A Statistical Study of the Long-Term Evolution of Coronal Hole Properties As Observed by SDO S

A&A 638, A68 (2020) Astronomy https://doi.org/10.1051/0004-6361/202037613 & c ESO 2020 Astrophysics

A statistical study of the long-term evolution of coronal hole properties as observed by SDO S. G. Heinemann1, V. Jerciˇ c´1,2, M. Temmer1, S. J. Hofmeister1, M. Dumbovic´1,3, S. Vennerstrom4, G. Verbanac5, and A. M. Veronig1,6

1 University of Graz, Institute of Physics, Graz, Austria e-mail: [email protected] 2 Centre for Plasma Astrophysics, KU Leuven, Leuven, Belgium 3 University of Zagreb, Faculty of Geodesy, Hvar Observatory, Zagreb, Croatia 4 National Space Institute, DTU Space, Denmark 5 University of Zagreb, Faculty of Science, Department of Geophysics, Zagreb, Croatia 6 Kanzelhöhe Observatory for Solar and Environmental Research, University of Graz, Graz, Austria

Received 29 January 2020 / Accepted 21 April 2020

ABSTRACT

Context. Understanding the evolution of coronal holes is especially important when studying the high-speed solar wind streams that emanate from them. Slow- and high-speed stream interaction regions may deliver large amounts of energy into the Earth’s magnetosphere-ionosphere system, cause geomagnetic storms, and shape interplanetary space. Aims. By statistically investigating the long-term evolution of well-observed coronal holes we aim to reveal processes that drive the observed changes in the coronal hole parameters. By analyzing 16 long-living coronal holes observed by the Solar Dynamic Obser- vatory, we focus on coronal, morphological, and underlying photospheric magnetic field characteristics, and investigate the evolution of the associated high-speed streams. Methods. We use the Collection of Analysis Tools for Coronal Holes to extract and analyze coronal holes using 193 Å EUV observations taken by the Atmospheric Imaging Assembly as well as line–of–sight magnetograms observed by the Helioseismic and Magnetic Imager. We derive changes in the coronal hole properties and look for correlations with coronal hole evolution. Further, we analyze the properties of the high–speed stream signatures near 1AU from OMNI data by manually extracting the peak bulk velocity of the solar wind plasma. Results. We find that the area evolution of coronal holes shows a general trend of growing to a maximum followed by a decay. We did not find any correlation between the area evolution and the evolution of the signed magnetic flux or signed magnetic flux density enclosed in the projected coronal hole area. From this we conclude that the magnetic flux within the extracted coronal hole boundaries is not the main cause for its area evolution. We derive coronal hole area change rates (growth and decay) of (14.2±15.0)×108 km2 per day showing a reasonable anti-correlation (ccPearson = −0.48) to the solar activity, approximated by the sunspot number. The change rates of the signed mean magnetic flux density (27.3 ± 32.2 mG day−1) and the signed magnetic flux (30.3 ± 31.5 1018 Mx day−1) were also found to be dependent on solar activity (ccPearson = 0.50 and ccPearson = 0.69 respectively) rather than on the individual coronal hole evolutions. Further we find that the relation between coronal hole area and high-speed stream peak velocity is valid for each coronal hole over its evolution, but we see significant variations in the slopes of the regression lines. Key words. Sun: corona – Sun: evolution – Sun: activity – Sun: magnetic fields – solar-terrestrial relations – solar wind

1. Introduction CIRs have been associated with large-scale coronal signatures, the CHs. Nolte et al.(1976) first found an empirical relation- Coronal holes (CH) are stable, long-lived structures usually ship between the CH area and the peak bulk velocity of the solar observed in the solar corona as regions of reduced emission in wind. The linear CH area–HSS speed relation is supported by extreme ultraviolet (EUV) or X-ray. Coronal holes are charac- many studies, although different slopes of the regression lines terized by an open magnetic field configuration along which are found (e.g., Nolte et al. 1978a; Vršnak et al. 2007; Tokumaru ionized atoms and electrons are accelerated into interplanetary et al. 2017; Heinemann et al. 2018a; Hofmeister et al. 2018). space, forming high speed solar wind streams (HSS; Krieger The long-term evolution of recurrent CH structures and et al. 1973; Nolte et al. 1976; Cranmer 2009). The interaction of the associated HSSs has rarely been investigated. Most studies HSSs with the preceeding ambient slow solar wind forms stream focus on a snap-shot of the CH during its lifetime in the form interaction regions (SIRs) which can develop into co-rotating of a case study (e.g., Gibson et al. 1999; Gopalswamy et al. interaction regions (CIRs; Wilcox 1968; Tsurutani et al. 2006) 1999; Zhang et al. 2007; Yang et al. 2009) or statistical stud- if the CH persists over multiple rotations. These transient fea- ies that do not separate the evolution of individual CHs (e.g., tures are the main source of usually weak to medium geomag- Harvey et al. 1982; Lowder et al. 2017; Hofmeister et al. 2017; netic storms at Earth (see, e.g., Alves et al. 2006; Verbanac et al. Heinemann et al. 2019). In the Skylab era, Bohlin(1977) and 2011a; Vršnak et al. 2017; Yermolaev et al. 2018; Richardson Bohlin & Sheeley(1978) proposed that the area and the mean 2018). Since the Skylab era, recurrent geomagnetic effects of magnetic flux density of a CH are dependent on its age and

