Large-scale horizontal flows in the solar photosphere V: Possible evidence for the disconnection of bi-polar sunspot groups from their magnetic roots
aa r X i v : . [ a s t r o - ph . S R ] A ug Astronomy&Astrophysicsmanuscript no. aa12422-09 c (cid:13)
ESO 2018November 21, 2018
Large-scale horizontal flows in the solar photosphere
V. Possible evidence for the disconnection of bi-polar sunspot groups from theirmagnetic roots
M. ˇSvanda , , , M. Klvaˇna , and M. Sobotka Max-Planck-Institut f¨ur Sonnensystemforschung, Max-Planck-Strasse 2, D-37191, Katlenburg-Lindau, Germanye-mail: [email protected] Astronomical Institute, Academy of Sciences of the Czech Republic (v. v. i.), Friˇcova 298, CZ-25165, Ondˇrejov, Czech Republice-mail: [email protected], [email protected] Astronomical Institute, Faculty of Mathematics and Physics, Charles University, V Holeˇsoviˇck´ach 2, Prague, CZ-18200, CzechRepublicReceived 5 May 2009 / Accepted 10 Aug 2009
ABSTRACT
In a recent paper (ˇSvanda et al., 2008, A&A 477, 285) we pointed out that, based on the tracking of Doppler features in the full-discMDI Dopplergrams, the active regions display two dynamically di ff erent regimes. We speculated that this could be a manifestationof the sudden change in the active regions dynamics, caused by the dynamic disconnection of sunspots from their magnetic roots asproposed by Sch¨ussler & Rempel (2005, A&A 441, 337). Here we investigate the dynamic behaviour of the active regions recordedin the high-cadence MDI data over the last solar cycle in order to confirm the predictions in the Sch¨ussler’s & Rempel’s paper. Wefind that, after drastic reduction of the sample, which is done to avoid disturbing e ff ects, a large fraction of active regions displays asudden decrease in the rotation speed, which is compatible with the mechanism of the dynamic disconnection of sunspots from theirparental magnetic structures. Key words.
Sun: photosphere – Sun: magnetic fields
1. Introduction
The dynamics of active regions in the solar photosphere and inthe close sub-photospheric layers is closely related to the so-lar dynamo process. The magnetic flux emerges from beneaththe surface and forms sunspots and other active phenomena. Atsome point, the magnetic field starts to disperse, the sunspotsdisappear, and the active region decays, forming the surge-likestructures of the trailing polarity expanding to the solar poles(Bumba & Howard, 1965), where they contribute to the solarfield reversals (see e.g. Wang et al., 1989).The measurements of the dynamic behaviour of active re-gions can bring forth new insights into what is happening tothe magnetic field under the surface. Many authors have stud-ied the variations in the rotation speed of sunspots. The rotationof the sunspots in relation to their morphological type was stud-ied by e.g., Balthasar et al. (1986), who found that more evolvedtypes of sunspots (E, F, G, and H types) rotate slower than lessevolved types. Ruˇzdjak et al. (2004) investigated the GreenwichPhotoheliographic Results for the years 1874–1976 and foundclear evidence for the deceleration of the sunspots in the photo-sphere with their evolution. Herdiwijaya (2002) found that theleading part of a complex sunspot group rotates about 3 % fasterthan the following part. The dependence of the rotation rate ofsunspots on their size and position in the bi-polar region wasinvestigated by D’Silva & Howard (1994). Their results showedthat smaller spots rotate faster than large ones. The authors ex-
Send o ff print requests to : M. ˇSvanda plained the observed behaviour through a subtle interplay be-tween the forces of magnetic buoyancy and drag, coupled withthe Coriolis force acting on rising flux tubes.The interpretations used in the explanation of the observeddynamics of active regions often involve the deep anchoring ofthe magnetic structures. From helioseismic inversions, we knowthat throughout the convective envelope, the angular velocitycontours at mid-latitudes are nearly radial. Near the surface, atthe top of the convection zone, there is a layer of a large radialshear in the angular velocity. At low and mid-latitudes, there isan increase in the rotation rate immediately below the photo-sphere that persists down to r ∼ . R ⊙ (where r is the radialcoordinate). The angular velocity variation across this layer isroughly 3 % of the mean rotation rate, and according to the he-lioseismic analysis of Corbard & Thompson (2002), the angularvelocity ω decreases within this layer approximately as r − . Athigher latitudes, the situation is less clear. The changing depthof the magnetic roots, e.g., by the rising motion, could explainthe deceleration of the sunspots during their evolution.One of the important properties observed in the bi-polarsunspot groups is their tilt with respect to the zonal direction(Hale et al., 1919). This tilt is believed to be generated by theCoriolis force, which acts to twist the flux-loop as it rises throughthe convection zone. The obvious question is, what happens tothe tilt when the flux eruption has ceased, because this impliesthat the twisting Coriolis force no longer exists? If the magneticfield remains connected to the deep toroidal field at the base ofthe convection zone, then the tilt should slowly diminish through M. ˇSvanda et al.: Large-scale horizontal flows in the solar photosphere V: A disconnection of bi-polar sunspot groups the action of the magnetic tension. However, this behaviour isnot observed, which challenges the solidity of the connection tothe deep magnetic field.A number of theories have been suggested (Fan et al., 1994;Sch¨ussler & Rempel, 2005) indicating that bi-polar magnetic re-gions may become disconnected from their magnetic roots andform an isolated island-like feature. The mechanism is basedupon the buoyant upflow of plasma along the field lines. Suchflows arise in the upper part of a rising flux loop during the finalphase of its buoyant ascent towards the surface. The combina-tion of the pressure build-up by the upflow and the cooling ofthe upper layers of an emerged flux tube by radiative losses at thesurface leads to a progressive weakening of the magnetic field atdepths of several Mm. When the field strength has become suf-ficiently low, convective motions ablate the flux tube into thin,passively advected flux fragments. The mechanism provides fora dynamical disconnection of the emerged part from its parentalmagnetic structure. This instant should be observed as a changein