Evolution of the magnetic field and flows of solar active regions with persistent magnetic bipoles before emergence

Abstract Magnetic active regions on the Sun are harbingers of space weather. Understanding the physics of how they form and evolve will improve space weather forecasting. Our aim is to characterise the surface magnetic field and flows for a sample of active regions with persistent magnetic bipoles prior to emergence. We identified 42 emerging active regions (EARs), in the Solar Dynamics Observatory Helioseismic Emerging Active Region survey (Schunker et al. 2016, A&A. 595, A107), associated with small magnetic bipoles at least one day before the time of emergence. We then identified a contrasting sample of 42 EARs that emerge more abruptly without bipoles before emergence. We computed the supergranulation-scale surface flows using helioseismic holography. We averaged the flow maps and magnetic field maps over all active regions in each sample at each time interval from 2 d before emergence to 1 d after. We found that EARs associated with a persistent pre-emergence bipole evolve to be, on average, lower flux active regions than EARs that emerge more abruptly. Further, we found that the EARs that emerge more abruptly do so with a diverging flow of 
$(3\pm 0.6) \times 10^{-6}$
 s 
$^{-1}$
 on the order of 50–100 ms 
$^{-1}$
 . Our results show that there is a statistical dependence of the surface flow signature throughout the emergence process on the maximum magnetic flux of the active region.


Introduction
Active regions are generally thought to be formed by coherent, arched magnetic flux tubes rising through the interior to manifest as roughly east-west aligned opposite polarity pairs at the surface of the Sun.In many dynamo models they are important to convert the Sun's global toroidal magnetic field to poloidal (Cameron and Schüssler 2015).Understanding the physics behind the emergence process is important to constrain their origins and connection to the Sun's large scale global field, as well as for space weather forecasting.
It is not clear from what depth these flux tubes originate, nor what causes them to rise.At the surface and below, the Sun's magnetic field is embedded in the convective flows, and as such can be modelled with the equations of magnetohydrodynamics. Below the surface, the plasma pressure is generally greater than the magnetic pressure.Understanding the dominant terms in these equations, particularly the flows and the magnetic field, is important to understand how active regions form.
Simulations of magnetic flux emergence show that thin flux tubes can rise a priori from the base of the convection zone due to magnetic buoyancy in the absence of convection (e.g.Fan, Fisher, and Deluca 1993;Weber, Fan, and Miesch 2011); or tubes of magnetic flux can be formed within the convection zone itself and brought up by convective upflows (e.g.Chen, Rempel, and Fan 2017;Hotta and Iijima 2020).It may also be possible for active regions to form without the presence of a flux tube (e.g.Brandenburg 2005;Brandenburg et al. 2014).For a full review see Fan 2021.
The thin flux tube models in Fan 2008 predict a retrograde flow at the peak of the flux tube just before emergence.In principle, local helioseismology could be used to measure this flow.Local helioseismology measures perturbations to the natural seismic oscillations driven by the turbulent convection at the surface of the Sun and infers the three-dimensional subsurface structure and dynamics in localised areas (see Gizon and Birch 2005, for a full overview).Birch et al. 2013 used helioseismic holography (Lindsey and Braun 2000) to measure the subsurface flows prior to the formation of one hundred active regions observed by the Global Oscillation Network Group (GONG; Harvey, Tucker, and Britanik 1998).They found that there were no statistically significant flows below the surface, however near the surface they found a statistically significant flow of about 15ms -1 towards the emergence location in the day preceding the active region formation. emerge.
From a practical perspective, perhaps most importantly for space weather, it would be useful to be able to predict the location and time an active region will emerge, and whether or not it is likely to have low magnetic flux or high magnetic flux.Some effort has been dedicated to this.Helioseismic studies have not resulted in a significant subsurface detection (see e.g.Komm et al. 2015), but Barnes et al. 2014 showed that in the day before emergence the strongest indication that an active region will emerge is the unsigned surface magnetic field itself.This was also reflected in more recent efforts using machine learning (Dhuri et al. 2020).
In this paper, we examine the magnetic field prior to emergence for two samples of active regions.In Section 2 we describe our database of emerging active regions.We then outline the data reduction, computation of the surface flows, how we measure the location of the polarities in each active region, and the ensemble averaging of the flow and magnetic field maps (Section 3).In Section 4 we describe the identification of active regions that show persistent pre-emergence bipole magnetic fields.In Section 5 we show that there is a distinct difference in the averaged surface flows and magnetic field from 2 days before the emergence to 0.6 days afterwards, and in Section 6 we discuss the implications of our results and possible avenues to make future progress.

