A statistical study of long-term evolution of coronal hole properties as observed by SDO

TL;DR

This study statistically analyzes the long-term evolution of coronal holes observed by SDO, examining their properties, magnetic fields, and associated high-speed solar wind streams, revealing correlations with solar activity and variability in solar wind speeds.

Contribution

It provides a comprehensive statistical analysis of long-lived coronal holes, highlighting the relationship between their evolution, magnetic properties, and solar wind signatures, with new insights into their dynamics.

Findings

Coronal hole area generally grows to a maximum then decays.

No correlation between area evolution and magnetic flux within CHs.

CH area change rates are anti-correlated with solar activity.

Abstract

The study of the evolution of coronal holes (CHs) is especially important in the context of high-speed solar wind streams (HSS) emanating from them. Stream interaction regions may deliver large amount of energy into the Earths system, cause geomagnetic storms, and shape interplanetary space. By statistically analysing 16 long-living CHs observed by the SDO, we focus on coronal, morphological and underlying photospheric magnetic field characteristics as well as investigate the evolution of the associated HSSs. We use CATCH to extract and analyse CHs using observations taken by AIA and HMI. We derive changes in the CH properties and correlate them to the CH evolution. Further we analyse the properties of the HSS signatures near 1au from OMNI data by manually extracting the peak bulk velocity of the solar wind plasma. We find that the area evolution of CHs mostly shows a rough trend of growing to a maximum followed by a decay. No correlation of the area evolution to the evolution of the signed magnetic flux and signed magnetic flux density enclosed in the projected CH area was found. From this we conclude that the magnetic flux within the extracted CH boundaries is not the main cause for its area evolution. We derive CH area change rates (growth and decay) of 14.2 +/- 15.0 * 10^8 km^2/day showing a reasonable anti-correlation (cc =-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) and the signed magnetic flux (30.3 +/- 31.5 * 10^18 Mx/day) were also found to be dependent on solar activity (cc =0.50 and cc =0.69 respectively) rather than on the individual CH evolutions. Further we find that the CH area-to-HSS peak velocity relation is valid for each CH over its evolution but revealing significant variations in the slopes of the regression lines.

Tables

Table 1. Table 1: Average change rates throuout the CH evolution. ”max” denotes the time intervall from 2012 − 2014 2012 2014 2012-2014 and ”min” the interval 2016 − 2019 2016 2019 2016-2019 .

	dA	dBs	d${\Phi }_s$
	${10}^8$ km2 day-1	mG day-1	${10}^{18}$ Mx day-1
Total	$14.2\pm 15.0$	$27.3\pm 32.2$	$30.3\pm 31.5$
Growth	$15.4\pm 18.5$	$24.4\pm 27.1$	$26.8\pm 25.9$
Decay	$13.2\pm 12.6$	$29.6\pm 37.6$	$34.0\pm 40.7$
Totalmax	$10.7\pm 8.9$	$28.1\pm 29.6$	$38.4\pm 36.1$
Growthmax	$12.2\pm 9.8$	$24.5\pm 25.1$	$34.4\pm 35.9$
Decaymax	$9.5\pm 8.9$	$30.9\pm 34.5$	$43.0\pm 40.4$
Totalmin	$17.5\pm 18.7$	$17.7\pm 17.0$	$26.4\pm 29.9$
Growthmin	$19.8\pm 23.6$	$17.8\pm 18.8$	$22.6\pm 16.5$
Decaymin	$15.6\pm 15.2$	$17.6\pm 16.8$	$30.1\pm 43.8$

Equations

$$P^{\ast }=\frac{1}{N}\sum _{i=0}^N{P}_i,$$

$${\sigma }^{\ast }=\sqrt{\frac{1}{N}\sum _{i=0}^N{\sigma }_{P_i}^2+\frac{1}{N-1}\sum _{i=0}^N(P_i-P\ast {)}^2}$$

$$d{P}_{i+1}=\frac{P_{i+1}-P_i}{t_{i-1}-t_i},$$

$$A_{\mathrm{geo}}=A_{CH}\times (1\text{leavevmode}-\text{leavevmode}|\text{leavevmode}{\phi }_{co}{(}^{\mathrm{o}})\text{leavevmode}|\text{leavevmode}/\text{leavevmode}61.4),$$

Full text

*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 Observatory, we focus on coronal, morphological and underlying photospheric magnetic field characteristics as well as investigate the evolution of the associated high–speed streams.

