of wave en-ergy. This is clearly reflected in the spectra of Fig. 4, where weobserve both a deviation of the oscillations from a sinusoidalform, and a large amplitude of the excursions. At these peri-odicities, the typical r.m.s. of chromospheric Doppler shifts isaround 1 km s − , vs. ∼ − of photospheric motions, cf.Reardon et al. (2008). However, many of the line shift episodesnot only display much stronger Doppler amplitudes, of the or-der of 5-6 km s − , but also exhibit a very abrupt change fromlarge redshift to large blueshift, often within a single 19-secondtemporal step in our sampling. Further, the maximum redshift ofthe line often coincides with a brightening episode just bluewardof the line core, lasting 50–70 s, with enhanced intensities up to1.5–2 times the average value at this wavelength. They are alsoassociated with an increased intensity in the extended line wings,that progresses in time from the far wings towards the core. Forthe wavelength range of our observations, this time is less thanabout 60 s. Clear examples in Fig. 4 occur at t = a , or at t = d .These features are analogous with those of the Ca II K V grains (Liu 1974; Cram et al. 1977; Cram & Dame 1983, RU91)which have been unequivocally identified as due to hydrody-namic shocks in the mid chromosphere (hereafter we will usethe terms grains and shocks interchangeably). A clear example of the resemblance between the temporal evolution of the Ca II Kand Ca II 854.2 lines in a non-magnetic atmosphere is providedby comparing Fig. 4 with Fig. 2 of Kamio & Kurokawa (2006):all the characteristics previously described for the IBIS data ap-pear very obvious in the latter high-resolution observations (notethe di ff erent axes of their Figure with respect to Fig. 4). TheDoppler shifts are clearer in the Ca II 854.2 line while the brightgrains and related wing enhancements are less prominent whencompared to the H and K lines. These di ff erences are a conse-quence of the di ff erent formation and wavelengths of the twolines: the Ca II 854.2 line has a much stronger Doppler sensi-tivity due to its longer wavelength and the Planck function (towhich the emissivity is related) has a much weaker temperaturedependence in the near-IR.To our knowledge, this is the first time that acoustic shocksin the quiet internetwork chromosphere are convincingly (andabundantly) observed in the Ca II 854.2 line, due to both thehigh spectral and spatial resolution of the IBIS data. Indeed, syn-thetic profiles calculated with the 1-D hydrodynamical code ofCS97 well agree with the features described above (Pietarila, pri-vate communication; Cauzzi et al. 2007). As further evidence,we show in Fig. 5 the development of Ca II 854.2 spectra of twoexample pixels, at several times during the passing of a shockwave. The profiles in the right panels are representative of alarge fraction of internetwork pixels, for which the character-istic shifts and asymmetries of the spectral line are in excellentagreement with the results of the simulations displayed in Fig.7of Pietarila et al. (2006). As an interesting case, we also showin the left panels the spectral profiles for a more extreme event,where a strong shock greatly deforms the whole line shape up tothe far blue wing. A. Vecchio et al.: The solar chromosphere at high resolution with IBIS
Fig. 6.
Spatial distribution of properties related to shocks. Top row: data set 1; bottom row: data set 2. Results shown in a through c , and e through g have been derived from the POD analysis. Axes are in arcsec. Panels a, e : binary “shock maps” at a time aroundthe middle of the sequence. Panels b, f : cumulative number of shocks within the whole observational sequence. Panels c, g : maps ofthe shocks’ cumulative amplitude over the whole duration of the observations. Panels d, h : spatial distribution of the Fourier powerfor chromospheric velocity, integrated over frequencies at and slightly above the acoustic cut- o ff (5.5 – 8.0 mHz).
4. Shock identification
Typically, shocks in extended FOV have been identified by usingan intensity threshold on Ca II H V or K V filtergrams. This takesadvantage of the larger temperature sensitivity of the Planckfunction in the blue. However, shocks are foremost a velocityphenomena, due to the steepening and rapid reversal of the up-ward propagating waves. Hence, the velocity signature is pre-sumably the most suitable means to identify their actual occur-rence. Given the properties reminded above, Ca II 854.2 appearsto be a reliable line with which to identify shocks in the solarchromosphere.We adopt two di ff erent methods that utilize the temporalsequence of the full spectral profiles to locate shocks in ourdatasets. For clarity of exposition, we shortly describe here onlytheir most relevant characteristics, with further details given inthe Appendix. The first method we call it the “velocity” method:analyzing the temporal profile of the chromospheric line-of-sightvelocity for each spatial position, we identify times of brusque,strong displacements from downward to upward motions. Themethod utilizes a threshold both in amplitude of the displace-ment, and in the temporal interval in which this displacementoccurs, set at a maximum of two time steps of the IBIS sequence(i.e. 38 s). The second method uses the “Proper OrthogonalDecomposition” technique (POD, Holmes et al. 1996), that sep-arates a time-series of spectral profiles into multiple orthogo-nal eigenmodes. These are then ordered in terms of decreasingenergy content, i.e. of their contribution to the whole intensityprofile. The periodic velocity shifts that produce the sawtoothshape in the temporal sequence of internetwork Ca II 854.2 spec-tra is clearly identified by the POD in a single antisymmetriceigenmode (see panel b of Fig. A.1), properly modulated by atemporal coe ffi cient. After finding all the spatial positions forwhich this eigenmode represents the dominant mode, we define the shock occurrence at the times when the positive peak of thefluctuation shifts from the red to the blue side of the line. Weapply the same temporal threshold as in the velocity method, butno amplitude threshold.For both methods we derive a time series of binary “shockmaps” defining the times of occurrence and spatial distributionof the shocks. An example of the POD results is given in Fig. 6 a and e . The results from the two methods are similar. As a generalcharacteristic, the POD identifies smaller shocks occurring morefrequently, most notably in the areas filled with fibrils, for whichthe velocity method essentially finds no shocks (see Sects. 5.1and 5.3 below). This can be attributed to the absence of a pre-scribed threshold for the amplitude of the shocks in the PODcase. We will point out other di ff erences and similarities as wedescribe the further results of the analysis.
5. Shock properties
From the shocks maps defined above, we can derive the size of ashock by measuring the area covered by contiguous pixels pos-sessing values of one. We discarded any shock area coveringless than 2 pixels in either direction, imposing an e ff ective lowerlimit of 0.3 × to their dimension. For both data setswe find average shock extents of 0.4 arcsec (using the PODmethod) to 0.8 arcsec . Under the assumption that the shocksare roughly circular, this corresponds to diameters of 0.7 arcsecto 1.0 arcsec. These values can be compared to the typical 1-2arcsec size of the K V grains as reported in the literature (e.g.RU91; Liu 1974; Tritschler et al. 2007), although a number offactors set apart our analysis from the more common intensitythreshold approach. . Vecchio et al.: The solar chromosphere at high resolution with IBIS 7 Fig. 5.