Sample of observed emerging active regions
The Solar Dynamics Observatory Helioseismic Emerging Active Region (SDO/HEAR) Survey currently consists of 182 emerging active regions (EARS) (for a full list see Schunker et al. 2016;Schunker et al. 2019) observed by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI, Scherrer et al. 2012) between May 2010 (the start of science grade SDO/HMI observations) and July 2014 (the declining phase of solar cycle 24).To avoid complications in interpreting local helioseismology results (e.g.Schunker 2010), the active regions selected for the HEAR survey specifically emerge into a relatively quiet area of the Sun's surface at least 20 • from any surrounding strong surface magnetic fields.
The emergence time for each active region, t = 0 days (see Appendix 1 and Appendix 2), is defined as the time when the absolute flux, corrected for line-of-sight projection, reaches 10% of its maximum value over a 36 hour interval following the first appearance of the sunspot (or group) in the National Oceanic and Atmospheric Administration (NOAA) record (Schunker et al. 2016).We emphasise that a small amount of flux from the EAR is present at the emergence time.A negative time indicates pre-emergence and a positive time indicates post-emergence for each EAR.
Each active region, labelled by its NOAA number, is paired with a corresponding control region (CR).The CR is assigned a mock-emergence time when the Stonyhurst coordinates of the CR was the same as the EAR at its (real) emergence time (see Table 1 and Table 2 in this paper, and Schunker et al. 2016, for a full description).The control region is necessary to ensure that the signal is not due to systematics from the SDO/HMI instrument or due to some line-of-sight observing effect.

Data reduction
Our data reduction closely follows what has already been published in Schunker et al. 2016, Birch et al. 2016and Birch et al. 2019.Here we outline the relevant details for this study.

Mapping and tracking
The HMI observes the full-disk continuum intensity, line-ofsight magnetic field and Doppler velocity at the photosphere with a cadence of 45 s.We track the location of the EARs and CRs at the Carrington rotation rate over time intervals (TI) of 6.825 h (547 frames with a cadence of 45 s).
Local helioseismology measures the travel time of a wave from one location on the surface until it appears at another location on the surface.Waves travel at the local sound speed, and generally waves that travel shorter distances do so over a shorter time.The waves we are interested in for this study have travel times less than about 6 hours, and so this is the length of time we chose for a single time interval and the corresponding datacube.
These datacubes are labelled with their time interval (TI) relative to the emergence time interval, TI+00.The emergence time is defined as τ = 0.0 days, and the midtime of time interval TI+00 corresponds to τ = 0.1 days (see Table B.1 in Schunker et al. 2019, which lists the mid-time of each TI relative to the time of emergence, τ = 0).The beginning of each time interval is spaced at 5.3375 h (320.25 min, 427 frames), and they have a 1.5 hour, or 120 frame, overlap (see Figure 5 in Schunker et al. 2016).Each active region is tracked up to 7 days before and after the emergence time, depending on their distance to central meridian at that time.
At each 45 s interval we projected the full-disk SDO/HMI observations onto 60 • × 60 • Postel projection maps.The projection is made to a 512 × 512 pixel grid with a pixel size of 1.39 Mm.The coordinates of the map centre are the flux-weighted centre of the line-of-sight magnetic field at the emergence time (see Schunker et al. 2016, for more details).In this article we examine the magnetic field maps averaged over each 6.825 hour time interval to correspond directly to the flows.