*Methods. *We use the Collection of Analysis Tools for Coronal Holes (CATCH) 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 correlate them to the 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 mostly shows a rough trend of growing to a maximum followed by a decay. No correlation of the area evolution to the evolution of the signed magnetic flux and signed magnetic flux density enclosed in the projected coronal hole area was found. 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 $(14.2\pm 15.0)\times 10^{8}$ km2 per day showing a reasonable anti–correlation (cc${}_{Pearson}=-0.48$) to the solar activity, approximated by the sunspot number. The change rates of the signed mean magnetic flux density ($27.3\pm 32.2$ mG day*-1*) and the signed magnetic flux ($30.3\pm 31.5$ $10^{18}$ Mx day*-1*) were also found to be dependent on solar activity (cc${}_{Pearson}=0.50$ and cc${}_{Pearson}=0.69$ respectively) rather than on the individual CH evolutions. Further we find that the coronal hole area–to– high–speed stream peak velocity relation is valid for each coronal hole over its evolution but revealing significant variations in the slopes of the regression lines.

1 Introduction

Coronal holes (CH) are stable, long-lived structures usually observed in the solar corona as regions of reduced emission in extreme ultraviolet (EUV) or X-ray. CHs are characterized by an open magnetic field configuration along which ionized atoms and electrons are accelerated into interplanetary space, forming high speed solar wind streams (HSS; Krieger et al., 1973; Nolte et al., 1976; Cranmer, 2009). The interaction of HSSs with the preceeding ambient slow solar wind forms stream interaction regions (SIRs) which can develop into co-rotating interaction regions (CIRs; Wilcox, 1968; Tsurutani et al., 2006) if the CH persists over multiple rotations. These transient features are the main source of usually weak to medium geomagnetic storms at Earth (see, e.g., Alves et al., 2006; Verbanac et al., 2011a; Vršnak et al., 2017; Yermolaev et al., 2018; Richardson, 2018). Since the Skylab-era, recurrent geomagnetic effects of CIRs have been associated with large scale coronal signatures, the CHs. Nolte et al. (1976) first found an empirical relationship between the CH area and the peak bulk velocity of the solar wind. The linear CH area – HSS speed relation is supported by many studies, however, different slopes of the regression lines are found (e.g., Nolte et al., 1978a; Vršnak et al., 2007; Tokumaru et al., 2017; Heinemann et al., 2018b; Hofmeister et al., 2018).

The long-term evolution of recurrent CH structures and the associated HSSs has rarely been studied. Most studies focus on a snap-shot of the CH during its lifetime in form of a case study (e.g., Gibson et al., 1999; Gopalswamy et al., 1999; Zhang et al., 2007; Yang et al., 2009) or statistical studies that do not separate the evolution of individual CHs (e.g., Harvey et al., 1982; Lowder et al., 2017; Hofmeister et al., 2017; Heinemann et al., 2019). In the Skylab-era Bohlin (1977) and Bohlin & Sheeley (1978) proposed that the area and the mean magnetic flux density of a CH are dependent on its age and Nolte et al. (1978a, b) used X-ray observations to show that CHs primarily evolve by sudden, large-scale shifts in the position of the boundaries. A change in the underlying photospheric magnetic field is believed to influence the appearance of the CHs in the corona (Wang & Sheeley, 1990; Gosling, 1996). In a more recent study Ikhsanov & Tavastsherna (2015) showed that there are two magnetic field systems (large scale high latitude and small scale low latitude magnetic field systems) that play a main role 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-term evolution of CHs and the associated wind streams is related to flux emergence in active regions and the subsequent flux transport processes. CHs themselves seem to form in response to local (low-latitudes) or global (polar, high-latitudes) changes in the magnetic field topology. At low-latitudes, small scale magnetic systems may manifest themselves as localized CHs that are the result of decaying local sunspot groups (Petrie & Haislmaier, 2013) or generated by other mechanisms that enable to open the magnetic field, such as coronal mass ejections (CMEs)/filament eruptions, flux accumulation, or flux emergence (e.g., Webb et al., 1978; Heinemann et al., 2018a). Heinemann et al. (2018b, a) give an in-depth view on the evolution of one particular CH in 2012 from which they identified a clear evolutionary pattern in combination with a correlation to the underlying magnetic field.