Temporal evolution of the Ca II 854.2 line during a shock,for two internetwork pixels. Intensity is given in arbitrary units.The time indicated in each panel is expressed in s from an arbi-trary zero point. The thin vertical line indicates the average posi-tion of the line core throughout the full spatio-temporal sample.Note the broadening of the line during the upward phase.The average number of shocks occurring at any time withina given area can also be estimated. To this end, we selected forboth data sets a 30” diameter area roughly covering the centerof a supergranulation cell centered at ( x , y ) = (14 ,
0) for dataset 1 and (( x , y ) = ( − , V bright grains in a typical supergranula-tion cell have been reported at between 10 and 20 in “the bestK V spectroheliograms” (RU91). Our average values are onlysomewhat higher than these previous findings, but we observelarge variations of the number of shocks during the course of theobservations, mostly correlated to the seeing conditions: duringmoments of good to excellent seeing, more than 30 shocks canbe identified within a single cell. We can further analyze the temporal behavior of the shock oc-currence by using two methods. The first one, described in theAppendix, shows that the spatial areas where shocks occur inlarge numbers are dominated by shock periodicities around thethree minutes typical of the chromosphere. We also take an-other approach here by calculating the histograms of the “wait-ing times” for the shocks, defined simply as the interval between
Fig. 7.
Distribution of waiting times between shocks, for data set1 (panel a ) and data set 2 (panel b ).one shock and the next. No significant di ff erence is found be-tween the two methods of shock identification.The results are shown in Fig. 7 where a strong peak around120–150 seconds is observed for both data sets, with a sharp de-cline at shorter time scales and a slower decrease towards longerperiods. The data do not show any evidence of shock periodici-ties below 120 s (i.e. frequencies above 8 mHz), although suchperiods would be observable with our data. The long tail of thecurves at longer periodicities highlights the fact that Ca II 854.2shocks do not occur in a continuous fashion, but often in sepa-rate bursts. At the same time, no obvious values of waiting timebetween bursts emerge from the curves, although a change in theslope of the distribution appears around 4–5 minutes. Assumingthis values as discriminant between shocks in the same burst,and between di ff erent bursts, we find that the average numberof shocks per burst is only 1.25, and that the average number ofbursts within the whole sequence is around 3.All of this bears on the total number of shocks observed ineach pixel, displayed in panels b, f of Fig. 6 (using the POD re-sults). From these maps it is clear that most of the internetworklocations only develop shock for a fraction of the observing se-quence: only between 25% and 30% of the “shocking pixels”display 5 or more shocks during the whole sequence. The maxi-mum number of shocks for any given pixel is around 15 for bothdata sets and methods, although this is attained only in a veryfew pixels. A striking result emerging from panels b, f in Fig. 6 is the ex-treme inhomogeneity of the spatial distribution of the total num-ber of shocks. In particular, large portions of the internetworkclustered around the magnetic elements experience very fewshocks, or none at all. The velocity method provides the samespatial patterns, but with even more extended regions displayingvery few shocks . In the maps of Fig. 6, more than 20% of thepixels in data set 1, and 30% in data set 2, do not experience anyshock throughout the whole course of the observations. Thesevalues increase to a surprising 50%, respectively 60%, for areaswith a total number of shocks ≤
2. These areas are significantlylarger than the area occupied by the photospheric magnetic ele-ments, less than 10% in both cases. These results highlight howchromospheric dynamical properties are poorly constrained by
A. Vecchio et al.: The solar chromosphere at high resolution with IBIS
Fig. 8.
Scatterplot of the cumulative amplitude of shocks vs.Fourier power of chromospheric velocities, integrated in a bandof frequencies just above the acoustic cut-o ff (5.5– 8.0 mHz).Both axes are in arbitrary units. To avoid pixel crowding, the 2-D distribution is represented by contours, in logarithmic levels.the usually adopted photospheric magnetic diagnostics, a factalready remarked in Paper I.We further note that these “very few shocks” areas are es-sentially coincident with the fibrils observed in the Ca II linecore images (compare Fig. 6 with Fig. 1), that are again revealedas a crucial player in shaping the chromospheric dynamics (cf.V07 and Paper I). Conversely, the highest number of shocks isrecorded in areas well removed from both the photospheric mag-netic network and the fibrils. These areas are consolidated insmall patches scattered within the internetwork. Panels c, g of Fig. 6 provide the cumulative amplitude of theshocks over the duration of the observations, again derived fromthe POD analysis (Sect. A.2).It is interesting to compare the amplitude maps with the dis-tribution of the chromospheric velocity Fourier power, integratedover the 5.5-8.0 mHz range just above the acoustic cut-o ff fre-quency. The latter is shown in panels d, h of Fig. 6. As discussedin V07 for a subset of the data utilized here, in such maps allthe magnetic elements are surrounded by areas of very low ve-locity power, corresponding to the “magnetic shadows” first in-troduced by Judge et al. (2001) in an analysis of chromosphericSUMER data. They are also coincident with the fibrillar struc-tures so prominent in Ca II core images and, as clear from Fig. 6,with the chromospheric regions where few shocks occur duringthe observational sequence.The scatterplots in Fig. 8 display a clear pixel by pixel rela-tionship between the velocity power and the cumulative shocksamplitude: a simple linear regression finds a correlation of about0.65. From these correlations, we surmise that a large fractionof what is commonly identified as the “3-minute chromosphericoscillations” signal in Fourier analysis (e.g. Orrall 1966; Noyes1967; Deubner & Fleck 1990) is due to the presence of shocks,even if they do occur with the intermittent character describedabove. In practice, the linear Fourier analysis identifies theshock periodicity and provides a measure of the amplitude of thevelocity fluctuations at this dominant frequency, even though thephysical phenomenon that produces this signal is very non lin-ear. Fig. 10.
Distribution of MDI longitudinal magnetic flux mea-sured in points undergoing a large (dotted line) and small (solid)number of shocks, respectively.
6. Shock occurrence vs. magnetic structures
Numerous observational studies have searched for a connectionbetween the occurrence of K V grains and the presence of mag-netic structures in the internetwork as evidence for a possibleexcitation mechanism (see e.g. the Introduction of Lites et al.1999). The majority of these have concluded that the grainsare essentially a hydrodynamical phenomenon, for which mag-netism plays a minor role at most. However, there remain someclaims about a tight correspondence between the presence ofsmall scale bipoles in the internetwork and K V grains, most re-cently by Sivaraman et al. (2000). Our comprehensive data sets,combining high-cadence spectral data over extended areas withactual magnetic field measurements, can be used to examine thisquestion.A coarse inspection of the magnetic maps of Fig. 1 and thecumulative shock maps of Fig. 6 immediately shows that shocksdo not occur at the locations of magnetic structures. A closer in-spection shows that the shocks apparently avoid even the small-est magnetic elements: in Fig. 9 we show again the cumulativeshocks maps for both data sets, overlaid with the contours of thetime-averaged MDI magnetic maps. While in the average MDImaps the noise is reduced to a level of about 5 G, in Fig. 9 themagnetic contour level is set at 8 G to allow visibility of theweak and / or transient structures (the network elements have anaverage magnetic flux of 200–300 G). ¿From Fig. 9, one infersthat even small magnetic structures impede the development ofthe shocks: one notes the small “shadows” in the shock mapssurrounding several tiny internetwork magnetic structures, forexample at positions ( − − − − −
33) in data set 2.A deeper analysis on this issue involves measuring the mag-nitude of the magnetic field in those areas that undergo shocks.We first selected, in both data sets, the quiet regions where thetemporal average of the MDI magnetic flux does not exceed 30G. We then divided these regions in two parts, one collecting thepixels where several shocks ( n ≥ ≤ n ≤ n = ff ectively avoids most of the magnetic shadows associatedwith the network elements (cf. Fig. 6). The magnetic flux distri- . Vecchio et al.: The solar chromosphere at high resolution with IBIS 9 Fig. 9.