the dynamic regime, as the “floating island” does not reflectthe deep dynamics any longer. We note that even in the modelswhich assume that the surface magnetic activity is a consequenceof the shallow dynamo action (e.g. Schatten, 2009), the separa-tion of the surface local magnetic field from the close subsurfaceone is required, in order to allow the magnetic flux to dispersetowards the solar poles. The model of Schatten (2009) howeverdoes not provide the predictions for the systematic dynamics ofactive regions in the photosphere.In the recent paper of ˇSvanda et al. (2008) we found thatsunspots in the equatorial region seem to show two di ff er-ent dynamical regimes. In one regime, the fast regime , thesunspots displayed an almost constant velocity of 1910 ± − .Furthermore, the sunspots embodying this regime were of ayounger type. The second group, the scattered group , containedmostly old and perhaps recurrent sunspot groups. In the ve-locity, this group showed a large scatter with the mean speedof 1850 m s − . At that time we did not have a tool to followa particular region on the Sun for any time of interest, there-fore we concluded that the existence of the above-mentionedregimes is compatible with the theory of dynamic disconnec-tion. Furthermore, the fact that all the young sunspots we ob-served depicted almost the same speed, led us to speculate thatthis behaviour is related to the assumption that the magneticfield emerges from a similar depth in the convection zone, inline with deep anchoring. Following the approximation of theradial rotation profile in Corbard & Thompson (2002), the ra-dius where the rotation corresponds to 1910 ± − is roughly0.946 ± R ⊙ .In the past year, we have developed a tool for the selectionof the active regions in the Michelson Doppler Imager (MDI;Scherrer et al., 1995) magnetograms. From the previous studieswe possess the datasets that cover all the MDI Dynamics cam-paigns in years 1996–2006, i.e., 502 days of high quality obser-vations. In each of these days, two full-disc 24-hours-averagedhorizontal velocity maps, with an e ff ective resolution of 60 ′′ sampled by 12 hours, were calculated. This allowed us to studythe evolution of the active region dynamics recorded in our ve-locity datasets, in particular the phenomenon of the dynamic dis-connection from the magnetic roots.
2. Data and Method
In recent papers (e.g. ˇSvanda et al., 2006) we introduced amethod to measure the large-scale dynamics in the solar photo-sphere. This method is based on supergranular-structures track- ing in the full-disc, processed Dopplergrams, measured by MDIon-board the SOHO spacecraft. The application of this methodallows one to compute the 24-hour averaged horizontal flowfields with resolution of 60 ′′ and noise level of 15 m s − . Inthe magnetised regions, this method makes it possible to mea-sure the apparent motion of supergranular-scale magnetic fea-tures ( ˇSvanda et al., 2009).The methodology consists of several steps. The main pur-pose of the pseudo-pipeline is to suppress disturbing e ff ects,to remap the data onto a suitable coordinate system, to com-pute the horizontal vector-displacement field, and to convert themap of the displacements into the horizontal velocity vectors.The method and its subsequent validation are described in thegreat detail in ˇSvanda et al. (2006). Here we provide a very briefoverview.The method processes 24-hour series of MDI full-discDopplergrams containing 1 440 frames. The one-day series firstundergoes noise substraction and the removal of other distortinge ff ects (Carrington rotation profile, p -modes). Then, the process-ing of averaged frames consists of two main steps. The first stepinvolves the calculation of mean zonal velocities using a veryapproximate local correlation tracking (LCT; November, 1986)algorithm. The obtained zonal velocities are fitted by a smoothfunction in a form of ω = c + c sin b + c sin b , and the se-ries is tracked with the computed rotation profile. The trackingwith the smooth velocity profile is done in order to minimise theaverage displacement of the supergranular structures caused bythe solar di ff erential rotation. Therefore the coe ffi cients c , c ,and c vary from series to series. In the second step, the LCTalgorithm, with an enhanced sensitivity, is applied to obtain alow-noise-level displacement map. Finally, the di ff erential rota-tion (obtained in the first step) is added to the vector velocityfield obtained in the second step. Both steps can be divided intoseveral sub-steps, which do not di ff er much in application.1. The data series containing 96 averaged frames is tracked us-ing a selected rotation profile (Carrington rotation in the firststep, di ff erential rotation in the second step), and the framesare transformed into the Sanson-Flamsteed coordinate sys-tem to remove the geometrical distortion caused by the pro-jection onto the disc. The Sanson-Flamsteed (also known as“sinusoidal”) pseudo-cylindrical projection conserves the ar-eas and is therefore suitable for the preparation of the dataused by LCT.2. The tracked datacube undergoes k – ω filtering with the cut-o ff velocity of 1 500 m s − to suppress the noise comingmostly from the evolutionary changes of the supergranules.3. The LCT is applied: the lag between the correlated framesis 4 hours, the correlation window has a FWHM of 60 ′′ , themeasure of correlation is the sum of the absolute di ff erencesof the frames, and the nine-point method for calculation ofthe subpixel value of displacements is used. The calculatedvelocity field is averaged over the period of one day. Themagnitudes of the vectors are corrected using formula v x , corrected v y , corrected ! = . v x , computed v y , computed ! −
15 m s − ! . (1)This formula results from the direct comparison between thesynthetic data and the results of the displacement measuring pro-cedure applied to these synthetic data (see ˇSvanda et al., 2006).The processed dataset contains 1004 full-disc flow maps in502 days, when high-cadence MDI data were available and of agood quality. The velocity maps consist of many components on . ˇSvanda et al.: Large-scale horizontal flows in the solar photosphere V: A disconnection of bi-polar sunspot groups 3 -60-40-20 0 20 40 60-40 -30 -20 -10 0 10 20 30 40 A c t i v e r eg i on t il t [ deg ] Heliographic latitude [deg] -60-40-20 0 20 40 60-40 -30 -20 -10 0 10 20 30 40 A c t i v e r eg i on t il t [ deg ] Heliographic latitude [deg]
Fig. 1.
