Height distribution of the power of 3-min oscillations over sunspots
N. I. Kobanov, D. Y. Kolobov, S. A. Chupin, V. M. Nakariakov
HHeight distribution of the power of 3-minoscillations over sunspots
N.I. Kobanov, D.Y. Kolobov, S.A. Chupin
Institute of Solar-Terrestrial Physics,Russia, 664033, Irkutsk p / o box 291; Lermontov st., [email protected] V.M. Nakariakov
Physics Department, University of Warwick, Coventry CV4 7AL, [email protected] September 2010, published in A&A 525, A41 (2011)
AbstractContext.
The height structure of 3-min oscillations over sunspots isstudied in the context of the recently discovered e ff ect of height inversion:over the umbra, the spatial location of the maximum of chromospheric 3-min oscillation power corresponds to the relative decrease in the power ofphotospheric oscillations. Aims.
We investigate whether the height inversion of the power of 3-minoscillations is a common feature of the spatial structure of the oscillationsfor the majority of sunspots.
Methods.
Spectrogram sequences of H α i Results.
The e ff ect of the height inversion is found in 9 of 11 analyzedactive regions. The interpretation of this e ff ect is possibly connected to boththe decrease in the level of photosphere in sunspot umbrae and the magneticfield topology. a r X i v : . [ a s t r o - ph . S R ] N ov Introduction
Powerful 3-min oscillations of the line-of-sight (LOS) velocity, detected in theDoppler shifts of the chromospheric spectral lines above sunspots have been sub-ject to intensive studies for several decades (Beckers and Tallant, 1969; Giovanelli,1972; Zirin and Stein, 1972; Lites, 1992). The interest in this phenomenon is jus-tified for several important reasons. First of all, it is connected to the transfer ofthe energy of photospheric motions by these waves to the corona. There is obser-vational evidence of 3-min field-aligned compressible waves in the corona oversunspots, usually seen in 171Å and 195Å passbands of TRACE (see, e.g. (DeMoortel, 2006)), which may be associated with the leakage of the 3-min sunspotoscillations. As the waves are interpreted as slow magnetoacoustic waves thatpropagate almost parallel to the magnetic field, their path highlights the mag-netic connectivity of the photospheric and coronal plasmas. In addition, thesewaves are a useful tool for probing solar coronal plasmas in the quickly devel-oping research field of coronal seismology (King et al. , 2003; Wang, Innes, andQiu, 2007). Moreover, the relationship between 3-min oscillations in sunspotsand the appearance of a similar periodicity in flaring energy releases has been es-tablished (Sych et al. , 2009). Another useful application of 3-min oscillations isin attempting to reveal the internal, sub-photospheric structuring of sunspots (e.g.(Zhugzhda, 2008)).3-min sunspot oscillations are presently studied in the optical band by bothfiltering and spectral methods, as well as in radio and UV bands (Gelfreikh et al. ,1999; O’Shea, Muglach, and Fleck, 2002; Rouppe van der Voort et al. , 2003;Bloomfield, Lagg, and Solanki, 2007; Nagashima et al. , 2007; Jess et al. , 2007;Tziotziou et al. , 2007; Balthasar and Schleicher, 2008). (Kobanov and Makarchik,2004; Kobanov, Kolobov, and Makarchik, 2006; Bloomfield, Lagg, and Solanki,2007) demonstrated that 3-min oscillations in the umbral chromosphere are notthe source of the running penumbral waves and concluded that the apparentlyhorizontally propagating waves correspond to the “visual pattern” scenario.Another identified peculiarity in the behaviour of 3-min oscillations has beenthe e ff ect of height inversion (Kobanov, Kolobov, and Chupin, 2008): at the chro-mospheric level, the spatial localisation of the maximum of 3-min oscillationpower, usually over the umbra, often corresponds to the minimum of these os-cillations at the photospheric level. One would expect that the spatial distributionof 3-min oscillations at both heights is similar, although at the photospheric levelthe oscillation power in the umbra is lower than in the penumbra and adjacent re-gions. This finding is consistent with the results of previous studies. In particular,2t was pointed out that in