Cumulative shock maps for dataset 1 (panel a ) and 2 (panel b ). Overlaidis the contour of the high resolutionMDI magnetic flux, averaged over thecourse of the IBIS observations. Thecontour level is set at 8 G. Comparehow even minute magnetic structureswithin the internetwork, probably oc-curring only for a fraction of the ob-servations, correspond to a decreasednumber of Ca II shocks. Spatial scale inarcsec.butions obtained from the temporally resolved MDI maps in thetwo classes of pixels are shown in Fig. 10. The vertical line at 15G represents the noise level for a single pixel in MDI maps. Inboth data sets, the distributions for the two classes of pixels startdiverging shortly after the noise value, with the pixels undergo-ing many shocks characterized by sensibly lower values of themagnetic flux.The curves diverge at the level of 10 − in relative occur-rence, i.e. only a small fraction of the pixels displays this e ff ect.Nevertheless, the di ff erence is clear. Combined with the mapsin Fig. 9, this shows that the internetwork magnetic fields actu-ally seem to have a negative e ff ect on the development of shocks.Magnetograms with higher sensitivity and spatial resolution thanthose of MDI might reveal if there is a critical area or flux valuebelow which this e ff ect no longer holds.
7. Shock occurrence vs. photospheric velocities
We now examine the relationship between the occurrence ofshocks and the underlying photospheric dynamics. We do soboth with classical Fourier analysis, and also using wavelet anal-ysis on photospheric velocities, which is a more e ffi cient way totake into account the highly intermittent character of the shocks. The spatially-averaged Fourier velocity power spectra for thesedata sets are displayed in Reardon et al. (2008) and Paper I,and are in general very similar to previously published spec-tra (e.g. Deubner & Fleck 1990): the photospheric curve showsa strong maximum around the classical 5 minute periodicity( ν ∼ . ∼ . a, b in Fig. 11 display the phase di ff erence spectrabetween the Fourier transforms of the chromospheric and photo-spheric velocities, obtained over the pixels that develop at least5 shocks throughout the observational sequence. The Figure isbuilt by plotting the binned phase di ff erence ∆ φ weighted by thecross-power amplitude and normalized per temporal frequencybin; for details see Krijger et al. (2001) and references therein.The noisier scatterplot for data set 1 is due to the worse seeingconditions with respect to data set 2. A positive phase di ff erencedescribes signals propagating upward in the solar atmosphere: the scatterplots thus clearly evidence the propagation of acous-tic waves from photosphere to chromosphere, up to about 10–12mHz. The bottom panels c, d provide the coherence spectra ofthe Fourier velocity signal (solid line). The coherence is veryhigh around the velocity power peak at 5–6 mHz (see Paper I),and falls below the confidence limit of 0.5 around 8–9 mHz.If we consider an equal-size sample of pixels characterizedby a smaller number of shocks, we obtain essentially the samephase di ff erences (not shown in Figure) and slightly lower coher-ence values (dashed line): the same photospheric piston mech-anism thus seems at the base of all quiet chromospheric os-cillations, regardless of whether other atmospheric propertiesare conducive to the development of many mid-chromosphericshocks or not. The coherence is instead much smaller if we usean equal sample of pixels belonging to the fibrillar areas (dottedline); these are areas where most pixels do not develop any chro-mospheric shocks, especially for data set 2. In these atmosphericregions, a direct (vertical) relationship between photospheric andchromospheric dynamics no longer holds.The coherence spectra display a curious bump around 7mHz, most evident in data set 2. Such a feature has alreadybeen reported by Deubner & Fleck (1990) in a spectrographicanalysis of a quiet region. Like these authors, we find no obvi-ous explanation for the feature. We suspect that it might be re-lated to the ”aureoles” of enhanced high frequency power some-times measured in both photospheric and chromospheric signa-tures around active regions or strong network elements (see e.g.Krijger et al. 2001, and references therein). The bump is indeedmore evident in data set 2, which has stronger magnetic fieldsand a more ”active region-like” magnetic configuration than dataset 1. In their analysis of K V grain formation, CS97 remarked thatphotospheric acoustic waves at or near the cut-o ff frequency playthe most important role for the development of shocks. In par-ticular, they stated that whenever photospheric velocities havesignificant power around 5 mHz, there will usually be signifi-cant bright grains. To check these statements, we performed awavelet analysis of the photospheric velocities. We concentrateon the spatio-temporal features showing enhanced power at pe-riodicities between 120 and 200 s (5–8 mHz), taken as valueslarger than the average over the whole sample (this accounts forabout 35% of the total number of pixels). Hereinafter we refer tothem as “areas”, even if they contain a temporal dimension. Fig. 11.
Panels a, b : Fourier spectra of phase di ff erences betweenthe photospheric and chromospheric velocities, for data set 1 and2, respectively. The diagram has been calculated over the pointsin the FOV that develop at least 5 shocks throughout the obser-vational sequence. Panels c,d : corresponding coherence spectra(solid line). Dashed lines refer to the coherence measured foran equally populated sample of pixels undergoing less than 5shocks; dotted lines to the coherence for the case of fibrils.Fig. 12 shows example that the mechanism outlined by CS97is most probably at work. In all panels the x -axis represents thespatial dimension along a horizontal cut within a quiet region inthe FOV, while the y -axis displays the temporal dimension overthe duration of the observations. Top panels refer to instancesin data set 1; bottom panels to data set 2. The small diamondsrepresent the occurrence of Ca II 854.2 shocks, while the con-tours outline the areas of enhanced photospheric velocity power(left and center panels), and the presence of magnetic features(right panels). In the left panels, most of the patches of strongphotospheric velocity power encompass the areas where shocksare observed, indicating a relationship between these two phe-nomena. The coincidence in the case of data set 1 is particu-larly striking, with photospheric contours enclosing the chromo-spheric shocks for the whole sequence over extended areas. Wenote that in order to obtain this coincidence a delay of about120 seconds (6 time steps) has been applied between the photo-spheric signal and the occurrence of shocks. This is consistentwith the idea that the photospheric perturbations propagate up-ward at the speed of sound over a ∼ ff er-ence.However, determining whether all areas of enhanced photo-spheric power indeed give rise to shocks, proved a di ffi cult task.As the presence of magnetic fields breaks the direct relationshipbetween the photospheric and chromospheric dynamics, one hasto carefully select the areas to scrutinize this phenomenon. Thecenter panels of Fig. 12 provide a clear example of this. Theplots have been obtained for spatial positions still well removedfrom the magnetic network, and in them we observe that in sev-eral instances, especially for the data set 2, areas of enhancedphotospheric power do not produce any shocks, contrary to theexpectations of the hydrodynamical modeling. The small mag- Fig. 13.
