Supergranulation Velocity Field from the MDI (SOHO) Data
IISSN 0016(cid:2)7932, Geomagnetism and Aeronomy, 2014, Vol. 54, No. 8, pp. 1–6. © Pleiades Publishing, Ltd., 2014.
1. INTRODUCTIONIn the study of long(cid:2)period oscillations in sunspotmagnetic field and radial velocities, we showed the fol(cid:2)lowing:(1) Long(cid:2)period sunspot oscillations have a multi(cid:2)mode character: oscillations are confidently detectedin the bands with periods of 60–80, 135–170, and220–240 min, with the oscillation power decreasingmonotonically with decreasing period.(2) The limiting (lowest frequency) mode of thesunspot magnetic field natural oscillations is the M M M
1 leads to the sunspotoscillation power spectrum having an even lower fre(cid:2)quency mode M
2, with a period of about 30–48 h. M M
1. The M
2 mode reflects, we believe, the quasi(cid:2)period of an external perturbing force attributed to thesunspot dynamic perturbations from the surroundingsupergranulation cells.The aim of this work is to detect in the quiet photo(cid:2)sphere oscillations with a period close to that of the M Michel(cid:2)son Doppler Image ( MDI ) on board the
Solar andHeliospheric Observatory (SOHO) (Scherrer et al.,1995). We used observation series recorded at 1(cid:2)mincadence. The
SOHO/MDI space data includes a timeseries of full solar disk Dopplergrams (http://soi.stanford.edu/data/). In each Dopplergram we selected a radialvelocity value strictly for one and the same point in thephotosphere throughout the whole multiday observa(cid:2)tion series. In order to construct these time series, itwas necessary to stabilize the image of an object (spot,pore, etc.) moving along the Sun’s surface. To thisend, we used magnetograms or intensitygrams of sta(cid:2)ble spots having a regular round shape without bridges.The images were stabilized using an extreme referencefor a distributed object that had been immersed in a strip , a limited fixed frame. After the first run, weobtained a pair of coordinate functions { X ( n ), Y ( n )} tocreate a scenario describing the motion of the refer(cid:2)ence (in our case, extreme) in the strip during theobservation period. Immersing the spot in a small Supergranulation Velocity Field from the MDI (SOHO) Data
L. D. Parfinenko, V. I. Efremov, and A. A. Solov’ev
Main (Pulkovo) Astronomical Observatory, Russian Academy of Sciences, St. Petersburg, Russiae(cid:2)mail: [email protected]
Received February 10, 2014
Abstract —Long (up to 100 hours) time series of
SOHO / MDI
Doppler data are analyzed. The power spectrumof radial velocity time series in the quiet photosphere is observed to have, along with the known 5(cid:2)min mode,a stable strong mode with a period of about 32 h, which is close to the supergranulation cell lifetime. The spa(cid:2)tial distribution of the amplitudes of these oscillations also coincides with the characteristic size scale ofsupergranulation (~35 Mm).
DOI:
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PARFINENKO et al. frame and making the frame boundaries move accord(cid:2)ing to the scenario, we stabilized the object. Then wecould construct the time series for a given parameter atany point in or near the spot. The processing tech(cid:2)nique is described in (Efremov et al. 2010; 2012;2014). Due to the low degree of structure and low con(cid:2)trast of the Dopplergrams, pegging the results to theextreme reference was very difficult even within a spot,to say nothing of the quiet photosphere.Hence, we used, along with the Dopplergrams, asynchronous series of magnetograms or intensity(cid:2)grams, which allow a relatively simple and reliablesunspot stabilization. The simultaneous observationshould provide the magnitudes of the radial velocity V r and magnetic field H (or continuum intensity I c ),which can be quite confidently pegged to the extremereference near the sunspot center. Then, synchroniz(cid:2)ing the data and using the sunspot motion scenario forthe magnetic field ( H ) or intensity ( I c ), we applied thescenario to the Dopplergrams ( V r ). Obviously, theresulting scenario can be used not only for the spot butalso for any point in the quiet photosphere movingacross the disk at the latitude of the selected spot in thesame time interval. 3. RESULTS AND DISCUSSIONOur assumption was that the M –800 900–4000400800 15 30 45 60 7564 15 30 45 60 75321684211/21/41/81/16 0 1 2Time, h P e r i o d , h V e l o s i t y , m / s Power ([ x ] ) ×
32 h5 m
Global Walvet
Wavelet Power Spectrum June 26–29, 2000, MDI/SOHO 90(cid:2)h series DopplergramS1 (N 09057) S3 (N 09055)
Fig. 1.
