Accelerating and Supersonic Density Fluctuations in Coronal Hole Plumes: Signature of Nascent Solar Winds
Il-Hyun Cho, Valery M. Nakariakov, Yong-Jae Moon, Jin-Yi Lee, Dae Jung Yu, Kyung-Suk Cho, Vasyl Yurchyshyn, Harim Lee
aa r X i v : . [ a s t r o - ph . S R ] A ug Draft version August 19, 2020
Typeset using L A TEX preprint style in AASTeX62
Accelerating and Supersonic Density Fluctuations in Coronal Hole Plumes: Signature of NascentSolar Winds
Il-Hyun Cho, Valery M. Nakariakov,
2, 3, 4
Yong-Jae Moon,
1, 2
Jin-Yi Lee, Dae Jung Yu, Kyung-Suk Cho,
5, 6
Vasyl Yurchyshyn, and Harim Lee Department of Astronomy and Space Science, Kyung Hee University, Yongin, 17104, Korea School of Space Research, Kyung Hee University, Yongin, 17104, Korea Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, CV4 7AL, UK Special Astrophysical Observatory, Russian Academy of Sciences, St. Petersburg, 196140, Russia Space Science Division, Korea Astronomy and Space Science Institute, Daejeon 34055, Korea Department of Astronomy and Space Science, University of Science and Technology, Daejeon 34055, Korea Big Bear Solar Observatory, New Jersey Institute of Technology, 40386 North Shore Lane, Big Bear City, CA92314-9672, USA (Received July 30, 2020; Revised Aug 11, 2019; Accepted Aug 18, 2020)
Submitted to ApJLABSTRACTSlow magnetoacoustic waves in a static background provide a seismological tool toprobe the solar atmosphere in the analytic frame. By analyzing the spatiotemporalvariation of the electron number density of plume structure in coronal holes above thelimb for a given temperature, we find that the density perturbations accelerate withsupersonic speeds in the distance range from 1.02 to 1.23 solar radii. We interpret themas slow magnetoacoustic waves propagating at about the sound speed with acceleratingsubsonic flows. The average sonic height of the subsonic flows is calculated to be 1.27solar radii. The mass flux of the subsonic flows is estimated to be 44.1% relative tothe global solar wind. Hence, the subsonic flow is likely to be the nascent solar wind.In other words, the evolution of the nascent solar wind in plumes at the low corona isquantified for the first time from imaging observations. Based on the interpretation,propagating density perturbations present in plumes could be used as a seismologicalprobe of the gradually accelerating solar wind.
Keywords:
Solar coronal plumes (2039); Solar wind (1534); Solar coronal seismology(1994) INTRODUCTIONSlow magnetoacoustic waves are useful seismological tool to probe the solar atmosphere (e.g.,Cho et al. 2017, 2019). MHD waves propagating in a flowing background with a constant speed are
Corresponding author: Yong-Jae [email protected]
Cho et al. faster than phase speeds of the waves in a static medium due to the Doppler effect, which was pre-dicted by theories (Goossens et al. 1992; Nakariakov et al. 1996) and observations (Chen et al. 2011;Feng et al. 2011; Decraemer et al. 2020). A wave propagation in a flowing background with a non-constant speed may not be analyzed analytically, but can be explored in a simulation (Griton et al.2020).Solar plumes are thin and ray-like structures rooted above networks and extended up to at least30 solar radii (Deforest et al. 1997; DeForest et al. 2001). Plumes are known to be cooler and denserthan their surrounding interplumes (Poletto 2015). It was found that a plume in extreme ultraviolet(EUV) bands disappears due to a density reduction rather than temperature decrease (Pucci et al.2014). It was also found that EUV intensities are enhanced above the enhanced spicular activity(Samanta et al. 2019). These structures are thought to be magnetic tubes that guide MHD waves(Nakariakov 2006; Banerjee et al. 2011; Poletto 2015) which were observed as periodically propagatingintensity disturbances in various wavelength bands (Ofman et al. 1997; DeForest & Gurman 1998;Ofman et al. 1999; Wang et al. 2009; Gupta et al. 2010; Krishna Prasad et al. 2011; Gupta et al.2012; Krishna Prasad et al. 2014, 2018), and/or mass-flows (McIntosh et al. 2010; Tian et al. 2011;Pucci et al. 2014).In this study, we provide evidence of wave propagations in an accelerating background with asubsonic speed in plume structures. For this, a propagation speed of density fluctuations in plumestructures is estimated and compared with the sound speed obtained from the electron temperaturegiven by the differential emission measure (DEM). In Section 2, we describe data and method todistinguish the plume structures in a plume line of sight (LOS). In Section 3, we perform the least-square fitting to the evolution of density fluctuation by the second-order polynomial and explore theproperty of background flow. Finally, we summarize and discuss our results. DATA AND METHOD2.1.
