Can High Frequency Acoustic Waves Heat the Quiet Sun Chromosphere?
Mats Carlsson, Viggo H. Hansteen, Bart De Pontieu, Scott McIntosh, Theodore D. Tarbell, Dick Shine, Saku Tsuneta, Yukio Katsukawa, Kiyoshi Ichimoto, Yoshinori Suematsu, Toshifumi Shimizu, Shin'ichi Nagata
aa r X i v : . [ a s t r o - ph ] S e p PASJ:
Publ. Astron. Soc. Japan , 1– ?? , c (cid:13) Can High Frequency Acoustic Waves Heat the Quiet SunChromosphere?
Mats
Carlsson Viggo H.
Hansteen
Bart
De Pontieu Scott
McIntosh
[email protected], [email protected], [email protected], [email protected]
Theodore D.
Tarbell Dick
Shine [email protected], [email protected] Saku
Tsuneta Yukio
Katsukawa Kiyoshi
Ichimoto Yoshinori
Suematsu Toshifumi
Shimizu Shin’ichi
Nagata [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Institute of Theoretical Astrophysics, University of Oslo, PB 1029 Blindern, 0315 Oslo Norway Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, CA 94304, USA Department of Space Studies, Southwest Research Institute, 1050 Walnut St, Suite 400, Boulder, CO 80302, USA High Altitude Observatory, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA National Astronomical Observatory of Japan, Mitaka, Tokyo, 181-8588, Japan ISAS/JAXA, Sagamihara, Kanagawa, 229-8510, Japan Kwasan and Hida Observatories, Kyoto University, Yamashina, Kyoto, 607-8471, Japan (Received 2007 June 11; accepted )
Abstract
We use Hinode/SOT Ca ii H-line and blue continuum broadband observations to study the presenceand power of high frequency acoustic waves at high spatial resolution. We find that there is no dominantpower at small spatial scales; the integrated power using the full resolution of Hinode (0.05” pixels, 0.16”resolution) is larger than the power in the data degraded to 0.5” pixels (TRACE pixel size) by only a factorof 1.2. At 20 mHz the ratio is 1.6. Combining this result with the estimates of the acoustic flux basedon TRACE data of Fossum & Carlsson (2006), we conclude that the total energy flux in acoustic wavesof frequency 5-40 mHz entering the internetwork chromosphere of the quiet Sun is less than 800 W m − ,inadequate to balance the radiative losses in a static chromosphere by a factor of five. Key words: waves, Sun: chromosphere
1. Introduction
Observations show that the solar chromosphere radi-ates more than is expected from radiative equilibrium.The extra energy needed to balance the radiative lossesmust be generated somewhere, transported to the chro-mosphere and dissipated there. Acoustic waves were sug-gested early on to play an important role (Biermann 1948;Schwarzschild 1948) because they are readily generatedin the convection zone, can easily propagate and are ex-pected to steepen and dissipate in shocks in the chromo-sphere.The estimates of the total radiative losses from thesolar chromosphere (and thus the required heating) aremodel dependent. Ulmschneider (1974), Athay (1976) andVernazza et al. (1981) found the total loss to be 2500-3300W m − , 2000-4000 W m − and 4300 W m − , respectively.More recently, Anderson & Athay (1989) compared theircomputed model solar chromospheres with the Vernazza,Avrett and Loeser models and found that the VAL-Cmodel is characterized by a total heat flux of 14000 Wm − , where about 90 % is dissipated near the base of thetemperature plateau. The above estimates of radiativelosses concerns the average solar chromosphere. For theinternetwork regions the losses will be lower, the VAL3Amodel constructed to fit the lowest intensities observed with Skylab has about 2.2 times lower radiative lossesthan VAL3C (Avrett 1981).Carlsson & Stein (1995, 1997) calculated synthetic spec-tra of the strong chromospheric Ca II H-lines. Theyshowed that the enhanced chromospheric emission, whichcorresponds to an outwardly increasing semi-empiricaltemperature structure, can be produced by wave mo-tion without any increase in the mean gas temperature.However, these simulations do not reproduce observationsof spectral features formed in the middle to upper chro-mosphere. The reason could be the lack of waves above20 mHz in the simulations. On the other hand, high-frequency acoustic waves, even if produced in abundancein the convection zone, are heavily radiatively damped inthe photosphere (Carlsson & Stein 2002): at 10 s periodonly 1% of the generated acoustic energy flux remains ata height of 500 km. In principle, waves with frequenciesabove what is easily observed from the ground (above 20mHz) and below what is very heavily damped in the pho-tosphere (below 50 mHz) could account for the energy fluxneeded to balance the radiative losses from the middle-upper chromosphere where the dynamic models fail. Suchwaves are by many believed to constitute the dominantheating mechanism of the chromosphere in non-magneticregions.The amount of acoustic energy contained in high fre- Carlsson et al. [Vol. ,quency waves is difficult to determine observationally fortwo reasons: First, image distortions from the Earth’s at-mosphere introduces