Article published by EDP Sciences A68, page 1 of 11 A&A 638, A68 (2020)

Nolte et al.(1978a,b) used X-ray observations to show that CHs – The last condition was that the CH did not originate as or primarily evolve by sudden, large-scale shifts in the position of from a polar CH. This was considered due to high uncertainties the boundaries. A change in the underlying photospheric mag- in determining the CH area in polar regions due to projection netic field is believed to influence the appearance of the CHs in and line–of–sight effects. Additionally the magnetic field obser- the corona (Wang & Sheeley 1990; Gosling 1996). In a more vations of these areas are highly unreliable. recent study, Ikhsanov & Tavastsherna(2015) showed that there By considering the stated constraints, we extracted 16 CHs are two magnetic field systems (large-scale high-latitude and fulfilling those requirements over most of the operational life- small-scale low-latitude magnetic field systems) that play major time of SDO from 2010 to 2019. roles in the evolution of the solar magnetic cycle and whose effects can be seen in the appearance of CHs. Wang & Sheeley (1990) showed in their current-free coronal model, that the long- 2.2. Coronal hole detection and extraction term evolution of CHs and the associated wind streams is related To identify and extract CHs we use the 193 Å filter of the AIA to flux emergence in active regions and the subsequent flux instrument onboard SDO as CHs can be well observed in the transport processes. Coronal holes themselves seem to form in emission of highly ionized iron (especially Fe xii: 193/195 Å). response to local (low-latitudes) or global (polar, high-latitudes) The high contrast with the surrounding quiet Sun enables a good changes in the magnetic field topology. At low-latitudes, small- extraction of boundaries. To capture the long-term evolution, we scale magnetic systems may manifest themselves as localized extract each CH and its characteristics at each solar disk passage CHs that are the result of decaying local sunspot groups (Petrie near the central meridian. Heinemann et al.(2018a,b) showed in & Haislmaier 2013) or are generated by other mechanisms a case study that one data point per rotation depicts the evolution- that enable to “open” the magnetic field, such as coronal mass ary trend sufficiently. We use the Collection of Analysis Tools for ejections (CMEs)/filament eruptions, flux accumulation, or flux Coronal Holes (CATCH; Heinemann et al. 2019). CATCH uses emergence (e.g., Webb et al. 1978; Heinemann et al. 2018b). a supervised threshold-based extraction that is modulated by the Heinemann et al.(2018a,b) provide an in-depth view of the evo- intensity gradient perpendicular to the CH boundary. For illus- lution of one particular CH in 2012 from which they identified trative purposes we show in the right panel of Fig.1 the extrac- a clear evolutionary pattern in combination with a correlation to tion of a CH from May 29, 2013. In analogy to the right panel the underlying magnetic field. of Fig.1, in Fig. A.1 we show a representative EUV image for To statistically obtain the evolutionary aspects of individual every CH. CHs in the photosphere and corona the current study investi- The CHs were extracted from point spread function (PSF) gates the evolution of 16 long-lived individual CHs in detail. deconvoluted, limb-brightening-corrected (Verbeeck et al. 2014) The observational CH data cover most of the Solar Dynamics AIA 193 Å EUV images that were rebinned to a pixel resolu- Observatory (SDO; Pesnell et al. 2012) era so far, starting from tion 1024 × 1024, corresponding to a plate scale of 2.4 arcsec September 2010 until April 2019. This enables us to obtain a per pixel. Reducing the size increases processing speed and more general insight into the evolutionary processes of CHs by has only negligible effects on the boundary extraction (e.g., see analyzing coronal and magnetic properties as well as the rates at Heinemann et al. 2019). Furthermore, the boundaries were which they change. Additionally, we investigate how changes in smoothed using morphological operators with a kernel of 2 × the observed CH on-disk characteristics affect the in-situ mea- 2 pixel size. sured HSS parameters near Earth, and check whether or not the To account for LoS, projection, and limb effects as well as for well-established CH area–HSS peak velocity relation holds over unreliable magnetograms near the poles, we only consider pixels individual CH evolutions. For this we used data from the Global at latitudes |λ| < 60◦ in our calculations, i.e. all pixels above 60◦ Geospace Science Wind satellite (Acuña et al. 1995) and the latitude were disregarded. Advanced Composition Explorer (ACE; Stone et al. 1998). The properties of the photospheric magnetic field underlying the extracted CH boundary were derived from de-projected 720 s 2. Methods LoS HMI magnetograms which were chosen over its 45 s equiv- alent due to the lower photon noise of ≈3 Gauss near the disk 2.1. Dataset center (Couvidat et al. 2016). The higher signal-to-noise ratio For this study, we focus on the long-term evolution of CHs and gives more reliable results for low magnetic field densities. The its properties. In order to derive significant correlations or trends, extracted CH boundaries were overlaid on the magnetograms to we properly chose the dataset applying the following constraints: calculate the properties. – We aim to analyze not only the intensity and morphological parameters of the CH evolution but also the change in the underlying photospheric magnetic field and enclosed magnetic 2.3. Coronal hole properties flux. We are therefore limited to observations for which remote All properties were derived using CATCH, which includes mor- sensing magnetic field data are available. For this reason, data phological properties like the CH area, shape, and position (cen- from the Atmospheric Imaging Assembly (AIA; Lemen et al. ter of mass), and properties of the underlying photospheric 2012) and the Helioseismic and Magnetic Imager (HMI; Schou magnetic field like the signed mean magnetic flux density and et al. 2012; Couvidat et al. 2016) on board SDO were chosen for magnetic flux. For more details about the extraction and calcula- the analysis. SDO was preferred over the Solar and Heliospheric tion of the parameters and uncertainties, we refer to Heinemann Observatory (SOHO; Domingo et al. 1995) due to the signifi- et al.(2019) and references therein. cantly lower noise in the line-of-sight (LoS) magnetograms of In this study we focus on the evolution of the primary param- HMI, which is very relevant for regions of low magnetic field eters of the CH: the CH area (A), the signed mean magnetic strength such as CHs. flux density (Bs), and the signed magnetic flux (Φs). The signed – To analyze the long-term evolution of CHs, only CHs that magnetic flux density is a good indicator of the magnetic fine showed a clear coronal signature for at least five consecutive structure of a CH as it is directly correlated to the abundance solar disk passages were considered. and coverage of strong unipolar magnetic elements within CHs.