Computing the surface flows
Local helioseismology is a tool that uses the acoustic waves in the Sun to map the three-dimensional subsurface structure and/or dynamics (for a review of the different methods and key results see Gizon and Birch 2005).For example, perturbations to the travel-times of the waves can be interpreted as a linear perturbation to the structure and dynamics of the interior of the Sun at the depths where that particular wave has sensitivity.By selecting waves that are sensitive to the near-surface of the Sun, we can infer the horizontal flows which we can then be used to identify supergranulation structures (e.g.Gizon, Duvall, and Schou 2003).
We filtered the tracked and remapped Doppler velocities with a phase-speed filter with a central phase speed of 17.49 km s -1 and a width of 2.63 km s -1 (filter 3 from Table 1 in Couvidat et al. 2005).This filter isolates waves that are most sensitive to the 3 Mm just below the photosphere.We then measured the north-south and east-west travel time differences using surface-focusing helioseismic holography (Lindsey and Braun 2000).We used an empirically determined conversion constant of -7.7 ms -2 to convert from travel time differences to surface flows (Birch et al. 2016).
We remove any remnant large scale velocities from the Sun's bulk rotation or orbital velocity of the SDO satellite (a constant offset) in the flows by subtracting a plane fit to each map, excluding a central region of radius 70 Mm (50 pixels) which is our region of interest where the active regions emerge.To remove high-wavenumber noise, we use a low-bandpass filter with a value of 1 for kR ⊙ < 140, a raised cosine from 1 to 0 in the region 140 < kR ⊙ < 220, and zero for kR ⊙ > 220.We then have surface flow maps, v x (x, y) and v y (x, y) at a 5.3375 h time interval, corresponding to the time-averaged magnetic field maps (described at end of Section 3.1).
To create ensemble averages, we treat all active regions as if they were in the northern hemisphere, so that positive y, is towards the pole (north); negative y is towards the equator (south); positive x is in the prograde (solar west) direction; and negative x is in the retrograde (solar east) direction.
We reversed the magnetic field polarity of the regions in the southern hemisphere, to account for Hale's law when averaging EARs, so that the leading polarity is always negative.Under the assumption that the magnetic field is radial at the solar surface, we approximately corrected for the magnitude of the magnetic field for the line-of-sight projection by dividing it by cos θ, where θ is the angular distance to disk centre.
For active regions in the southern hemisphere, we flipped the averaged magnetic field and flow maps in the latitudinal direction to account for the pole-to-equator symmetry, and reversed the direction of the flows in the north-south direction, so that the poleward flows are in the positive y-direction.We then computed the divergence of the flows, ∇ • v h where v h = (v x , v y ), as the most representative way to show the location of the supergranules, which are the tops of convection cells.

Measuring the location of the bipoles
The magnetic field associated with an emergence can have significant proper motion compared to the Carrington rotation rate.To analyse the evolution of the flows associated with the EARs, we measured the location of the active region magnetic field at each time interval.
We tracked the position of the centroid of the positive and negative polarity in the active region as described in Schunker et al. ( 2019), and we outline the process here.We first measured the location of the roughly circular polarities with a threshold magnetic field strength of 20 G at time interval TI+02 (τ = 0.6 days).We used a feature recognition algorithm (feature.procopyright 1997, John C. Crocker and David G. Grier) designed to determine the centroid position of roughly circular features in an image to determine the location of both polarities individually.Moving forward and backwards in time, we repeated the process and selected the x and y-centroid closest to the polarity location in the previous time interval.
If the location of the bipole at some time interval is not defined (e.g. a bipole cannot be detected), then we linearly interpolated for the x and y-centroid locations from the nearest time intervals.For times before a clear bipole is detected, we extrapolate the first measured location of the bipole.Similarly, for times after emergence when a clear bipole can no longer be detected, e.g. after decay, we extrapolate the last measured location of the bipole.
We shifted the averaged magnetic field and flow maps, using a bi-linear interpolation (over the nearest four pixels), for each EAR to the point half-way between the centroid locations at each time interval.The shifts are typically on the order of up to 5 pixels.The shifting of the maps at each time interval removing the proper motion of the bipole is unique to the analysis method in this paper, and is required to get a well-defined mean of the absolute magnetic field prior to emergence.

