Statistical Approach on Differential EmissionMeasure of Coronal Holes using the CATCH Catalog
Stephan G. Heinemann, Jonas Saqri, Astrid M. Veronig, Stefan J. Hofmeister, Manuela Temmer
SSolar PhysicsDOI: 10.1007/ ••••• - ••• - ••• - •••• - • Statistical Approach on Differential EmissionMeasure of Coronal Holes using the CATCH Catalog
Stephan G. Heinemann •• · Jonas Saqri •• · Astrid M. Veronig •• · Stefan J. Hofmeister •• · Manuela Temmer •• © Springer ••••
Abstract
Coronal holes are large-scale structures in the solar atmosphere thatfeature a reduced temperature and density in comparison to the surroundingquiet Sun and are usually associated with open magnetic fields. We perform adifferential emission measure analysis on the 707 non-polar coronal holes col-lected in the Collection of Analysis Tools for Coronal Holes (CATCH) catalogto derive and statistically analyze their plasma properties (i.e. temperature,electron density, and emission measure). We use intensity filtergrams of the sixcoronal EUV filters from the
Atmospheric Imaging Assembly onboard of the
Solar Dynamics Observatory , which cover a temperature range from ≈ . to 10 . K. Correcting the data for stray and scattered light, we find that allcoronal holes have very similar plasma properties with an average temperatureof 0 . ± .
18 MK, a mean electron density of (2 . ± . × cm − , and amean emission measure of (2 . ± . × cm − . The temperature distributionwithin the coronal hole was found to be largely uniform, whereas the electrondensity shows a 40 % linear decrease from the boundary towards the inside of thecoronal hole. At distances greater than 20 (cid:48)(cid:48) ( ≈
15 Mm) from the nearest coro-nal hole boundary, the density also becomes statistically uniform. The coronalhole temperature may show a weak solar cycle dependency, but no statisticallysignificant correlation of plasma properties to solar cycle variations could bedetermined throughout the observed time period between 2010 and 2019.
Keywords:
Corona; Coronal Holes; Solar Cycle (cid:66)
[email protected] University of Graz, Institute of Physics, Universit¨atsplatz 5, 8010 Graz, Austria Kanzelh¨ohe Observatory for Solar and Environmental Research, University of Graz,9521 Treffen, Austria Columbia Astrophysics Laboratory, Columbia University, New York, USA
SOLA: main_clean.tex; 1 March 2021; 1:32; p. 1 a r X i v : . [ a s t r o - ph . S R ] F e b .G. Heinemann et al.
1. Introduction
Coronal holes are large-scale magnetic structures that extend from the solarphotosphere into interplanetary space and are characterized by their open-to-interplanetary-space magnetic field configuration. This distinct magnetic topol-ogy enables plasma to be accelerated to high speeds of up to 780 km s − andescape along the open field lines (Schwenn, 2006). Coronal holes are defined bya lower density and temperature in comparison to the surrounding corona andand are thus observed as large-scale regions of reduced emission in X-ray andextreme ultraviolet (EUV) wavelengths (see reviews by Cranmer, 2002, 2009,and references therein).Studies using differential emission measure (DEM) techniques on spectro-scopic data from the EUV imaging spectrometer onboard Hinode(Hinode/EIS;Hahn, Landi, and Savin, 2011) and the Solar Ultraviolet Measurements of Emit-ted Radiation on the Solar and Heliospheric Observatory (SOHO/SUMER; Landi,2008) as well as on SDO/AIA EUV filtergrams (Saqri et al. , 2020) revealed thatcoronal holes have a peak in the emission at a temperature of T ≈ . . . et al. (2020)used Hinode/EIS and SDO/AIA data to derive DEM profiles and revealed thatbesides the dominant contribution at around 0 . ≈ . . . − . × cm − (Fludra, Del Zanna,and Bromage, 1999; Warren and Hassler, 1999; Hahn, Landi, and Savin, 2011;Saqri et al. , 2020). Using coronagraphic white-light images, Guhathakurta andHolzer (1994) showed that the density in coronal holes varies in height abovethe solar surface but not over latitude.The plasma properties (i.e., emission measure, temperature, and density) ofcoronal holes have been been analyzed using different observations and methods;however, it has been done only in the scope of observational campaigns or casestudies but not in the scope of a large statistical approach. By using long-termEUV observations from 2010 to 2019 covering nearly the full Solar Cycle 24, weare able to statistically investigate the distributions of the plasma properties fora large variety of coronal holes of different sizes, and whether these propertieschange over the solar cycle.In this study, we performed differential emission measure (DEM) analysis us-ing data from the Atmospheric Imaging Assembly (AIA: Lemen et al. , 2012) on-board the
Solar Dynamics Observatory (SDO: Pesnell, Thompson, and Cham-berlin, 2012) on coronal holes of the extensive Collection of Analysis Tools for
SOLA: main_clean.tex; 1 March 2021; 1:32; p. 2
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Coronal Holes (CATCH) catalog (Heinemann et al. , 2019). We derive the dis-tribution of plasma properties and their dependence on the solar cycle, and werelate them to the primary coronal hole parameters such as area and magneticfield density.