To statistically obtain the evolutionary aspects of individual CHs in the photosphere and corona the current study investigates in detail the evolution of 16 long-lived individual CHs. The observational CH data covers most of the Solar Dynamics Observatory (SDO; Pesnell et al. 2012) era so far, starting from September 2010 until April 2019. This enables us to obtain a more general insight into the evolutionary processes of CHs by analyzing coronal and magnetic properties as well as the rates at which they change. Additionally we investigate how changes in the observed CH on-disk characteristics affect the in–situ measured HSS parameters near Earth as well as check if the well established CH area – HSS peak velocity relation holds over individual CH evolutions. For this we used data from the Global Geospace Science Wind satellite (Acuña et al., 1995) and the Advanced Composition Explorer (ACE; Stone et al. 1998).

2 Methods

2.1 Dataset

For this study, we focus on the long-term evolution of CHs and its properties. In order to derive significant correlations or trends, we properly chose the dataset applying the following constraints:

• •

We aim not only to analyze intensity and morphological parameters of the CH evolution but also the change in the underlying photospheric magnetic field and enclosed magnetic flux. As such we are limited to observations for which remote sensing magnetic field data is available. For this reason, data from the Atmospheric Imaging Assembly (AIA; Lemen et al., 2012) and the Helioseismic and Magnetic Imager (HMI; Schou et al., 2012; Couvidat et al., 2016) on board SDO was chosen for the analysis. SDO was preferred over the Solar and Heliospheric Observatory (SOHO; Domingo et al., 1995) due to the significantly lower noise in the line–of–sight (LoS) magnetograms of HMI, which is very relevant for regions of low magnetic field strength such as CHs.

• •

To analyze the long–term evolution of CHs, only CHs which showed a clear coronal signature for at least five consecutive solar disk passages were considered.

• •

The last condition was, that the CH did not originate as or from a polar CH. This was considered due to high uncertainties in determining the CH area in polar regions due to projection and line–of–sight effects. Additionally the magnetic field observations of these areas are highly unreliable.

By considering the stated constraints we extracted $16$ CHs fulfilling those requirements over most of the operational life-time of SDO from $2010$ to $2019$.

2.2 Coronal Hole Detection and Extraction

To identify and extract CHs we use the 193Å filter of the AIA instrument on–board of SDO as CHs can be well observed in the emission of highly ionized iron (especially Fe XII: 193/195Å). The high contrast to the surrounding quiet Sun enables a good extraction of boundaries. To capture the long–term evolution, we extract each CH and its characteristics at each solar disk passage near the central meridian. Heinemann et al. (2018b, a) showed in a case study that one data point per rotation depicts the evolutionary trend sufficiently. We use the Collection of Analysis Tools for Coronal Holes (CATCH; Heinemann et al., 2019). CATCH uses a supervised threshold-based extraction that is modulated by the intensity gradient perpendicular to the CH boundary. Exemplary we show in the right panel of Figure 1 the extraction of a CH from May 29, 2013. In analogy to the right panel of Figure 1 we show in the Appendix (Figure 10) for every CH a representative EUV image.

The CHs were extracted from point spread function (PSF) deconvoluted, limb-brightening corrected (Verbeeck et al., 2014) AIA 193Å EUV images that were rebinned to a pixel resolution $1024\times 1024$, corresponding to a plate scale of $2.4$ arcseconds per pixel. Reducing the size increases processing speed and has only negligible effects on the boundary extraction (e.g., see Heinemann et al., 2019). Furthermore, the boundaries have been smoothed using morphological operators with a kernel of $2\times 2$ pixel size.

To account for LoS, projection and limb effects as well as for unreliable magnetograms near the poles we only consider pixels at latitudes $|\lambda|<60^{\mathrm{o}}$ in our calculations, e.g., all pixels above $60^{\mathrm{o}}$ latitude were disregarded.

The properties of the photospheric magnetic field underlying the extracted CH boundary were derived from de-projected 720s LoS HMI magnetograms which were chosen over its 45s equivalent due to the lower photon noise of $\approx 3$ Gauss near the disk center (Couvidat et al., 2016). The higher signal–to–noise ratio gives more reliable results for low magnetic field densities. The extracted CH boundaries were overlaid on the magnetograms to calculate the properties.

2.3 Coronal Hole Properties

All properties were derived using CATCH, which includes morphological properties like the CH area, shape, position (center of mass) and properties of the underlying photospheric magnetic field like the signed mean magnetic flux density and magnetic flux. For more details about the extraction and calculation of the parameters and uncertainties we refer to Heinemann et al. (2019) and references therein.