Distribution of photospheric velocity power between120 and 200 s periodicity for positions undergoing shocks (thickcurves) and not (thin curves). Panel a refers to data set 1; panel b to data set 2. The overall higher power values in data set 2 aredue to better seeing conditions.netic structures responsible for this lack of shocks are outlinedin the right panels, at a level of ∼
30 G: it is obvious how theshocks generally avoid both the magnetic elements proper, andsome surface around them, as for the larger network shadows.We hence attempted to identify the quietest portions of theFOV for both data sets, by combining the series of MDI mapswith the Ca II 854.2 core intensity maps (see also Fig. 14). Inboth cases we selected a 8” ×
13” area (50 ×
80 spatial pixels, con-sidered independent) positioned almost at the center of the FOV,that displayed the least magnetic flux in MDI maps and no ob-vious evidence of fibrils in Ca II core images. For these regions,we find that more than 80% of the areas with enhanced pho-tospheric velocity power contain shocks. Further, the numberof shocks measured in each area is directly proportional to thespatio-temporal extent of that area: the development of acousticshocks appears to be continuos as long as photospheric condi-tions are favorable. As a rough estimate of the influence of mag-netic structures, we compare the total number of shocks mea-sured in these quietest portions of the FOV, taken as prototypesfor the undisturbed acoustic shocks mechanism, with those mea-sured in the whole supergranular cells defined in Sect. 5.1. Wefind that the quietest regions produce, per unit area, from almost2 (data set 1) up to 3 (data set 2) times more shocks than thesupergranular cells as a whole.We have shown that high photospheric velocity power at thecut-o ff periodicity is certainly responsible for the developmentof shocks. But do all shocks occur in areas of high power? Toanswer this question, we show in Fig. 13 the distribution of thephotospheric velocity power for both data sets. The curves havebeen calculated for all the pixels undergoing shocks (thick line)and pixels where shocks are not observed (thin line). Again adelay of 120 seconds has been applied between photosphericand chromospheric signals. The photospheric power is obviouslystronger in the former case than in the latter, as expected fromthe results described above, with an average value 45% largerfor data set 1, and 35% for data set 2. By measuring the area en-closed below the curves, we find that in both data sets over 55%of shocks occur in areas with photospheric power larger than theaverage value (the latter accounting for 35% of the total pixels,as stated before). This is to be considered a lower limit, as shocksthat are part of a common pattern sometimes lie just outside ofthe areas defined by the photospheric level, as clearly seen in Fig.12. Thus, a large fraction of shocks is due to enhanced power in . Vecchio et al.: The solar chromosphere at high resolution with IBIS 11 Fig. 12.
Examples of spatio-temporal occurrence of chromospheric shocks (small diamonds) in relation to the photospheric velocitypower at periodicities between 120 and 200 s (left and center panels) and magnetic features from MDI (right panels). Velocity powercontour levels are set at the average value over the whole FOV plus half standard deviation. Top row refers to data set 1; bottom rowto data set 2. The temporal axis is shorter than the full IBIS observational sequence as wavelet maps are not reliable in the initial andfinal temporal samples, and because of the delay applied between photospheric and chromospheric signal. The x – axes coordinatesare given in the same units as in the FOV of Figs. 1, 6, 9. Left panels correspond to y =
5, 0 for data set 1 and data set 2, and definequiet areas with strong correspondence between photospheric dynamics and shocks’ occurrence. Center panels correspond to y = ff . Possible causesfor shocks not accounted by this mechanism could be the addi-tional contribution from high-frequency waves when waves nearthe acoustic cuto ff frequency are weak (CS97), as well as someinstances of non-vertical propagation.
8. Summary and Discussion
The temporal sequences of internetwork Ca II 854.2 nm spectrashow compelling evidence for abundant acoustic shocks in themid-chromosphere (Sect. 3). The evolution of spectral charac-teristics of the Ca II 854.2 line during these events is in com-plete analogy with the more famous Ca II K V grains, clearlyexplained by CS97 as due to weak acoustic shocks in the mid-chromosphere. We have set out to provide a comprehensive viewof the occurrence of these shocks, by combining a large ar-ray of complementary diagnostics, including spectral informa-tion in both photospheric and chromospheric lines; high spatialresolution over an extended field-of-view; simultaneous high-resolution magnetic maps from MDI; and observations of twodi ff erent quiet Sun targets with di ff erent magnetic topologies,for a period of about 1 hr each, at high cadence. We surmise that such a dataset is rather unique, and indeed provided muchinsight into the issue. Shock identification . We have identified the spatio-temporal lo-cations of chromospheric shocks by using a velocity criterion onthe Ca II 854.2 nm line, namely the abrupt displacement of theprofile from red to blue. This approach provides several intrin-sic advantages over the more commonly used intensity thresholdmethods (see e.g. Tritschler et al. 2007, and references therein):Using a velocity determination avoids confusion between bright-enings from shocks and those due to transient small-scale mag-netic structures within the internetwork. The latter correspondto what has been termed “magnetic grains” (RU91) or “per-sistent flashers” (Brandt et al. 1992; de Wijn et al. 2008), and,while as bright as the internetwork grains, they are character-ized by longer evolutionary timescales. Analysis of filtergramsin Ca II H and K may confuse the intensity signature from thesetwo di ff erent processes. Our shock identification technique alsoidentifies the start time of each shock, assuring that they arecounted only once during the temporal sequence, something thatcan be di ffi cult with threshold methods. Finally, by using thefull spectral profile, we reduce the influence of spatially andspectrally scattered light and photometric errors. The velocitymethod for identifying shock relies on a threshold for the am- plitude of the red-to-blue Doppler shift, but while some of theshock parameters did show a dependence on the threshold value(in particular the size, and total number), others, such as the tem-poral characteristics and spatial distribution, did not. Shocks ′ properties . Many of the properties that we derive forthe Ca II 854.2 shocks are analogous to those reported in theliterature for K V grains, confirming that the two phenomenarepresent the same physical process. In particular, we find thatthe Ca II 854.2 shocks often appear in bursts, with the typicalinterval between shocks ranging from ∼ ∼ V emission for about 60–80 s for eachevent (e.g. Beck et al. 2008), this rate of occurrence translatesinto a measurable K V emission for about 6–10% of the totalspatio-temporal sample, in agreement with earlier works (e.g.von Uexkuell & Kneer 1995; Ste ff ens et al. 1996). Recently, us-ing high resolution Ca II H spectra acquired with POLIS,Beck et al. (2008) claimed that in quiet Sun regions the core ofthe Ca II H resonance line spends about half of the time in emis-sion. This is probably misleading, as they implicitly assumedthat shocks occur everywhere and continuously with the typical3 minutes periodicity, an assumption obviously not fulfilled onthe Sun.The average shock size of 0.7”–1.0” arcsec measured fromthe Ca II 854.2 data is sensibly smaller than the 1”–2” arcsectypically reported for K V grains. We believe our measurementcomes closer to the true size of the shocks due to the higher spa-tial resolution reached with IBIS with respect to older works,the limited influence of instrumental scattered light on our mea-surements, and the reduced scattering in the solar atmospherefor the Ca II 854.2 line with respect to the H and K. A small ex-tension of the shocks explains why earlier spectral observationsof the Ca II 854.2 nm in the quiet internetwork, obtained with a0.6” pixel size, did not display the clear sawtooth behavior suchas that seen in Fig. 4 (cf. Fig. 3 in Deubner & Fleck 1990). Thesmaller e ff ective size of the Ca II 854.2 shocks, together with theoverall better resolution, accounts for the larger occurrence ratethat we measure in a typical supergranular cell ( >
20 in our case,vs. 10-20 in the “best spectroheliograms”, cf. RU91).