The Joy’s law in our sample of active regions.
Left – calculated for the sample of active regions, which emerged in CMDless than 60 degrees.
Right – the same for active regions, that emerged in CMD less than 60 degrees and spent at least 4 days withinCMD less than 60 degrees, so due to the averaging in time the measured tilts are less noisy.various spatial scales that cannot be reliably and unambiguouslyseparated. On the largest scales, the di ff erential rotation and themeridional circulation operate. We assume that these large-scalecomponents vary slowly with the time, but their changes mayinfluence the measurements of the proper motions of the activeregions. Therefore, from each velocity map we subtracted the13-day running average to remove the systematic changes in theflows on the largest scales. We assume that other componentswithin our resolution of 60 ′′ are the components of our inter-est. The removal of the long-term average will also suppress anypossible systematic errors.Based on the daily bulletins coming from the SpaceEnvironment Center of the National Oceanic and AtmosphericAdministration (SEC NOAA) we identified 564 labelled activeregions in these maps. From which 522 were observed in morethan one flow map. The theory predicts that the change in thedynamic regime should occur within a few (perhaps three) daysafter the magnetic regions has emerged in the photosphere. Fromthe sample we therefore have to choose only those active regionsthat have emerged in the visible hemisphere within a reasonabledistance from the central meridian, to avoid the influence of theedge e ff ects. Only 194 active regions in the dataset were seen forthe first time less than 60 degrees from the central meridian. Thisunfortunately means that the particular region could already beup to 1 day old at that time. Therefore, we included the mea-surements from the previous two days of the same region on theSun into the analysis. From this set, we selected 72 bi-polar re-gions that survived at least 4 days within the central meridiandistance (CMD) of less than 60 degrees. This drastic reductionof the sample was necessary in order to avoid the edge e ff ects.Furthermore, to show that the disconnection-like behaviour iscommon among active regions showing significant changes intheir dynamics over the lifespan, we chose another reduced sam-ple of active regions which possessed a standard deviation of therotation speed of more than 10 m s − over the lifespan. We have18 such active regions in the sample. Note that the 10 m s − cri-terion is arbitrary.The 24-hour averaged velocity maps and correspondingmagnetograms typically contain more than one active regionat once. Thus, the selection of individual active regions isneeded. This selection is based on the masks applied to thefull-disc displacement maps and magnetograms. The masks foreach active region were obtained in a semi-automatic way. Firstly, from the daily reports from the SEC NOAA ′′ , which created the final mask.This mask was then applied to the set of displacement maps andmagnetograms corresponding to days when the particular activeregion was recorded in the SEC NOAA reports, and two daysbefore.For each active region in the sample of 72, we computed theproperties suitable for a detailed investigation. To study the evo-lution of flows in the active regions and the properties describ-ing these active regions, we calculated the large-scale flow fieldin the area covered by the magnetic field (with the threshold of100 G), and the total unsigned flux. As additional parameters, wecomputed the mean magnetic field intensities in both the leadingand trailing polarities, the coordinates of the gravity centre ofboth polarities, and the mean proper motions of both polaritiesin the frame co-rotating with the mean rotation rate of the activeregion. All these properties are sampled by 12 hours and coverthe whole interval, when the particular active region was locatedwithin a CMD of 60 degrees.We searched for any significant changes in the dynamics,which could be caused by the disconnection of the magneticstructures from their deeper roots. The expected change shouldreveal itself as a sudden deceleration of the proper motion of theactive region, because the radial gradient of the mean plasma ro-tation is negative in near-surface subphotospheric layers. All theactive regions in the sample underwent this investigation in or-der to obtain a homogeneous set of active regions properties toexamine.