In this study we focus on the evolution of the CH’s primary parameters. The CH area (A), the signed mean magnetic flux density (Bs) and the signed magnetic flux ($\Phi_{s}$). The signed magnetic flux density is a good indicator for a CHs magnetic fine–structure as it is directly correlated to the abundance and coverage of strong unipolar magnetic elements within CHs. It has been found that they are the main contributors to the signed CH flux (Hofmeister et al., 2019; Heinemann et al., 2019).

The average parameters over a CH’s evolution, denoted by a ”*”, are derived by calculating the mean over the CH’s evolution considering the uncertainties given by:

[TABLE]

[TABLE]

$P_{i}$ represents a CH property for every rotation ($i$) and $\sigma_{P_{i}}$ its uncertainty. The spread of the values over the whole evolution, $\sigma^{*}$, is calculated by adding the mean uncertainty (first term) and the standard deviation of the mean (second term). The change rates of CH properties were calculated as follows:

[TABLE]

with P again representing a CH property (i.e., A, Bs, $\Phi_{s}$) and t being the time of observation.

2.4 In–Situ Data

To make more complete interpretation of the evolutionary effects of CHs on the in–situ measured signatures, we investigated the associated HSSs near 1au using 5 minute plasma and magnetic field data provided by the OMNI111https://omniweb.gsfc.nasa.gov/ database. OMNI in–situ measurements are propagated to the Earth’s Bow Shock Nose.

HSSs signatures were classified using the criteria given by Jian et al. (2006, 2009) and cross-checked with ready HSS lists (maintained by S. Vennerstroem for 2010–2019). The association of an identified HSS structure to an extracted CH was done (1) by comparing the dominant polarity of the HSS (as given in Neugebauer et al., 2002) with the dominant polarity of the CH. Small scale turbulences (as reported in the Parker Solar Probe results by Bale et al. 2019) were neglected. And (2) by considering the travel time of the HSS according to its speed (e.g., Vršnak et al., 2007). Time ranges covering ICME signatures were removed using ready-catalogs maintained by Richardson and Cane222http://www.srl.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm for ACE (see Richardson & Cane, 2010, for a description of the catalog). CHs that could not be associated with a HSS signature were excluded from the HSS analysis.

For each CH we derive, if possible, for each solar disk passage the associated HSS speed peak and the plasma density and magnetic field at the same time. From the peak we define the plateau speed as the averaged peak speed of the HSS within an interval of $[-2,+6]$ hours around the identified peak. The asymmetrical averaging interval was chosen to consider the asymmetry in the speed profile of HSSs and to avoid contribution from the stream interaction region. The plasma density and magnetic field magnitude for the identical time interval were also calculated in the same way.

Here, the aim was to verify if and how the CH area – HSS speed relation (Nolte et al., 1976; Vršnak et al., 2007; Rotter et al., 2012; Tokumaru et al., 2017; Hofmeister et al., 2018) relates to the CH evolution. It has been found that there is a latitudinal dependence in CH area – HSS speed relation and because we are interested in the CH area that affects Earth, the geoeffective CH area, we correct for it. It can be calculated using the relation derived by Hofmeister et al. (2018):

[TABLE]

with $\varphi_{co}$ being the latitudinal separation angle between the center of mass of the CH and the observing spacecraft. According to this statistical relation, there is no contribution to the HSS from CHs above a latitude of $\approx 60^{\mathrm{o}}$, which seems to be valid in a first order approximation (Vršnak et al., 2007). Consequently, we consider CH areas below $60^{\mathrm{o}}$.

2.5 Correlations

The analysis of different parameters, e.g., by correlation coefficients was done using a bootstrapping method (Efron, 1979; Efron & Tibshirani, 1993) to derive errors that take into account the low sample size within each evolution (between $5$ and $18$).

3 Results

By examining a sample of $16$ long–lived CHs throughout the SDO-era and its associated HSSs we obtained the following results:

3.1 Lifetime

We define a CH’s life from the time of its first observed central meridian passage to its last. This gives a lower boundary of the lifetime of the analyzed CHs. The accurate time of birth and death of a CH is generally a rarely observed phenomenon, mostly due to the limited coverage of the solar surface. Figure 2 depicts the 16 recurrent CHs that were under study. The length of the bar represents the lifetime, the position the date, and the number gives the count of rotations the CH was observable. The profile depicts the individual CH area evolution. In the background the smoothed sunspot number provided by WDC-SILSO333Royal Observatory of Belgium, Brussels: http://www.sidc.be/silso/, a proxy for the solar activity, is shown.