2. Methodology
For the presented statistical study we used the CATCH catalog, which con-tains 707 observations of well-defined non-polar coronal holes extracted fromSDO/AIA 193 ˚A filtergrams. The catalog contains the extracted boundariesand properties of the coronal holes such as area, intensity, signed and unsignedmagnetic field strength and magnetic flux including uncertainty estimates. Thecoronal holes are distributed between latitudes of ± ◦ and cover nearly the fullSolar Cycle 24 from 2010 to 2019. A description of the catalog has been givenby Heinemann et al. (2019). For the DEM analysis the level 1.6 data (processed with aia_prep.pro andpoint-spread-function-corrected) of the six coronal channels of AIA/SDO (Lemen et al. , 2012) was used, namely 94 ˚A (Fe xviii ), 131 ˚A (Fe viii , xxi ), 171 ˚A (Fe ix ), 193 ˚A (Fe xii , xxiv ), 211 ˚A (Fe xiv ) and 335 ˚A (Fe xvi ). To enable us topre-process all coronal holes in a reasonable amount of time and to enhance thesignal-to-noise ratio for the DEM analysis, the data were rebinned by a factorof eight to a plate scale of 4 . (cid:48)(cid:48) per pixel. From previous DEM studies of coronal holes it is known that stray light andscattered light significantly affects the analysis, since the emission in coronalholes is much lower than the surrounding quiet Sun and active regions (Wendelnand Landi, 2018; Saqri et al. , 2020). Therefore, we use the point spread function(PSF) correction available in the SolarSoftware package of the Interactive DataLanguage (SSW IDL) aia psf ( aia_calc_psf.pro written by M.Weber, SAO),to remove contributions from bright sources as well as possible.We tested the performance of the PSF corrections using lunar-eclipse observa-tions. At the eclipse boundary, the counts should drop to zero and all measuredcounts are due to stray light and noise. A well-performing PSF correction shouldshow such a behavior. To verify, we analyzed ≈
20 lunar eclipses that occurredbetween 2010 and 2019 in all six wavelengths. Figure 1 shows for each AIA filter,superposed light profiles of level 1.6 data across the boundaries of multiple solar Vizier Catalog: vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/other/SoPh/294.144
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Table 1.
Mean lunar eclipse counts (DN) of level 1.5 and level 1.6 data for all wavelengthsderived from the light profiles in Figure 1, the resulting eclipse correction as well as the meancounts of the 707 coronal holes using the level 1.6 data94˚A 131˚A 171˚A 193˚A 211˚A 335˚Alevel 1.5 0 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . . . . . . . ± . . ± . . ± . . ± . . ± . . ± . eclipses. We find that for all channels, some counts remain, however, withoutan obvious correlation to the solar cycle or the mean intensity of the solar disk.The hot channels (94 ˚A , 131 ˚A , 335 ˚A) show no dependence on the distance fromthe transition, and we assume the remaining counts to be primarily isotropicnoise. This seems especially true for the 94˚A filter, where the remaining eclipsecounts may be in the order of the quiet-Sun counts. The 171 ˚A, 193 ˚A, and 211 ˚Achannels display a weak dependence on the distance, which indicates the presenceof some uncorrected long-range scattered light (Wendeln and Landi, 2018). Wefound no working solution to correct for this; however, we can account for theremaining counts in the DEM analysis by increasing the input error of the counts(DN) in each pixel (see Saqri et al. , 2020). For each filter, we derive the remainingcounts by averaging over the lunar eclipse light profiles (as shown in Figure 1) ata distance between 50 (cid:48)(cid:48) to 200 (cid:48)(cid:48) from the eclipse boundary. These distances werechosen to avoid contribution of the transition and associated boundary effects inthe eclipse data (50 (cid:48)(cid:48) ) and because there are no coronal hole pixels with distancesexceeding 200 (cid:48)(cid:48) . The average eclipse counts for level 1.5 and level 1.6 are listedin Table 1. We find that the level 1.6 data shows strongly reduced remainingeclipse counts in the 171 ˚A, 193 ˚A, and 211 ˚A channels. The other channels areprimarily dominated by isotropic noise and comparable between level 1.5 and 1.6data. The eclipse correction for the DEM input is given as the mean remainingeclipse counts (as stated above and shown in Table 1) plus one sigma. Note, thatwith this method we ignore the distance dependence and possible effects such asthe roughly one-sided illumination of the eclipse in contrast to coronal holes inthe center of the disk. This is done because we cannot reliably make an estimatefor such effects. Differential emission measures analysis is the reconstruction of the plasma prop-erties from observed intensities in different wavelengths. The DEM is defined asthe emission of optically thin plasma in thermodynamic equilibrium for a specifictemperature along the line-of-sight (LoS) and is given byDEM( T ) = n e ( T ) d h d T , (1)
SOLA: main_clean.tex; 1 March 2021; 1:32; p. 4
EM of Coronal Holes with n e the electron number density as function of the temperature T and h the LoS distance over which the emission observed is integrated (see Mariska,1992, Chapter 4). According to Hannah and Kontar (2012), from the observedintensities of each filter [ I λ ] the DEM can be estimated by solving the inverseproblem I λ = (cid:90) T K λ ( T ) DEM( T ) d T, (2)with K λ being the instrumental response functions. By following Equation 6from Cheng et al. (2012) the electron number density ( n e ) for coronal holes canbe calculated from the DEM as follows: n e = (cid:114) EM h , (3)with the emission measure EM = (cid:82) DEM d T and the LoS integration length [ h ]which we approximate with the hydrostatic scale height h = k B T m gµ . Due to theopen magnetic field that does not vertically constrain the plasma, we assume thehydrostatic scale height to be valid as a first-order approximation. However thisis only valid for the regime where the field is mostly vertical and approximatelyuniform i.e., it is not valid outside of coronal holes. In quiet Sun regions, aheight-dependent DEM model using a scale height approximation modeled withan ensemble of multi-hydrostatic loops might be used (Aschwanden, 2005). Weuse g = 274 ms − , a proton mass of m = 1 . × − kg (Aschwanden, 2005), µ = 0 .