high frequency noise in ground basedobservations. Second, the width of the intensity formationregion of any spectral diagnostic feature smears out thesignal of a short wavelength (high frequency) wave in bothground and space based data. Fossum & Carlsson (2005a)showed that the response function of the 1600 ˚A passbandfilter of the TRACE (Handy et al. 1999) spacecraft is suf-ficiently narrow to allow the detection of waves at leastup to 40 mHz frequency. Fossum & Carlsson (2005b)used TRACE data to determine the acoustic energy fluxof waves in the 5-38 mHz range at the formation heightof the 1600 ˚A passband integrated intensity and found avalue of 0.44 kW m − . A specially optimized observingsequence for TRACE permitted a more detailed study ofthe acoustic wave power as function of frequency (Fossum& Carlsson 2006): a value of 0.51 kW m − in the 5-50 mHzrange was found (note that the originally published valueof 0.255 kW m − is too low by a factor of two becauseof an error in a reduction routine). This value is too lowby a factor of 4-10 to balance the radiative losses of theinternetwork chromosphere as deduced from static models(Avrett 1981; Anderson & Athay 1989). As pointed outin their paper, “The major uncertainty in the analysis isthe possibility of high frequency power with spatial scalessmaller than the resolution element of TRACE.” Cuntzet al. (2007) argues that, indeed, the high frequency powerat small scales is sufficient to make acoustic heating ofthe solar chromosphere locally dominant. They base thisconclusion on theoretical calculations of wave power gen-eration, on 1D simulations of acoustic waves (where highfrequency waves can account for a temperature increas-ing with height but where other aspects of the simulationthat do not agree with observations have to be attributedto the 1D limitation of the simulation) and on syntheticimages from 3D simulations where they refer to the workof Wedemeyer-B¨ohm et al. (2007). It is obvious that highresolution observations would go a long way to answeringthe question whether a significant acoustic energy flux ishidden in spatial scales smaller than the resolution ele-ment of TRACE.We here present such observations obtained with theHinode spacecraft at 0.16” spatial resolution (pixel size0.05”). In Section 2 we present the observations and datareduction, in Sect. 3 we discuss the power spectra of theobservations at various spatial scales and we conclude inSect. 4.
2. Observations and Data Reduction
The TRACE 1600 passband is rather ideal for studyingthe input of acoustic energy flux into the chromospherebecause the response of the passband integrated intensityto perturbations in temperature is not very wide with aweighted mean formation height of 430 km (Fossum &Carlsson 2005a), placing the sensitivity right at the lowerboundary of the chromosphere. As pointed out above, the drawback is the large pixel-size of 0.5”. With the SolarOptical Telescope (SOT) (Tsuneta et al. 2007) of Hinode(Kosugi et al. 2007) we have a much higher spatial reso-lution, the diffraction limit ( λD ) is 0.16” with 0.054” pixelsize, but can we find a filter that is sensitive to temper-ature fluctuations at the lower end of the chromosphere?The prime candidate is the filter centered at the long-ward of the two resonance lines of singly ionized calcium— the Ca ii H-line. This filter is rather wide with analmost Gaussian shape with FWHM of 0.22 nm, so thesignal may be dominated by the photospheric wings ofthe strong absorption line. To investigate the suitabil-ity of using Ca ii H-line filtergrams for studies of chro-mospheric dynamics we have determined the intensity re-sponse function for the Hinode filter to perturbations ofthe temperature. We follow the procedure of Fossum &Carlsson (2005a). In general, a response function mea-sures the response of an observed quantity to a given per-turbation (Magain 1986). In this case the response func-tion, R I,T ( h ), measures the response of the relative changein intensity, ∆ II , given a perturbation in the temperature,∆ T ( h ), as function of height in the atmosphere, h . Thefunction is defined from∆ II = Z ∞−∞ R I,T ( h ) ∆ T ( h ) T dh. (1) R I,T ( h ) is derived numerically from using a step func-tion to introduce a change of 1 % in the temperature of agiven reference atmospheric model up to a given point inthe atmosphere and varying this point. For each such per-turbation, the full non-LTE equations are solved for a sixlevel model atom of Ca ii with the code MULTI (Carlsson1986), the resulting intensity profile of the H-line was mul-tiplied with the Hinode filter transmission profile and inte-grated and the resulting Hinode intensities were derivatedwith respect to depth giving the response function. Itis obvious that this approach has its limitations — theresponse is assumed to be linear and we may get a signif-icant contribution from heights where the acoustic waveshave actually shocked, violating the assumption of linear-ity. Furthermore, the