CHs having a lifetime from $5$ up to $18$ rotations were observed. The 2 CHs with the significantly longest lifetimes ($17$ and $18$ rotations) were observed during the solar minimum ($2017-2019$) but this is obviously not a general trend. Note, that this only regards CHs already considered long–living and in a sample where polar CHs are excluded. We nearly continuously observe long–living CHs throughout the solar cycle with only one notable exception near the maximum in the solar activity (between $2014$ and $2015$).

3.2 Coronal Hole Evolution in A, Bs and $\Phi_{s}$

By examining a sample of $16$ long–lived CHs throughout the SDO-era, we found that $13$ show a steady change in area, characterized by an approximately monotonic increase in the area followed by a roughly monotonic decrease (with scatter). Such a general trend is often visible, but the relative position of the peak, the maximum and minimum area, and the lifetime significantly vary. This shows the individuality in each CH’s evolution. Figure 3 shows the evolution of the CH area (black–red) of all 16 CHs studied. The blue line represents the evolution of the photospheric magnetic flux density within the projected CH area. Note, that large jumps in the area might be caused by merging/splitting with/into CHs, connection to polar CHs or nearby filament eruptions that abruptly open additional field lines.

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

Figure 4 shows the average properties over each CHs evolution. On the top the CH area, in the middle the flux density and on the bottom the signed flux. We find only mild variations in the mean parameters (A*,Bs**,$\Phi_{s}$) represented by the mid–point of each vertical bar. The varations over each evolution however may strongly vary. The CH areas over the entire CH evolution may vary slightly ($\sim 2-3\times 10^{10}$ km2) or strongly ($>10\times 10^{10}$ km2) around the mean. We find magnetic flux densities ranging from $\sim 1$ G up to $\sim 9$ G with usual variations over a CHs lifetime of about $\pm(1-2)$ G around the mean. The value of the mean magnetic flux of CHs over their evolutions seems to be similiar for all CHs, however the variation throughout the evolution seem to be in the order of the mean.

3.3 Change Rates

Apart from the evolutionary profile in the CH properties we investigated the average rates at which CH properties change (a) to evaluate if CHs evolve at similar rates or differ significantly from each other and (b) as an important information on how the open magnetic field changes as CHs are a major contributor of open magnetic flux (in regards to the open flux problem). Figure 5 shows the average change rates of the individual CH evolutions separated into growth rates (positive change rates, red) and decay rates (negative change rates, blue). Averaged over all CH evolutions, we find an area change rate (Figure 5, top panel) of $(14.2\pm 15.0)\times 10^{8}$ km2 day*-1* that can be divided into an area growth rate of $(15.4\pm 18.5)\times 10^{8}$ km2 day*-1* and a similar area decay rate of $(13.2\pm 12.6)\times 10^{8}$ km2 day*-1*. This suggests that, on average, the CH grows and decays at a similar rate. We observe a possible solar cycle dependence of the area change rates as in and near the solar maximum ($2012-2014$) we find change rates of $(10.7\pm 8.9)\times 10^{8}$ km2 day*-1*. During the descending phase and solar minimum ($2016-2019$) the average area change rates are higher at around $(17.5\pm 18.7)\times 10^{8}$ km2 day*-1*.

The second panel in Figure 5 shows the change rates for the mean signed magnetic flux density. We find similar rates for both growth and decay in each CHs evolution, on average $27.3\pm 32.2$ mG day*-1*. We again observe a difference in the rates between CHs near solar maximum (2012-2014) and CHs near the solar minimum (2016-2019). During the former, the flux density growths at an average rate of $24.5\pm 25.1$ mG day*-1* and decays at a similar rate of $30.9\pm 34.5$ mG day*-1*. During the later interval the change rates drop by up to factor 2 to $17.8\pm 18.8$ mG day*-1* for growth and $17.6\pm 16.8$ mG day*-1* for decay.

From the bottom panel of Figure 5 we can deduce that a CHs magnetic flux, on average, evolves at a rate of $(30.3\pm 31.5)\times 10^{18}$ Mx day*-1*. Interestingly we find that for most CHs the average negative flux change rate is between $20-30\%$ higher than the average positive change rate. It is not clear if this an effect dominated by a CHs area evolution or magnetic field evolution.