60 (Asplund et al. , 2009), and the median DEM temperature (Equation 4)for the hydrostatic scale height. The input error of each pixel was calculatedusing aia_bp_estimate_error.pro considering shot-, dark-, read-, quantum-,compression- and calibration noise to which the eclipse correction is added (seeTable 1).To investigate the plasma properties of the coronal holes, we applied a regular-ized inversion technique developed by Hannah and Kontar (2012) to reconstructthe DEM from the six optically thin EUV channels of SDO/AIA. As Equa-tion 2 does not yield a unique solution without further constraints, the code byHannah and Kontar (2012) gives the DEM solution with the smallest amountof plasma required to explain the observed emission (zeroth-order constraint).The instrument response function [ K λ ( T )] was calculated assuming photosphericabundances (CHIANTI 9 database: Dere et al. aia_get_response.pro ). We preferphotospheric over coronal abundances as it was shown that the elemental abun-dances in chromospheric and coronal layers of coronal holes strongly resemble thephotospheric ones (Feldman, 1998; Feldman and Widing, 2003). For every pixelin each coronal hole we use 60 equally spaced temperature bins (in log space)between log ( T ) = 5 . ( T ) = 6 . SOLA: main_clean.tex; 1 March 2021; 1:32; p. 5 .G. Heinemann et al. curve the EM-weighted median temperature is calculated as such that: (cid:90) T median . DEM d T = EM2 . (4)The median temperature was chosen over a mean or EM-weighted mean temper-ature because it better describes the asymmetrical DEM profile and thus betterrepresents the dominant emission from coronal holes (also see DEM curves inSaqri et al. , 2020). For each pixel i , we derive the EM-weighted median temper-ature [ T median ,i ], and calculating the mean of all pixels in a coronal hole givesthe average coronal hole temperature as T CH = N (cid:80) T median ,i with N being thenumber of coronal hole pixels.In Figure 2, we show the DEM solutions for a coronal hole observed on May 29,2013 for level 1.5, level 1.6 data and level 1.6 plus applying the eclipse correction.The non-PSF-deconvolved solution shows a peak at high temperatures, whichis lower in the PSF-corrected solution and reduces further when considering theremaining counts derived from the Lunar eclipse analysis. This finding supportsthat the contribution of coronal hole emission at quiet Sun temperatures, alsofound by Hahn, Landi, and Savin (2011) and Saqri et al. (2020), is mainly dueto stray light from regions outside the coronal hole.When calculating the uncertainties, three components have to be considered:the error from the DEM calculation [ σ dem ], which comes from the method andthe initial uncertainties in the observations, the variation of the individual pixelvalues [ σ ch : standard deviation of pixel values] and the variation of the coronalhole mean values [ σ total : standard deviation of coronal hole mean values]. Theresulting uncertainty can be given as follows:¯ σ = (cid:118)(cid:117)(cid:117)(cid:116)(cid:18) N j N j (cid:88) j =0 (cid:113) ¯ σ dem ,j + σ ch ,j (cid:19) + σ total , (5)with ¯ σ dem ,j being the mean DEM error and the index j running over all coronalholes. The correlation analysis was done using a bootstrapping method (Efron, 1979;Efron and Tibshirani, 1993) with > repetitions to derive Pearson correlationcoefficients that take into account the uncertainties of the parameters. Addition-ally, to show that the correlations found do not depend on the data preparation,i.e., on the choice of the PSF nor the estimated correction for the remainingcounts, we calculated all correlations with two different PSF deconvolutions( aia psf and a PSF by Poduval et al. SOLA: main_clean.tex; 1 March 2021; 1:32; p. 6
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3. Results
We derived the plasma properties of a set of 707 coronal holes by performing aDEM analysis using the coronal EUV observations by SDO/AIA and obtainedthe following results.