derived response function dependson the reference model atmosphere. Nevertheless, such aresponse function give an indication as to what heights canbe diagnosed by intensity variations observed in a givenfilter.Figure 1 shows the deduced temperature responsefunction for the SOT/BFI filters Ca ii H (centered at396.86 nm with FWHM of 0.22 nm), G-band (centeredat 430.64 nm with FWHM of 0.63 nm), blue-continuum(centered at 450.51 nm with FWHM of 0.23 nm) (all wave-lengths in air) using the FALC model of the average quietsolar atmosphere (Fontenla et al. 1990) as reference modelatmosphere. It is clear that the Ca ii H filter samplesthe highest regions (average response height of 247 km)while the G-band filter has a photospheric response witha upper photospheric tail (because of the numerous spec-tral lines in the passband, primarily from CH) with anaverage response height of 74 km and the blue contin-uum has a clean photospheric response with an averageo. ] High frequency acoustic waves 3
Fig. 1.
Response functions for the SOT/BFI filters Ca ii H( solid ), G-band ( dot-dashed ) and blue-continuum ( dashed ) us-ing the FALC model of the average quiet solar atmosphere asreference model atmosphere. response height of 14 km. The response function of theCa ii H filter is particularly wide with a long tail extendinginto the middle chromosphere. The width of the responsefunction will tend to attenuate the response to a waveperturbation — more so for high frequency waves withsmaller wavelength. The attenuation as function of fre-quency of the waves is given by the Fourier transform ofthe response function (Fossum & Carlsson 2006). For theHinode calcium filter and the FALC atmosphere we expectvery little power beyond 20 mHz (only 5% of the ampli-tude remains). Note, however, that small scale verticalinhomogeneities would substantially increase the sensitiv-ity to high frequency waves. The blue continuum gives thecleanest photospheric response and has a sharp responsefunction. For this study we therefore choose to observewith high cadence in the calcium filter and the blue con-tinuum filter.
The dataset analyzed in detail here was obtained onMarch 3 2007 between 05:48:03 and 07:09:29 UT and con-sists of 765 image pairs in the Ca ii H filter and the bluecontinuum filter. The cadence is strictly fixed at 6.4 swith 3.2 s between the blue continuum and the calciumimage. We read out only the central 1024x512 pixels ofthe detector (to keep the high cadence within the teleme-try restrictions) thus covering an area of 55”x28” at Suncenter. Exposure times were 0.41 s for the calcium im-ages and 0.1 s for the blue continuum. After 736 framesthere was a shift in the spacecraft pointing of 12” and wethus restrict the analysis to the first 736 frames in eachchannel, covering a timespan of 1 h m . We correct the data for dark current and camera arti-facts using the IDL routine fg prep , which is part of theHinode tree of solarsoft (Tarbell et al. 2007). We also needto correct for CCD sensitivity variations by flat-fieldingthe data. At the time of analysis, there were no flat-
Fig. 2.
Residual image jitter after the correlation tracker cor-rections, calculated from cross-correlation frame to frame. field data in the Hinode tree of solarsoft and we thereforeconstructed our own flat-fields. This was done by extract-ing all the synoptic observations from disk-center in theperiod November 2006 to April 2007. Frames that werecloser in time than 10 minutes were discarded as wereframes containing pores or sunspots. The flat-field wasconstructed from a mean of the remaining 440 frames.The calcium images have a solar rms variation of 16%.The averaging of 440 independent frames brings this downto an rms variation of solar origin of 0.8%, much smallerthan the rms variation of the flat-field image of 3%.The SOT correlation tracker removes most of the jitterintroduced by the spacecraft but visual inspection of thetimeseries reveals there is some remaining jitter. This isremoved by performing a rigid-co-alignment using cross-correlation from image to image and applying the cumu-lative offsets to the whole timeseries. Figure 2 shows thededuced image to image shift for the time-series show-ing that the residual image motion after the correlationtracker corrections is on the order of 0.1 pixels or 0.005”(one standard-deviation). The larger jumps are caused bythe replacement of the reference frame of the correlationtracker approximately every 40 s (Shimizu et al. 2007).The shifts calculated from the calcium images and thosecalculated from the blue continuum images are highly cor-related. From this we conclude that the deduced rms isactually uncorrected image motion and not errors in thecross-correlation method. There is drift over the wholetimeseries of about 30 pixels or 1.7”. This means thatthere is an area close to the edge of the field of view wherewe don’t have data for the whole timeseries. This area isexcluded from the further analysis.
