Three-phase Evolution of a Coronal Hole. I. 360° Remote Sensing and In Situ Observations

CHs can be well observed in the emission of highly ionized elements, especially iron (e.g., Fe xii: 193/195 Å or Fe xiv: 211 Å). Based on the high contrast between CHs and the surrounding quiet corona, the EUV wavelength of 193 Å from the Atmospheric Imaging Assembly (AIA/SDO) and 195 Å from the EUV Imager (EUVI/STEREO) is best suited to extract the CH boundaries from the different spacecraft. The observed light is emission from Fe XII ions with a peak response temperature of 1.4–1.6 · 10⁶ K (Aschwanden & Boerner 2011; Lemen et al. 2012). The data was acquired at a 1 hr cadence through the Joint Science Operations Center and the Virtual Solar Observatory (VSO).

For the in situ measurements, level 2 data for the three different viewpoints are used. For Earth position, these are the high-resolution (5 minutes) plasma and magnetic field measurements provided by OMNI https://omniweb.gsfc.nasa.gov/ and averaged over 1 hr. OMNI data is taken by different satellites (e.g., WIND and ACE) at various positions (e.g., L1) and then propagated to the Earth's Bow Shock Nose. For the two STEREO positions, we use 1 hr resolution solar wind magnetic field data from IMPACT (Acuña et al. 2008; Luhmann et al. 2008) and plasma parameters from PLASTIC (Galvin et al. 2008).

To prepare the EUV images for multi-instrument calibration, the images were prepared to level 1.5 and 1 for SDO and STEREO, respectively, using standard SSW-IDL routines. For a common size of the images and to enhance the processing speed, full resolution images from SDO (4096 × 4096) and STEREO (2048 × 2048) were both resized to 1024 × 1024 pixels. In order to combine EUV image data from the different instruments, STEREO (195 Å) and SDO (193 Å) are intercalibrated following the procedure described by Caplan et al. (2016). To be able to consistently extract CH areas based on their intensity over the solar disk, an inter-instrument intensity normalization is applied and center-to-limb variations (e.g., limb-brightening in EUV) are corrected. A robust Limb-Brightening-Correction (LBC) is derived by using unbiased long-term averages of intensity bins. To correct for the different satellite orbits, instruments and instrument conditions, an Inter-Instrument-Transformation (IIT) was applied. The source code for the data based transformations (LBC, IIT) was supplied by the Predictive Science Team in MATLAB and was converted into IDL. For further information about the LBC and IIT, we refer the reader to Caplan et al. (2016).

The CH under study was chosen for reasons that were primarily based on the position of the different spacecraft. For a continuous tracking, STEREO and Earth-view satellites needed to be equally separated, which was only possible around the year 2012. During that time, this particular CH was outstanding, as it had a long lifespan, a reasonable size, and was located at a low-latitudinal position.

For the extraction of individual CHs on the solar disk, an intensity method with a threshold based on the median intensity of the solar disk is used. As threshold, a value of 35% of the median intensity of the solar disk was applied. Compared to the mean intensity, the median intensity is more robust and stable over time against the influence of bright and dark structures. By applying the threshold method onto EUV images, a binary map is created that is then smoothed by a median filter of 15 pixels (which equals ∼30 arcsec in the center of the solar disk) in order to remove fragments and very small dark structures and to smooth the edges of the CH. The binary map is then segmented into the different detected CHs. This threshold-based method has already been used and intensively tested by Reiss et al. (2014) and Hofmeister et al. (2017) for SDO images and by Rotter et al. (2012) for EIT images. To reduce projection effects when CHs are close to the limb of the solar disk (Timothy et al. 1975), CHs where the center of mass (CoM; see Section 2.4) is outside of −45° and +45° degrees longitude measured from the central meridian of the current spacecraft are disregarded.

The tracking of the CH under study in each image was done using a semi-automatic tracking algorithm. The CH was identified in the first image of the time series and then automatically compared to the following images. To identify the CH under study in each image, the CoM and area of all extracted CHs are compared to the forward rotated position of the CH in the previous image. If none or multiple similar CHs were detected, manual input was requested to identify the correct structure. This process was applied to all (>4000) images. Manual input was only needed in <5% of the images.