All change rates of CH area, mean signed magnetic flux density and magnetic flux are listed in Table 1.

3.4 Correlations

After deriving various evolutionary CH parameters we investigated possible correlations. Figure 6 shows the three primary CH properties (averaged over the CH lifetime), namely area (top, red), flux density (middle, orange) and flux (bottom, blue), and their change rates as function of CH lifetime. We find moderate correlations for the average CH area ($cc_{Pearson}=0.52$) and the average flux density ($cc_{Pearson}=-0.46$), however strongly influenced by the two very large and long living CHs during solar minimum (2 datapoints on the far right). No correlation with the CH lifetime is visible in the change rates nor in the average magnetic flux.

Figure 7 investigates a possible dependence of average CH parameters and change rates on solar activity. As a proxy for the solar activity, the average sunspot number was used. We define the average sunspot number of a CHs evolution as the mean of SIDC sunspot number over the time interval in which the CH was observed. We find weak (anti-)correlations to solar activity of the average CH area and flux density as well as their change rates. Parameters that show the highest correlation with the solar activity are the average magnetic flux ($cc_{Pearson}=0.50$) and the flux change rate ($cc_{Pearson}=0.69$).

In Figure 8 we investigated a possible correlation of the CH area to the flux density. The top panel shows the flux density as function of the CH area for all individual CHs (black) and the average over each evolution (red). We find a weak anti–correlation for the whole sample ($cc_{Pearson}=-0.33$) and a strong anti–correlation for the averages ($cc_{Pearson}=-0.70$). Note, that the strong anti–correlation of the average CH area and mean magnetic flux density is due a smoothing effect of the whole sample and not a causal relation. The middle panel shows the correlation coefficients for each individual CH evolution. We find CHs in which the evolutionary profile of the area seems quite strongly correlated with the flux density evolution ($3/16$), some that show no correlation at all ($6/16$) and about half that show a weak to strong anti–correlation ($7/16$). We note here that the slopes of the regression line of some CH evolutions are very low due to an only slightly changing magnetic flux density throughout the lifetime. This can artificially enhance the Pearson correlation coefficient without a causal relation being present. All CHs retain the same polarity over their evolution. The change rates of CH area and flux density (Figure 8,bottom panel) do not seem to be correlated (average over all evolutions: $cc_{mean}=-0.15$).

3.5 High Speed Stream Velocity Evolution

Here we investigate if the well–established CH area – HSS peak velocity relation is visible over individual CH evolutions. Using the geoeffective CH area, calculated from Equation 4, we derive a Pearson correlation coefficient of $cc_{Pearson}=0.46$ with a $90\%$ confidence interval of $[0.36,0.55]$ for the full sample. If considering each evolution individually we find a large range of correlation coefficients between medium and strong correlations (see Fig. 9). Possible reasons for this will be discussed later. The mean correlation coefficient of all 16 individual evolution correlation coefficients comes to $cc_{mean}=0.59\pm 0.26$. The slopes of the individual regression lines vary largely around $(3-44)\times 10^{-10}$ km*-1* s*-1* with accordingly different y–intercepts. For large CHs (A $>10\times 10^{10}$ km2) we find a saturation effect in the peak velocity. For ”patchy” CHs (large fragmented CHs with weakly defined boundaries) the maximum peak velocity seems to be lower than one would expect for CHs of such area. We investigated in–situ measured plasma density and magnetic field magnitude at the position of the velocity plateau and did not find any correlations to the CH area or magnetic field properties.

4 Discussion

Using EUV full–disk observations by AIA and HMI magnetograms throughout most of the operational lifetime of SDO between $2010$ and $2019$ we studied the evolution of a sample of $16$ long–living CHs and their associated HSSs.

We find that $13$ out of $16$ CHs follow a visible trend in the area evolution covering roughly a growing phase until a clear maximum is reached followed by a decay phase. Only $3$ CHs show an erratic behavior, e.g., revealing multiple peaks in the area or a maximum area at the birth or decay. From this we deduce that the majority of CHs ($>80\%$) reveal an area evolution that follows a pattern of growth and decay. However, we note that due to the small sample we cannot comment on the significance. The proposed 3-phase evolution (Heinemann et al., 2018b) might be rather the exception as it was only clearly observed for one CH.

We find a moderate correlation of the average CH area and flux density but the correlation is not significant. Also, the change rates seem independent of the lifetime.