3. Power Spectra
The distribution of power is known to be different innetwork areas and in internetwork regions. The currentdataset is very quiet and does not contain any plage orpore but two small network patches. The area of thesepatches is so small that the mean power is not affected Carlsson et al. [Vol. ,
Fig. 3.
Power of intensity fluctuations as function of fre-quency for the SOT/BFI Ca ii H filter timeseries at variousspatial binnings (colour code in the legend). whether they are included or not. To facilitate compar-isons with various degrees of rebinning, we include thewhole area in the following. For each point we calculatethe power of the intensity fluctuations relative to the meanintensity (∆
I/ < I > ) and take the mean. To determinethe power as function of spatial resolution, we redo the ex-ercise several times after rebinning the data to 2x2, 4x4,8x8 and 16x16 original pixels per new pixel.Figure 3 shows the one-sided power (the power at neg-ative and positive frequencies added together) for the cal-cium timeseries. Significant power can be seen up to about30 mHz. The maximum power is at low frequencies, de-creasing to 2.5 mHz and then increasing through a localmaximum at 4-5 mHz before decreasing again. The noiselevel goes down with rebinning but very little power is lostby the rebinning at 5-20 mHz: The integrated power inthe 5-20 mHz range is 90% of the original value for thedata binned to 0.43” pixels and 58% for the data binnedto 0.86”.The largest power is at the lowest frequencies. This isprobably caused by the granular evolution rather than bywaves. We have tried to separate the two components byperforming a filtering of the timeseries in the space-timedomain with a conical filter. We separate all componentsthat have a horizontal velocity smaller than 7 km s − (theapproximate sound speed) from those with a larger veloc-ity. Sound waves that propagate horizontally should havea phase speed of the intensity signal equal to the soundspeed. For an inclined wave, the phase speed will be larger(infinite for a vertically propagating wave). All acousticwaves should thus be contained in the high-pass part of thefiltered data while granular evolution (and gravity waves)will be in the low-pass part. Figure 4 shows the originaldata and the two filtered components for one snapshot.The original data have some intensity modulations of largespatial scale that disappear in the low-pass filtered image(e.g. a dark patch at [10,7] and a bright patch at [2,0]).We find these patches in the high-pass component. It isalso clear that the smallest spatial scales are in the low- Fig. 4. Ca ii H filter image at 06:32:44 UT ( top ), same snap-shot with features moving slower ( middle ) and faster ( bottom )than 7 km s − . pass component. Figure 5 shows the same for the bluecontinuum filter.Figure 6 shows the power in the original data and thetwo filtered components. The high power at low frequen-cies is totally dominated by the low-pass component (evo-lution and gravity waves) while the acoustic wave compo-nent gives rise to the peak at 5 mHz and dominates upto 20 mHz. The two components are of equal importanceat 30 mHz while the noise is dominated by the high-passcomponent (where spatially uncorrelated photon countingnoise is).The power of the high-pass filtered data (where we ex-pect the acoustic waves to be) is shown in Fig. 7 which alsoshows the integrated power in the 5-20 mHz range com-pared with the 2x2 binned data (we compare with the 2x2binned data because the unbinned data has high velocitycomponents from alignment interpolations that cancel outwhen the data is first binned to 2x2. Furthermore, the 2x2binned data has identical power spectrum as the originaldata apart from the noise level, see Fig. 3). The powerratios are similar to the case for the unfiltered data exceptthat the high-pass power at low frequencies is identical forthe various binnings, showing that the differences at lowo. ] High frequency acoustic waves 5 Fig. 5.
Blue continuum filter image at 06:32:40 UT ( top ),same snapshot with features moving slower ( middle ) andfaster ( bottom ) than 7 km s − . Fig. 6.