Different CH properties, as the de-projected area, the mean intensity, the CoM, and the orientation, were calculated from the extracted binary structure. As pixels closer to the solar limb represent a larger area, the binary maps were pixel-wise corrected for the projected area on the spherical solar surface:

$$\begin{eqnarray}&&{A}_{i,\mathrm{corr}}=\displaystyle \frac{{A}_{i}}{\cos ({\alpha }_{i})},\end{eqnarray} \tag{ 1 }$$

with A_i being the area per pixel and α_i the angular distance to the center of the solar disk. The total area was calculated by summing the corrected area of all CH pixels by

$$\begin{eqnarray}&&A=\displaystyle \sum _{i}^{N}{A}_{i,\mathrm{corr}}.\end{eqnarray} \tag{ 2 }$$

The area is given in square kilometers, km². Using the de-projected area of the CH, the CoM is calculated pixel wise by weighing the pixels based on their area. We further calculate the longest diagonal of the CH that passes through the CoM, from which we define the orientation (ϕ) of the CH as the counterclockwise angle of its longest diagonal with respect to the solar equator. The mean intensity of the CH is calculated by

$$\begin{eqnarray}&&\bar{I}=\displaystyle \frac{1}{N}\displaystyle \sum _{i}^{N}{I}_{i}.\end{eqnarray} \tag{ 3 }$$

With I_i being the intensity value of each CH pixel.

To identify from the in situ solar wind data high-speed streams associated with the CH under study, we have to take into account the propagation time from the Sun to Earth. A CH that is centrally located on the solar disk shows a strong increase in density and magnetic field after about 1–2 days, and its peak in the solar wind plasma speed on average after 2–6 days (e.g., Vršnak et al. 2007). We therefore use the central meridian passage (CMP) of the CoM as reference and open a time-window in the in situ data set of −4 to +8 days (minus to account for E–W elongated CHs). After manually identifying the stream, the values of the solar wind plasma (peak velocity and total perpendicular pressure) and magnetic field (peak in the total magnetic field at the compression region, and magnetic field at the time when the speed peaks) were manually extracted. The total perpendicular pressure (sum of the magnetic pressure and the perpendicular plasma thermal pressure) was calculated using the formula given by Jian et al. (2006): ${P}_{{\rm{t}}}={B}^{2}/(2{\mu }_{0})+{\sum }_{j}{n}_{j}{{kT}}_{\mathrm{perp},j}$, where j represents protons, electrons, and α particles. For both OMNI and STEREO data, we assume a constant electron temperature of 130,000 K and a constant ratio of α particles to protons of 4%. To account for the temporal extension of the stream, we averaged the in situ data of each parameter over ±12 hr around the manually extracted peak value.

Figure 2 shows three examples of the in situ data that was used. Within the defined time-window, after the marks for the CMP of the west boundary and the CoM (gray vertical lines), we looked for typical HSS signatures using the criteria as given by Jian et al. (2009). A HSS signature can usually be identified by a pile-up of the total perpendicular pressure and a steep peak (shock) in the proton density followed by a rise in the bulk velocity that usually peaks a couple of hours/days later and then slowly decreases (upper panel). The compression affects the density, pressure, as well as the magnetic field, which usually also is sheared (lower panel). Also, the polarity of the magnetic field of the HSS must be considered, as it has to match the polarity of the source region, i.e., the CH, which is found to be negative for our event under study (see Heinemann et al. 2018). The HSS polarity was calculated using the formula given by Equation (1) in Neugebauer et al. (2002) and appears as the red and blue bar below the velocity-pressure plot. The red bars in each plot mark the manually extracted peak (triangle) and the ±12 hr interval over which the parameter was averaged. For each disk passage of the CH observed in the three different satellites (i.e., 29 disk passages in total), we extract one HSS signature with its respective properties.

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Possible CME signatures in the HSS were cross-checked by using ready-catalogs maintained by Richardson & Cane³ for ACE (see Richardson & Cane 2010 for a description of the catalog) and for STEREO from L. Jian⁴ (see Jian et al. 2018, for a description of the catalog). From a total of 29 data points, we excluded 5 from the analysis: (1) 2012 March 5 because it was a CME-HSS interaction event, and the HSS signatures could not be properly separated from the CME, (2) 2012 August 5 because only a CME signature is visible, and (3) 2012 August 14, (4) 22 and (5) 2012 October 14 were excluded as no clear HSS signature could be identified associated with the CH under study.