3. Results
The aim of this section is to show that the sample of active re-gions we have available displays the widely-accepted statisticalproperties of the magnetic field in the solar photosphere and is
M. ˇSvanda et al.: Large-scale horizontal flows in the solar photosphere V: A disconnection of bi-polar sunspot groups therefore suitable for more detailed analysis of the proper dy-namics of active regions. We have selected two basic propertiesto test: the Joy’s law and the polarity separation evolution.As first noted by Hale et al. (1919), the bi-polar sunspotgroups are tilted with respect to the zonal direction. The lati-tudes of the leading polarities are on average lower than the lat-itudes of the trailing ones. The so-called
Joy’s law shows that,statistically, the bi-polar regions are more tilted, if they are lo-cated at higher latitudes than the ones located at lower latitudes.The tilts are considered essential by kinematic dynamo mod-els (e.g. Leighton, 1969; Wang et al., 1991) and are often ex-plained as the action of the Coriolis force on rising flux tube(e.g. D’Silva & Choudhuri, 1993).To test the Joy’s law in our sample, we calculated the averagemagnetogram for each active region that emerged and remainedin a CMD of less than 60 degrees. The tilt was measured from thecentre-of-mass position of both polarities. The results are shownin Fig. 1. We clearly see that the tilts are mostly positive on thesouthern hemisphere and negative on the northern hemisphere,i.e., the leading parts of the bi-polar active regions are closer tothe equator than the following ones. Joy’s law itself is not nicelyrecovered. However, as pointed out in Kosovichev & Stenflo(2008), Joy’s law holds only statistically and we cannot expectmuch better results than those presented in Fig. 1. Our resultsare very similar to those in Kosovichev & Stenflo (2008). Othere ff ects, such as a dependence on the phase of the solar cycleas noted by Ulrich et al. (2002) may also take place. To sepa-rate such subtle e ff ects the sample we have at our disposal is toosparse.Another property tested was the evolution of the separationdistance between the leading and the following polarity in thespot group. Many works (e.g van Driel-Gesztelyi & Petrovay,1990; Moreno-Insertis et al., 1994; Sobotka & Roudier, 2007)pointed out that during the evolution, the separation betweenthe leading and the following polarities grows. The active re-gion increases its size in the longitudinal direction. It is ofteninterpreted as the result of the stretch caused by the di ff erentialrotation on the tilted region. The trailing polarity is at higherlatitudes, therefore it senses a slower rotation than the leadingpart. We used our sample to measure this quantity. The separa-tion of the leading polarity from the following one is defined asthe distance between the gravity centres of both polarities in theCarrington coordinate system. We constructed the histogram ofthe separation speeds based on the sample of 194 active regions.The results are shown in Fig. 2. We see that, on average, the sep-aration of polarities in the active regions is increasing with time,with the median speed of 0.3 heliographic degree per day, whichcorresponds to 45 m s − on the solar equator. As Ruˇzdjak et al. (2004) showed in a nice paper, based on thelong-term observations of sunspots at Greenwich observatorycovering more than a century, that rotation of sunspots usuallyslowed down during their evolution. In fact, this observationwas initially shown by Tuominen (1962). These papers primarilydeal with the deceleration of sunspots in term of linear relation-ship with time. However, there is no principal reason to assumethat in a highly dynamic layer, such as is the convection zone,the deceleration should be monotonic. Sivaraman et al. (2003),using Kodaikanal data, found an opposite behaviour, i.e. that therotation rates of spot groups increase with their age. They sortedthe sunspot groups according to their life spans from one to eightdays, and found that the rotation of the groups on the first day F r equen cy [ % ] Average increase of polarity separation [hel. deg/day]
Fig. 2.
The histogram of the polarity-separation speed for thesample of 194 active regions. It is evident that for most of thebi-polar active regions, the polarities are continuously separat-ing. The characteristic (median) speed is overplotted by verticalline and it is roughly 0.3 heliographic degree per day.of their life-cycle is the slowest. They then proceed to acceler-ate with age and reach the maximum velocity of rotation the daybefore dissolution.We studied the evolution of the proper velocities of thesunspots with respect to the averaged large-scale background,with a sampling of 12 hours. This sampling allowed for animprovement of the statistics compared to the simple averageover the active region lifespan. Four di ff erent trends, which arepresent in the sample, are displayed in Fig. 3. The error-barsrepresent the statistical errors showing the 1- σ scatter of the ve-locities over the whole active region.We observe that for two of these trends, i.e., continuousacceleration and variable behaviour, the change in the rotationspeed is below 20 m s − . On the contrary, the other two casesdisplay more significant changes. Table 1 contains the detailed -40-30-20-10 0 10 20 30 40
50 60 -1 0 1 2 3 4 5 6 7 8 9 A v e r age r o t a t i on r a t e [ m s - ] Days after appearance
NOAA 8183
NOAA 8038NOAA 9408NOAA 8523
Fig. 3.
Four di ff erent trends in the active region speed evolu-tion, which are present in our data sample. The regions arecontinuously decelerating (NOAA 8183), or continuously ac-celerating (NOAA 8038). Less clear trends are also noticed,such as the early acceleration followed by a rapid deceleration(NOAA 9408) and very variable behaviour (NOAA 8523). . ˇSvanda et al.: Large-scale horizontal flows in the solar photosphere V: A disconnection of bi-polar sunspot groups 5 A R a v e r age r o t a t i on s peed [ m / s ] A R a v e r age r o t a t i on s peed [ m / s ] −4 −2 0 2 4 6 8−200204060 Days from maximum A R a v e r age r o t a t i on s peed [ m / s ] A R a v e r age r o t a t i on s peed [ m / s ] Fig. 4.