The upper left panel shows the radial velocity time series at the photosphere point marked by an arrow (right panel). Thelower left panel shows the time series wavelet.EOMAGNETISM AND AERONOMY
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SUPERGRANULATION VELOCITY FIELD FROM THE MDI (SOHO) DATA 3
To investigate the oscillations, we applied waveletanalysis (Torrence et al., 1998), using a fifth orderMorlet wavelet as an analyzing function. Trends in theradial velocity time series were approximated withfourth(cid:2)order polynomials.Preliminary studies were conducted for observa(cid:2)tions made in the period from June 26 to June 29, 2000(SOHO/MDI 90(cid:2)hour series). Figure 1 shows theradial velocity time series at an arbitrary point in thequiet photosphere (marked by an arrow) and the cor(cid:2)responding wavelet. The power spectrum of the radialvelocity time series in the quiet photosphere turnedout to have, along with the known 5(cid:2)min mode (Lei(cid:2)bacher and Stein, 1971), a strong low(cid:2)frequency modewith a period of about 33 h.For a more detailed study, we selected the 100(cid:2)hSOHO/MDI series for the period from March 31 toApril 4, 2002 in the area of NOAA 09887. The power spectra of radial velocity oscillations atarbitrarily selected points in the quiet photosphere(Fig. 2) are observed to have a strong low(cid:2)frequencymode with a period of about 30 h, which is close to thatof M
2. The wavelet for the spot center shows no 5(cid:2)minmode but is observed to have a technical artifact (a~16(cid:2)min mode). The latter was described by Efremovet al. (2010; 2012). The spot image moves across thematrix due to the Sun’s rotation. The artifact appearswhen the maximum field strength point, or maximumvelocity point, moves from one pixel to another in thematrix because of a large magnetic field or velocitygradient in the spot (produces a short jump in the sig(cid:2)nal). In the quiet photosphere, the velocity gradient issmall and the artifact does not manifest itself.Our next step was to study the spatial distribution ofthe M H H VrSpot
Wavelet Power Spectrum Global Walvet Wavelet Power Spectrum Global Walvet Wavelet Power Spectrum Global WalvetWavelet Power Spectrum Global Walvet Wavelet Power Spectrum Global Walvet Wavelet Power Spectrum Global Walvet P e r i o d , m i n P e r i o d , m i n P e r i o d , m i n P e r i o d , m i n P e r i o d , m i n P e r i o d , m i n Time, min Time, min Time, minTime, min Time, min Time, minPower ([ x ] ) ×
106 Power ([ x ] ) ×
106 Power ([ x ] ) × x ] ) ×
106 Power ([ x ] ) ×
106 Power ([ x ] ) × Fig. 2.
The upper panel shows the position of the analyzed fragment in the full solar disk magnetogram. In the middle and on theright is shown, on a larger scale, the analyzed fragment of the magnetogram and Dopplergram. The points are indicated at whichvelocity oscillations were analyzed: six points in the photosphere and one point at the spot center. The middle and lower panelspresent the corresponding wavelets for the radial velocity time series for points , , , , and in the photosphere and the centralpoint of the spot. GEOMAGNETISM AND AERONOMY
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PARFINENKO et al. in the photosphere in the vicinity of the sunspot.Then, collecting a sequence of scans for the wholeobservation, we first built an L – T map, which is thetimebase of the radial velocities in each selected scan,and then used the resulting L – T map to build Ω – L maps. In these maps the Y axis plots the oscillation fre(cid:2)quency and the X axis plots the scan number. This is ahighly visual representation of the process, ensuring its readability: we see both the spatial distribution of theprocess power, i.e., the localization of the power inspace, and the temporal distribution of the process,i.e., its characteristic periodicity (Efremov et al.,2007).Figures 3 and 4 show the results of our study for thedirection along the meridian and parallel. It is clearthat the oscillation power can be grouped into clusters Ω –L maps F r e q u e n c y , m H z F r e q u e n c y , m H z F r e q u e n c y , m H z F r e q u e n c y , m H z Frame 150 ×
80 110100 120
H(cid:2)canal V(cid:2)canal L–T map (line 100)Time, min L i n e , p x
32 hN scan N scanN scan N scan
Fig. 3.