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Fig. 1. Example of an in-situ signature of the solar wind data provided by the OMNI database (left), as a CH under study was observed near the center of the solar disk by SDO on May 29, 2013, at 18 UT (right). The black line shows the solar wind bulk velocity and green line represents the plasma density. The purple triangle represents the peak velocity and the horizontal bar the average interval to show the plateau speed. The colored bar on the top represents the in-situ polarity calculated after Neugebauer et al.(2002), with red being positive and blue negative polarity. Right panel: snapshot of the CH that is associated with this HSS, and the time of the SDO observation corresponds to the yellow vertical line in the left panel. The red line is the extracted CH boundary (using CATCH) and the yellow x represents the center of mass of the CH.

It has been found that they are the main contributors to the signed results by Bale et al. 2019) were neglected –; and second by con- CH flux (Hofmeister et al. 2019; Heinemann et al. 2019). sidering the travel time of the HSS according to its speed (e.g., The average parameters over the evolution of a CH, denoted Vršnak et al. 2007). Time ranges covering ICME signatures were by an asterisk, are derived by calculating the mean over the evo- removed using ready-catalogs maintained by Richardson and lution of a CH considering the uncertainties given by: Cane2 for ACE (see Richardson & Cane 2010, for a description of the catalog). Coronal holes that could not be associated with 1 XN a HSS signature were excluded from the HSS analysis. P∗ = P , (1) N i For each CH, we derive, if possible, the associated HSS i=0 speed peak and the plasma density and magnetic field at the same tuv time, for each solar disk passage. From the peak, we define the XN XN ∗ 1 2 1 2 plateau speed as the averaged peak speed of the HSS within an σ = σ + (Pi − P∗) , (2) N Pi N − 1 − i=0 i=0 interval of [ 2, +6] hours around the identified peak. The asym- metrical averaging interval was chosen to consider the asymme- try in the speed profile of HSSs and to avoid contribution from where Pi represents a CH property for every rotation (i) and σPi its uncertainty. The spread of the values over the whole evo- the stream interaction region. The plasma density and magnetic lution, σ∗, is calculated by adding the mean uncertainty (first field magnitude for the identical time interval were also calcu- term) and the standard deviation of the mean (second term). The lated in the same way. change rates of CH properties were calculated as follows: Here, the aim was to verify whether or not and how the CH area–HSS speed relation (Nolte et al. 1976; Vršnak et al. 2007; Pi+1 − Pi Rotter et al. 2012; Tokumaru et al. 2017; Hofmeister et al. 2018) dPi+1 = , (3) ti−1 − ti relates to the CH evolution. It has been found that there is a latitudinal dependence in CH area–HSS speed relation, and because with P again representing a CH property (i.e., A, Bs, Φs) and t we are interested in the CH area that affects Earth, that is, the being the time of observation. geoeffective CH area, we correct for it. The geoeffective CH area can be calculated using the relation derived by Hofmeister et al. (2018): 2.4. In-situ data A = A × (1 − |ϕ (◦)|/61.4), (4) To make a more complete interpretation of the evolutionary geo CH co effects of CHs on the in-situ measured signatures, we investi- with ϕco being the latitudinal separation angle between the cen- gated the associated HSSs near 1 AU using five-minute plasma ter of mass of the CH and the observing spacecraft. According and magnetic field data provided by the OMNI1 database. OMNI to this statistical relation, there is no contribution to the HSS in-situ measurements are propagated to the Earth’s bow shock from CHs above a latitude of ≈60◦, which seems to be valid in nose. a first-order approximation (Vršnak et al. 2007). Consequently, HSSs signatures were classified using the criteria given by we consider CH areas below 60◦. Jian et al.(2006, 2009) and cross-checked with ready HSS lists (maintained by S. Vennerstroem for 2010−2019). Identified HSS structures were associated to extracted CHs in two ways: first, 2.5. Correlations by comparing the dominant polarity of the HSS (as given in The analysis of different parameters, for example using cor- Neugebauer et al. 2002) with the dominant polarity of the CH – relation coefficients, was done using a bootstrapping method small-scale turbulences (as reported in the Parker Solar Probe 2 http://www.srl.caltech.edu/ACE/ASC/DATA/level3/ 1 https://omniweb.gsfc.nasa.gov/ icmetable2.htm