the umbra, at the photospheric height, 3-min oscillationsare either not detected at all (Balthasar, Kueveler, and Wiehr, 1987) or of very lowamplitude relative to the level of noise (Lites and Thomas, 1985). We note thatthe suppression of the photospheric oscillation power in active regions has alsobeen detected by the helioseismological methods (Braun and Duvall, 1990; Braun,1995; Nicholas, Thompson, and Rajaguru, 2004). The analysis of the brightnessfluctuations observed in the G-band with Hinode / SOT detected the decrease in thebroadband oscillation power in central parts of sunspots (Nagashima et al. , 2007).The aim of this paper is to perform a comparative analysis of 3-min oscilla-tions for a number of sunspots, demonstrate that the height inversion is a statisti-cally significant and reproducible e ff ect, and contribute to its interpretation. Ourapproach is based on the use of high cadence optical data, with the time resolu-tion of about 2 s, and upon the consideration of 3-min oscillations in a narrowband, 4.7–6.7 mHz. The paper is organised as follows. In the next section, wedescribe the instrument used in the observations and data reduction. In Section3, we present the results obtained. The results obtained are summarised in theconclusions. We use data obtained with the Horizontal Solar Telescope at the Sayan Solar Ob-servatory, Russia (Kobanov et al. , 2009). The diameter of the mirror of the instru-ment is 80 cm, hence the theoretically possible spatial resolution is 0.2 (cid:48)(cid:48) . However,because of the Earth’s atmospheric conditions the resolution is usually about 1 (cid:48)(cid:48) .The guiding system carries out targeting and object capturing with a precision noworse than 1 (cid:48)(cid:48) . In observations, an astronomical CCD of the resolution 256 × × (cid:48)(cid:48) , defined by the slit of the spectrograph. For each spatialelement, we obtain the spectrum of the width of 8.5Å (for the spectrograph dis-persion of the fifth order in the vicinity of the H α i ff er. Displacingthe slits to make their intensities equal allows one to determine the new locationof the line. Since this method is based upon the determination of the relative posi-tion of the line, it is not a ff ected by the variation in the intensity in time, from onespectrogram to another.In the processing of the observational sequences obtained with the deflector,the LOS velocity is determined by the Doppler formula directly from the displace-ment of H α line, as the splitting of the line by the deflector is insignificant. In thecase of another line used in this study, Fe i , it is completely split by the deflectorinto the σ − and σ + components. The LOS velocity is proportional to the sum ofthe displacements of these components, while the magnetic field is proportionalto the di ff erence in the displacements. The magnetic field is then calculated ac-cording to the Zeeman e ff ect for a simple triplet. Telluric line near H α was usedto eliminate the spectrograph noise.A possible error in the determination of the line position may be related to theasymmetry of the line shape. The asymmetry can be caused by blending of theH α line, or by the variation in the LOS speeds between the heights covered by theoptically thick H α line. However, as in this study we consider not the absolutevalues of the LOS speeds, but the frequencies of their time variations, the lattere ff ect not being likely to cause significant error. In this paper, we did not discussthe results of the magnetic field measurements.4igure 1: An example of the spectrograph slit orientation in the observations ofthe sunspot NOAA 791 (the scale of the slit is not kept). -20 0 2005 p o w e r , a r b i t r a r y u n i t s -20 0 20 arcsecs i n t e n s i t y , a r b i t r a r y u n i t s -20 0 20 t i m e , m i n Figure 2: The distribution of the wavelet power of the LOS velocity in the range4.7–6.7 mHz in the chromosphere of NOAA 810 observed in H α . Left panel:time-spatial dynamics of the 3-min oscillations. Central panel: Profile of the time-averaged spatial distribution of the wavelet power. Right panel: the profile of theintensity observed in the continuum. The