Are the brightest coronal loops always rooted in mixed-polarity magnetic flux?
Sanjiv K. Tiwari, Caroline L. Evans, Navdeep K. Panesar, Avijeet Prasad, Ronald L. Moore
DD raft version F ebruary
23, 2021Typeset using L A TEX twocolumn style in AASTeX63
Are the brightest coronal loops always rooted in mixed-polarity magnetic flux? S anjiv K. T iwari , C aroline L. E vans , N avdeep K. P anesar , A vijeet P rasad , and R onald L. M oore
Lockheed Martin Solar and Astrophysics Laboratory, 3251 Hanover Street, Bldg. 252, Palo Alto, CA 94304, USA Bay Area Environmental Research Institute, NASA Research Park, Mo ff ett Field, CA 94035, USA Department of Physics, Davidson College, Box 6910, Davidson, NC 28035, USA Department of Physics, North Carolina State University, Raleigh, NC 27695, USA Center for Space and Aeronomic Research, The University of Alabama in Huntsville, 320 Sparkman Drive, Huntsville, AL 35805, USA NASA Marshall Space Flight Center, Mail Code ST 13, Huntsville, AL 35812, USA
ABSTRACTA recent study demonstrated that freedom of convection and strength of magnetic field in the photosphericfeet of active-region (AR) coronal loops, together, can engender or quench heating in them. Other studies stressthat magnetic flux cancellation at the loop-feet potentially drives heating in loops. We follow 24-hour moviesof a bipolar AR, using EUV images from SDO / AIA and line-of-sight (LOS) magnetograms from SDO / HMI,to examine magnetic polarities at the feet of 23 of the brightest coronal loops. We derived FeXVIII emission(hot-94) images (using the Warren et al. method) to select the hottest / brightest loops, and confirm their foot-point locations via non-force-free field extrapolations. From 6” ×
6” boxes centered at each loop foot in LOSmagnetograms we find that ∼
40% of the loops have both feet in unipolar flux, and ∼
60% of the loops have atleast one foot in mixed-polarity flux. The loops with both feet unipolar are ∼
15% shorter lived on average thanthe loops having mixed-polarity foot-point flux, but their peak-intensity averages are equal. The presence ofmixed-polarity magnetic flux in at least one foot of majority of the loops suggests that flux cancellation at thefootpoints may drive most of the heating. But, the absence of mixed-polarity magnetic flux (to the detectionlimit of HMI) in ∼
40% of the loops suggests that flux cancellation may not be necessary to drive heating incoronal loops – magnetoconvection and field strength at both loop feet possibly drive much of the heating, evenin the cases where a loop foot presents mixed-polarity magnetic flux.
Keywords:
Sun – chromosphere – corona – photosphere, magnetic field INTRODUCTIONMagnetic energy dissipated in coronal loops by unknownprocesses heats the Sun’s corona to millions of Kelvin. Thebrightest and hottest extreme ultraviolet (EUV) and X-ray so-lar coronal loops are rooted in strong magnetic flux in ac-tive regions (ARs) (Golub et al. 1980; Fisher et al. 1998;Dahlburg et al. 2018; Ugarte-Urra et al. 2019; Asgari-Targhiet al. 2019). These loops have temperatures of 2-6 MK,or more. The processes for heating them to these temper-atures remain ill-determined (Zirker 1993; Schrijver et al.1998; Moore et al. 1999; Aschwanden 2005; Katsukawa &Tsuneta 2005; Klimchuk 2006; Reale 2014; Hinode ReviewTeam et al. 2019). The two most well-known mechanismsthat could explain these temperatures are magentohydrody-namic (MHD) waves (e.g., van Ballegooijen et al. 2011, andreferences therein) and nanoflare heating (Parker 1972, 1983,1988).In both cases, magnetoconvection most probably drives themagnetic energy input (e.g., Tiwari et al. 2017). Photosphericconvection can produce MHD waves that transport energy to higher parts of the Sun’s atmosphere (Priest et al. 1994,2002). Photospheric convective motion can also randomlyshu ffl e the feet of the coronal loops so that they become en-tangled and braided, dissipating the magnetic energy by cur-rent sheet dissipation in the higher solar atmosphere (Parker1983, 1988). Recent observations of an AR and modellingshow evidence of braided magnetic structures in the corona(Cirtain et al. 2013; Thalmann et al. 2014; Tiwari et al. 2014;Pontin et al. 2017).Some studies (Falconer et al. 1997; Tiwari et al. 2014,2017, 2019; Chitta et al. 2017, 2018; Priest et al. 2018) findthe presence of mixed-polarity magnetic flux at the feet of thebrightest coronal