Spatial distribution and magnetic shadows . An important re-sult of our analysis is the extreme inhomogeneity of the spatialdistribution of the shocks (Sect. 5.3). It has long been known thatshocks can be relatively rare and widely dispersed in the super-granular cells (e.g. Lites et al. 1994). Indeed we find that up to50–60% of the FOV display zero or very few shocks, even for thecase of data set 1 which, being situated at the edge of a coronalhole, arguably has one of the weakest possible magnetic config-uration. However, with our data we clearly show that the shocksconcentrate in the internetwork but away from the regions wherechromospheric fibrils are present. The local magnetic topologyoutlined by the fibrils is very di ff erent for the two data sets, withmany short loops closing back from the network elements to thenear internetwork regions in set 1 and longer and more stable fib-rils nearly spanning the supergranular cell in set 2 (Fig. 3). Thisnature of the canopy and the spatial distribution of the shocks isnot easily predicted using only photospheric indicators such as the granulation in the continuum, or the location of the networkmagnetic elements.A second interesting result is that the total amplitude ofthe shocks over the course of the observations is directly re-lated to the magnitude of the Fourier power of chromosphericvelocities with periods around 3 minutes (Fig. 8). Thus, theshocks represent an important, if not dominant, contribution tothe “3- minute chromospheric oscillations” (e.g. Orrall 1966;Noyes 1967), even if they do occur with an intermittent char-acter. Because the shocks are related to large excursions of thespectral line, corresponding to several km s − when parametrizedin terms of line core Doppler shifts, they can contribute a largefraction of the velocity signal around the acoustic cuto ff fre-quency in classical Fourier analysis, even if they do not occurcontinuously. The two quantities are essentially equivalent, atleast in the quiet Sun.These two results fit in nicely with several pieces of evi-dence reported in the literature about the so-called “magneticshadows”, and allow us to form a coherent explanation of theirexistence. First introduced by Judge et al. (2001), the shadowsare regions of reduced Fourier oscillatory power at the 3-minuteperiodicity, often observed in low- and mid-chromospheric sig-natures around (but not coincident with) magnetic network el-ements. They have been reported in intensity observations ofthe continuum at 119 nm obtained with SUMER (Judge et al.2001), and of the continuum at 160 nm obtained with TRACE(Krijger et al. 2001), as well as in Fourier analysis of chromo-spheric velocities by V07 and Lites et al. (1994).All these works invoke the presence of horizontal magneticfield lines (the “canopy”) to somehow disturb the propagationof normal acoustic waves towards the outer solar atmosphere,for example by means of wave scattering or mode conver-sion (Judge et al. 2001; McIntosh & Judge 2001; McIntosh et al.2003). With our data, we prove that the shadows correspond toa strong suppression of the number of acoustic shocks. Further,we show that the shadows are tied to the presence of chromo-spheric fibrils, i.e. to structures with a very distinct physicalstructure with respect to the surrounding atmosphere. Indeed,we believe they are best compared to the H α mottles and fib-rils observed around quiet Sun magnetic network, that can beexplained either by elevated structures such as spicules, or “em-bedded” ones (see e.g. the discussion in Al et al. 2004). Hence,the upward propagating acoustic waves may be disturbed not somuch by the horizontal field itself, but by the di ff erent stratifica-tion of the atmosphere. This should be taken into account in thediscussions in terms of high- or low- plasma β (the ratio of ki-netic to magnetic pressure) as the main discriminant between an‘acoustically-dominated’ and a ‘magnetically-dominated’ atmo-sphere. An estimate of β that uses the classical, semi-empiricaltemperature and density values (e.g. from VAL) might not beappropriate in these regions. In the case of elevated structures,it is also possible that the acoustic shocks develop normally inthe low chromosphere whenever photospheric conditions are fa-vorable, and the higher-lying fibrils simply act as a mask, hidingthe lower layers from view. Some support for this scenario canbe gathered in de Wijn et al. (2007) as well as from Movie 2 inPaper I, where the lateral motions of the fibrils at times “un-cover” the presence of bright grains, especially towards the endof their horizontal extension (see also Fig. 14). Photospheric drivers . The analysis of Sec. 7.1 clearly showsthat the Ca II 854.2 shocks partake in the general chromosphericdynamics, responding to acoustic waves propagating from lowerlayers. The phase relationships between photospheric and chro- . Vecchio et al.: The solar chromosphere at high resolution with IBIS 13
Fig. 14.
Maximum (top row) and minimum (bottom row) intensity of the Ca II line core throughout the 55 minute sequences.Left: data set 1; right: data set 2. The scale has been set in radiation temperature (K, see text for details). This representation ofthe data immediately provides a distinction among the three major chromospheric components: the bright network; the acousticchromosphere where acoustic shocks show up as tiny bright points; and the magnetic chromosphere threaded by slanted fibrils thatcan appear as either dark or bright.mospheric velocities in regions undergoing shocks are fully con-sistent with earlier results obtained for general internetwork ar-eas, proving the propagation of acoustic waves up to 10–12 mHz(Deubner & Fleck 1990). The occurrence of shocks in this gen-eral oscillation pattern must then be triggered by complementarycircumstances. By means of a wavelet analysis we find that in-stances of high photospheric velocity power at periodicities be-tween 120 and 200 s (5–8 mHz) are well correlated with theoccurrence of chromospheric shocks. Tellingly, the correlationis maximized when allowing for a delay of ∼