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Fig. 2. Temporal evolution of all the CHs under study. The length of the bars represents the lifetime from the first to the last observation near the central meridian. The profile displays the area evolution (scale in the left corner of the figure). The red triangle marks the peak in the CH area. If no clear central peak was detected, the mark was omitted. The number in front of the bars shows how many times the CH was observed passing the central meridian. The solar activity, approximated by the smoothed sunspot number (Source: WDC-SILSO, Royal Observatory of Belgium, Brussels), is shown in the background.

(Efron 1979; Efron & Tibshirani 1993) to derive errors that take CHs with a lifetime from 5 to 18 rotations were observed. into account the low sample size within each evolution (between The two CHs with the longest lifetimes (17 and 18 rotations) 5 and 18). were observed during the solar minimum (2017−2019) but this is obviously not a general trend. We note that this only regards CHs already considered long-living and in a sample where polar 3. Results CHs are excluded. We almost continuously observe long-living By examining a sample of 16 long-lived CHs throughout the CHs throughout the solar cycle with only one notable excep- SDO era and its associated HSSs we obtained the following tion near the maximum in the solar activity (between 2014 and results. 2015).

3.1. Lifetime 3.2. Coronal hole evolution in A, Bs, and Φs We define the life-time of a CH as the time between its first By examining a sample of 16 long-lived CHs throughout the observed central meridian passage and its last. This gives a lower SDO era, we found that 13 show a steady change in area, which boundary of the lifetime of the analyzed CHs. The accurate time is characterized by an approximately monotonic increase in the of birth and death of a CH is generally a rarely observed phe- area followed by a roughly monotonic decrease (with scatter). nomenon, mostly due to the limited coverage of the solar surface. Such a general trend is often visible, but the relative position of Figure2 depicts the 16 recurrent CHs studied here. The length the peak, the maximum and minimum area, and the lifetime vary of the bar represents the lifetime, the position gives the date, and significantly. This demonstrates the individuality in the evolution the number gives the count of rotations during which the CH was of each CH. Figure3 shows the evolution of the CH area (black- observable. The profile depicts the individual CH area evolution. red) of all 16 studied CHs. The blue line represents the evolution The background shows the smoothed sunspot number provided of the photospheric magnetic flux density within the projected by WDC-SILSO3, which is a proxy for the solar activity. CH area. We note that large jumps in the area might be caused by merging or splitting with or into CHs, connection to polar 3 Royal Observatory of Belgium, Brussels: http://www.sidc.be/ CHs, or nearby filament eruptions that abruptly open additional silso/ field lines.

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Fig. 3. Evolution of the area (black–red) and magnetic ﬂux density (blue) of all CHs under study. The error bars represent the uncertainties. The vertical dashed guidelines represent the ﬁrst day of each month and the yellow pin marks the peak in the observed CH area (if a clear peak was associated).

CHs are usually considered to be large-scale structures that As shown in Fig.3, the evolution of the mean signed magnetic are defined by their magnetic field topology, the predominantly flux density of different CHs does not follow a uniform trend open field configuration. Therefore, we analyze the photospheric but displays various kinds of behavior. We find CHs that seem magnetic field underlying the extracted boundary to investigate to have a visual correlation of area and flux density evolution as the relation between magnetic field evolution and area evolution. well as some with a supposed anti-correlation and ones without

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25 ] 2 20 km

10 15

A [10 10

0 0 5 10 15

6 | [G] s

|B 4

0 0 5 10 15

40 Mx] 20 30 Fig. 5. Average change rates (growth: red; decay: blue) for each CH | [10 s

Φ 20 | evolution individually. Top panel: average CH area change rates, mid-

10 dle: CH ﬂux density change rates, and bottom panel: change rates of the signed ﬂux. The purple triangles mark values calculated from only 1 or 0 0 5 10 15 NrCH 2 measurement points, making them less reliable.