Identification of persistent magnetic bipoles before emergence.
Active regions are defined by their dark appearance in the intensity of light from the surface of the Sun.This is due to the strong concentrations of magnetic field, that appear in an east-west aligned pair of opposite polarities on the solar surface, and increases in size and field strength as more flux emerges (see, for example, Figure 1 in Schunker et al. 2019).It takes about 2 days on average from the time of emergence for an active region to reach its maximum flux (see Figure 2 in Weber et al. 2023).
By inspection, we identified 42 EARs (listed in Appendix 1) as having persistent magnetic bipoles at least one day before emergence associated with the eventual bipole structure of the active region.The persistent polarities are characterised by their roughly east-west orientation and the proximity as a pair as they are buffeted by the convection.The bipoles do not change significantly in size (on the order of 10 Mm, see Figure 1, first panel) until the main emergence process begins closer to t = 0. Some active regions, such as AR 11182 and AR 11969, show magnetic bipoles up to 2.8 days (TI-12) before emergence.An example of an EAR with a clearly associated preemergence bipole more than 2 days before emergence is AR 11702 shown in the top row of Figure 1.
For a contrasting sample, we selected an equal number (42) of EARs that, by inspection, are not associated with any magnetic field bipoles prior to t = -0.3days (listed in Appendix 2).One example is AR 11697 shown in the bottom row of Figure 1.These two samples may constitute the extremes of a continuum allowing us to clearly identify any fundamental differences in their evolution.
Any EARs with dense, small-scale magnetic field within ≈ 50 Mm radius of the emergence location were excluded from either sample since they may obscure the identification of any pre-emergence bipole.In Schunker et al. 2016, the authors defined a P-factor, where 0 represents an emergence into a very quiet region; a P-factor of 1 or 2 indicates emergence into increasing amounts of magnetic field nearby (but not directly at) the subsequent emergence location; and a P-factor of 3 or higher indicates the region may be compromised by pre-existing field at the emergence time and location.We cross-checked the P-factor for the active regions identified in our two samples, and found that neither of the samples we identified have a dominant P-factor, and were mostly 0 or 1.
In summary, we have averaged line-of-sight magnetic field maps, B(x, y), flow maps, v x (x, y) and v y (x, y), and flow divergence maps ∇ • v h with a 5.3375 h cadence, centred on the bipole location at each time interval for 42 EARs with persistent pre-emergence bipoles, and 42 EARs without preemergence bipoles.

Evolution of the average magnetic field and flows
We averaged the magnetic field maps and the flows for each sample of EARs (with and without persistent pre-emergence bipoles).Figures 2 and 3 show the average surface flows at each time interval for the two samples.The equivalent maps for the control regions are in Figures 5 and 6 in Appendix 3.
The sample of EARs with persistent pre-emergence bipoles (Figure 2) shows a converging flow at the location of the bipoles (centre of the map) prior to the emergence time.The growth of the bipole is shown in the contours of the mean magnetic field.The sample without pre-emergence bipoles (Figure 3) does not show a statistically significant converging flow, but does show a statistically significant diverging flow from the time of emergence.
At each time interval we computed the spatially averaged magnetic flux within a central disk of radius 35 Mm for each active region.We chose a fixed radius that encompasses the contour of the average |B los | = 20 G as the active region grows in size to τ = 0.6 days (see Figure 2).The top panel of Figure 4 shows the mean and standard error of the magnetic flux over the sample of active regions with (blue), and without (orange), a pre-emergence bipole.The expected difference in magnetic flux prior to the emergence of the active regions is clear.Then, after about -0.3 days, the averaged magnetic flux of the regions that emerge abruptly becomes higher than for the regions with pre-emergence bipoles.This shows that the active regions with pre-emergence bipoles evolve to have significantly lower flux than those without preemergence bipoles.
We then averaged the surface flows in the central 11 Mm (8 pixels) radius for each active region and time interval.We chose this radius by inspection of the maps in Figure 3 to include only the flows associated with the emergence, and note that it is on the order of supergranulation scales, but is considerably smaller than the radius of the area over which the magnetic flux was averaged (35 Mm).The lower three panels of Figure 4 show the evolution of the averaged flow divergence, east-west velocity, and north-south velocity.The averaged flow divergence follows a similar evolution for both populations apart from an offset of about 3×10 -6 s -1 .The mean flow in both samples is converging up until 0.5 days before emergence, ⟨∇ • v h ⟩ = (-2.9± 0.5) × 10 -6 s -1 for regions with a pre-emerging bipole, and ⟨∇ • v h ⟩ = (0.03 ± 0.4) × 10 -6 s -1 for those without.From about 0.5 days before emergence until about 0.1 days after emergence, the divergence increases in both samples.
The flows for both samples are strongest in the east-west direction, ⟨v x ⟩, and peak close to the time of emergence at about 70 ms -1 .The flows in the north-south direction, ⟨v y ⟩, are consistent with zero and do not vary significantly, due to averaging over the antisymmetric flow in the north-south direction (see Figure 2).
Most of the surface of the Sun consists of the diverging flows of granules and supergranules.Statistically, it is more likely that a randomly selected location on the surface will be a diverging flow, rather than the narrower inflow lanes.This is reflected in Figures 5 and 6 (which shows the averaged surface flow maps of the control regions), and the orange dashed curve in the second panel of Figure 4.The averaged divergence signal close to the emergence time in Figure 4 is equivalent in magnitude to other diverging flows in the map (see Appendix 3), showing that it is not significant compared to the background signal.Because we averaged the flows over a relatively small sample of active regions and the averaging area (diameter of about 20 Mm) is the size of a supergranule, we have captured the evolution of supergranulation-scale flows.

