Flows around Averaged Solar Active Regions

TL;DR

This study analyzes near-surface flows around solar active regions using helioseismic holography, revealing converging and retrograde flows that influence global solar flow patterns, with validation from MHD simulations.

Contribution

It provides the first comprehensive statistical analysis of flow properties around active regions, linking local flows to global solar dynamics.

Findings

Converging flows extend up to 10 degrees from active regions.

Retrograde flows flank active regions, with ~10 m/s speeds.

Active-region flows can influence global-scale solar flow variations.

Abstract

We explore the general properties of near-surface flows around solar active regions. Helioseismic holography is applied to HMI Dopplergrams yielding nearly 5000 flow measurements of 336 unique active regions observed by the Solar Dynamics Observatory between 2010 and 2014. Ensemble averages of the flows, over subsets of regions sorted on the basis of magnetic flux, are performed. These averages show that converging flows, with speeds about 10 m/s and extending up to 10 degrees from the active region centers, are prevalent and have similar properties for all regions with magnetic flux above 10^21 Mx. Retrograde flows are also detected, with amplitudes around 10 m/s, which predominantly, but not exclusively, flank the polar side of the active regions. We estimate the expected contribution of these active-region flows to longitudinal averages of zonal and meridional flows and demonstrate the plausibility that they are responsible for at least some component of the time-varying global-scale flows. The reliability of our flow determination is tested using publicly available MHD simulations of both quiet-Sun convection and of a sunspot. While validating the overall methodology in general, the sunspot simulation demonstrates the presence of artifacts which may compromise quantitative flow inferences from some helioseismic measurements.

Tables

Table 1. Table 1: properties of magnetic flux groups

group	$\Phi$ range	${\Phi }_{\mathrm{med}}$	number
	(${10}^{22}$ Mx)	(${10}^{22}$ Mx)
a	0.1 – 0.5	0.27	773
b	0.5 – 1.0	0.71	733
c	1.0 – 1.67	1.34	1234
d	1.67 – 2.35	1.97	1088
e	$>2.35$	3.01	1097

Full text

1 Introduction

The detection of flows with amplitudes of order 10 m s*-1* or more and converging towards active regions (hereafter ARs) was an early discovery in local helioseismology (Gizon et al., 2001; Haber et al., 2004; Zhao & Kosovichev, 2004). However, their general characteristics, including their detailed variation with magnetic properties of the associated magnetic regions, remain largely uncharted. These flows appear to provide a link between convection and magnetism, two critical processes governing the solar convection zone. Possibly lasting (at least) as long as the magnetic regions themselves, the flows are suspected of affecting larger circulation patterns, particularly the meridional and zonal flow components of global circulation. For example, converging flows in active region latitudes appear to modulate and reduce the amplitude of the meridional flow pattern (Chou & Dai, 2001; Gizon, 2003; Zhao & Kosovichev, 2004). The meridional flow is involved critically in the process that leads to polar field polarity reversals (Wang et al., 2002) and the ability to predict properties of subsequent solar cycles (e.g. as reviewed by Jiang et al., 2014). The modulation associated with active latitudes, and which may include AR-related inflows, is believed to provide critical nonlinear feedback, preventing eventual decay or growth of subsequent solar cycles (e.g. Jiang et al., 2010; Cameron & Schüssler, 2012; Martin-Belda & Cameron, 2017). The role of this modulation has been explored as a contributor to the recent extended solar minimum and weak cycle 24 (Upton & Hathaway, 2014).

Early measurements were made of the subsurface flows beneath individual active regions (Zhao & Kosovichev, 2004; Haber et al., 2004), which are described as a toroidal-like circulation with converging flows extending down to depths of about 10 Mm and diverging flows below this depth. As reviewed by Gizon et al. (2010) this scenario is far from established and relevant systematic surveys have been sparse. Some general properties of the flows and their relation to other AR properties have been studied (Komm et al., 2007, 2011; Komm & Gosain, 2015), albeit with helioseismic methods with relatively low spatial resolution (i.e. having spatial scales on the order of 15*∘*, which is comparable to the AR sizes). The ring-diagram based survey performed by Hindman et al. (2009) focused on the near-surface ($<2$ Mm deep) flow properties, including inflow and circulation speeds, of $\sim$ 100 active regions at somewhat higher spatial resolution ($\sim 2^{\circ}$) .

Studies of near-surface flows using helioseismic methods with greater spatial resolution are hampered by the strong flows associated with supergranulation. Supergranules with peak flows $\sim$ 300 m s*-1* (Rincon & Rieutord, 2018), and root-mean-squared fluctuations $\sim 100$ m s*-1*, effectively act as noise and dominate the weaker flows associated with ARs. Ensemble averaging, consisting of identifying and averaging coaligned flow measurements of features with (expected) similar properties provides one method for increasing the signal-to-noise ratio. Löptien et al. (2017), using a local-correlation tracking method applied to the granulation pattern, carried out such averaging over more than 200 active regions. In this work, we carry out a high-spatial resolution ($\sim 1^{\circ}$) survey of active regions flows, using helioseismic holography (hereafter HH) applied to Dopplergrams obtained from the Helioseismic and Magnetic Imager (HMI). Our intent is to measure and compare ensemble-averaged AR flows across a wide range of magnetic flux. To accomplish this, we use both existing (Braun, 2016) flow measurements of 252 large (NOAA numbered) ARs, as well as additional measurements of flows around regions with magnetic fluxes as low as $10^{21}$ Mx. Our survey is discussed in §2, which includes a description of AR identification (§2.1), and the magnetic properties of the complete sample (§2.2). The “calibrated helioseismic holography” method, employed to infer the near-surface flows, is described in §2.3. Results are presented in §3, followed by a discussion in §4.