We find a correlation of the average CH properties as well as change rates with the solar activity. Especially the change rate of the magnetic flux in CHs is strongly correlated to the average sunspot number during the CH life time. We suspect that depending on magnetic activity (magnetic pressure) in quiet sun areas and active region, near the CH, the open field is able to expand accordingly.

Specifically, we found that near and during solar maximum ($2012-2014$), the area change rate was found to be $(10.7\pm 8.9)\times 10^{8}$ km2 day*-1* (similar for both growth and decay rates) and during solar minimum the rate was around $60\%$ larger at $(17.5\pm 18.7)\times 10^{8}$ km2 day*-1*. Our results for the solar maximum match the area change rates found by Bohlin (1977) with $(13.0\pm 3.5)\leavevmode\nobreak\ 10^{8}$ km2 day*-1* quite well. Nolte et al. (1978a) used Skylab X–ray observations of long–living coronal holes during the descending phase of solar cycle 20 and derived rates of $(7.3\pm 1.4)\leavevmode\nobreak\ 10^{8}$ km2 day*-1*, which is lower than the values found in our study. Large deviations between the rates from previous studies can be primarily found in the CH evolutions during low solar activity where much larger average rates were derived. The growth and decay rates were found to be rather stable between long–living CHs observed during times of similar solar activity. The consistent average rates suggest that discrete events that may cause sudden large–scale changes in the CHs, like filament eruptions that permanently open magnetic field lines (e.g., Kahler & Moses, 1990), are rare events and that CHs evolve more gradually. This might explain the discrepancy between Nolte et al. (1978a), who claimed that most of a CHs area evolution can be explained by discrete boundary changes of sizes larger than $2.7\leavevmode\nobreak\ 10^{8}$ km2, and Kahler & Moses (1990) who found no such sudden large–scale changes. When comparing the average rate at which CHs evolve with results from flux transport calculations by Leighton (1964) we are in good agreement during the solar maximum and off during low solar activity.

A similar picture can be deduced from the change rates of the mean signed magnetic flux density enclosed within the projected CH boundary. For evolutions of individual CHs the rate at which the flux density changes stays at rather similar values but the percentual scatter is larger than in the area change rates. We show that the change rates of the flux density is higher during enhanced solar activity, for the timerange of $2012-2014$ (near and at solar maximum) we derive rates of ($28\pm 30$ mG day*-1*) and over $30\%$ lower rates of $18\pm 17$ mG day*-1* near solar minimum ($2016-2019$). This hints towards a small imbalance between flux appearance and flux removal rates as well as low rates in general. Gošić et al. (2016) found average net flux density change rates of $5.0\pm 5.8$ G day*-1* in internetwork elements of two supergranular cells in the quiet sun using $38$ hour continuous HINODE observations. Smitha et al. (2017) report values about a factor 10 larger using SUNRISE data. We note, that comparison should be treated cautiously as the rates derived by both Gošić et al. (2016) and Smitha et al. (2017) are from internetwork elements and the ones in this study from the total extracted CH area. Also, HINODE and SUNRISE obtain their magnetograms in a much higher resolution and sensitivity than HMI/SDO which might explain the difference to the results gathered in this study.

Zhang et al. (2007) found that in a decaying CH a decrease of flux is caused by the emergence of opposite polarity flux within the CH boundaries and also that nearly no flux transport across the CH boundary is observed. According to this, changes in the magnetic flux density in CHs are caused by processes within the CH boundaries, e.g, flux emergence rate. The average CH area and average flux density over the CH evolutions seem to be correlated, however this is simply a smoothing effect and does not imply a causal correlation (see Figure 8). From the statistical distribution of small unipolar magnetic elements within CHs, that have been found to define a CHs magnetic topology, it can be simply deduced that only smaller CHs might have higher flux densities (but also can have small flux density). Whereas in large CHs the flux density tends to converge to a mean flux density of about $1-3$ G (see Heinemann et al., 2018a, 2019; Hofmeister et al., 2019). As such the derived anti–correlation is no evolutionary effect. Larger statistical studies of CH properties show no correlation between the CH area and its magnetic flux density (Hofmeister et al., 2017; Heinemann et al., 2019).