Discussion
From our classification of two samples of EARs based on their pre-emergence bipole signatures we found that these samples also form distinct post-emergence populations of active regions.The sample of active regions with persistent pre-emergence bipoles evolve to be, on average, lower flux active regions a , and those that emerge more abruptly are higher flux active regions.It is not clear why this is the case, but suggests that there is some flux-dependence in the growth and evolution of active regions.
Our results are consistent with Birch et al. 2019 who show that active regions tend to emerge into regions of converging flow, but we add that the amplitude and sign of the flow divergence is flux dependent.We find that the sample with persistent pre-emergence bipoles emerges into strong converging flows and these flows begin more thsn two days prior to emergence.Pre-emergence bipoles confined to the converging flow lanes between supergranules is not surprising since small, lower flux magnetic features are buffeted by the flows at the surface of the Sun.
Secondly, Birch et al. 2016 showed that the upward rise speed of flux tubes that form active regions must be on the order of the convective flow velocities (≲ 100 ms -1 ), based on the lack of any diverging flow signature in a single observed active region.In our statistical analysis, we have shown that some samples of active regions are associated with a diverging flow, although the magnitude is on the order of supergranulation velocities (≈ 100 ms -1 ) and not as strong as the diverging flows produced by simulations of a traditional thin flux tube (up to 500 ms -1 Birch et al. 2016) .
Furthermore, this sample of EARs shows that higher flux active regions emerge with stronger diverging flows.This may suggest that it is easier to form a large active region where the converging (down) flow is weak, and/or that the magnetic flux is brought up in the upflows of newly forming supergranules.On the other hand, it could also suggest that tubes with higher magnetic flux rise faster, driving a moderate surface diverging flow at the time of emergence, however this can only be properly explored once the emergence process of the full sample of active regions is (better) understood.
a. We do note, however, that although the largest active region in our sample, AR 11158, falls in this category, it is a double emergence where two bipoles emerge close to one another and then recombine to form a large, complex active region.In this study, we have effectively only followed the central bipole.
We suspect that these active regions with pre-emergence bipoles are responsible for the conclusions of Barnes et al. 2014 andDhuri et al. 2020 that the best predictor of an imminent active region emergence is the surface magnetic field itself.It may also be that these active regions are at the sites of active region 'nests' (Işık et al. 2020) or active longitudes (e.g.Berdyugina and Usoskin 2003) supplementing the surface small-scale magnetic field from below.A larger sample of active regions will help to explore this idea.
We also note that we are limited by our resolution of 1.39 Mm per pixel, which is four times coarser than the nominal HMI resolution.From inspection of some of the full resolution line-of-sight magnetograms for these active regions, the onset of the bipoles before emergence and their motions can be tracked more precisely.
Hotta and Iijima 2020 have successfully formed a small active region by placing a flux tube at some depth in their three dimensional numerical magnetohydrodynamic simulations where the near-surface convective flows have brought the flux to the surface.The key to the formation of their active region is placement in an upflow region sandwiched between two downflow regions.The emergence in an upflow region is consistent with our sample of EARs with higher flux, but without pre-emergence bipoles.These simulations are computationally expensive, and while an equivalent statistical sample of emerging active regions to compare with is prohibitive, such simulations are crucial to probe the subsurface mechanisms of active region formation.