To compare and relate the CH evolution, observed in the remote sensing data, to the in situ data, the area of the CH was processed. Based on the time of the CMP of the CoM, the area was averaged over ±18 hr (${A}_{\mathrm{CH},n}$) to derive a CH area to associate with the in situ measured HSS signature (a summary of the parameters defined in Section 2 can be found in Table 1):

$$\begin{eqnarray}&&{A}_{\mathrm{SW}}=\displaystyle \frac{1}{N}\displaystyle \sum _{n}{A}_{\mathrm{CH},n}.\end{eqnarray} \tag{ 4 }$$

To visualize the different spacecraft, the CH evolution plots show three different vertical lines. The dashed line marks the STEREO-A spacecraft, the dashed–dotted line STEREO-B, and the dark red dashed line SDO. Each of those lines represents the CMP, hence, the time when the CoM of the CH passes the central meridian of the respective spacecraft. These are featured in the Figures 7, 8(a), 9 and 10(a), (c), (d).

Table 1.  Overview of Parameters Defined in Section 2

Parameter	Definition	Description
ACH	$={\sum }_{i}{A}_{i,\mathrm{corr}}$	CH Area
ICH	$=\tfrac{1}{N}{\sum }_{i}{I}_{i}$	CH Mean EUV Intensity
ϕCH		CH Orientation
vSW		SW Peak Bulk Velocity
ρSW		SW Number Density
BSW		SW Magnetic Field Strength
Pt	=B2/(2μ0)	SW Total Perpendicular
	$+{\sum }_{j}{n}_{j}{{kT}}_{\mathrm{perp},j}$	Pressure
ASW	$=\tfrac{1}{N}{\sum }_{n}{A}_{\mathrm{CH},n}$	Processed CH Area

Download table as:  ASCIITypeset image

For correlating various parameters, the Pearson correlation coefficient and the Spearman correlation coefficient including the confidence intervals (CIs) have been calculated by bootstrapping (Efron 1979; Efron & Tibshirani 1993) the data set with over 10⁵ repetitions. For each repetition, a subset with replacement was drawn from the initial set, with each data point in this subset coming from a Gaussian distribution of itself plus its standard deviation. From the resulting subset, the correlation coefficients were calculated. The given correlation coefficients are the mean values of all repetitions. The CI for the correlation coefficients (90%, 95%, 99%) were calculated using the respective quantiles (e.g., for the 95% CI the quantiles are 2.5% and 97.5%). Detailed results of the Pearson and Spearman correlation coefficients calculated for the intensity--area relation as well as the solar wind speed--area relation are reported in Table 2 which can be found in the Appendix.

The CH under study became continuously detectable starting with 2012 February 3–4 after two consecutive filament eruptions that have evacuated material and opened the magnetic field lines (see Figure 6). This is observed in STEREO-A off-limb and in STEREO-B very close to the limb. Signs for the emergence of a structure of reduced intensity can already be seen before in STEREO-A and SDO; however, no continuous extraction of the structure was possible nor could we associate an HSS in the in situ data to this structure. Thus, we consider the double filament eruption event as the "formation" of the CH, and as such, it marks the start time of our analysis. Because the position of the formation of the CH is close to the solar limb, a detailed analysis of the opening process was not feasible.

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Figure 7 shows the evolution of the CH area as measured from the three different spacecraft. The black line represents the calculated area from the extracted CHs, the blue line is a smoothed curve (running median of 100 images ≈4 days) to make the trend visible and to remove outliers. Extreme outliers are marked with the green roman numbers and are caused by the extraction algorithm that gives a false merging and splitting of the CH with fractions of other low-intensity areas close to the CH. From the derived profile, we find that the area evolves with a pattern that can be divided into three distinct phases.