Figure 3 shows an example of the plasma properties (i.e. temperature, density,and emission measure) of a coronal hole and the surrounding quiet Sun areason September 8, 2015. The temperature shows only small variations around amean value of T CH = 0 . ± .
05 MK, and is is statistically uniformly distributedinside the coronal hole. The density and emission measure maps show a gradientfrom the boundary inward with regions of lesser emission and density at somedistance from the boundaries. We confirm this statistically in Section 3.4.Figure 4 shows the median and the 80th and 90th percentiles of the superposedmean DEM curves of all coronal holes to present the range of values found (notethat the errors in the DEM are not shown for this figure). We found that theDEM of a coronal hole is gaussian shaped around a peak temperature of roughly0 . . et al. , 2012, for filter sensitivityand response curves). The superposed DEM curve shows that the shape is verysimilar for all coronal holes, the major variation is in the height of the peakwhich can vary up to a factor of two. A contribution at quiet Sun temperatures( ≈ . . T ] of 0 . ± .
18 MK, with a derived minimum of 0 .
86 MKand a maximum of 1 .
32 MK. For all coronal holes under study, the averagetemperature [ T CH ] is significantly lower than average quiet Sun temperatures.The electron density is distributed around (2 . ± . × cm − , with aminimum of 1 . × cm − and a maximum of 3 . × cm − . The emissionmeasure was found in a range between 1 . × cm − and 5 . × cm − with a mean of (2 . ± . × cm − . Due to the large number of coronal hole observations in the CATCH catalog thatspan from 2010 to 2019, we can study the plasma properties over almost the fullSolar Cycle 24 and investigate a possible dependence on solar activity. In Fig-ure 6 we present the calculated plasma properties together with the internationalsunspot number (bottom panel) as functions of time. The coronal hole temper-ature shows small variations over time, which seem to follow the solar activity
SOLA: main_clean.tex; 1 March 2021; 1:32; p. 7 .G. Heinemann et al. cycle. When considering the uncertainties of the average coronal hole plasmaproperties, we find only a very weak correlation to solar activity as approximatedby the smoothed sunspot number provided by WDC-SILSO with a Pearsoncorrelation coefficient of cc T = 0 .
13 within a 90 % confidence interval [CI ] of[0 . , . − − σ T , max = 0 .
06 MKand σ T , min = 0 .
03. It is worth mentioning that when neglecting the uncertaintiesand only considering the average values of the plasma parameters derived, a faircorrelation of the temperature to the average sunspot number can be found( cc T = 0 .
57, CI = [0 . , . cc n e = 0 .
04, CI = [ − . , .
10] and cc em = 0 . = [0 . , . To investigate how plasma properties are correlated to morphological and mag-netic coronal hole properties, we plot the average coronal hole temperature[ T CH ], electron density [ n e ] and emission measure [ EM ] as function of coro-nal hole area and signed mean magnetic field density, which were obtainedfrom the CATCH catalog. This is shown in Figure 7. The left column showsthe plasma properties plotted against the coronal hole area and the right col-umn against the magnetic field density. The Pearson correlation coefficients forthe plasma properties against the coronal hole area reveal no correlation, with cc T = − .
04, CI = [ − . , . cc n e = − .
01, CI = [ − . , . cc em = − .
01, CI = [ − . , .
06] for temperature, electron density, and emis-sion measure respectively. With a Pearson correlation coefficient of cc n e = − . = [ − . , − .
04] and cc em = − .
13, CI = [ − . , − .
07] the densityand emission measure show no clear correlation to the mean magnetic field den-sity. The average coronal hole temperature shows a weak trend in the averagevalues when neglecting the uncertainties ( cc T = 0 .
34, CI = [0 . , . cc T = 0 .
11, CI = [0 . , . In addition to the average coronal hole plasma properties, we investigated howthe properties are spatially distributed within the coronal hole. To this aim,we calculated for each coronal hole pixel the distance to the closest coronalhole boundary [ d in arcsec] and derived the temperature, electron density, and SOLA: main_clean.tex; 1 March 2021; 1:32; p. 8
EM of Coronal Holes emission measure of each individual pixel as function of the distance, which isshown in Figure 8. In each vertical bin of a size of 5 (cid:48)(cid:48) , the pixel distribution of T median , n e , and EM is given. Each bin is normalized to reflect the probabilityfor a pixel in a given distance bin to have a certain value. Additionally to thepixels within the coronal holes, the DEM for pixels surrounding the coronalhole boundary was calculated (represented by negative distances) to show thegeneral trend outside of the coronal hole. We note that the calculations outsideare not reliable as they were calculated in the same way as for coronal holepixels, but here the assumptions of a hydrostatic scale height and photosphericabundances are not valid. Figure 8 shows that the temperature (top panel)within the coronal holes is very uniform and does not depend on the distancefrom the EUV extracted boundary. Near the boundary, small variations are seen(within ≈ (cid:48)(cid:48) ) and the temperature does not change strongly at the coronalhole boundary. For the electron density as well as for the emission measurewe find a dependence on the distance to the closest coronal hole boundary.Within a distance of 20 (cid:48)(cid:48) from the coronal hole boundary, on average the electrondensity drops by a factor of ≈ . . × cm − and theemission measure by a factor of ∼ . . . × cm − . At distances > (cid:48)(cid:48) the dependence ceases and the individual pixel are distributed around(1 . ± . × cm − for the density and around (2 . ± . × cm − for the emission measure (also considering the individual DEM errors). Thesevalues were derived for all pixels that are located at distances larger than 20 (cid:48)(cid:48) from the closest coronal hole boundary inside coronal holes. When comparing theaverage pixel values for the electron density and emission measure at distancessmaller and larger than 20 (cid:48)(cid:48) from the closest coronal hole boundary, we findthat the mean pixel densities close ( d < (cid:48)(cid:48) ) to the boundary are a factor 1 . d > (cid:48)(cid:48) ). For the emission measure we find a factorof 1 .