vertical dashed lines indicate the umbra-penumbra boundary. In our study, we analysed 11 active regions (AO) observed during 2002–2007. Alist of the AO with their locations on the solar disk, the time of the observation,and results is presented in Table 1. The duration of each sequence is about onehour, where P p and P c are the ratios of the mean power of the 3 min oscillationsin the spot umbra to the mean power in the penumbra for the photospheric ( P p )and chromospheric ( P c ) level correspondingly.The spatial localisation of the 3-min oscillations of the LOS velocity has beenstudied using both Fourier and wavelet analyses. In both cases, the analysed spec-tral interval was taken to be from 4.7 to 6.7 mHz. Figure 2 shows a typical waveletspectrum that gives the time-spatial dynamics of the 3-min oscillation, as well asthe time-averaged spatial distribution of the oscillation power.5able 1: Observational sequences studied in this paper.NOAA Solar coordinates Date Start time, UT P p / P c
051 S17E01 02.08.2002 00:45 0.5 / / / / / / / / / / / / / / / / / / / / / / /
10 0 10 -20 -10 0 10 20 30 -10 0 100 -10 0 10 -10 0 10-10 0 10 -10 0 10 -10 0 105-5 arcsecs p o w e r , a r b i t r a r y u n i t s NOAA 051 NOAA 613NOAA 105 NOAA 791NOAA 657 NOAA 661NOAA 810 NOAA 963NOAA 794 -15 -5 5 -5-15 5 15 5-5-15 -5 155 -15 -5 5 15-5 5-5 5 15
Figure 3: The e ff ect of the height inversion for the power of 3-min oscillations insunspot umbrae. The panels show time-averaged spatial profiles of 3-min oscilla-tions of the LOS velocity measured in di ff erent active regions. Thin lines corre-spond to the photospheric signal (Fe i ), and the thick curves to the chromosphericsignal (H α ). The vertical dashed lines indicate the umbra-penumbra boundary.7 o w e r , a r b i t r a r y u n i t s space, arcsecs t i m e , m i n -20 0 20051234 -10 3010-20 0 20051234 -10 30104080120 Fe , Photosphere
I-20 0 200 -10 30101002060 -20 0 20
Hα, Chromosphere -10 3010408012010020600
Figure 4: The absence of the height inversion e ff ect for the leading sunspot ofNOAA 791 in the observational sequences on 2005 July 26, 03:27–5:40 UT. Inthe same sunspot, the e ff ect of the height inversion is presented in other five timeseries (one of them is shown in Figure 3). The figure shows the spatial distri-bution of the wavelet power of the LOS oscillations in the band 4.7–6.7 mHz. Top panels:
Time-spatial dynamics of the wavelet spectra.
Bottom panels : Time-averaged profiles of the wavelet spectra. The vertical dashed lines indicate theumbra-penumbra boundary. 8ur analysis demonstrated that at the chromospheric level in all consideredsunspots except the small sunspot NOAA 621, the maxima of 3-min oscillationpower are situated near the centres of the umbrae. At the photospheric level, inthe most considered time series, these regions were found to correspond to thesuppression of the 3-min oscillation power (see Figure 3). The criterion used inthe detection of the e ff ect of the height inversion is the occurrence of a local min-imum in the spatial distribution of the photospheric narrowband power and itsabsence at the chromospheric level. The spatial coordinates in all plots of Fig-ure 3 were restricted by the external boundaries of the penumbra. The e ff ect canbe quantified by the ratio of the mean power in the umbra (averaged over the wholeumbra) to the mean power in the penumbra (averaged over the whole penumbra).In the chromosphere, this ratio was found to be greater than one, while in the pho-tosphere it is smaller than one (see P p / P c , Table 1). We analysed 24 time seriesfrom 11 active regions. In 18 series, we found the e ff ect of height inversion, in 3series the situation was the opposite, and for 2 series we derived uncertain results(the photospheric mean power ratio was 0.9–1.1). One time series of NOAA 621shows the absence of the 3-min LOS velocity oscillations in the chromosphere.We should also point out that in certain time intervals in some sunspots the maxi-mum of 3-min oscillations at the photospheric level can be found in the umbra. Forexample, for NOAA 791, in six analysed time sequences, the e ff ect of the heightinversion