The division of the sample of the active regions into four dynamically di ff erent groups is based on the di ff erent shape ofthe trend of the active regions proper rotation speed with time. We divided 72 active regions in the group showing the continuousacceleration (upper left), continuous deceleration (upper right), acceleration followed by a sudden deceleration (bottom left), andthe varying rotation speed (bottom right). With the thick line, the average trend among the displayed active regions is overplotted.Except for the third case, individual plots were not aligned. In the case with the possible dynamical disconnection imprint, wealigned the plots in time on the significant feature in the active regions lifetime, which is denoted by the one-to-two days lastingpeak.results for all active regions in the sample. The sample is dividedinto four types based on the dynamic behaviour: The active re-gion is continuously accelerating ( A ), decelerating ( D ), showsthe signs of the dynamic disconnection ( DC ), or behaves errati-cally ( var ).The tabulated results show that 33 % of the active regionsin our sample first accelerate and then suddenly decelerate. In13 % of cases the active regions depict a continuous acceleration,while in 15 % of cases a continuous deceleration is observed.Finally, in the remaining 39 % a variable behaviour is presentwhen the proper velocity does not change significantly or sys-tematically in the active region lifespan. The active regions ac-celerate mostly during the first few days of their lifespan. Table 1also contains a number of other values describing the character-istic properties of the active regions. These include the measureof the average slope of the deceleration or acceleration in timefor active regions falling in the corresponding category, the vari-ance of the rotation speed over the life-cycle of the active regionsshowing variable behaviour in their rotation speed. The measure-ments obtained for the active regions showing first accelerationand then deceleration can also be found in the same table, andare discussed in the following sections.Given the number of active regions in the sample, it is notfeasible to demonstrate the exact trends in proper rotation evo-lution for each active region we studied. Instead, we associatethese trends to the above-mentioned corresponding groups, with-out making explicitly clear which plot belongs to which activeregion. These plots can be seen in Fig. 4 and they demonstrate the overall trend in each selected group. Except for the thirdgroup, no alignment of the individual curves were done. Thethird group however contains a significant feature in the trend,a large peak lasting one to two days. The curves were thereforealigned in time using this feature. The thick solid line indicatesthe averages of all the trends contained in the panels. Using thisaverage trend we are able to clearly distinguish di ff erent regimesfor active regions showing continuous deceleration and for thoserepresenting the disconnecting group. Although it is di ffi cult toclearly see the di ff erence between the group with the assignedcontinuous acceleration and the variable behaviour, in the for-mer case one can see the overall increasing rotation speed withtime when following individual trends. From the sample, 18 active regions display a variance of speedevolution larger than 10 m s − , and from this 18, 78 % are of thetype which display an initial acceleration followed by a suddendeceleration. We assume that these active regions are represen-tative of the sample which contain clear signatures of dynamicdisconnection.We assume that disconnection is exhibited as a sudden de-crease in the proper speed, shortly before the maximum in areais reached. We further assume that the disconnection takes placeat the instant of sudden decrease in speed. The upper part of theformer flux-tube continues to rise and feeds more magnetic fluxinto the photosphere. Therefore the area of the magnetic field M. ˇSvanda et al.: Large-scale horizontal flows in the solar photosphere V: A disconnection of bi-polar sunspot groups −60−40−20 0 20 40 60 0 2 4 6 8 10 A v e r age r o t a t i on r a t e [ m s − ] Days after appearance
Active region rotation rate
NOAA 8524 , first on 1999.04.25, l=29 o , b=21 o A r ea [ he li og r aph i c deg r ee s ] Days after appearance
Areas in active region (thresh 20 Gauss)
Active region averageLeading polarityFollowing polarity−40−20 0 20 40 0 2 4 6 8 10 P o l a r i t y s peed [ m s − ] Days after appearance
Polarities proper motion in the co−rotating frame
0 2 4 6 8 10 T o t a l f l u x [ W b ] Days after appearance
Total flux evolution
Leading polarity statistics M agne t i c f i e l d i n t en s i t y [ k G au ss ] Following polarity statistics
Fig. 6.
The example of the evolution of flows, active region area, the total flux, and the histogram of the magnetic field intensities. Wesee the overall acceleration in first two days (in this phase, the polarities separate rapidly), and sudden deceleration after this instant.The area of the active region continues to grow for another two days, the total flux in the active region for three days (however,usually the maximum in the area corresponds with the maximum in the total flux). In the bottom row of figures, in each column thehistogram of the magnetic field strength in the region-of-interest in the particular part is displayed in by colours. The evolution ofthe dynamics seems very symmetrical, which is not true for the histograms of the magnetic field strength. The actual evolution ofthe flows in this particular active region is displayed in Fig. 7.in the photosphere keeps growing until the disconnected part isfully emerged, after which the flux starts to disperse and the ac-tive region area decreases. In Fig. 5 we display the speed at theassumed disconnection point (the disconnection speed , v dis ) and the speed in the following minimum (the relaxed speed , v relax ),these numbers are also summarised in Table 1. The thick linesemphasise the set of 14 active regions which display a signifi- . ˇSvanda et al.: Large-scale horizontal flows in the solar photosphere V: A disconnection of bi-polar sunspot groups 7 H e li g r a ph i c l a t i t ud e [ d e g ] Heligraphic longitude [deg] day 9day 8day 7 day 6day 5day 4 day 3day 2day 1
Fig. 7.