5. The gradient in the electron density and emission measure shows thatthe coronal hole boundary extracted using an intensity threshold technique is agood tracer for an area of reduced density.
4. Discussion
The coronal hole properties derived from the presented statistical DEM study arein good agreement with the results of individual case studies and observationcampaigns. Fludra, Del Zanna, and Bromage (1999) used the CDS on SOHOto derive coronal hole densities and temperatures as a function of height. Thetemperatures range from 0 .
75 MK at a radial distance of 1 . (cid:12) to 0 .
85 MK at aradial distance of 1 . (cid:12) . This approximately agrees with the results derived inthis study ( T = 0 . ± .
18 MK). The derived average coronal hole temperaturesare also in good agreement with the 0 . et al. (2020).Further, it is notable that the temperature is almost uniformly distributed( σ T = 0 .
05 MK) within the coronal holes.When using the DEM analysis to derive electron densities, multiple assump-tions have to be made. The densities are calculated over the emission of a LoS
SOLA: main_clean.tex; 1 March 2021; 1:32; p. 9 .G. Heinemann et al. column, which we defined as the hydrostatic scale height, which is believed tobe a reasonable first-order approximation due to the open field lines in coronalholes. In the quiet Sun a hydrostatic scale height cannot be used due to theabundance of primarily closed fields. As the magnetic topology at the coronalhole boundaries is not well known, it is unclear how valid our assumptionsare in this regime. Additionally, it is known that stray light in EUV imagescan contribute up to 40 % of the derived electron density value (Shearer et al. ,2012), and it is unclear, even after a correction, how much stray and scatteredlight still remains in the images (Poduval et al. , 2013). The derived electrondensities of (2 . ± . × cm − are in fair agreement with the DEM studyof the evolution of one particular coronal hole performed by Saqri et al. (2020),who derived values between 1 . . × cm − , and Warren and Hassler(1999), who derived values between 1 . . × cm − . Hahn, Landi, andSavin (2011) used Hinode/EIS spectroscopy of a polar coronal hole and deriveddensity values of 1 . × cm − and 1 . × cm − from the Fe viii and Fe xiii line ratios, respectively. They suggested that the density derived from thecooler lines (Fe viii ) probes the cool coronal hole plasma and the hotter linesshow a contribution from quiet Sun plasma. This also agrees with the results byPascoe, Smyrli, and Van Doorsselaere (2019) that estimated coronal hole electrondensities to be around ∼ cm − . Figure 8 shows that the density decreases asa function of the distance from the coronal hole boundary up to d ≈ (cid:48)(cid:48) . Underthe assumption that the PSF correction used does indeed remove most of thestray light, this result suggest that the extracted coronal hole boundary does notrepresent a vertical separation of two magnetic regimes but rather the positionwhere the emission drop is the strongest. Thus, the LoS column might represent amixture of coronal hole plasma emission and quiet Sun plasma emission, maybedue to field lines that are bent rather than radial (e.g. forming an inclinedseparation between coronal hole and quiet Sun). We notice that the decrease inelectron density from the coronal hole boundary to d ≈ (cid:48)(cid:48) within the coronalhole is approximately 30 %, which is smaller than the 50 % that has been foundby Doschek et al. (1997).The plasma properties show no correlation with the area and magnetic fielddensity of coronal holes. This suggests that the size of a coronal hole does notdetermine the plasma properties nor vice versa (we find this to be valid fornon-polar coronal holes). A trend can be seen in the correlation of the meanmagnetic field density and the average coronal hole temperature, however thisis not significant ( cc T = 0 .
11, CI = [0 . , . et al. (2019) found that the mean193˚A intensity and the mean magnetic field density show a dependence on solaractivity and so does the long-term evolution of large coronal holes (Heinemann SOLA: main_clean.tex; 1 March 2021; 1:32; p. 10
EM of Coronal Holes et al. , 2020). Only the average coronal hole temperature does show some varia-tion, which might be linked to the solar cycle where slightly higher spreads duringsolar maximum are observed than during solar minimum. However, the Pearsoncorrelation coefficient does only show a very weak correlation of cc T = 0 .