Fig. 4. Average properties over the evolution of each CH. The middle Table 1. Average change rates throughout the CH evolution. represents the average property (A*, Bs*, Φs*), the colored bar the 1σ “max” denotes the time interval 2012−2014 and “min” the interval range, and the whiskers show the full range of values of the parameter 2016−2019. observed over the evolution. Top, middle, and bottom panels: CH area, CH flux density, and signed flux, respectively. dA dBs dΦs 108 km2 day−1 mG day−1 1018 Mx day−1 noticeable correlation. We quantify these correlations and anti- correlations below. Total 14.2 ± 15.0 27.3 ± 32.2 30.3 ± 31.5 Figure4 shows the average properties over each CHs evo- Growth 15.4 ± 18.5 24.4 ± 27.1 26.8 ± 25.9 lution. We find only mild variations in the mean parameters Decay 13.2 ± 12.6 29.6 ± 37.6 34.0 ± 40.7 ± ± ± (A∗,Bs*,Φs*), represented by the mid-point of each vertical bar. Totalmax 10.7 8.9 28.1 29.6 38.4 36.1 However, the variations over each evolution may strongly vary. Growthmax 12.2 ± 9.8 24.5 ± 25.1 34.4 ± 35.9 The CH areas over the entire CH evolution may vary slightly Decaymax 9.5 ± 8.9 30.9 ± 34.5 43.0 ± 40.4 10 2 10 2 (∼2−3×10 km ) or strongly (>10×10 km ) around the mean. Totalmin 17.5 ± 18.7 17.7 ± 17.0 26.4 ± 29.9 We find magnetic flux densities ranging from ∼1 G up to ∼9 G Growthmin 19.8 ± 23.6 17.8 ± 18.8 22.6 ± 16.5 with usual variations over the lifetime of a CH of about ±(1−2) G Decaymin 15.6 ± 15.2 17.6 ± 16.8 30.1 ± 43.8 around the mean. The value of the mean magnetic flux of a CH over its evolution seems to be similar for all CHs, but the varia- tion of the mean magnetic flux throughout individual the evolu- During the descending phase and solar minimum (2016−2019) tion seems to be on the order of the mean. the average area change rates are higher at around (17.5±18.7)× 108 km2 day−1. 3.3. Change rates The second panel in Fig.5 shows the change rates for the mean signed magnetic flux density. We find similar rates In addition to the evolutionary profile in the CH properties, we for both growth and decay in each CHs evolution, on average investigated the average rates at which CH properties change (a) 27.3 ± 32.2 mG day−1. We again observe a difference in the rates in order to evaluate whether CHs evolve at similar rates or differ between CHs near solar maximum (2012−2014) and CHs near significantly from each other and (b) to gather important infor- the solar minimum (2016−2019). During the former, the flux mation on how the open magnetic field changes, as CHs are a density increases at an average rate of 24.5 ± 25.1 mG day−1 and major contributor of open magnetic flux (in regards to the open decreases at a similar rate of 30.9 ± 34.5 mG day−1. During the flux problem). Figure5 shows the average change rates of the later interval, the change rates drop by up to a factor of two to individual CH evolutions separated into growth rates (positive 17.8 ± 18.8 mG day−1 for growth and 17.6 ± 16.8 mG day−1 for change rates, red) and decay rates (negative change rates, blue). decay. Averaged over all CH evolutions, we find an area change rate From the bottom panel of Fig.5 we can deduce that the mag- (Fig.5, top panel) of (14 .2 ± 15.0) × 108 km2 day−1 that can be netic flux of a CH evolves at an average rate of (30.3 ± 31.5) × divided into an area growth rate of (15.4 ± 18.5) × 108 km2 day−1 1018 Mx day−1. Interestingly, we find that for most CHs the aver- and a similar area decay rate of (13.2 ± 12.6) × 108 km2 day−1. age negative flux change rate is 20−30% higher than the average This suggests that, on average, the CH grows and decays at positive change rate. It is not clear whether this an effect dom- a similar rate. We observe a possible solar cycle dependence inated by the area evolution of a CH or by magnetic field evo- of the area change rates, as in and near the solar maximum lution. All change rates of CH area, mean signed magnetic flux (2012−2014) we find change rates of (10.7±8.9)×108 km2 day−1. density, and magnetic flux are listed in Table1.

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20 20

] 15 ] 15 2 2 km km

10 10 10 10 [10 [10 * *

A 5 A 5

cc = 0.52 cc = -0.29 Pearson Pearson 0 0 ] ] -1 -1 30 30 day day 2 2

km 20 km 20 8 8

10 10 |dA| [10 |dA| [10

ccPearson = 0.16 ccPearson = -0.48 0 0 0 100 200 300 400 500 600 0 20 40 60 80 100 120 140 Lifetime [days] Average Sunspot Number 7 7 6 6 5 5 4 4 | [G] | [G] * * s 3 s 3 |B |B 2 2 1 1 cc = -0.46 cc = 0.45 Pearson Pearson 0 0 60 60 ] ] -1 50 -1 50 40 40 30 30 | [mG day | [mG day s s 20 20 |dB |dB 10 10 ccPearson = -0.17 ccPearson = 0.45 0 0 0 100 200 300 400 500 600 0 20 40 60 80 100 120 140 CH Lifetime [days] Average Sunspot Number 40 40

30 30 Mx] Mx] 20 20 20 20 | [10 | [10 * * s s Φ Φ

| 10 | 10

cc = 0.15 cc = 0.50 Pearson Pearson 0 0 ] ]