was found in five cases, while in one case the photospheric maximum ofthe 3-min oscillations was localised in the umbra, hence exactly coincident withthe chromospheric maximum (see Figure 4). Wavelet spectra of the photosphericand chromospheric signals are shown in the upper panels. At first glance, theincreases and decreases in the oscillation power at those heights seem to occursimultaneously. However, the detailed phase analysis discussed below does notsupport this impression.We are thus inclined to conclude that in the majority of the observed cases thespatial location of the maxima of 3-min chromospheric oscillations correspond tothe suppression of these oscillations at the photospheric level. One possible inter-pretation of this e ff ect may be the decrease in the photospheric level observed inFe i ff erence in heights, associated with the Wilson de-pression, is responsible for the observed decrease in the oscillation amplitude bya factor of two.According to Balthasar and Woehl (1983) and Watson et al. (2009), the depres-sion ( τ =
1) of the umbral photosphere with respect to the penumbra (the Wilson9 ff ect) is about 700 km. This di ff erence in height can lead to the decrease in the3-min oscillation amplitude by a factor of 2 (Lites et al. , 1998). This decreaseis consistent with the 3-min LOS velocity power distribution at the photosphericlevel (Figure 3), at least within the order of the magnitude.Parnell and Beckers (1969) used the formation depth of the line Fe I 6569to study the granulation. They determined the upper limit to the line formationheight to be 250 km. According to the broadly used atlas of the solar spectrum(Moore, Minnaert, and Houtgast, 1966), this line is suppressed in sunspots, henceone can assume that its optical thickness in the umbra is not higher. In the Fe I6569 line, the Wilson e ff ect is as pronounced as in the continuum.The observed e ff ect may also be caused by the topology of the sunspot mag-netic field. If we assume that a horizontally extended source of 3-min oscillationsis situated below the photosphere, in the umbra, the oscillations in the form of slowmagnetoacoustic waves would be guided by the vertical magnetic field lines up-wards and reach the chromosphere. At the edge of the umbra and in the penumbra,the magnetic field lines are inclined from the vertical direction, preventing the freepropagation of the short period waves (Bogdan and Judge, 2006). Thus, under thecanopy 3-min waves are able to propagate in the vertical direction up to the mag-netic dome only. Finsterle et al. (2004) pointed out that the 7-mHz oscillations arereflected by the active region canopy. The partial reflection of the waves from themagnetic dome can lead to the observed accumulation of the wave energy at thephotospheric level under the regions with a horizontal magnetic field. This mayexplain the relative increase in the 3-min photospheric oscillation power in theregions outside the umbra, and the corresponding decrease in the chromosphericoscillation power in these regions.Moreover, it is necessary to consider a possible contribution of the “powerhalo”(Lindsey and Braun, 1999; Braun and Lindsey, 1999). Our observationswere focused on the sunspots, and, unfortunately, studying the sunspots’ vicinitiesis beyond the scope of the data for most time series.In the majority of the observational sequences, the power of photospheric 3-min oscillations in the umbra was low, thus it was impossible to estimate thephase delay between the photospheric and chromospheric oscillatory motions inthe umbra. However, the above-mentioned unusual observational sequences ofNOAA 791, containing the umbral maximum of the photospheric 3-min oscilla-tions, allows us to carry out the analysis of the phase shifts between the signalsat di ff erent heights. Unfortunately, the direct comparison of the photospheric andchromospheric signals does not provide us with any conclusive results. Figure 5shows that there is no stable phase di ff erence between narrowband photospheric10 time, min -40-2002040 v e l o c i t y , a r b i t a r a y u n i t s
120 130-40-2002040 c o rr e l a t i o n Figure 5:
Left panel.