13 andCI = [0 . , . et al. (2010) showed that the temperature in coronalholes varies with the solar cycle between 0 . .
04 insolar maximum, which we find to be in fair agreement with this study whenconsidering the average values in the correlation, without taking into accountthe uncertainties ( cc T = 0 .
57, CI = [0 . , .
5. Summary and Conclusions
In this statistical study on the DEM analysis of coronal holes we investigatedtemperature, electron density, and emission measure of the 707 coronal holesfrom the CATCH catalog and analyzed their distribution, variability over SolarCycle 24, and correlations to the coronal hole area and magnetic field density.Our major findings can be summarized as follows.i)
DEM:
The shape of the average DEM curve for coronal holes is very stableand resembles a Gaussian profile centered around a peak temperature withan extended tail towards higher temperatures.ii)
Temperature:
We find that coronal holes show a EM-weighted median tem-perature of 0 . ± .
18 MK, which is in accordance with previous studies.Additionally, we found that the temperature is spatially very uniform insidethe coronal hole.iii)
Electron Density:
Using the DEM analysis we derive electron number densi-ties for the coronal holes to be (2 . ± . × cm − . The density profile withincoronal holes decreases from the boundary to 20 (cid:48)(cid:48) by ≈
30 % and approachesa constant level further inside.iv)
Solar Activity:
We observe only small variations in the temperature, elec-tron number density, and emission measure during the period from 2010to 2019 but these appear not to be correlated to changes in solar activity.Although the average coronal hole temperature may hint toward some solarcycle dependence, due to the uncertainties this dependence is not significant.From the statistical analysis we find that coronal holes show a strong similarityin their DEM curves and derived properties. Thus, coronal holes can be canbe clearly defined by their plasma properties. This not only enables a deeperunderstanding of the structure of coronal holes but can also serve to constrainthe input for models (e.g. solar wind models such as: Odstrˇcil and Pizzo, 1999;Pomoell and Poedts, 2018) and studies of coronal waves interacting with coronalholes (e.g. Podladchikova et al. , 2019; Piantschitsch, Terradas, and Temmer,2020).
SOLA: main_clean.tex; 1 March 2021; 1:32; p. 11 .G. Heinemann et al. C o un t s [ D N ] C o un t s [ D N ] -400 -200 0 200 400Distance [arcsec]0.11.010.0100.01000.0 C o un t s [ D N ] -400 -200 0 200 400Distance [arcsec]0.11.010.0 Å Å Å Å Å Å Figure 1.
Superposed intensity profiles across the solar disk during ≈
20 lunar eclipses of level1.6 data for different wavelengths. The eclipse border is centered on 0, the negative directionmarks the visible solar disk and the positive direction the part covered by the lunar eclipse. K]012345 D E M [ c m - ] Level 1.5 (no PSF)Level 1.6 (PSF)Level 1.6 (PSF + Eclipse Correction)
Figure 2.
Average coronal hole DEM for May 29, 2013 using level 1.5 data (red line), level1.6 (PSF-corrected; blue line), and level 1.6 with eclipse correction (green line). The error barsrepresent the uncertainties from the DEM calculations of all pixels of the coronal hole. Notethat the error bars are shown only for every third bin for better visualization.
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Figure 3.
Example of the DEM analysis of a coronal hole on September 8, 2015. The left panelshows the map of peak temperature, the middle panel the electron density, and the right panelthe emission measure. The white contour is the coronal hole boundary as extracted by CATCH(Heinemann et al. , 2019). The temperature is distributed around a mean of T CH = 0 . ± . Figure 4.
Median, 80th and 90th percentiles of 707 superposed mean coronal holes DEMcurves. The black line gives the median, the blue shaded area the 20th and 80th percentiles,and the gray shaded area the 10th and 90th percentiles.
Acknowledgments
The SDO image data are available by courtesy of NASA and the re-spective science teams. S.G. Heinemann, M. Temmer and A.M. Veronig acknowledge fundingby the Austrian Space Applications Programme of the Austrian Research Promotion AgencyFFG (859729, SWAMI). J. Saqri acknowledges the support by the Austrian Science Fund FWF(I 4555).
SOLA: main_clean.tex; 1 March 2021; 1:32; p. 13 .G. Heinemann et al. e [10 cm -3 ]020406080100120 N cm -5 ]020406080100120 N N Binsize = 10 KBinsize = 1 x 10 cm -3 Binsize = 2 x 10 cm -5 Figure 5.
Distribution of the average coronal hole plasma properties derived from the entiresample of 707 coronal holes. From top to bottom: the temperature, the electron density, andthe emission measure. In the temperature histogram we use an overflow bin for all values > . SOLA: main_clean.tex; 1 March 2021; 1:32; p. 14
EM of Coronal Holes
Figure 6.