loops and suggest a third manner of drivingheating – by flux cancellation at the loop feet. According tothese studies, the brightest AR coronal loops most frequentlyhave at least one footpoint in a region of mixed-polarity mag-netic flux. This implies that over time, magnetoconvectioncauses an increase in the injection of free magnetic energyinto the brightest coronal loops via some consequence ofthe opposite-polarity flux, which is most probably magnetic a r X i v : . [ a s t r o - ph . S R ] F e b flux cancellation, often accompanied by small-scale mag-netic flux emergence (Tiwari et al. 2019; S¸ ahin et al. 2019).Magnetic reconnection events taking place very low in thechromosphere, accompanied by magnetic flux cancellation,evidenced by fine-scale explosive events and chromosphericinverted-Y-shaped jets in the lower solar atmosphere at thesesites, can feed energy and hot plasma into the corona (Chittaet al. 2017; Tiwari et al. 2019; Panesar et al. 2019, 2020).Magnetic flux cancellation is most probably the result ofsubmergence of lower reconnected loops (e.g., Tiwari et al.2019, and references therein). Priest et al. (2018) have de-scribed a theoretical model of how chromospheric and coro-nal heating of loops might depend on flux cancellation speed,flux size, and field strength in the loop (see also Syntelis &Priest 2020). An observational test supporting this model wasrecently performed by Park (2020).Tiwari et al. (2017) demonstrated that photospheric mag-netic rooting plays an important role in determining theamount of heating in AR coronal loops – freedom of con-vection and strength of magnetic field in the loop-feet, to-gether, can enhance or suppress heating in coronal loops. Us-ing EUV observations and non-linear force-free modelling oftwo ARs they found that the hottest loops of an AR are theones connecting sunspot umbra / penumbra at one end to (a)penumbra, (b) unipolar plage, or (c) mixed-polarity plage onthe other end. The loops connecting dark sunspot umbra atboth ends were not visible in EUV images. Thus, these loopsare the coolest loops, despite being rooted in the strongestmagnetic field regions. They concluded that both the fieldstrength and freedom of convection at the loop feet play cru-cial role in determining the heating magnitude of the loop. Asmentioned earlier, some recent investigations stress more onthe loop-foot mixed-polarity (above-mentioned connectivity‘c’), suggesting that flux cancellation is involved in heatingchromospheric and coronal loops. In the present work we in-vestigate whether all or most of the hottest loops of an ARhave mixed-polarity magnetic flux at their feet. If not, whatpercentage of them are rooted in unipolar magnetic flux ateach end of the loop?If it turns out that at least one foot of each hot loop hasmixed-polarity magnetic flux, then it would provide strongevidence to the idea of flux cancellation being involved indriving heating of coronal loops. The presence of unipolarfield at both feet of hot loops will support the idea that (ir-respective of polarity mixture at the loop feet) heating of thehottest coronal loops depends primarily on the freedom ofconvection at the loop feet, together with the strength of themagnetic field there (Tiwari et al. 2017), not primarily on fluxcancellation. DATA AND MODELLING We examine EUV / UV images of NOAA AR 12712 ob-tained with Atmospheric Imaging Assembly (AIA: Lemenet al. 2012) on-board Solar Dynamics Observatory (SDOPesnell et al. 2012) to investigate the hot emissions cen-tered on the Fe XVIII line (6-8 MK), by treating the datato omit the 1 MK plasma detection. To isolate the brightestand hottest coronal loops of the AR in question, we use themethod laid out in Warren et al. (2012) to subtract out thewarm component of the 94 Å intensity: I warm = . (cid:88) i = a i (cid:34) f I + (1 − f ) I . (cid:35) i , (1)where I and I are the respective intensities of AIA 171Å and AIA 193 Å; f is determined to be 0.31; a i are, in order, − . × − , . × − , . × − , and 2 . × − .We refer to Fe XVIII emission images calculated by theabove method as hot 94 images. To create the hot 94 im-ages, we downloaded 94 Å, 171 Å, and 193 Å AIA data at athree-minute cadence for the 24 hours of May 29, 2018 fromJoint Science Operations Center (JSOC) with two im patchparameters: (1) a center at -230”, 270” and (2) a box heightand width of 600” (Figure 1). The EUV