120 s betweenthe photospheric and chromospheric signal, indicating a photo-spheric perturbations propagating upward at the speed of soundover a ∼ ff erence.The small dimension of the shocks is not completely corre-lated with the piston’s size – the analysis of Sect. 7.2 shows howareas of coherent photospheric oscillations at the relevant peri-odicity have lateral sizes of up to several arcsec. However, it isimportant to note that these areas completely encircle the ma-jority of the pixels that develop shocks (left panels in Fig. 12).All of these results are consistent with the analysis of CS97 thatstate how the appearance of the bright grains, including theirsize, is fully determined by powerful waves near or just abovethe acoustic cuto ff frequency interfering with higher frequency waves. The interference pattern that determines the actual sizeand recurrence of shocks will be contained within, but not nec-essarily coincident with, the regions of enhanced photosphericvelocity at the dominant frequencies.The strength of photospheric motions is not the only fac-tor shaping the “quiet” chromosphere and its dynamics. We findthat the presence of magnetic structures has a profound influ-ence on what occurs in the lower chromosphere and, in particu-lar, whether the acoustic mechanism outlined above can operateundisturbed. Many areas with suitable photospheric dynamicsdo not develop shocks (the “shadows”) and show a decreasedcoherence between the vertical photospheric and chromosphericvelocity signals at all frequencies (panels c and d of Fig. 11).The dynamics of the fibrils present in the shadows’ areas prob-ably is most-closely related to the oscillatory behavior at theirfootpoints than to the directly underlaying layers. Interestingly,we note that pixels developing a small number of shocks havea lower coherence than the ones developing many shocks; weassume that this is related to a mechanism similar to the shad-ows, just operating on smaller scales. Several hints support thishypothesis, such as: the di ff use appearance of the Ca II line coreimages (Fig. 1, especially panel d ) that might betray short, un-resolved fibrils; the correlation between the presence of small, transient magnetic structures observed in the MDI HR maps andthe reduction in total shocks numbers (Fig. 9); the lack of chro-mospheric shocks in areas corresponding to enhanced photo-spheric velocity power patches, if there exist nearby small scalemagnetic structures (Sect. 7.2). Vertical propagation . Throughout this paper, we searched forcorrelations between photospheric and chromospheric signal un-der the assumption of vertical propagation. This is of course alimitation of our analysis and has been invoked often as oneof the major problems in the CS97 study of K V grains (e.g.Ulmschneider et al. 2005). However, there are several indica-tions that this assumption is not misguided. First, the level ofcoherence between the photospheric and chromospheric veloci-ties at the dominant frequency of ∼ ◦ ) would also not cause any drastic di ff erence in ourresults.The wavelet analysis shows that in some instances chromo-spheric shocks are measured even in absence of high photo-spheric power; these could be obvious candidates for a searchon the e ff ects of inclined propagation, and deserve further in-vestigation. They could also be related to the presence of highfrequency waves or photospheric power just below our cuto ff forenhanced power. Still, it appears that small magnetic structuresrepresent a more important factor in the shaping of the 3-D chro-mospheric dynamics, reducing the overall number of shocks bylarge amounts (Sect. 7.2). Three quiet chromospheres . From our results, we propose thatthe “quiet” lower-chromosphere should be considered to com-prise at least three components, as somewhat anticipated inJudge et al. (2001) and remarked in Paper I. These three com-ponents are: 1- the purely acoustic chromosphere, where thestrong photospheric motions at frequencies near the acoustic cut-o ff can propagate upwards undisturbed and develop into shocks;2- the network and internetwork magnetic elements, that openup partially from the photosphere and are heated by a mecha-nism still unexplained (see Hasan & van Ballegooijen 2008, andreferences therein); and 3- the inclined fibrils that magneticallyconnect horizontally separated areas. The fibrils can span as longas a supergranular cell (as in data set 2) or as short as few arcsec-onds (as in the smallest shadows in Fig. 6 d ); in any case they de-fine chromospheric volumes with very di ff erent dynamical prop-erties than the other two components. In particular, they show areduced chromospheric vertical velocity power at all frequen-cies (see also Paper I); distinctly longer evolutionary timescales(V07); a lack of vertical coherence between the photospheric andchromospheric signals (Sect. 7.1).These three components can be immediately identified byusing maps of the Ca II 854.2 line core intensity, a reliable indi-cator of temperature (Cauzzi et al. , in preparation). In particular,we show in Fig. 14 the maximum (top row) and minimum (bot-tom row) value of the line core intensity, measured for each spa-tial pixel within the 55 min observing sequences. In the Figure the intensity has been converted to radiation temperature by scal-ing the average intensity computed over the full spatio-temporalsample to the calibrated atlas intensity of Neckel (1999) and ap-plying the inverse Planck function (the average intensity corre-sponds to 3800 K). Obviously this definition does not representthe real kinetic temperatures as the line is not formed in LTE, butit does provide an indication for the magnitude of the variations.In Fig. 14 the acoustic shocks stand out clearly in the maximumintensity maps as bright specks with a quasi-granular appearance(but with smaller dimensions) and temperatures up to 4200 K. Attimes, especially in data set 2, the shocks can even be discernedin amongst the long fibrils, supporting the idea of the latter op-erating as a switch in between the lower chromosphere and theobserver. The canopy-free internetwork regions where there aresignificant numbers of shocks are also the regions of the low-est intensity, and presumably lowest temperature, in the entiresequence, with radiation temperature values as low as 3400 K.The magnetic elements appear also as distinct point-like sources,but larger and brighter than the acoustic shocks, with tempera-ture excursions ranging from a minimum of 4000 to maxima of4700 K. Finally, the slanted fibrils have a very di ff erent morphol-ogy and might be better defined as the “di ff use” sources in boththe maximum and minimum intensity maps. Two things aboutthem are particularly remarkable: they are the component whoseintensity (temperature) changes the least between maximum andminimum values, with largest values close to the network pointsand cooler ends towards the internetwork; and they cover a largefraction of the FOV, even for data set 1. The magnetic influenceappears very pervasive over the quiet Sun.Finally, it would appear that Fig. 14 also o ff ers a defini-tive statement on the issue of the spatial correspondence be-tween small scale magnetic structures and K V bright points (e.g.Sivaraman et al. 2000). Indeed, many such small magnetic con-centrations are visible in the internetwork portion of the FOV inboth of our data sets, and they do correspond to enhanced bright“points”, some of them only 1–2” wide. However, they also areclearly distinguished from the acoustic grains by the di ff use co-coon around them, made up most probably of unresolved fibrils.They appear just like miniature versions of normal network ele-ments (Krijger et al. 2001). The analysis of Sect. 6 makes it clearthat these bright structures do not participate in the typical dy-namics of acoustic shocks, making them K V bright “points”, butnot K V bright grains! Claims to the contrary, such as those ofSivaraman et al. (2000), stem from the limited coverage of theavailable datasets or the limited number of co-spatial magneticand K V measurements.