The upper panel shows a fragment of the magnetogram and Dopplergram with the meridional sections used to analyze thespatial distribution of velocity oscillations. On the right is shown the L – T map for the 100th section. The middle and lower panelspresent the Ω – L maps for 80, 100, 110, and 120 sections.EOMAGNETISM AND AERONOMY Vol. 54
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SUPERGRANULATION VELOCITY FIELD FROM THE MDI (SOHO) DATA 5 at a period of about 32 h, with the distance between theneighboring clusters being about 35 Mm.These results allowed us to the estimate the height h of the supergranulation cell. Taking into account thecontinuity of flows in the convective cell, the averagetime of gas lift in the cell may be assumed to be equal to that of its horizontal flow: R / ≈ h / , where R is the radius of the convective cell; h is its character(cid:2)istic thickness (height); and and are the aver(cid:2)age velocities of the radial flow and gas lift, respec(cid:2)tively. Based on the data obtained, we can assume that V ˜ rad V ˜ lift V ˜ rad V ˜ lift × × L i n e , p x Time, min1000 2000 3000 4000 50005 2065 80Contour map Contour mapContour map Contour map Ω –L maps N scanN scan N scanN scan 32 h F r e q u e n c y , m H z F r e q u e n c y , m H z F r e q u e n c y , m H z F r e q u e n c y , m H z Fig. 4.
The upper panel shows a fragment of the magnetogram and Dopplergram with the sections made along the parallel to ana(cid:2)lyze the spatial distribution of velocity oscillations. On the right is shown the L – T map for the 20th section. The middle and lowerpanels present the Ω – L maps for 2, 20, 65, and 80 sections. GEOMAGNETISM AND AERONOMY
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PARFINENKO et al. the characteristic gas lift velocity is = 100 m/s andtake the known values of 200 m/s to 400 m/s for theaverage horizontal gas flow velocity. Then we have R ≈ (2–5) h . Since the radius R of the supergranulation cellcross(cid:2)section is on average ~17.5 Mm, then the heightof the cell is h = (3–8)Mm; i.e., supergranulation cellsprove to be planar formations occurring in the upperlayers of the convective zone. This is independent evi(cid:2)dence supporting the hypothesis that supergranulationis induced by convective instability in the area of He+recombination at a depth of (2–8)Mm (Simon andLeighton, 1964). However, it might be possible thatthe observed supergranulation pattern is due to thesuperimposition of wave and oscillation processesupon the hydrodynamics of convective transport.It should be noted that in this study we did not usedata from SDO / HMI , which has a better spatial reso(cid:2)lution, because the data for the target frequency rangemay have a daily Doppler artifact attributed to thisinstrument. (The
SDO / HMI data can be used to studylong(cid:2)period sunspot oscillations if the sunspot mag(cid:2)netic field intensity is less than 2000 G, at which thereare no apparent manifestations of the artifact(Smirnova et al., 2013)). As to the
SOHO / MDI instru(cid:2)ment, we showed previously (Efremov et al., 2010;2014) that the observations series recorded at 1(cid:2)mincadence in the target low(cid:2)frequency spectral regionhave no significant artifacts.4. CONCLUSIONS(1) The quiet photosphere velocity field is observedto have vertical plasma oscillations with a characteris(cid:2)tic period of T ~ 32 h.(2) The oscillation power is distributed across thephotosphere as clusters with a characteristic spatialscale of L ~ 35 Mm, both along the meridian and alongthe parallel.(3) The amplitude of radial velocity oscillations inthese clusters is approximately 100 m/s.(4) The oscillation clusters discovered in the mag(cid:2)netic field(cid:2)free photosphere have the same spatial andtemporal characteristics as supergranulation cells,which is substantial evidence for the physical identifi(cid:2)cation of these phenomena.(5) Presumably, it is the motions of superconvectivecells that induce M T ~ 32 h in the power spectra of the sunspot mag(cid:2)netic field and radial velocity oscillations.ACKNOWLEDGMENTSWe thank Dr. P.H. Scherrer and the SOHO team forthe opportunity to use the
SOHO / MDI observationdata.This work was supported by the Presidium of theRussian Academy of Sciences, project nos. P(cid:2)21 andP(cid:2)22; the Science School Support Program, project no. NSh(cid:2)1625.2012.2, and the Russian Foundationfor Basic Research, project no. 13(cid:2)02(cid:2)00714.REFERENCES
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Translated by A. KobkovaV ˜ liftlift