-1 6 -1 6 5 5 4 4 Mx day Mx day 19 3 19 3 | [10 | [10

s 2 s 2 Φ Φ

|d 1 |d 1 ccPearson = -0.01 ccPearson = 0.69 0 0 0 100 200 300 400 500 600 0 20 40 60 80 100 120 140 Lifetime [days] Average Sunspot Number

Fig. 6. Scatterplot of the average evolutionary CH properties and their Fig. 7. Scatterplot of the average evolutionary CH properties and their absolute change rates against the CH lifetime. Top panel (red): CH area absolute change rates against the average sunspot number as a proxy (A∗, |dA|), middle panel (orange): mean signed magnetic flux density for solar activity. Top panel (red): CH area (A∗, |dA|), middle panel (Bs*, |dBs|), and bottom panel (blue): signed magnetic flux (Φs*, |dΦs|). (orange): mean signed magnetic flux density (Bs*, |dBs|), and bottom panel (blue): signed magnetic flux (Φs*, |dΦs|).

3.4. Correlations define the average sunspot number in the evolution of a CH as After deriving various evolutionary CH parameters, we inves- the mean SIDC sunspot number over the time interval in which tigated possible correlations. Figure6 shows the three primary the CH was observed. We find weak (anti-)correlations between CH properties (averaged over the CH lifetime), namely area (top, average CH area, flux density, and their change rates to solar red), flux density (middle, orange) and flux (bottom, blue), and activity. Parameters that show the highest correlation with solar their change rates as a function of CH lifetime. We find moderate activity are the average magnetic flux (ccPearson = 0.50) and the correlations between the average CH area (ccPearson = 0.52) and flux change rate (ccPearson = 0.69). the average flux density (ccPearson = −0.46), albeit strongly influ- Figure8 shows CH area versus flux density. We find a weak enced by the two very large and long-living CHs during solar anti-correlation for the whole sample (ccPearson = −0.33) and minimum (two data points on the far right). No correlation with a strong anti-correlation for the averages (ccPearson = −0.70). the CH lifetime is visible in the change rates or in the average We note that the strong anti-correlation between the average magnetic flux. CH area and the mean magnetic flux density is attributable to Figure7 investigates a possible dependence of average CH a smoothing effect of the whole sample and is not a causal rela- parameters and change rates on solar activity. The average tion. Also, we find CHs in which the evolutionary profile of the sunspot number was used as a proxy for the solar activity. We area appears to be quite strongly correlated with the flux density

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10 800

8 ccPearson = -0.33 700 cc = -0.70 6 Pearson | [G] * s |B 4 ]

-1 600

[km s "Patchy CHs"

HSS 500 0 v 0 5 10 15 20 25 * 10 2 A [10 km ] 1.0 400

ccPearson = 0.46 |] s 0.5 90% CI : [0.36,0.55] 300 0 5 10 15 20 0.0 10 2

[A vs. |B A [10 km ] geo 1.0 Pearson -0.5 cc

-1.0 0 5 10 15 0.5 Nr CH 1.0 |] s 0.5 0.0

0.0 [|dA| vs. |dB -0.5 -0.5 Pearson Pearson Correlation Coefficient cc

-1.0 0 5 10 15 -1.0 NrCH 0 5 10 15 NrCH Fig. 8. Scatterplot of the absolute value of the signed mean magnetic Fig. 9. Correlation plot of the CH area vs. the plateau bulk velocity of flux density of CHs as a function of the CH area. Top panel: all obser- the associated HSS. Top panel: all observations and bottom panel: evo- vations (in red the average values over each evolution). Middle panel: lution of each individual CH. The green circle marks the “patchy” CHs evolution of each CH individually. Bottom panel: correlation between that have large uncertainties in their area. Bottom panel: the median of change in area and change in magnetic flux density for each CH evo- the bootstrapped sample for each evolution is represented by the hor- lution individually. Middle and bottom panels: the median of the boot- izontal line in the bar, the green and blue bars represent the 80% per- strapped sample for each evolution is represented by the horizontal line centiles, and the whiskers the 90% percentiles. The dotted line gives the in the bar, the green and blue bars represent the 80% percentiles, and mean values. the whiskers the 90% percentiles. The dotted line gives the mean of the median values. CHs with an area of this size. We investigated in-situ measured evolution (3/16), some that show no correlation at all (6/16), plasma density and magnetic field magnitude at the position of and a significant proportion that show a weak to strong anti- the velocity plateau and did not find any correlations to the CH correlation (7/16). We note here that the slopes of the regression area or magnetic field properties. line of some CH evolutions are very low due to an only slightly changing magnetic flux density throughout the lifetime. This can 4. Discussion artificially enhance the Pearson correlation coefficient without a causal relation being present. All CHs retain the same polarity Using EUV full-disk observations by AIA and HMI magne- over their evolution. The change rates of CH area and flux den- tograms throughout most of the operational lifetime of SDO sity (Fig.8, bottom panel) do not seem to be correlated (average between 2010 and 2019 we studied the evolution of a sample over all evolutions: ccmean = −0.15). of 16 long-living CHs and their associated HSSs. We find that 13 out of 16 CHs follow a visible trend in the 3.5. High speed stream velocity evolution area evolution covering roughly one growing phase until a clear maximum is reached followed by a decay phase. Only 3 CHs Here we investigate whether or not the well-established CH show erratic behavior, for example revealing multiple peaks in area–HSS peak velocity relation is visible over individual CH the area or a maximum area at the birth or decay. From this we evolutions. Using the geoeffective CH area calculated from deduce that the majority of CHs (>80%) undergo an area evo- Eq. (4), we derive a Pearson correlation coefficient of ccPearson = lution that follows a pattern of growth and decay. However, we 0.46 with a 90% confidence interval of [0.36, 0.55] for the full note that due to the small sample size we cannot comment on the sample. When considering each evolution individually, we find significance of this finding. The proposed three-phase evolution a large range of correlation coefficients between medium and (Heinemann et al. 2018a) might be rather the exception as it was strong correlations (see Fig.9). Possible reasons for this are dis- only clearly observed for one CH. cussed below. The mean correlation coefficient of all 16 individ- We find a moderate correlation between the average CH area ual evolution correlation coefficients comes to ccmean = 0.59 ± and flux density, but the correlation is not significant. Also, the 0.26. The slopes of the individual regression lines vary signifi- change rates seem independent of the lifetime. cantly around (3−44) × 10−10 km−1 s−1 with accordingly differ- We find a correlation between solar activity and the average ent y-intercepts. For large CHs (A > 10 × 1010 km2) we find a CH properties and their change rates. In particular, the change saturation effect in the peak velocity. For “patchy” CHs (large rate of the magnetic flux in CHs is strongly correlated with the fragmented CHs with weakly defined boundaries), the maxi- average sunspot number during the CH life-time. We suspect mum peak velocity seems to be lower than one would expect for that the open field of CHs is only able to expand in response