Power of intensity fluctuations as function of fre-quency for the SOT/BFI Ca ii H filter timeseries ( solid ), forthe low-pass filtered component (features moving slower than7 km s − ) ( dashed ) and for the high-pass filtered component(features moving faster than 7 km s − ) ( dotted ). Fig. 7.
As Fig.3 but with the data first filtered to removefeatures that move more slowly than 7 km/s horizontally. Theintegrated power in the 5-20 mHz range compared with theunbinned data is also given. frequencies in Fig. 3 are caused by slow motion/evolutionof sharp features. The integrated power 5-20 mHz is 90%of the 2x2 binned power at 0.43” binning and still 69% at0.86” binning. The high percentages are because the in-tegrated power is dominated by the low frequencies closeto 5 mHz where the difference between the different bin-nings is very small. The acoustic power will have a slowerdecline with frequency because the intensity signal is de-pressed at higher frequencies from the significant widthof the response function (Fossum & Carlsson 2006). Onewould thus expect that the small spatial scales are moreimportant for the integrated acoustic power than for theintegrated intensity power. As an extreme case one canuse the ratio of the intensity power at 20 mHz as the ratiofor the integrated acoustic power. This ratio is 69% at0.43” binning and 43% at 0.86” binning.The Ca ii H-line is a scattering line with a broad re-sponse function. It could be argued that the spatial scalesin the intensity response of this line will be larger thanthe actual acoustic waves scales and larger than for theTRACE 1600 filter. We have therefore repeated the exer-cise for the blue continuum that has a much more narrowresponse function. The response is from the photosphereso we expect the waves to have a much lower amplitudethan in the calcium filter. Figure 8 shows this to be thecase. The power is lower than for the calcium filter intensi-ties and there is a distinct 3 mHz peak from p-mode oscil-lations. However, the spatial scales of the high frequencysignal is very similar in the two filters: for the blue contin-uum the integrated power in the 5-20 mHz band is 87% for0.43” binning and 60% at 0.86” binning. At 20 mHz thecorresponding numbers are 65% and 40%, respectively.For a proper comparison with TRACE, our data shouldfirst be smeared with the PSF of TRACE and then re-binned to 0.5” pixel size. The PSF is poorly known butis probably wider than the diffraction limit. The apertureat the 1600 band of TRACE is set by the 11.2 cm diam-eter of the filter. This corresponds to a diffraction limitof 0.3”. TRACE is thus severly undersampled and the Carlsson et al. [Vol. ,
Fig. 8.
As Fig.7 but for the blue continuum filter.
PSF would have to be much broader than the diffractionlimit to add smearing beyond the pixel sampling. We thusfeel that the proper comparison is with the Hinode datarebinned to 0.5”. As the numbers above show, even re-binning to 0.86” pixel size does not change the integratedmean power of the timeseries much.
4. Conclusions
We have calculated the power of intensity variations asobserved with Hinode SOT/BFI Ca ii H and blue con-tinuum filters at high, strictly regular, cadence. We findthat intensity power corresponding to propagating acous-tic waves is largest close to the acoustic cutoff frequency.Furthermore, the spatial scales of the intensity variationsare predominantly larger than the TRACE pixel size of0.5”: The integrated intensity power in the 5-20 mHzrange is 83% of the original power when the data is re-binned to the TRACE pixel size. Even at 20 mHz thepower of the rebinned data is 64% of the original power.There is no large, unseen, pool of high frequency waves atsmall spatial scales. Combining this result with the workof Fossum & Carlsson (2005b, 2006) we conclude that thetotal energy flux in acoustic waves of frequency 5-40 mHzentering the internetwork chromosphere of the quiet Sun isless than 800 W m − , inadequate to balance the radiativelosses in a static chromosphere by a factor of five. We are grateful to the Hinode team for their effortsin the design, building and operation of the mission.Hinode is a Japanese mission developed and launched byISAS/JAXA, with NAOJ as domestic partner and NASAand STFC (UK) as international partners. It is oper-ated by these agencies in co-operation with ESA and NSC(Norway). SOT was developed jointly by NAOJ, LMSAL,ISAS/JAXA, NASA, HAO and MELCO. This work wassupported by the Research Council of Norway grants170926/V30 and 170935/V30. B.D.P. was supported byNASA contracts NNG06GG79G, NNG04-GC08G, NAS5-38099 (TRACE) and NNM07AA01C (HINODE). SWMwas supported by grants from the NSF (ATM-0541567)and NASA (NNG05GM75G, NNG06GC89G).