The mosaic of the evolution of the flow field in the active region NOAA 8524. The background colours represent the large-scale magnetic field in the region, the grey arrows the the flows in the area. The di ff erently coloured arrows in the magnetized areasrepresent the velocities that were used for the studies of the dynamics of this particular active regions.cant change in proper speed during their evolution, and whichalso exhibit the signs of disconnection.The typical drop of the speed during disconnection is ∼
50 m s − . This value corresponds well with the bi-modal distri-bution of the equatorial rotation rates in the presence of sunspots -30-20-10 0 10 20 30 40
50 60 70
50 100 150 200 250 300 350 400 450 500 550 600 R o t a t i on s peed [ m s - ] Area [hel. degrees ]Disconnection speedRelaxed speed Fig. 5.
The jump in the speed, which can be caused by the dy-namic disconnection. For 23 active regions from the sample of72 we see that the speed in the pre-disconnection phase is bysome 50 m s − larger than in the post-disconnection phase. Thisvalue does not depend on the active region area. By the thicklines, active regions belonging to the subsample showing signif-icant change in the speed during the lifespan is emphasised. (with velocities clustered around 1850 m s − and 1910 m s − ), asfound by ˇSvanda et al. (2008). A quick check using the sunspotdrawing archives showed that the “fast” group contained mostlythe young and growing regions (which corresponds to the pre-disconnection phase in the current study), while the second“scattered” group contained mostly old and dispersing regions.In the current study this corresponds to the post-disconnectionphase.Although our analysis is based on the mean rotation rate con-sidered for the whole active region, the signatures of the dis-connection should be detectable in both polarities. However, itis di ffi cult to measure this phenomenon, because the motionsof polarities in the co-rotating frame are an order of magnitudefaster. The dynamics in the co-rotating frame (as displayed e.g.in Fig. 6) is usually very symmetrical in both polarities. Takinga careful look at this issue we found that in some 70 % of ac-tive regions in the sample showing clear signatures of the dis-connection, the disconnection features can be detected in bothpolarities, while in 30 % it is clear only in one polarity. For afew cases, the time when disconnection occurs in opposite po-larities di ff ers by approximately 1 day. This issue is probablyrelated to the configuration and asymmetry of the magnetic fieldin the particular active region. The disconnection is proposed forflux-tubes that form sunspots or pores, this does not apply to themagnetic field forming the plage. Unfortunately, as our methodallows the measurement of large-scale features, we cannot ad-dress this issue properly, and it can possibly a ff ect our results. M. ˇSvanda et al.: Large-scale horizontal flows in the solar photosphere V: A disconnection of bi-polar sunspot groups
We observe a systematic shift t lag between the time of the dy-namic regime change and the time of the maximum in the area(see e.g. Fig. 6). We interpret this lag as the time which the fluxtube forming the magnetic island rises from its parental mag-netic structure to the surface after the disconnection. After thedisconnection takes place, no more magnetic field is fed into themagnetic island and after its entire emergence the photosphericmagnetic field starts to diminish. In all but two cases this lagis positive, therefore fulfilling the above mentioned assumption(see Table 1).The average lag is 1 . ± . v rise , which is unknown andmust be determined for each case, e.g., by numerical simulations(such as in e.g. Fan et al., 1993). We may roughly estimate thisrising speed by various characteristic speeds in the convectionzone, to put limits on the disconnection depth. Various speeds inthe upper 70 Mm of the convection zone are displayed in Fig. 9.The most reasonable estimate of the rising speed is theAlfven speed, c A , c A = B √ µρ , (2)because the perturbations in the magnetic field usually propagatewith this speed (e.g. Parker, 1975). In the above equation B is theintensity of the magnetic field, µ is the permeability, and ρ is theplasma density. Based on the solar plasma parameters containedin the standard Model S (Christensen-Dalsgaard et al., 1996) at-mosphere, we may estimate the rising time t rise of the flux tubefrom the given depth in the convection zone R start onto the sur-face: t rise = R ⊙ Z R start d rc A ( r ) = R ⊙ Z R start p µρ ( r ) B d r . (3)Assuming a constant 1-kG flux-tube emerging with theAlfven speed, the theoretical t lag is 180 days if the flux-tubeemerges from the bottom of the convection zone, and 7 dayswhen emerging from the subsurface shear at 0.95 R ⊙ . Even the10 -G field would rise from the base of the convection zone forapproximately one month. Although these numbers represent avery rough estimate, they show that a measured time-lag slightlymore than 1 day corresponds to the disconnection location in theshallow subsurface layers.In Fig. 8 we show the theoretical rising time depending onthe initial depth and the strength of the flux tube that is con-sidered constant during the rising process. The measured lag isdisplayed in contours. We have to consider our theoretical resultsas an estimate, because the calculation does not include the flux-tube expansion, which naturally influences the rising speed. Theprecise modelling and the reproduction of the situation wouldbe very di ffi cult, because the initial properties of the flux tubedeep in the convection zone are unknown. We believe that ourestimate shows the essence of the problem. Inverting (3) with t rise ∼ t lag we can estimate the disconnection depth for the par-ticular active region.The Alfven speed gives the smallest disconnection depthestimate. Buoyant ascent of the flux tube requires the super-equipartition field, e.g., c A > v c , where v c is a convection speed.Using the convection speed as the rising speed after the assumeddisconnection in our study therefore provides the largest discon-nection depth estimate. It is clear that the presence of the strong R i s i ng t i m e [ da ys ]
0 10 20 30 40 50Depth [Mm]01000200030004000 F l u x - t ube s t r eng t h [ G au ss ] Fig. 8.