A68, page 8 of 11 S. G. Heinemann et al.: A statistical study of the long-term evolution of coronal hole properties as observed by SDO to the magnetic activity (magnetic pressure) in quiet Sun areas unipolar magnetic elements within CHs that have been found to and active regions in the vicinity. define the magnetic topology of a CH, it can be simply deduced Specifically, we found that near and during solar maximum that only smaller CHs might have higher flux densities (but also (2012−2014), the area change rate was found to be (10.7 ± can have small flux density). Alternatively, in large CHs the flux 8.9) × 108 km2 day−1 (similar for both growth and decay rates) density tends to converge to a mean flux density of about 1−3 G and during solar minimum the rate was around 60% larger at (see Heinemann et al. 2018b, 2019; Hofmeister et al. 2019). As (17.5 ± 18.7) × 108 km2 day−1. Our results for the solar max- such, the derived anti-correlation is not an evolutionary effect. imum match the area change rates found by Bohlin(1977) of Larger statistical studies of CH properties show no correlation (13.0 ± 3.5) × 108 km2 day−1 relatively well. Nolte et al.(1978a) between the CH area and its magnetic flux density (Hofmeister used Skylab X-ray observations of long-living coronal holes dur- et al. 2017; Heinemann et al. 2019). ing the descending phase of solar cycle 20 and derived rates of As such, the evolution of the magnetic flux density and mag- (7.3±1.4)×108 km2 day−1, which is lower than the values found netic flux cannot explain the evolutionary behavior of the CH in the present study. Large deviations between the rates from pre- area. We propose that the area evolution of CHs is not primarily vious studies can be primarily found in the CH evolutions during caused by the evolution of the mean signed magnetic flux den- low solar activity where much larger average rates were derived. sity within the projected CH boundary as extracted from EUV The growth and decay rates were found to be relatively stable observations. Possible processes that might play a role in the across long-living CHs observed during times of similar solar area evolution include interchange reconnection (see Shelke & activity. The consistent average rates suggest that discrete events Pande 1984; Wang & Sheeley 2004; Madjarska et al. 2004; Fisk that may cause sudden large-scale changes in the CHs, like fila- 2005; Madjarska & Wiegelmann 2009; Edmondson et al. 2010; ment eruptions that permanently open magnetic field lines (e.g., Krista et al. 2011; Yang et al. 2011; Ma et al. 2014; Kong et al. Kahler & Moses 1990), are rare events and that CHs evolve more 2018) and/or the change in the global and local magnetic field gradually. This might explain the discrepancy between Nolte configuration outside the CH. et al.(1978a), who claimed that most of the area evolution of In addition to the evolutionary trend derived from remote a CH can be explained by discrete boundary changes of sizes sensing data, we investigated the evolution of the in-situ mea- larger than 2.7×108 km2, and Kahler & Moses(1990) who found sured peak velocity of the associated HSS. Using the geoeffec- no such sudden large-scale changes. When comparing the aver- tive CH area, we derive a mean correlation coefficient of the indi- age rate at which CHs evolve with results from flux transport vidual CH evolutions of ccPearson,mean = 0.59 ± 0.26, which is in calculations by Leighton(1964) we are in good agreement dur- the range of previous statistical studies of the CH area–HSS peak ing the solar maximum but are not in agreement during low solar velocity relation (Karachik & Pevtsov 2011: ccPearson = 0.41 to activity. 0.65; Vršnak et al. 2007; Abramenko et al. 2009; Verbanac et al. A similar picture can be deduced from the change rates of 2011a,b; Rotter et al. 2012; Tokumaru et al. 2017; Hofmeister the mean signed magnetic flux density enclosed within the pro- et al. 2018: ccPearson = 0.62 to 0.80). Our results are also in good jected CH boundary. For evolutions of individual CHs, the rate agreement with those of Heinemann et al.(2018a), who found a at which the flux density changes stays at similar values but the correlation coefficient of ccPearson = 0.77 in their case study of a percentage scatter is larger than in the area change rates. We long-living CH. We find a saturation effect in the peak velocity– show that the change rates of the flux density are higher during CH area relation, where the peak velocity of large CHs does not enhanced solar activity; for the time range of 2012−2014 (near follow a linear trend but rather converges to a speed of roughly and at solar maximum) we derive rates of (28±30 mG day−1) and 700 km s−1. This might be related to the longitudinal saturation over 30% lower rates of 18 ± 17 mG day−1 near solar minimum found by Garton et al.(2018). (2016−2019). This hints towards a small imbalance between flux We conclude that the CH area–HSS peak velocity relation is appearance and flux removal rates as well as low rates in general. clearly visible within the evolution of each CH, but the slopes Gošic´ et al.(2016) found average net flux density change rates of the linear regression lines vary significantly. We identify three of 5.0 ± 5.8 G day−1 in internetwork elements of two supergran- possible causes for the varying slopes: (1) The in-situ measured ular cells in the quiet Sun using 38 h of continuous HINODE bulk velocity depends not only on the CH but also on the precon- observations. Smitha et al.(2017) report values about a factor ditioning of the interplanetary space (e.g., Temmer et al. 2017). of ten larger using SUNRISE data. We note that comparison HSS or CMEs near or before the arrival of the HSS under study should be treated cautiously as the rates derived by both Gošic´ can significantly influence the measured speeds. This may lead et al.(2016) and Smitha et al.(2017) are from internetwork ele- to enhanced scatter in the relations. (2) The relation between ments and the ones in this study are from the total extracted CH CH area and HSS peak velocity is individual for each CH. (3) area. Also, HINODE and SUNRISE obtain their magnetograms It might be possible that the CH area and the HSS peak velocity at a much higher resolution and sensitivity than HMI/SDO are not directly causally related. It is known that the geometry of which might explain the difference between the results gath- CHs plays an important role in defining the 3D shape of the HSS ered in this study and those found by the latter two mentioned (e.g., Garton et al. 2018). authors. Zhang et al.(2007) found that in a decaying CH a decrease 5. Conclusions of flux is caused by the emergence of opposite polarity flux within the CH boundaries and also that almost no flux trans- In this statistical study, we investigate the evolution of 16 long- port is observed across the CH boundary. According to this, living CHs between 2010 and 2019 and the associated evolution changes in the magnetic flux density in CHs are caused by pro- of the HSS peak velocity at 1AU. Our major findings can be cesses within the CH boundaries, such as for example changes summarized as follows. in flux emergence rate. The average CH area and average flux – We find that the general CH area evolution (>80% of the density over the CH evolutions seem to be correlated, however studied cases) exhibits a rough evolutionary profile showing this is simply a smoothing effect and does not imply a causal a rise to a clear peak in the observed CH area followed by a correlation (see Fig.8). From the statistical distribution of small decay.