9. Conclusions
In our analysis, we reach two main conclusions, both of whichare represented in Fig. 14.The first is that temporally resolved spectra of the Ca II 854.2nm provide a comprehensive picture of the occurrence of acous-tic shocks in the quiet solar atmosphere. We determine that theseshocks are a fundamental part of the general chromospheric dy-namics, as they essentially make up the bulk of the three-minuteoscillations in the middle chromosphere. We find that the shocksoccur in direct response (after a 120 second delay) to power-ful photospheric oscillations near the acoustic cuto ff frequency,with a primarily vertical propagation. No major role is found forwaves with periods below 120 seconds or with a slanted prop-agation, consistent with the 1-D purely hydrodynamical simu-lations of Carlsson & Stein (1997). Portions of the quiet chro-mosphere are then the site of brief episodes when the acoustic . Vecchio et al.: The solar chromosphere at high resolution with IBIS 15 shocks dramatically enhance the temperature (Fig. 14 a and b )mixed with extended periods of lower temperatures (Fig. 14 c and d ), as opposed to the steady-state mean temperature rise typ-ically assumed in semi-empirical models (see the discussion inCarlsson & Stein 1995; Carlsson 2007).The second, more important conclusion is that these acousticprocesses are very often significantly disturbed by the presenceof magnetic field, even in the quiet Sun. Both at the network and(surprisingly) at internetwork scales, the signature of acousticshocks is suppressed both in and around the footpoints of mag-netic structures. Hence the distribution of shocks is considerablyreduced compared to what would be inferred from the amplitudeof the photospheric oscillations alone. The main player in thisrespect appears to be the magnetic topology, and in particularwhether the field has an open or closed configuration. The ar-eas of modified acoustic behavior coincide with the presence ofchromospheric fibrils, betraying an atmosphere that is stratifieddi ff erently with respect to the classical 1-D view.These results provide an important hint concerning thelongstanding controversy about why the dynamical model ofCS97 fails to predict the ubiquitous emission observed in UVlines (e.g. Kalkofen et al. 1999; Kalkofen 2001; Carlsson 2007;Avrett & Loeser 2008). Our analysis is based on observations inthe Ca II 854.2 nm line, a spectral signature formed relativelylow in the atmosphere. Our data provide uncontroversial evi-dence that even at these heights the quiet atmosphere is highlystructured by pervasive magnetic fields that connect di ff erent lo-cations. The presence of fibrils is a clear testimony of these inter-connections . It is then natural to assume that other spectral di-agnostics forming in higher, less dense parts of the atmosphere,experience such a magnetic structuring to an even larger extent,much as advocated by Ayres (2002).Far UV lines and continua are one such diagnostic, and theyfigure prominently in the derivation of the temperature structurein semi-empirical models, often as spatial and temporal averages(e.g. Avrett & Loeser 2008). It follows that a substantial fractionof the UV flux could originate in magnetic structures, even in the quiet internetwork chromosphere. This could happen either be-cause of the volume filling of the magnetic field at these heights,or because of the dominant weight of magnetic-related bright-ness in the averages: Fig. 14 illustrates how magnetic concentra-tions introduce a brightness component with a di ff erent spatialdistribution and temporal evolution than for the purely acousticcase. This happens on spatial scales at the limit of the resolutionof many modern instruments, including SUMER. Any averagedor marginally resolved observation of the chromospheric fluxmight then contain a sizable magnetic component, in ways notimmediately predictable by using only photospheric indicators.A dominance of the magnetic topology in the quiet upper chro-mosphere would also explain why UV observations obtainedwith SUMER have produced so many disparate results. Theserange from the clear signature of upward propagating acousticwaves reported by Wikstøl et al. (2000) all the way from thephotosphere up to the base of the corona, as could happen in thecase of a coronal hole, to instances of complete disconnectionbetween the observed lower and upper chromospheric dynamics(Judge et al. 2001, 2003), as would be the case for regions witha locally closed magnetic topology. In this scenario, obviouslythere is no need to reconcile the predictions of CS97, a purely We note that this magnetic structuring has been observed fordecades in H α , a diagnostics that has figured little in the discussionon chromospheric heating. non-magnetic model, with the UV observations, as they pertainto completely di ff erent physical regimes.We thus conclude that the radiative losses in the “non-magnetic” (quotes are necessary at this point) solar chro-mosphere are strongly influenced, and possibly dominated,by processes related to magnetic fields. We remark that thissame conclusion has been reached by Judge and collaborators(Judge & Carpenter 1998; Judge et al. 2003, 2004), in a preciseanalysis of UV emission lines for both the case of the Sun andother stars with convective envelopes. The presence of fibrilsin large fractions of the quiet atmosphere provides a plausibleagent for such dominance. On the one hand, they disrupt thenormal vertical propagation of acoustic waves from lower lay-ers, strongly reducing the e ff ects of a purely acoustic mech-anism in shaping the chromosphere. On the other, they pro-vide the means to transport energy of magnetic origin, or me-diated by the magnetic elements, from the network footpointstowards the center of the supergranular cells. We note that thisidea is consistent with several recent works that have calledinto question whether the photospheric acoustic flux at high fre-quencies is su ffi cient to compensate the chromospheric radia-tive losses (Fossum & Carlsson 2005, 2006) or, even more perti-nent, whether di ff erent energy sources such as low- frequenciesmagneto-acoustic waves, or atmospheric gravity waves, mightplay a more important role (Je ff eries et al. 2006; Straus et al.2008). Acknowledgements.
This work was partially supported by PRIN-INAF 2007:“Scientific exploitation of the Interferometric Bidimensional Spectrometer(IBIS). Magnetic structuring of the lower solar atmosphere.”The authors are grateful to the DST observers D. Gilliam, M. Bradford andJ. Elrod, whose patience and skills are greatly appreciated. IBIS was built byINAF–Osservatorio Astrofisico di Arcetri with contributions from the Universit`adi Firenze and the Universit`a di Roma Tor Vergata. Further support for IBISoperation was provided by the Italian MIUR and MAE, as well as NSO. NSOis operated by the Association of Universities for Research in Astronomy, Inc.(AURA), under cooperative agreement with the National Science Foundation.SOHO is a project of international cooperation between ESA and NASA.Wavelet software was provided by C. Torrence and G. Compo, and is availableat http://atoc.colorado.edu/research/wavelets/ . We made much useof the NASA’s Astrophyics Data System.
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Appendix A: Identification of shocks
A.1. The velocity thresholdapproach
A way to identify acoustic shocks “events” is through the sawtooth peaks inthe velocity field, defined via the Doppler shift of the line intensity minimum.The small white crosses in Fig. 4 panel a show this parameter for the particu-lar pixel. As apparent from both Fig. 4 and 5, during the upward phases of theshock the spectral line broadens considerably in the blue wing, probably lead-ing to an underestimate of the actual value of the vertical velocity by using thesimple Doppler shift of the minimum. However, such an e ff ect does not seemparticularly severe (compare for example Fig. 7 in Pietarila et al. 2006), and thesign of the recovered velocity is always correct.Following the temporal behavior of the velocity, for each spatial pixel ashock event is then defined to occur at the time when the velocity experiences anabrupt jump from large positive to large negative values (downward to upwardmotion). As a temporal threshold for this velocity jump, we utilize a maximuminterval of two time steps, i.e. a 38 s window. The threshold for the amplitude ofthe velocity jump is set at a value of 4 km s − . This is safely above the r.m.s valueof ∼ − measured for chromospheric velocities at the dominant periodic-ity, and allows us to identify the most energetic events. Experiments with lowerand higher values of the velocity threshold cause a di ff erent number of shockevents to be counted, but do not alter the main conclusions about their overallspatio / temporal distribution.With these two combined criteria we can identify the presence of an acousticshock at any given time or location within the FOV, and hence derive a temporalseries of binary maps defining their spatial distribution, similar to the examplesdisplayed in Fig. 6 a and e . A value of the shock strength can also be definedas the maximum velocity di ff erence between downward and upward velocitiesduring the shock. Given the limitations of the Doppler shift of the intensity min-imum, described above, both of these values can be considered as lower limits tothe actual distributions. A.2. The ProperOrthogonal Decompositionapproach
As an independent validation of the results obtained through the velocity thresh-old method, we also attempted a more general approach, based on an analysisof the whole spectral shapes. This approach makes use of the Proper OrthogonalDecomposition (POD) technique, initially developed to study coherent structuresin channel flow turbulence and recently applied to various astrophysical prob-lems (Rees et al. 2000; Carbone et al. 2002; Lawrence et al. 2004; Vecchio et al.2005; Vecchio 2006). As the POD technique is not yet widely known, we willdescribe it in some detail in the following.