The theoretical time-shift between the disconnection timeand the time when the maximum in area is reached, based onthe assumption that flux-tube rises with the Alfven speed as thefunction of depth and flux-tube strength. The measured time-shift including the error is displayed in contours. This very roughestimate shows that the disconnection cannot occur deeper thansome 40 Mm for 4-kG flux-tube to reproduce the observed be-haviour. The Alfven speed computation is based on Model S ofChristensen-Dalsgaard et al. (1996). The real rising speed of anexpanding flux-tube should not di ff er from the Alfven speed inthe order of magnitude.magnetic field alters convection and therefore probably changesthe convection speed. However, the main purpose of this calcu-lation is to bound the disconnection depth, therefore the use ofthe model convection speed without the influence of the mag-netic field is justified. Again, without proper modelling it is notpossible to go beyond presented estimates.The mixing-length (e.g. Stix, 1989) convection speed in theSun can be computed from a known solar model (e.g., Model Sin our case) using the following formula: v c = r − Gm ( r ) r A ∗ ( r ) α H p ( r ) , (4)where m ( r ) is the total mass in the sphere with radius r , α is themixing-length parameter, H p is a pressure scale height, and A ∗ is a convection parameter, A ∗ ( r ) = γ ( r ) d ln p ( r )d ln r − d ln ρ ( r )d ln r , (5)where γ , p , and ρ represent the adiabatic exponent, pressure, anddensity. The rise of the flux-tube with a convection speed impliesthat the strength of the field is the equipartition one.In Table 1 we provide the range of the disconnection depthsfor each active region studied. We observed that the disconnec-tion occurs within a few tens of Mm in depth. The maximumintensity of the magnetic field used for the calculation of theAlfven speed is determined from the MDI magnetograms. Weneed to keep in mind that the actual strength of the original fluxtube (also the rising time) may be di ff erent from the estimatedone.
4. Conclusions
We conclude that the observed dynamical behaviour of a signif-icant fraction of active regions in the homogeneous sample inthe past solar cycle is compatible with a dynamic disconnectionof the bi-polar active regions from their parental magnetic roots. . ˇSvanda et al.: Large-scale horizontal flows in the solar photosphere V: A disconnection of bi-polar sunspot groups 9
In our sample, 33 % of active regions display the signs of thedisconnection. In the reduced sample with significant changes inthe dynamics, 78 % show the desired behaviour. The disconnect-ing active regions display a lag between the disconnection timeand the instant when the maximum in area is established. If weassume that this lag is caused by the continuous rise of the dis-connected magnetic field up to the photosphere, we may estimatethe depth where disconnection takes place. We estimate that dis-connection takes place within few tens of Mm below the solarsurface, not in disagreement with 1-D simulations conducted bySch¨ussler & Rempel (2005).The numerical simulations done by Sch¨ussler & Rempel(2005) predict that the disconnection should happen for the sig-nificant fraction of bi-polar active regions, if not for all of them.However, our results show the clear attributes of the disconnec-tion in only one third of the studied cases. We speculate that inother cases, disconnection does not occur during the observedspan (e.g. before emergence into the photosphere in the case ofcontinuously decelerating active regions) or that the influenceof the proper motions of the magnetic features by the turbulentbackground is too high. Therefore we cannot reliably separatethe attributes of the disconnection from other motions.The mechanism of the dynamic disconnection is proposedfor strong flux-tubes that form sunspots or pores. With our in-vestigation method we unfortunately do not have su ffi cient reso-lution to distinguish between the motion of magnetic structuresin, e.g. sunspots, from the ones in the plage region, which prob-ably embody di ff erent dynamic properties.Our present study does not provide a definitive answer onthe question of whether the origin of magnetic activity is in thedeep or shallow dynamo action. Both approaches require someform of disconnection of the surface magnetic field to allow thedispersed flux to migrate towards the solar poles. The deep dy-namo based model assumed by Sch¨ussler & Rempel (2005) pro-vides predictions for particular active regions dynamics, whichwe have tested. Although the results of this test favour the modelassumed, they are not robust enough to rule out other interpreta-tions. The phenomenon of dynamic disconnection requires fur-ther investigation using high resolution methods and by localhelioseismology, which proves its power in investigating deep S peed [ m / s ] Depth [Mm]Alfven speed [100 G]Alfven speed [1 kG]Alfven speed [5 kG]Convection speed
Fig. 9.
The trends in various speeds in the upper part of the solarconvection zone. The Alfven speed and the convection speed areused to estimate the limits in depths, where the disconnectiontakes place. The computation of the speed trends is based onmodel S. structure of sunspots (e.g. Moradi et al., 2009). Clear, deep mag-netic field signatures would rule out a group of models assuminga shallow dynamo and provide other tests for rising flux-tubesmodels.