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– The strength and evolution of the photospheric magnetic flux Gosling, J. T. 1996, ARA&A, 34, 35 and flux density enclosed in the projected CH boundary is Gošic,´ M., Bellot Rubio, L. R., del Toro Iniesta, J. C., Orozco Suárez, D., & found to be largely independent of the evolution of the CH Katsukawa, Y. 2016, ApJ, 820, 35 Harvey, K. L., Sheeley, N. R., Jr., & Harvey, J. W. 1982, Sol. Phys., 79, 149 area. This suggests that the mean signed flux density of CHs Heinemann, S. G., Temmer, M., Hofmeister, S. J., Veronig, A. M., & is not the main cause for the observed evolution in the CH Vennerstrøm, S. 2018a, ApJ, 861, 151 area. Heinemann, S. G., Hofmeister, S. J., Veronig, A. M., & Temmer, M. 2018b, ApJ, – Area growth and decay rates within CHs over their evolu- 863, 29 Heinemann, S. G., Temmer, M., Heinemann, N., et al. 2019, Sol. Phys., 294, tion seem to only vary over the solar cycle, with higher rates 144 during lower solar activity. The calculated rates for the high Hofmeister, S. 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Appendix A: Snapshot of coronal holes under study Figure A.1 shows a snapshot of every coronal hole analyzed in this study. The red line represents the extracted CH boundary using CATCH and the yellow x is the center of mass.

Fig. A.1. Example snapshot of CH under study. The extracted CH boundary is given by the red line and the center of mass is represented by the yellow x. The blue shaded areas represent the uncertainties as calculated by CATCH.

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