channels have a 12-second temporal cadence and a 1.2” resolution (0.6” pixelsize) (Lemen et al. 2012). However a 3-minute cadenceworked well for our purpose because most of the hottestloops lived well beyond 3-minutes, the shortest one livingfor about 12 minutes (see Table 1).The 94 Å channel captures the characteristic emission ofFe XVIII from plasma at 6-8 MK, but also captures emis-sion of plasma around 1 MK (Warren et al. 2012). The 171Å channel detects the characteristic emission of the Fe IXline from plasma at about 0.8 MK and the 193 Å channelshows the characteristic emission of Fe XII from plasma ataround 1.5 MK (Reale et al. 2011; Lemen et al. 2012). Allimages were normalized by dividing each image by its expo-sure time.For investigating photospheric magnetic flux polarity at theloop feet, we downloaded line-of-sight (LOS) magnetogramsfrom the Helioseismic and Magnetic Imager (HMI: Schouet al. 2012; Scherrer et al. 2012), also onboard SDO, of thesame field of view (FOV) as AIA EUV images at a 3-minutecadence, the same cadence as used for AIA images. In Fig-ure 1, we show our active region NOAA 12712 in UV, EUV,processed AIA images and a processed HMI magnetogram.This AR is of interest because it is a bipolar region observedclose to the solar disk center during an otherwise quiet Sun.This AR was also observed on this day (May 29, 2018) byHi-C 2.1 (Rachmeler et al. 2019).All our generated maps (AIA and HMI) were processedand de-rotated using SolarSoft routines (Freeland & Handy1998). We discarded the one time frame in this set that showsvery large noise. We examined the UV AIA data at 1600 Å Figure 1.
Context images of the NOAA AR 12712 on 29-May-2018 at about 05:03 UT. The six image panels contain six di ff erent wavelengths– Top Left:
94 Å,
Top Center:
171 Å,
Top Right:
193 Å,
Bottom Left: our created hot 94,
Bottom Center:
HMI LOS magnetogram,
BottomRight: to confirm alignment between each of the EUV wavelengthsand LOS magnetograms. After these data treatments we fol-lowed each hot loop in our 24-hour span of observationsto select the most clearly visible hot loops, which are suf-ficiently isolated from other hot loops in the surroundings.This led to selection of 23 hot loops in the 24 hours of data.For each loop, we made a light curve of the emission in a 2”x 2” box placed on the brightest segment of the loop top toobtain the loop’s start, peak-brightness, and end times.Note that in a few cases there are two loops tangled in theway that they have a single foot on one end. Because theseloops are spatially isolated from other bright loops, we in-cluded them in our study and counted these as two separateloops.After visual identification of the footpoints of the hottestcoronal loops using a zoomed-in FOV, we chose the loca-tions and placed boxes (of size 6” × ×
2” box duringthe peak time of each loop. The box was placed at severalplaces along the loop to find out the maximum value of theintegrated intensity. For each loop, we used the light curveof the 2” x 2” box to find the start time, the peak-brightnesstime, and the end time of the loop, and to obtain the intensityof the emission in the box at the peak-brightness time (theloop’s peak intensity given in Table 1). The light curves forthree loops are shown in Figure 3. RESULTSWe found 23 of the brightest coronal loops that qualify un-der our selection criterion for loops described in Section 2(e.g., loops should be bright and hot enough to be clearlyvisible in hot 94, they should be fairly isolated from otherloops in the surroundings, and peak well in light curves). InTable 1, we list the 23 selected hot coronal loops, three ofwhich are presented in detail in Figures 2, and 4. Each of the23 loops is marked by pink arrows in Movie1.mp4, in threeframes (during the peak intensity time, on a frame just beforethe peak intensity time, and on a frame just after the peak in-tensity time). Our use of the hot 94 technique ensures thatthe selected loops are over 1 MK (Warren et al. 2012).In Table 1, we give the start, peak, and end times of eachloop found via visual tracking of the loops as well as fromlight curves, and also give the overall lifetime of each loop.We followed each loop from their peak time in forward andbackward directions in time, visually and in light curves, todefine the loop start / end time, which is when the loop gets al-most invisible (or shows the lowest intensity in light curves)in hot 94 images in backward / forward time from their peaktime. The lifetimes of di ff erent hot loops vary from 12 min-utes to two hours, with an average lifetime of 46 ± ×