Acknowledgements.
The authors were supported by the Grant Agency ofAcademy of Sciences of the Czech Republic under grant IAA30030808.The Astronomical Institute of ASCR is working on the Research projectAV0Z10030501 (Academy of Sciences of CR), the Astronomical Institute ofCharles University on the Research program MSM0021620860 (Ministry ofEducation of CR). SOHO is a project of international cooperation between ESAand NASA. The authors thank the referee Roger K. Ulrich, whose comments andsuggestions significantly improved the quality of the study and its presentation,and also Hamed Moradi for correcting the English.
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Table 1.
The studied properties of 72 active regions in our sample. Active regions of type DC show signatures of dynamic disconnection. NOAA From To Type Max. intensity v dis v relax Slope Variance t lag Disc. depth
Gauss m s − m s − m s − day − m s − days Mm0651 2004 / /
13 2004 / /
22 var 700 5 . / /
24 2004 / /
03 DC 100 16(3) − − . . . / /
27 2005 / /
05 DC 1300 14(6) − − . . . / /
29 2005 / /
09 DC 1300 31(9) − − . . . / /
28 2005 / /
06 var 800 6 . / /
22 2005 / /
31 A 1400 0 . / /
27 2005 / /
04 DC 700 29(9) 0(0) − . . . / /
01 1996 / /
11 var 200 3 . / /
02 1996 / /
12 var 700 4 . / /
14 1997 / /
19 var 500 4 . / /
06 1997 / /
16 A 700 1 . / /
15 1997 / /
25 DC 800 18(7) − − . . . / /
29 1997 / /
09 var 1000 15 . / /
08 1997 / /
18 var 300 4 . / /
10 1997 / /
19 A 400 0 . / /
02 1997 / /
10 D 200 − . / /
10 1998 / /
18 D 1300 − . / /
18 1998 / /
26 var 300 3 . / /
20 1998 / /
28 var 800 4 . / /
24 1998 / /
02 A 300 0 . / /
06 1998 / /
13 D 400 − . / /
11 1998 / /
21 D 1200 − . / /
13 1998 / /
20 var 200 4 . / /
16 1998 / /
21 A 300 0 . / /
21 1998 / /
01 A 1000 − . / /
22 1998 / /
02 DC 800 19(6) − − . . . / /
05 1998 / /
15 var 1000 4 . / /
07 1998 / /
16 var 200 6 . / /
11 1998 / /
21 D 800 − . / /
18 1998 / /
28 D 100 − . / /
19 1998 / /
26 var 800 3 . / /
25 1998 / /
02 DC 200 42(11) − − . . . / /
30 1998 / /
07 var 500 6 . / /
02 1998 / /
09 var 1800 4 . / /
03 1999 / /
12 var 200 5 . / /
05 1999 / /
14 var 500 8 . / /
06 1999 / /
16 var 1300 4 . / /
07 1999 / /
17 var 800 6 . / /
08 1999 / /
17 var 800 4 . / /
11 1999 / /
19 D 800 − . / /
23 1999 / /
02 DC 300 3(2) − − . . . / /
23 1999 / /
02 DC 1200 42(19) 2(5) − . . . / /
27 1999 / /
07 var 200 3 . / /
01 1999 / /
12 D 500 − . / /
05 1999 / /
14 var 1100 5 . / /
28 2000 / /
07 DC 900 28(10) − . . . / /
31 2000 / /
08 var 400 3 . / /
03 2000 / /
13 A 500 − . / /
03 2000 / /
13 DC 600 12(2) − − . . . / /
07 2000 / /
15 DC 500 10(5) − − . . . / /
09 2000 / /
19 DC 600 10(3) − − . . . / /
15 2000 / /
23 DC 500 16(10) − − . . . / /
21 2000 / /
29 var 500 5 . / /
25 2000 / /
05 var 600 3 . / /
01 2001 / /
06 DC 500 46(10) 0(0) 0 . . . / /
23 2001 / /
30 A 400 5 . / /
25 2001 / /
03 D 1300 − . / /
27 2001 / /
03 DC 1600 38(7) − − . . . / /
08 2001 / /
16 DC 700 33(14) − − . . . / /
10 2001 / /
18 var 700 7 . . ˇSvanda et al.: Large-scale horizontal flows in the solar photosphere V: A disconnection of bi-polar sunspot groups 11 Table 1. continued.
NOAA From To Type Max. intensity v dis v relax Slope Variance t lag Disc. depth
Gauss m s − m s − m s − day − m s − days Mm9431 2001 / /
16 2001 / /
26 DC 700 23(5) − − . . . / /
16 2001 / /
24 DC 900 19(8) − − . . . / /
26 2001 / /
05 DC 1200 21(11) − − . . . / /
26 2001 / /
06 D 400 4 . / /
17 2002 / /
24 DC 1200 25(15) − − . . . / /
22 2002 / /
29 var 1500 3 . / /
22 2002 / /
01 A 200 − . / /
01 2002 / /
11 var 500 4 . / /
01 2002 / /
10 D 500 0 . / /
01 2002 / /
10 DC 400 13(4) − − . . . / /
10 2002 / /
19 var 700 5 . / /
26 2002 / /
02 DC 1500 0(3) − − . . ..