Evolution of the coronal hole plasma properties as a function of time. Panel ashows the average coronal hole temperature, panel b the mean electron density, and panel cthe mean emission measure of the coronal holes. The orange lines represent the mean of theaverage values, the shaded area represents the 1 σ uncertainty. The vertical bars represent theuncertainties of each coronal hole (= (cid:112) ¯ σ dem + σ ch ). In panel d the daily sunspot number (grayline) and smoothed daily sunspot number (black line) as provided by the SIDC/SILSO areshown. SOLA: main_clean.tex; 1 March 2021; 1:32; p. 15 .G. Heinemann et al. km ]12345 E M [ c m - ] T [ M K ] n e [ c m - ] s | [G] cc = -0.04; CI [-0.10, 0.02]cc = -0.01; CI [-0.07, 0.06]cc = -0.01; CI [-0.07, 0.06] cc = 0.11; CI [ 0.05, 0.17]cc = -0.10; CI [-0.16,-0.05]cc = -0.13; CI [-0.19,-0.07]cc* = -0.14; CI [-0.18,-0.10]cc* = -0.01; CI [-0.06, 0.04]cc* = -0.02; CI [-0.07, 0.04] cc* = 0.34; CI [ 0.25, 0.45]cc* = -0.21; CI [-0.27,-0.15]cc* = -0.28; CI [-0.33,-0.23] Figure 7.
Scatter plots of average coronal hole temperature, density and emission measureagainst area (left) and the mean of the signed magnetic field density (right) from the CATCHcatalog (Heinemann et al. , 2019). The Pearson correlation coefficients claculated with (cc) andwithout uncertainties (cc*) are given in each respective panel. E M [ c m - ] QS CH0.91.11.31.5 T [ M K ] n e [ c m - ] P x D i s t r [ % ] P x D i s t r [ % ] P x D i s t r [ % ] y - Binsize = 50 kKx - Binsize = 5 arsecy - Binsize = 3 x 10 cm -3 x - Binsize = 5 arsecy - Binsize = 5 x 10 cm -5 x - Binsize = 5 arsec Figure 8.
Distribution of the plasma properties of individual pixels as a function of thedistance to the nearest coronal hole boundary [ d ]. For each vertical bin (of a size of 5 (cid:48)(cid:48) ) thenormalized distribution of pixels and their temperature, density, and emission measure (fromtop to bottom) value was calculated. A darker shade represents a higher percentage of pixelsin the according bin. Note that the distributions with d > (cid:48)(cid:48) are very uncertain because ofthe low amount of pixels available. Thus, the focus is on the region between 0 to ≈ (cid:48)(cid:48) . Sucha large minimum distance to the coronal hole boundary is only possible in very large coronalholes, which are rare. The negative distances represent pixel outside of the coronal hole, whichshould be considered with care as discussed in Section 3.4 SOLA: main_clean.tex; 1 March 2021; 1:32; p. 16
EM of Coronal Holes
Table 2.
Pearson correlation coefficients for the average coronal hole temperature against coronalhole area, signed mean magnetic field density, and solar activity approximated by the internationalsunspot number and calculated from different input configurations. The correlation coefficientsare given as calculated with and without uncertainties. In the square brackets the CI aregiven. Pearson Correlation Coefficients with UncertaintiesCorrection T vs. A T vs. | B s | T vs. SSNr aia psf − .
05 [ − . , .
01] 0 .
12 [0 . , .
01] 0 .
16 [0 . , . aia psf + corr a − .
04 [ − . , .
02] 0 .
10 [0 . , .
02] 0 .
13 [0 . , . aia psf + Saqri et al. – corr b − .
05 [ − . , .
01] 0 .
16 [0 . , .
01] 0 .
16 [0 . , . et al. PSF − .
04 [ − . , − .
02] 0 .
12 [0 . , − .
02] 0 .
15 [0 . , − . et al. PSF + corr a − .
03 [ − . , − .
01] 0 .
10 [0 . , − .
01] 0 .
14 [0 . , − . | B s | T vs. SSNr aia psf − .
15 [ − . , − .
11] 0 .
35 [0 . , − .
11] 0 .
51 [0 . , − . aia psf + corr a − .
14 [ − . , − .
09] 0 .
34 [0 . , − .
09] 0 .
52 [0 . , − . aia psf + Saqri et al. – corr b − .
12 [ − . , − .
08] 0 .
43 [0 . , − .
08] 0 .
51 [0 . , − . et al. PSF − .
10 [ − . , − .
08] 0 .
27 [0 . , − .
08] 0 .
41 [0 . , − . et al. PSF + corr a − .
09 [ − . , − .
07] 0 .
27 [0 . , − .
07] 0 .
41 [0 . , − . a Stray-light correction derived from lunar eclipse data as given in Table 1. b Stray-light correction derived from Venus transit data as given given by Saqri et al. (2020).