6” boxed area centered at eachfoot to obtain LOS magnetogram histograms at each foot.The 6” ×
6” size of the box ensures that the loop foot is com-pletely covered within the box.We have three categories of loops: 1. loops having unipo-lar magnetic flux in both feet, 2. loops having mixed-polaritymagnetic flux in both feet, and 3. loops having one foot inmixed-polarity flux and the other foot in unipolar magneticflux. Of the 23 loops that we examined, ∼
40% (9 /
23) haveboth feet in unipolar magnetic flux, ∼
4% of loops (1 /
23) haveboth feet in mixed-polarity flux, and ∼
56% (13 /
23) have onefoot in unipolar and one in mixed-polarity flux.We have considered the presence of mixed-polarity onlywhen the LOS magnetogram at the loop foot contains values ≥
20 G of positive or negative minority polarity flux. Therandom noise level in the LOS magnetograms is about 7 G(Couvidat et al. 2016), fairly well below our selected lowerlimit. We would have counted footpoint 2 of our only cat-egory 2 loop as unipolar if there was no minority-polaritypixel with a negative B z value larger than 20 G, i.e., if therewere no pixel in the second bin (in 20–40 G range, bin size is20 G) on the negative / minority polarity side of the zero linein this footpoint box’s histogram in Figure 5. This case is themost marginal one in our sample – in all other mix-polaritycases there are several to many minority-polarity pixels withthe magnitude of B z larger than 20 G.Because there is only one loop in the category of both loop-feet having mixed-polarity flux, in our discussions we oftencount that in the category of loops having at least one foot inmixed-polarity flux region.In Figure 2 we show three example loops, one from eachof the three categories. In the top row of Figure 2, we showan example loop that has both feet in unipolar magnetic flux(category 1); the peak time in the hot 94 image comes at05:02:59 and the associated LOS HMI magnetogram is ob- Table 1.
23 Selected Hot Coronal Loops from AR 12712 on May 29, 2018Loop Start Time Peak Time End Time Lifetime a Footpoint 1 Footpoint 2 Peak IntensityIndex UT UT UT Minutes Coord b & Polarity c Coord b & Polarity c DN s − − , mix (-281, 246) + (-240, 251) − (-280, 274) + − , mix (-260, 242) + (-227, 254) − ( − , mix (-230, 251) − (-265, 259) + (-228, 252) − (-262, 258) + (-223, 251) − (-255, 258) + − , mix ( − , mix − , mix (-252, 247) + (-216, 253) − ( − , mix (-212, 251) − (-243, 259) + − , mix (-239, 257) + (-202, 252) − ( − , mix − , mix (-230, 258) + − , mix (-215, 243) + − , mix (-207, 242) + (-171, 251) − (-209, 259) + − , mix (-204, 271) + − , mix (-195, 249) + (-150, 252) − (-190, 273) + (-150, 251) − (-195, 259) + (-121, 243) − (-149, 250) + d
21 : 38 : 59 22 : 44 : 59 23 : 38 : 59 120 ( − , mix (-96, 245) + ± e – – 1221 ± f a The uncertainty in the measurement of lifetime of a coronal loop can be up to six minutes, twice the 3-min cadence of AIA dataused for the presented analysis. b Coordinates of the center of the box outlining the footpoint. c Footpoint 1 of each loop is rooted in dominantly negative magnetic polarity flux region. Footpoint 2 of each loop is rooted indominantly positive magnetic polarity flux region. d This loop has the most prolonged heating (displaying several sequential pulses) of our 23 loops. e The mean lifetime of these 23 loops is 46 min and the standard deviation of that mean is ± ± ± ∼ f Average peak intensity for the loops having mixed-polarity flux at foot one or both feet comes out to be 1222 ±
200 DN s − , andthat for the loops having unipolar flux at both feet comes out to be 1220 ±
120 DN s − . This shows that there is insignificantdi ff erence in the peak intensities of the loops having mixed-polarity flux or unipolar flux at their feet.N ote —The table contains information for each loop investigated in this study. The given coordinates for each loop foot are foreach foot’s center on the photosphere. Times of interest (start, peak, end) are given in addition to total lifetime of each loop.Coordinates of unipolar feet are in bold font for easy identification. Peak intensities are the integrated intensity inside a 2” × Category 1Category 3Category 2 a bc de f b1b2d1d2f2f1
Figure 2.