Comparison of phases of chromospheric (thick line) andphotospheric (thin line) narrowband (4.7-6.7 mHz) LOS velocity signals in thecentre of the umbra of NOAA 791 (the leading spot) in di ff erent time intervals. Right panel.
Correlation between the chromospheric and photospheric signals ofthe LOS velocity for the whole time series.and chromospheric signals. In some time intervals (e.g. 45–50 min), the chromo-spheric signal even precedes the photospheric signal. There are also time intervals(e.g. 112–130 min) when the time lag gradually increases from 20 s to 140 s. Thecorrelation between the signals for the whole time series is presented in the rightpanel of Figure 5.A similar negative result comes from the comparison of the power maximaof the photospheric and chromospheric signals (Figure 6). The detuning of thesignals is so pronounced that one has the impression that the photospheric andchromospheric signals are disconnected. Thus, the data obtained does not allowus to measure the phase lag between the photospheric and chromospheric 3-minoscillations directly, to derive the phase speed. However, the average time lag be-tween the appearance of the maxima of the oscillation power at those two heightscould be measured and is about 150 s. Taking the distance between the heightsof observations to be 2000 km (Vernazza, Avrett, and Loeser, 1981; White andWilson, 1966), we obtain the vertical group speed of about 13 km s − .11
20 40 60 80 100 12005 p o w e r , a r b i t r a r y u n i t s time, min c o rr e l a t i o n Figure 6: The time variation in the power of the chromospheric (thick line) andphotospheric (thin line) narrowband (4.7-6.7 mHz) LOS velocity signals in theumbra of the leading spot of NOAA 791. The upper panel shows the signals ofthe spatial element of 1 (cid:48)(cid:48) at the centre of the umbra. The bottom panel showsthe signals averaged over the 10 (cid:48)(cid:48) region in the umbra. Right panel shows thecorrelation between the signals presented in the upper panel.On the other hand, taking into account the correlogram shown in the rightpanel of Figure 6, the group speed can be estimated as 6 km / s. This discrepancyis due to the ambiguity of the phase connection between the photospheric andchromospheric signals. Moreover, the observed correlation coe ffi cient is ratherlow, about 0.35, and is observed only in one case. Thus, the present study doesnot allow us to make confident and statistically-significant conclusions about thewave connectivity at the photospheric and chromospheric levels, based upon thecorrelation analysis. One possible reason for the apparent out-of-phase behaviourof the photospheric and chromospheric oscillations may be the partial reflectionof the slow magnetoacoustic waves from the density gradient over the umbra,which causes a complicated time-dependent superposition of the propagating andstanding waves in the photosphere. 12 Conclusions
We have analysed the spatial distribution of narrowband 3-min oscillations of theLOS velocity at the photospheric and chromospheric levels in eleven sunspots.The observations dedicated to this study were carried out with the 80 cm Hor-izontal Solar Telescope at the Sayan Solar Observatory in the Fe i α ff ect may betermed a height inversion of 3-min oscillations in sunspots. Phase shifts betweennarrowband 3-min amplitude photospheric and chromospheric signals were foundto vary in time, as well as between the maxima of their power. The e ff ect of heightinversion may be attributed to the wave reflection caused by the inclined mag-netic fields in the peripheral regions of sunspots or to the Wilson depression ofthe photospheric level in the umbra. However, detailed theoretical study of thesephenomena is needed. Acknowledgements
The work is supported in part by the grant RFBR 08-02-91860-KO a, the Royal Soci-ety British-Russian International Joint Project, grant 10-02-00153-a and grant of FederalAgency for Science and Innovation (State Contract 02.740.11.0576). Wavelet softwarewas provided by C. Torrence and G. Compo, and is available at http: // paos.colorado.edu / research / wavelets. We would like to thank anonymous referee for the detailed considera-tion of our paper and for the constructive comments. eferences Balthasar, H., Schleicher, H.: 2008,
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