2 Survey

The starting point of our flow survey is the helioseismic holography analysis by Braun (2016). This prior survey, carried out to probe the relationship between flows and solar flares, produced approximately 4000 sets of near-surface flow maps of 252 unique NOAA numbered sunspot regions present between 2010 May and 2014 December. The use of the largest sunspot groups (as ranked by sunspot areas) was appropriate for studies of solar flares, but for the present work we have extended the AR sample to include weaker regions. The method used to identify these additional regions is described below.

2.1 Selection

To achieve a representative sample of ARs for a given solar rotation we start with HMI synoptic magnetograms. Taking the absolute value of the magnetic flux density, we applied spatial smoothing with a two-dimensional Gaussian function with a full-width at half-maxima (FWHM) of 10*∘. We located all of the peaks in this smoothed map, where a peak is defined to have a pixel value greater than the eight neighboring pixels. Sorting the peaks from highest to lowest magnetic flux density, we discard those which are situated within 20∘* of any larger peak. The total unsigned flux of each candidate AR (contained within a 20*∘* $\times$ 10*∘* bounding box) were assessed from the synoptic magnetogram, and only regions with a total flux greater than $10^{21}$ Mx (the lower limit of this survey) were retained. While the method is not intended to identify all possible magnetic regions, it does select ones which are more spatially separated from each other. This allows the flows associated with those regions to be more readily isolated.

We employ this procedure to six Carrington rotations, spaced ten rotations apart, and spanning the time range of the Braun (2016) survey (specifically, these included Carrington rotation numbers CR 2099, 2109, 2119, 2129, 2139, and 2149). An example of the regions identified for CR 2149 (the most active rotation) is given by Figure 1. A total of 104 ARs are identified in this manner during the six rotations, of which 20 are part of the Braun (2016) survey. Our complete sample thus contains 336 unique ARs: 252 from the original flare survey plus 84 new regions.

2.2 Magnetic Properties

Datacubes of Dopplergrams and magnetograms, centered on the AR locations determined using the procedure described above, are constructed identically to those employed by Braun (2016). Specifically, full-disk HMI magnetograms and Dopplergrams are remapped to Postel coordinates ($x_{p}$, $y_{p}$) with a tangent point centered on the AR location, tracked with a fixed Carrington rate, and spanning 30*∘* by 30*∘* with a pixel spacing of 0.0573*∘*. The choice of the Carrington rate, historically derived from observations of sunspots and defined as one rotation per 27.2753 days as viewed from Earth, is motivated by the desire to minimize spatial drifting of ARs in the Doppler and magnetogram time series. Further analysis to remove contributions from large-scale flows, including departures from the Carrington rotation rate, is described in §3.1. We use full-disk Dopplergrams with the full cadence of 45 seconds for the HH analysis of flows discussed in §2.3.

The magnetic properties of each AR are studied from remapped full-disk magnetograms sampled every 68 minutes. The passage of each AR across the disk is divided into 16 non-overlapping intervals each spanning 13.6 hr. To ensure the quality of the helioseismic analysis, intervals for which the AR position was farther than 60*∘* from disk center, or for which gaps in the HMI Dopplergram data exceeded 30% of the 13.6 hr period are excluded from further study.

For each AR, the Postel-remapped magnetograms are averaged over each of the 13.6 hr intervals. For the purpose of coalignment necessary for ensemble averaging, positions defining the center of mass (centroid) of the unsigned magnetic flux density, relative to the Postel-projection center, are obtained. During this step, the net unsigned flux (corrected for the cosine of the heliocentric angle) is also integrated and recorded. To reduce the effect of magnetogram noise, only pixels with flux density greater than 50 G present in a 20*∘* $\times$ 10*∘* bounding box are retained in the centroid and flux determinations. The statistics of these position offsets were examined, and a rejection of time intervals for which the offset (in either the $x_{p}$ or $y_{p}$ coordinate of the Postel frame) exceeded the mean by plus-or-minus three standard-deviations was carried out. Values of the standard deviations are 1.2*∘* and 0.6*∘* in the $x_{p}$ and $y_{p}$ directions, respectively.

After the analysis and data rejection described above, we are left with 4925 measurement sets which exceed $10^{21}$ Mx flux. A histogram of the fluxes is shown in Figure 2. The distribution is divided into five flux groups as separated by the vertical lines in the figure. Some properties of the groups are listed in Table 2.2, including the defining flux range, the median flux (${\Phi}_{\mathrm{med}}$) for each group, and the number of measurements within each group. The magnetic flux in most ARs change over the 9 days they are tracked, resulting in most regions being included in more than a single flux group. Magnetograms of ARs, randomly selected from each group, are shown in the top row of Figure 3. Coaligned averages over each group of the signed line-of-sight magnetic flux density are shown in the bottom row of Figure 3. For the averaging, we adapt a coordinate system ($x$,$y$) with an origin at the center-of-mass, $x$ increasing in the westward (prograde) direction, and $y$ increasing towards the pole of the hemisphere in which the AR resides. Thus, ARs in the southern hemisphere are spatially flipped around the $x_{p}$ axis. In accordance with Hale’s polarity law, regions in the southern hemisphere also have their polarity switched. The group averages clearly show the two polarities, tilted by Joy’s law, and having an asymmetry in peak flux density between polarities.