Three example loops depicting the three alternative categories. The left column (panels a, c, e) presents a close view of the loops(from Movie1.mp4) in hot 94 and the right column (panels b, d, f) presents the same FOV of LOS magnetograms. Insets b1, b2, d1, d2 and f1,f2 are each a further zoomed-in view of the LOS magnetogram of each loop foot. White / black / grey colours in the LOS magnetograms are forpositive / negative / zero field. Category 1 (uppermost row) has two unipolar feet – shown example is Loop 6 in Table 1; Category 2 (middle row)has two mixed-polarity feet – shown example is Loop 8 in Table 1; Category 3 (bottom row) has one unipolar and one mixed-polarity foot –shown example is Loop 4 in Table 1. Pink boxes on the hot 94 images and on the LOS magnetograms outline the 6” x 6” area examined in theLOS magnetograms and give the corresponding field-strength and polarity histograms (see Fig. 5). Yellow boxes on the loop outline the 2” x2” area integrated over to obtain the peak intensities listed in Table 1. N o r m a li ze d i n t e n s i t y a N o r m a li ze d i n t e n s i t y b N o r m a li ze d i n t e n s i t y c Figure 3.
Panels a, b, and c show normalized intensity curves (lightcurves of hot 94) integrated over the area inside the yellow box forthe three loops shown in Figure 2a, c and e, respectively. The dashedvertical lines in each panel mark the start and end times of the loop(also verified with the visual inspection of each loop). tained at 05:02:52. The light curve for this loop in Figure 3aalso shows another (weaker) peak, at 04:50:59. In such caseswe count peak brightness at the time of the brightest intensitypeak, e.g., at 05:02:59 in this case. In Figure 4 (top panel),we show the extrapolated loop with the correct perspective ofthe loop, given by means of VAPOR. Its time is 05:02:52 (top
Figure 4.
Sample 3D loop reconstructions shown by the VAPORsoftware. The three panels present each of the three example loopsin Figure 2. Yellow lines represent the extrapolated field lines. Redboxes in each panel are the same as those in Figure 2. Note thatour extrapolated field lines are rotated to the viewing angle of theobserved AR. panel in Figure 4). In Figure 5, top row, we plot histogramsfor each footpoint (labelled in the figure) of this loop.Figure 2 further shows a loop where both feet have mixed-polarity flux (category 2). The peak-intensity time for thisloop is 05:41:59 (the displayed LOS HMI magnetogram hasa time of 05:41:52). The middle panel of Figure 4 showsthe extrapolated field lines obtained from the HMI SHARPvector magnetogram at 05:36:00. The histograms for the feetof this example loop are plotted in the middle row of Figure5.
Histogram for a Category 1 Loop,Footpoint 1 Histogram for a Category 1 Loop, Footpoint 2Histogram for a Category 2 Loop, Footpoint 1 Histogram for a Category 2 Loop, Footpoint 2Histogram for a Category 3 Loop, Footpoint 1 Histogram for a Category 3 Loop, Footpoint 2B z (Gauss) B z (Gauss) Figure 5.