Conclusions
We have identified two distinct samples of emerging active regions: one sample with a persistent magnetic bipole more than one day prior to emergence, and one sample with no distinct magnetic signature until the emergence time.There are 42 active regions in each sample, which may constitute the extremes of a continuum.
We found that both samples of active regions are associated with converging flows prior to emergence, but that the magnitude of the convergence was statistically significantly different, with the sample of active regions with a persistent preemergence bipole emerging into strongly converging flows.We also found a statistical dependence on the post-emergence flux of the active regions, where the sample of active regions with a persistent pre-emergence bipole evolved into lower flux active regions, with an average flux of (19 ± 1.3) × 10 20 Mx, and those without evolved into stronger active regions, with an average flux of (24 ± 1.8) × 10 20 Mx.
Furthermore, we found that the higher flux active regions are associated with a diverging flow at the time of emergence, whereas the lower flux active regions did not show any significant flow signature.The ensemble averages of the flows for both samples show the same profile of the diverging flows in time, offset by about 3 × 10 -6 s -1 (and about 30 ms -1 in the averaged east-west flows).
We have presented a new observational constraint for flux emergence models, and a potential quantity to predict the Active regions with pre-emergence bipoles tend to evolve to be lower magnetic flux active regions post-emergence.The second panel shows the averaged flow maximum magnetic flux of an emerging active region.A full interpretation of these intriguing results requires both a more in-depth observational analysis of a broader sample of active regions coupled with numerical simulations of rising flux tubes with a range of magnetic fluxes.This will help to understand whether the flux dependence of the flows in these samples we have identified are distinct or are the extremes of a continuum of EARs governed by a single emergence mechanism.
Table 1.Emerging active regions with associated pre-emergence bipoles and their associated control region tracking locations and emergence time (adapted from Table A.1. in each of Schunker et al. 2016;Schunker et al. 2019).The left panel of the table lists the NOAA active region number, emergence time, Carrington latitude, Carrington longitude, central meridian distance (CMD) at the time of emergence and the P-factor.The middle panel lists the emergence time and Carrington longitude of the control region.The right panel lists the difference in B-angle, ∆B = B0(CR) -B0(EAR), and the rounded difference in days ∆T = t 0 (CR) -t 0 (EAR).Active regions with a maximum flux larger than the median of the entire HEARS are marked with an asterisk.There is a diverging flow at the centre of the map near the artificial emergence time, however, neither the size nor magnitude is significantly different than other surrounding regions.We note that most of the Sun's surface consists of supergranulation cells of diverging flows, and so this is statistically not unexpected.

Figure 1 .
Figure1.Time averaged line-of-sight magnetic field maps for an example EAR with a bipole associated with the emerging flux more than two days before the emergence time (top row, AR 11702).And an example of an EAR without an obviously associate pre-emergence bipole (bottom row, AR 11697).The greyscale is saturated at ±15 G.Note that these maps have not been shifted to the emergence location.

Figure 2 .Figure 3 .
Figure 2. Averaged divergence flow maps over N active regions with pre-emergence bipoles at different time intervals.Blue represents converging flows and red represents diverging flows.The arrows indicate the direction and magnitude of the flows.Solid (dashed) black lines contour the -20 G (+20 G) of the averaged line-of-sight magnetic field maps.There is a significant converging flow prior to emergence.

Figure 4 .
Figure 4. Averaged magnetic flux and flows as a function of time for active regions with pre-emergence bipoles (blue) and those without (orange).The top panel shows the average magnetic flux within a central 35 Mm radius of the emergence location as a function of time.The error bars show the standard error in the average magnetic flux over the active regions at each time interval.The dashed lines show the corresponding control regions with shaded standard errors.Active regions with pre-emergence bipoles tend to evolve to be lower magnetic flux active regions post-emergence.The second panel shows the averaged flow

Figure 5 .
Figure 5. Averaged divergence flow maps of the control regions associated with pre-emergence bipole regions.Blue represents converging flows and red represents diverging flows.The arrows indicate the direction and magnitude of the flows.Solid (dashed) black lines contour the -20 G (+20 G) of the averaged line-of-sight magnetic field maps.There are no significant flows.

Figure 6 .
Figure 6.Averaged divergence flow maps of the control regions associated with active regions without pre-emergence bipoles.Blue represents converging flows and red represents diverging flows.The arrows indicate the direction and magnitude of the flows.There is a diverging flow at the centre of the map near the artificial emergence time, however, neither the size nor magnitude is significantly different than other surrounding regions.We note that most of the Sun's surface consists of supergranulation cells of diverging flows, and so this is statistically not unexpected.

Table 2 .
Emerging active region and control region tSchunker et al. 2019) emergence time (adapted fromTable A.1. in each of Schunker et al. 2016;Schunker et al. 2019).The left panel of the table lists the NOAA active region number, emergence time, Carrington latitude, Carrington longitude, central meridian distance (CMD) at the time of emergence and the P-factor.The middle panel lists the emergence time and Carrington longitude of the control region.The right panel lists the difference in B-angle, ∆B = B0(CR) -B0(EAR), and the rounded difference in days ∆T = t 0 (CR) -t 0 (EAR).Active regions with a maximum flux larger than the median of the entire HEARS are marked with an asterisk.