Appendix
The PSF and eclipse corrections could be introducing systematic biases, whichmight affect the correlations between the coronal hole plasma parameters withthe other coronal hole parameters and the solar activity. To verify that weare not introducing such biases, we calculated the DEM using different inputconfigurations. We used two different PSF kernels: firstly the PSF provided inthe SSWIDL, which we used throughout the study, and secondly the PSF byPoduval et al. (2013). We then performed the analysis using different valuesfor the stray-light correction: We used the PSF-deconvoluted images withouteclipse correction, with the eclipse correction as derived in Section 2.3, andadditionally with the method used by Saqri et al. (2020; with a correction factorof [0 . , . , . , . , . , .
0] DN for the six SDO/AIA wavelengths respectively),who derived the correction from the 2012 Venus transit. The calculations wereperformed on a plate scale of 9 . (cid:48)(cid:48) (in contrast to the 4 . (cid:48)(cid:48) in the main study,which explains the small discrepancy to the values presented above) to completethe analysis in a reasonable amount of time. The resulting bootstrapped Pearsoncorrelation coefficients for the average coronal hole temperature, electron den-sity, and emission measure are presented in Tables 2, 3, and 4 respectively. Wefind that the data preparation, i.e. which PSF was used and what correction isapplied, does not significantly change the correlations, and as such the resultsare reliable. SOLA: main_clean.tex; 1 March 2021; 1:32; p. 17 .G. Heinemann et al.
Table 3.
Pearson correlation coefficients for the coronal hole electron density, against coronalhole area, signed mean magnetic field density, and solar activity approximated by the internationalsunspot number and calculated from different input configurations. The correlation coefficientsare given as calculated with and without uncertainties. In the square brackets the CI aregiven. Pearson Correlation Coefficient with UncertaintiesCorrection n e vs. A n e vs. | B s | n e vs. SSNr aia psf − .
01 [ − . , . − .
14 [ − . , .
05] 0 .
03 [ − . , . aia psf + corr a − .
02 [ − . , . − .
12 [ − . , .
05] 0 .
04 [ − . , . aia psf + Saqri et al. – corr b − .
02 [ − . , . − .
12 [ − . , .
04] 0 .
06 [ − . , . et al. PSF − .
02 [ − . , . − .
11 [ − . , .
04] 0 .
01 [ − . , . et al. PSF + corr a − .
02 [ − . , . − .
11 [ − . , .
04] 0 .
03 [ − . , . n e vs. A n e vs. | B s | n e vs. SSNr aia psf − .
03 [ − . , . − .
28 [ − . , .
03] 0 .
07 [0 . , . aia psf + corr a − .
04 [ − . , . − .
26 [ − . , .
02] 0 .
11 [0 . , . aia psf + Saqri et al. – corr b − .
04 [ − . , . − .
25 [ − . , .
01] 0 .
15 [0 . , . et al. PSF − .
03 [ − . , . − .
16 [ − . , .
03] 0 .
02 [ − . , . et al. PSF + corr a − .
04 [ − . , . − .
17 [ − . , .
03] 0 .
06 [ − . , . a Stray-light correction derived from lunar eclipse data as given in Table 1. b Stray-light correction derived from Venus transit data as given given by Saqri et al. (2020).
Table 4.
Pearson correlation coefficients for the coronal hole emission measure against coronalhole area, signed mean magnetic field density, and solar activity approximated by the inter-national sunspot number, and calculated from different input configurations. The correlationcoefficients are given as calculated with and without uncertainties. In the square brackets theCI are given. Pearson Correlation Coefficient with UncertaintiesCorrection EM vs. A EM vs. | B s | EM vs. SSNr aia psf − .
02 [ − . , . − .
09 [ − . , .
04] 0 .
09 [0 . , . aia psf + corr a − .
01 [ − . , . − .
09 [ − . , .
05] 0 .
09 [0 . , . aia psf + Saqri et al. – corr b − .
02 [ − . , . − .
08 [ − . , .
05] 0 .
10 [0 . , . et al. PSF − .
02 [ − . , . − .
09 [ − . , .
05] 0 .
08 [0 . , . et al. PSF + corr a − .
01 [ − . , . − .
10 [ − . , .
05] 0 .
08 [0 . , . | B s | EM vs. SSNr aia psf − .
04 [ − . , . − .
17 [ − . , .
02] 0 .
21 [0 . , . aia psf + corr a − .
03 [ − . , . − .
19 [ − . , .
03] 0 .
21 [0 . , . aia psf + Saqri et al. – corr b − .
03 [ − . , . − .
17 [ − . , .
02] 0 .
25 [0 . , . et al. PSF − .
03 [ − . , . − .
15 [ − . , .
03] 0 .
16 [0 . , . et al. PSF + corr a − .
02 [ − . , . − .
18 [ − . , .
04] 0 .
18 [0 . , . a Stray-light correction derived from lunar eclipse data as given in Table 1. b Stray-light correction derived from Venus transit data as given given by Saqri et al. (2020).
SOLA: main_clean.tex; 1 March 2021; 1:32; p. 18
EM of Coronal Holes
Disclosure of Potential Conflicts of Interest
The authors declare that they have noconflicts of interest.
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