A.2.1. The POD method
In the framework of the POD, a spatio-temporal field u ( r , t ) is decomposed as P ∞ j = a j ( t ) Ψ j ( r ). The orthonormal basis functions, Ψ j , are not given a priori butobtained from the experiment, and can hence assume the proper functional shapeof the phenomenon. The time coe ffi cients a j ( t ), computed from the projection ofthe data on the corresponding basis functions, represent the time evolution ofthe j -th mode associated with that eigenfunction. The modes are then orderedaccording to a parameter, the “energy” content of fluctuations associated withthem, quantifying the relative contribution of each mode to the signal reconstruc-tion. The most energetical mode ( j =
0) is associated to the average contributionto the signal. For more details, we refer to the text by Holmes et al. (1996).
A.2.2. Application of POD to Ca II 854.2 profiles
We apply the POD to analize the temporal evolution of the spectral profiles (likethose shown in Fig. 4) for each pixel of the FOV separately, considering the(wavelength- dependent) intensity fluctuations around the mean profile. Thus, inour application the the POD decomposition of a wavelength-time spectrum will . Vecchio et al.: The solar chromosphere at high resolution with IBIS 17 be s ( λ, t ) = ∞ X j = a j ( t ) Ψ j ( λ )namely, the role of spatial coordinate is played by the wavelength. For most ofthe pixels, we find that the 99% of the total energy is contained in the first fourPOD modes (including the average, j = e in Fig. A.1 displays, as an example, the actual temporal evolutionof the spectrum corresponding to an internetwork pixel in data set 1, where wefind evidence for several shocks. Panel a shows the corresponding POD eigen-function Ψ ( λ ) of the mode j =
0, i.e. the temporally averaged spectrum. Thechromospheric steepening of acoustic oscillations, which eventually will lead toshock development, induce an intensity fluctuation characterized by a well de-fined behavior, i.e. a large displacement of the line from the average position,with an asymmetric contribution in the two wings. The POD analysis isolatesthis behavior in a single mode, whose eigenfunction has the typical shape shownin panel b of Fig. A.1. It is characterized by two opposite lobes of di ff erent ampli-tude, indicating positive and negative contribution to the average profile towardsthe blue and the red wavelengths. The sign of the time coe ffi cient (to be multi-plied to the eigenfunction) selects when the positive contribution is in the red orin the blue part of the spectrum.Thus for each pixel the mode associated to the (possible) shock contributioncan be identified by looking at the shape of the eigenfunctions, including thelobe asymmetry. Suppose that for the spectrum of Fig. A.1 e this is the mode j = i . The wavelength-time intensity contribution of this mode to the actualspectral evolution can be expressed as a i ( t ) Ψ i ( λ ), and is shown in panel f ofFig. A.1 (for clarity we have displayed only its positive part). It illustrates howthe modifications to the spectral profiles induced by this mode are in generalstronger and more extended in the blue wing of the line, as well as the fact that,on average, the variations in the red wing last longer than in the blue wing. Thelatter property is present also in the simulations of CS97. For this particular pixel, i =
1, i.e. the mode characterizing the eigenfunction Ψ i ( λ ) is the one with thehighest “energy” content of fluctuations. A.2.3. Dominant POD modes and periodicities
Obviously, not all the pixels within the FOV have spectra similar to those dis-played in panel e of Fig. A.1. Panel g of the same Figure provides an illuminatingexample, showing the temporal evolution of the spectrum for a pixel pertainingto a fibril within the FOV of data set 1. The average spectrum (POD eigenfunc-tion of the mode j =
0) is given in panel c , the “shock-mode” eigenfunctionfor j = i is shown in panel d , and the POD reconstruction for this mode is dis-played in panel h . For this case, the mode characterizing the eigenfunction Ψ i ( λ )is i =
3, i.e. with a much lower energy than the example of panel e .Panels a and b of Fig. A.2 display the spatial distribution, for both data sets,of the mode i defined above. (As said before, modes with i > i =
1, i.e. the “shock-mode” is the most energetic component of the in-tensity fluctuation. However, there exist large portions of the FOV, apparentlypertaining to the photospheric internetwork but surrounding quite extensivelythe magnetic elements, for which the relevant eigenfunction corresponds to themode i =
2. Their typical energy fluctuation content is less than half that pertain-ing to the pixels with shock-mode i =
1. This e ff ect is more prominent in dataset 2, in correspondence to a larger extension of the fibrillar structures visible inthe line core images.The coe ffi cients a j ( t ) provide the temporal behavior of the di ff erent PODmodes for each spatial pixel. For example, the coe ffi cients used in the recostruc-tions of Fig. A.1 f and h are plotted in the same figure (panels i and j ), and showthat for the first case the “shock” eigenfunction has a clear periodicity near-ing 150 s, while for the second one the temporal coe ffi cient has a more erraticbehavior. Maps of the dominant periodicities in the a j ( t ) coe ffi cients, for eachpixel and for the shock-associated j = i POD mode, are reported in panels c and d of Fig. A.2. They have been derived from a Fourier analysis of the coef-ficients, but the same result is obtained if using a wavelet analysis of the timeseries, by considering the wave period containing the highest number of wavepackets with significant power. In both data sets, for most of the pixels charac-terized by the i = ∼
200 s and slightlyshorter (frequencies between 5 and 7 mHz). This is consistent with the typicalchromospheric periodicity of ∼ p -modes. The association between i = ff erences in this association, with a more fragmented distributionof the short-periodicity areas, and a stronger presence of longer periodicities (4mHz or less) in data set 2. We further note that some spatial locations within the magnetic networkareas display “shock- associated” eigenfunction i = A.2.4. POD shocks
Finally, in order to identify the occurrence of shocks from a pattern such as thatdisplayed in Fig. A.1 f or h , we can simply count the events characterized by a redpeak followed by a blue peak, with the jump occurring within the same temporaldelay defined before (38 s), without applying any threshold to the amplitude ofthe events. Rather, an amplitude can be defined as the intensity di ff erence of thetwo peaks of the eigenfunction ( a i ( t ) Ψ i ( λ )) on either (temporal) side of the shock.Such di ff erence is related to the variations induced by the shock over an averageprofile for the pixel, and is then again a measure of the strength of the event. Asin the velocity analysis, repeating this calculation for each pixel we can derivea temporal series of binary maps, displaying the shocks’ spatial distribution, aswell as maps of their amplitudes. Panels a and e of Fig. 6 show typical “shocksmaps”, for a time around the middle of the temporal sequence. Fig. A.1.
Example of POD analysis for two pixels from data set 1. Panels a–b, e–f refer to a pixel displaying a large number ofshocks with 3 min periodicity. a : Eigenfunction of the mode j = b : Eigenfunction describing the shockscontribution, displaying the typical asymmetric shape. Since the eigenfunction are orthonormal their amplitude is arbitrary. e : Actualmeasured spectra. f : Contribution to the profiles in e reconstructed using only the POD mode associated to an eigenfunction like b (mode 1 in this case). For clarity, only the positive portion of the reconstructed function is displayed. Panels c–d, g–h : As before,but for a pixel where only few, energetically unimportant shocks are found by the POD analysis (shock mode = i–j : PODtemporal coe ffi cients used in the reconstructions of panels f and h . A 3 minute periodicity is evident in panel i . . Vecchio et al.: The solar chromosphere at high resolution with IBIS 19 Fig. A.2.
Panels a and b : maps of mode pertaining to the shock eigenfunctions, for data set 1 and 2. c and d : maps of dominantperiodicity in coe ffi cients a i ( tt