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The growing phase is related to an increase in area (>6 · 10¹⁰ km²) from February until the middle of March ([1]) where the area decreases to ∼2 · 10¹⁰ km². From the observations, we find that this decrease may be explained by interchange reconnection with a small emerging active region near the southern part of the CH and/or by overlying coronal loops and stray light from active regions nearby that obscure the CH. After this drop, again a steady increase is observed until the area reaches the maximum phase (>9 · 10¹⁰ km²) around 2012 May 13 ([2]). This maximum is very stable (with only slight variations, e.g., the dip around the start of June ([3]) that lasts until around 2012 July 03 ([4])). After the maximum,⁵ we observe the decaying phase during which the CH area steadily declines to < 2 · 10¹⁰ km² ([5]) until the small CH cannot be detected anymore after 2012 October 17.

In the following, the three-phase evolution found in the area is used as a reference, and we investigate the other CH parameters in comparison to that result. Figure 8(a) shows the smoothed mean intensity together with the smoothed area. We find that the smoothed mean intensity of the CH changes by about a factor of 2.5 and that it is anti-correlated with the area evolution. The minimum of intensity corresponds with the maximum in the area. In Figure 8(b), the CH areas are plotted against their respective mean intensities. The data points of the different evolution phases are color-marked (green: growing phase, red: maximum phase, blue: decaying phase). We find a good (anti-)correlation, expressed through a Spearman correlation coefficient of −0.60 with a 95% CI of [−0.58, −0.62]. The different stages in the evolution occupy different areas in the plot, separating the phases most notably for the growing and maximum phase. The decaying phase is more scattered, showing some overlap with the growing phase.

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Figure 9 shows different properties of the CH motion patterns. The latitudinal position over time (Figure 9(a)), the velocity of the CoM in form of the Carrington longitude (Figure 9(b)), and the CH orientation (Figure 9(c)).

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The latitude of the CoM is located first in the southern hemisphere at around 20° and moves successively upwards into the northern hemisphere until the maximum phase. A subsequent slow movement toward the equator coincides with the decay of the area. During September, a fast northward movement (>25°) is derived, before the CH cannot be observed anymore. Note that the motion of the CoM carries no information of the shape and extension of the CH.

In Figure 9(b), the angular rotation speed of the CoM of the CH with respect to the Carrington rotation is shown. A constant Carrington longitude would refer to a rotation speed matching the Carrington rotation ω_Carr = 1418 day⁻¹ (Ridpath 2012). We obtain that the rotation speed changes over the lifetime of the CH (between 137 day⁻¹ and 148 day⁻¹). We observe a decrease in angular velocity until the middle of the maximum phase. There, a sudden increase in the angular velocity can be observed, which is most likely a result of the recession of the area in the northern part of the CH that causes the CoM to shift toward the equator. Thereafter, a constant angular rotation speed can be observed.

Figure 9(c) shows the change in the orientation of the CH. The orientation is defined as the counterclockwise angle of the longest CH diagonal to the equator. We find a good correspondence to the three phases as observed in the CH area, especially visible is the transition from the maximum to the decaying phase. A linear fit from 2012 February until 2012 July reveals a near constant counterclockwise rotation around its CoM with 042 day⁻¹ after a starting angle of ∼70°. This rotation can be observed until the end of the maximum phase; after that, coinciding with the decrease in CH area, the shape of the CH starts to become roundish. For a roundish CH, the orientation is not a well-defined parameter and therefore gives no reasonable results but causes strong fluctuations in the orientation angle derived.

Most prominently, the three-phase evolution is derived in the CH area. The growing phase is mainly defined by a steady increase in area with a duration of about three months, until the transition to the maximum phase takes place. Compared to the other phases, the maximum phase is characterized by a larger CH area (Figure 7), lower mean EUV intensity (Figure 8), a steady high solar wind speed of the associated HSS, and a stronger density/magnetic field compression of the CIR (Figure 10). The parameter values are rather stable during the maximum phase but only for a limited duration of around one month (the shortest of the three evolutionary phases). Around 2012 July 03, a significant drop in CH area and in situ solar wind speed heralds the last phase, the decaying phase in the CH lifetime. The decay continues for more than 3 months during which the CH area decreases and finally cannot be unambiguously identified anymore.