Histograms of the LOS magnetic field strength and polarity at each footpoint of the three example loops displayed in Figure 2, oneloop for each of the three alternative categories. From Table 1, the example loop for category 1 is Loop 6, the example loop for category 2 isLoop 8, and the example loop for category 3 is Loop 4. The left panels present histograms of footpoints 1 of the three loops (the foot located inthe negative majority polarity region) and the right panels present histograms of footpoints 2 of the three loops (the foot located in the positivemajority polarity region). The vertical pink line in each panel marks B z = The last set of images in Figure 2 show an example loophaving one footpoint in unipolar magnetic flux and the otherfootpoint in mixed-polarity flux (category 3). The peak timein the hot 94 image is 04:44:59 and the closest LOS HMImagnetogram is at 04:44:52. The bottom panel in Figure 4contains the extrapolated field lines. The bottom row of Fig-ure 5 shows the histograms of the two feet of this loop.Our non-force-free field extrapolations match well with theobserved loops, confirming the selection of footpoint loca- tions (e.g., in Figure 4). Histograms of LOS magnetogramsclearly show whether a loop foot has a unipolar, or mixed-polarity magnetic field (e.g., in Figure 5). All of our resultsare listed in Table 1.We also measured the peak intensity of each loop inside a2” ×
2” box during its peak intensity time (see yellow boxesin Figure 2) and list the values in Table 1. The peak intensitytime for each loop was selected based on visual inspection ofloops in the hot 94 movie. The location of the area for calcu-lating peak intensity was also decided via visual inspection ofthe loops. To make sure the selected area was on the bright-est location of the loop, we placed our 2” ×
2” box at severalplaces, as needed, along each loop. There is no significantdi ff erence in the peak intensities of two major categories ofloops (i) having unipolar flux at both of their feet or (ii) hav-ing at least one foot in mixed-polarity magnetic flux (see Ta-ble 1, comment ‘e’ ). DISCUSSION AND CONCLUSIONSWe performed our observational analysis and modellinge ff orts to investigate if magnetic flux cancellation (inferredfrom the presence of mixed-polarity magnetic flux) at theloop feet could be a significant heating mechanism for thehottest and brightest loops in the solar corona of the NOAAAR 12712.Our finding that 60% of the loops (14 out of 23 loops un-der investigation) contain HMI-detected mixed-polarity mag-netic flux at least at one of their feet is consistent with theidea of magnetic flux cancellation being involved in heatingthese loops. The magnetic flux cancellation at a footpointplausibly resulted from magnetic reconnection in the lowersolar atmosphere of coronal loops releasing stored magneticenergy (Tiwari et al. 2014; Chitta et al. 2018; Tiwari et al.2019). Recent examinations of magnetic flux cancellation,such as that of Chitta et al. (2018), note that only part of thedissipating magnetic energy reaches into the corona – somereaches only into the chromosphere.However, the absence of HMI-detected mixed-polaritymagnetic flux from the feet of about 40% of the loops inves-tigated here challenges this idea and allows the possibilitythat magnetoconvection, in tandem with the magnetic fieldstrength at the loop footpoints, could alone be responsiblefor loop heating (Tiwari et al. 2017). The same mechanismmight dominate in heating the loops having mixed-polaritymagnetic flux at one or both of their feet.We did not visually notice any significant magnetic fluxemergence and / or cancellation near the loop-feet during life-times of any loop. Furthermore, we could not establish mag-netic flux emergence and / or cancellation at the feet of theloops over time because of not being able to track the adja-cent opposite-polarity flux adequately for this purpose. Thisreason is also described in Tiwari et al. (2019) for several ofthe loops found in the core of the same AR.The process of loop selection benefited significantly by theuse of hot 94 emission. Most of the times hotter loops werevery cleanly isolated in hot 94 images and were not so clearlyisolated in AIA 94, 193 or 171 Å images. Many loops wereclearly identifiable in the hot 94 images, but not in 94 Å, 193Å, or in 171 Å images. We selected the loops partially alsoby our ability to perform non-force-free loop extrapolations– we were forced to throw out the cases in which the VAPOR software presented too many small loops making it di ffi cultto isolate the loop of interest.The AR investigated is at the peak of its lifetime during the24-hour movie, and starts decaying during or immediately af-ter the observations we use in our study. Thus, it is suitablefor investigations such as those presented here, avoiding ef-fects of pervasive flux emergence (found in the early phase ofARs) or obvious cancellation (found in the decaying phase ofARs).The peak intensities of the loops with unipolar flux atboth feet versus the loops with mixed-polarity flux at leastat one foot do not show a significant di ff erence, thus sug-gesting that polarity mixture at a loop-foot (or at