As such the evolution of the magnetic flux density and magnetic flux cannot explain the evolutionary behaviour of the CH area. We propose that the area evolution of CHs is not primarily caused by the evolution of the mean signed magnetic flux density within the projected CH boundary as extracted from EUV observations. Possible processes that might play a role in the area evolution include interchange reconnection (see Shelke & Pande, 1984; Wang & Sheeley, 2004; Madjarska et al., 2004; Fisk, 2005; Madjarska & Wiegelmann, 2009; Edmondson et al., 2010; Krista et al., 2011; Yang et al., 2011; Ma et al., 2014; Kong et al., 2018) and/or the change in the global and local magnetic field configuration outside the CH.

Additionally to the evolutionary trend derived from remote sensing data, we investigated the evolution of the in–situ measured peak velocity of the associated HSS. Using the geoeffective CH area, we derive a mean correlation coefficient of the individual CH evolutions of $cc_{Pearson,mean}=0.59\pm 0.26$, which is in the range of previous statistical studies of the CH area – HSS peak velocity relation (Karachik & Pevtsov 2011: $cc_{Pearson}=0.41$ to $0.65$; Vršnak et al. 2007; Abramenko et al. 2009; Verbanac et al. 2011c, b; Rotter et al. 2012; Tokumaru et al. 2017; Hofmeister et al. 2018): $cc_{Pearson}=0.62$ to $0.80$). We are also in good agreement with Heinemann et al. (2018b), who found in their case study of a long–living CH a correlation coefficient of $cc_{Pearson}=0.77$. We find a saturation effect in the peak velocity – CH area relation, where the peak velocity of large CHs does not follow a linear trend but rather converges to a speed of roughly $700$ km s*-1*. This might be related to the longitudinal saturation found by Garton et al. (2018).

We can conclude that the CH area – HSS peak velocity relation is clearly visible within each CH’s evolution, but the slopes of the linear regression lines vary strongly. We identify 3 possible causes for the varying slopes: (1) The in–situ measured bulk velocity depends not only on the CH but also on the preconditioning of the interplanetary space (e.g., Temmer et al., 2017). HSS or CMEs near or before the arrival of the HSS under study can significantly influence the measured speeds. This may lead to an enhanced scatter in the relations. (2) The relation between CH area and HSS peak velocity is individual for each CH. (3) It might be possible that the CH area and the HSS peak velocity are not directly causally related.. It is known that geometry of CHs plays an important role in in defining the 3D shape of the HSS (e.g., Garton et al., 2018).

5 Conclusions

In this statistical study we investigated the evolution of $16$ long–living CHs between $2010$ and $2019$ and the associated evolution of the HSSs peak velocity at 1au. Our major findings can be summarized in the following:

1. i

We found that the general CH area evolution ($>80\%$ of the studied cases) exhibit a rough evolutionary profile showing a rise to a clear peak in the observed CH area followed by a decay. 2. ii

The strength and evolution of the photospheric magnetic flux and flux density enclosed in the projected CH boundary was found to be largely independent of the evolution of the CH area. This suggests that the mean signed flux density of CHs is not the main cause for the observed evolution in the CH area. 3. iii

Area growth and decay rates within CHs over their evolution seem to only vary over the solar cycle, with higher rates during lower solar activity. The calculated rates for the high solar activity match flux transport rates derived by Leighton (1964). Sudden large–scale changes in the area seem to be rare events. 4. iv

The rates at which the magnetic flux and flux density changes seems to be related to the activity of the Sun. We find higher rates during enhanced solar activity than during periods of low solar activity as approximated by the sunspot number. 5. v

We find no correlation between the CH area and magnetic flux density changes rates. This hints that the rate at which the magnetic flux density of a CH evolves is independent from the CHs area evolution and and we suspect that this is caused by changes of the signed flux within the projected CH boundary (e.g., flux accumulation and cancellation due to flux emergence). 6. vi

It was shown that the well known CH area – HSS also persists over each individual CH evolution with varying correlation coefficients and varying slopes of the linear regression line.

Acknowledgements.

The SDO image data and the ACE in–situ data is available by courtesy of NASA and the respective science teams. S.G.H., M.T. and A.M.V. acknowledge funding by the Austrian Space Applications Programme of the Austrian Research Promotion Agency FFG (859729, SWAMI). V.J. acknowledges support from University of Zagreb, Croatia, Erasmus+ program. M.D. acknowledges support by the Croatian Science Foundation under the project 7549 (MSOC). S.J.H. thanks the OEAD for supporting this research by a Mariett-Blau-fellowship. S.G.H. would like to thank A.H.-P. for his endless supply of coffee, great motivation and helpful discussions.

Appendix A Snapshot of coronal holes under study

Figure 10 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.