In each phase, the CH exhibits a different behavior; especially noticeable is the difference between the growing and the decaying phase. Though the CH has in both phases similar values of area and similar solar wind plasma and magnetic field values, the solar wind plasma stream emanating from the decaying CH behaves more erratic compared to the CH growing phase. This leads us to the assumption that the physical processes that are responsible for the opening and closing of a CH have a different influence on the HSS peak velocity (see also Temmer et al. 2018).

The CH main latitudinal movement direction is northwards with a slight decrease in CoM latitude at the end of the maximum phase and the start of the decaying phase, which seems to be caused by the asymmetric (north–south direction) decline of the area (Figure 9). Structural changes of the CH, hence, changes in the CoM and its latitudinal movement, are supposed to be strongly related to the rearrangement of the global magnetic field structure (Bilenko 2002 and Bilenko & Tavastsherna 2016).

The CH main axis exhibits a counterclockwise rotation (Figure 9(c)), which might be caused by the differential rotation of the Sun acting differently on different parts of the CH. The CH is located mostly in the northern hemisphere stretching from the equator up to latitudes of 30° and higher. The faster rotation rates at the equator and the lower rotation rates at higher latitudes deform the CH, which becomes apparent as a counterclockwise rotation. This effect is especially noticeable when the CH has an elongated shape in the north–south direction. This finding shows that an extended CH does not rotate rigidly as a static body, but rather different parts have different rotation speeds, faster at the equator and slower at higher latitudes. A coronal differential rotation in CHs has also been found by Insley et al. (1995).

Solar wind HSSs and related CIRs are a major contributor to space weather due to their recurrence and the fact that they are more predictable than impulsive, sporadic space weather events (e.g., CMEs). With the well-derived linear relation between CH areas and HSS peak speed (e.g., Nolte et al. 1976; Vršnak et al. 2007; Rotter et al. 2012; Tokumaru et al. 2017; Hofmeister et al. 2018), a forecasting seems to be straightforward. In this study, we show that these correlations are strongly related to the evolution of the CHs (Figure 10). During the growing phase, the peak velocity of the associated HSS steadily increased from 500 km s⁻¹ to >680 km s⁻¹ in the maximum phase. With the decrease in area in the decaying phase, the speed drops to below 400 km s⁻¹. The correlation, as shown by the Pearson correlation coefficient, is 0.77 with a 95% CI of [0.57, 0.89].

From our regression analysis, we obtain a linear relation with a slope of 31.5 ± 2.2 km s⁻¹/(10¹⁰ km²). By comparison, Tokumaru et al. (2017) derived a smaller slope with 4.31 ± 0.15 km s⁻¹/(10¹⁰ km²) and Nolte et al. (1976) a higher slope with 80 ± 2 km s⁻¹/(10¹⁰ km²). We are in basic agreement with the study by Hofmeister et al. (2018) with a slope of 23.2 ± 4.5 but a higher y-intercept. These strong variations in the slope in different studies may be explained by the different CH data sets used. In a recent statistical study by Hofmeister et al. (2018), a further dependence of the measured HSS speed (alternatively, of the measured slopes) on the co-latitudinal position between the spacecraft and the solar CH was found. However, as our case study only covers a low-latitude CH within the co-latitudinal range of ±20°, such a correlation is not visible. Studies with only near equatorial CHs are expected to yield a different slope than those covering CHs over all latitudinal ranges. This assumption also applies to this study of the evolution of one CH. Nevertheless, as could be shown here, the degree of correlation is likely dependent on the evolutionary phase of the CH. We find similar slopes during the growing and decaying phase but with different base levels (lower speed and larger spread for the decaying phase). During the maximum phase, the linear correlation is the same as the overall correlation.

The in situ measured density peak, magnetic field, and therefore total perpendicular pressure of the interaction region and the magnetic field measured at the speed peak show a general evolutionary trend, with higher values during the maximum of the CH lifetime than during its beginning and end (Figure 10). For the total perpendicular pressure, we find large variations between the three spacecraft that may be caused by (a) instrumental effects (sensitivity, age, type) or (b) the three-dimensional structure of the HSS. However, we find no direct dependence on the co-latitude of the spacecraft to the CoM of the CH. We suppose that the plasma and magnetic field compression between fast and slow solar wind is likely influenced by the interplay between the CH structure itself (shape of the CH and its changes) and the ambient structures (nearby active regions and their activity, but also global changes in the magnetic field).