bothfeet) probably does not provide additional heating to theloops. On the other hand, the loops having no HMI-detectedmixed-polarity flux at either foot had marginally signifi-cantly shorter lifetime than the loops having some HMI-detected mixed-polarity flux at one foot or both feet. Thissuggests that shorter-lived below-HMI-detectability mixed-polarity flux might have been present at the apparently unipo-lar feet of these loops and might have been the main driverof the shorter-lived coronal heating in these loops. We notehowever that the brightness of the loops depends on otherfactors such as loop length, and area expansion with height(e.g., Klimchuk 2006; Winebarger et al. 2008; Reale 2014;Dahlburg et al. 2018; Hinode Review Team et al. 2019),which have not been taken into account. Thus, the loop-heating problem requires extensive further investigation.In the AR investigated here, there are no fully developedsunspots, as compared to the ARs studied in Tiwari et al.(2017). Therefore the loops selected here have mostly plage-to-plage connections, and no sunspot connections as were de-scribed in Tiwari et al. (2017). We have therefore studiedhere coronal loops having plage-to-plage connections (onlyone class of those described in the above-mentioned study),and explored what percentage of such loops have mixed-polarity flux at their base and what percentage are unipolarat both feet. We note that this percentage depends heavily onthe selection criterion of loops. Thus, our results have limitedabsolute significance and cannot be extended to all loops, noteven to hot ones only.There are two possibilities from the present study: ei-ther (i) future studies using new generation telescopes giv-ing higher spatial resolution and higher sensitivity magne-tograms will confirm that the presence of mixed-polaritymagnetic flux, thus flux cancellation, is universal for coro-nal loop heating, or (ii) the heating is mainly from unipolarflux and it does not matter much whether the loop feet con-tains a mixed-polarity flux or not —mainly field strength andconvective freedom at the loop feet determine how much theloop is heated.0Our loop extrapolations serve to confirm where the foot-points are for each of the loops investigated. Given the ca-dence di ff erence between the HMI LOS and HMI SHARPmagnetograms, some error might result. However, given thatthe loop lifetimes are usually ≥
24 minutes, the small dif-ference in time between the HMI LOS and vector magne-tograms is probably negligible. The excellent visual agree-ment between the loops of interest as seen on the hot 94 im-ages and the extrapolated loops viewed with VAPOR fromthe correct orientation calculated from the outward normal atthe patch center gives us a high degree of confidence in ourselection of the boxes surrounding the footpoints.Further, the size of the box of 6” by 6” probably includesthe footpoint and little more. The selected foot area is slightlylarger to make sure any part of the loop foot is not missed forthe histograms. Thus, it is possible that we counted a fewpixels of surrounding area not in the foot of a loop. As a re-sult we might have over-estimated the number of loops witha foot (or both feet) in mixed-polarity. Thus, the number ofloops with a mixed-polarity foot in our study can be consid-ered to be at the upper limit, while the ones with both feetunipolar can be considered to be at their lower limit. Thiswould then result into a larger number of loops with unipo-lar flux at both of their feet, thus providing further strengthto the idea that only magnetoconvection, together with thestrength of magnetic field at the loop feet (irrespective of thepresence / absence of mixed-polarity magnetic flux), drivesmost of the loop heating. In this scenario both pictures –MHD waves and nanoflares, can contribute significantly tothe bright-loop heating in AR 12712.Further, Reale et al. (2019) found that hot spots in the tran-sition region are the footpoints of very hot and transient coro-nal loops, which often show strong magnetic interactions andrearrangements. Thus, they concluded that hot bright loops often result from magnetic tangling and presumably by largeangle reconnection, see also Testa et al. (2014, 2020) andTesta & Reale (2020). A similar scenario is possible at leastin a few of our loops that are entangled (see, e.g., loops peak-ing at 05:41:59, 06:47:59, and 12:53:59 UT).Two main limitations of the present study are 1. limitedsample of loops, and 2. limited spatial resolution of the HMILOS magnetograms. We also do not know if these resultsbased on one AR’s loops are valid for other larger and morecomplicated ARs. Similar isolated ARs with proximity todisk center would be suitable candidates for further investi-gation. Future research using bigger samples of loops fromdi ff erent ARs and better magnetogram data, e.g., from theDaniel K. Inouye Solar Telescope (Tritschler et al. 2016),should validate or challenge the present results.We thank the referee for constructive comments. S.K.T.,N.K.P. and R.L.M acknowledge the support from NASAHGI program. S.K.T. gratefully acknowledges support byNASA contract NNM07AA01C (Hinode). 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