Plume structures in the plume LOS
We use narrow-band filtergram images at 94, 131, 171, 193, 211, 335 ˚A taken by the AtmosphericImaging Assembly (AIA) (Lemen et al. 2012) on board the Solar Dynamics Observatory (SDO)(Pesnell et al. 2012) on 2017-Jan-03 00:00 UT – 24:00 UT. During the observation day, the entireSun was very quiet. Each image is rotated based on the solar P angle and re-sized to have the pixelresolution of 0.600 arcseconds at the distance of 1.496 × km which is the reference distance givenin data. The intensity is scaled according to the changes in pixel resolution and the disk size.Plumes are embedded in interplume background. To minimize the effects from interplume emissionon the estimation of the density and temperature, we define the plume line of sight (LOS) andinterplume LOS separately, as in Figure 1. We define slits which indicate the boundaries of plumeand interplume LOSs based on the 1-day averaged intensity of the AIA 171 ˚A band (Figure 1c).The slits on the intensity images for the other five bands are the same with that of the intensityimage of 171 ˚A. The plume was inclined to ∼ ◦ relative to the direction normal to the solar surface.The interplume was also inclined, but the axis looks to be curved. Both the positions of straightand curved lines are determined by 1st- and 2nd- order polynomial fittings from several locationsthat were visually determined. Along the slits, the intensities of the (inter)plume LOS betweenboundaries at the (right)left are averaged for a given height and frame. For example, the averageintensity of 171 ˚A band on the plume LOS at the distance of 1.2 solar radii is determined from ropagating Density Fluctuations in Solar Coronal Holes Figure 1.
One-day averaged intensities of 94, 131, 171, 193, 211, 335 ˚A bands taken by the SDO/AIA forthe south polar region (a – f). Two white lines on the left and right in each panel are boundaries of plumeLOS and interplume LOS. From these region, intensities for plume and interplume LOSs are constructed asa function of heliocentric distance and time. The blue horizontal lines indicate the height of 1.2 solar radii. intensities along the positions indicated by the blue line on the left in Figure 1c, and that on theinterplume is from the positions indicated by the blue line on the right. Note that slit distances inthe plume and interplume LOSs are different from each other at a given height. The distance in ourstudy represents the heliocentric distance corresponding to the inclined slit distance of the plumeLOS. 2.2.
Differential emission measure
The DEM represents the amount of emission of plasma, and gives an electron number density fora given temperature and length of the LOS. The intensity of the filtergram with narrow ranges ofwavelength on EUV taken by the SDO/AIA ( I i ) can be modeled as R T R i ( T )DEM( T ) dT , where I i and R i represent intensity and temperature response for a certain channel. Temperature responsefunctions are slightly different for different abundances (e.g., Lee et al. 2017). It is likely that abun-dance enhancements are not able to be built up in an open magnetic field structure of coronal holes.Hence, we use the photospheric abundance (Caffau et al. 2011) which gives the temperature response Cho et al.
Figure 2.
Examples of DEMs for plume LOS (black) and interplume LOS (red) at an arbitrary time anddistance (a), their difference (b), the map of electron number density (c), temporal averages of the electronnumber density and temperature as a function of distance (d, e). The vertical bars in panel a represent ± σ DEM
Plume LOS and ± σ DEM
Interplume LOS . The vertical bars in panel b represent ± σ ∆DEM defined by q σ DEM + σ DEM . The red-dashed line in panel b indicates the zero DEM. The gray areain panel d and e represent ± σ n e and ± σ T e . The blue-solid line in panel d is the diameter of a single plume. of 171 ˚A at around 0.8 MK to be lower ∼ ropagating Density Fluctuations in Solar Coronal Holes Plume LOS ( t, h, T ) and DEM Interplume LOS ( t, h, T ), where t , h , and T are the time, height, andtemperature bin, respectively. DEMs are 1-min averaged to enhance the signal-to-noise ratios. Fromthis, we define the DEM of plume structures DEM Plume as DEM
Plume LOS − DEM
Interplume LOS . Asnapshot of DEM
Plume LOS , DEM
Interplume LOS , and DEM
Plume are presented in Figures 2a and 2b,which are taken from the position indicated by the cross in Figure 2c. As shown in Figure 2a, bothDEMs have two bumps at around 0.8 MK and 2 MK, but the latter bumps are identical in both LOSs.It was found that the temperature of the equatorial coronal holes is ∼ ∼ Interplume LOS from DEM
Plume can minimize a contributionto plume emissions from the background, but also reduces emissions from plumes along the plumeLOS.The emission measure, EM
Plume ( t, h ), is defined as R T DEM
Plume ( t, h, T ) dT . The electron numberdensity, n e ( t, h ), is defined as q EM Plume ( t,h ) dl ( h ) , and presented in Figure 2c. The LOS length of plumes, dl ( h ), is set to be the length of chord (2 h tan θ ) for a single plume, where h is the height, θ is halfof the angular width of a plume (1 ◦ ), which corresponds to 24 – 30 Mm. The calculated numberdensity seems to be consistent with the measurement from on-disk coronal holes (Saqri et al. 2020).The electron temperature, T e ( t, h ), is defined as R T DEM
Plume
T dT R T DEM
Plume dT . The temporal averages of n e and T e for a given distance are presented in Figures 2d and 2e. These quantities are used for the estimationof the mass flux and sound speed. RESULTS3.1.
Evolution of propagating density disturbances
We analyze δn e ( t, h ) defined by the electron number density ( n e ) sequentially subtracted by theprevious one, for a given height (Figure 3a). We perform the median smoothing with 3 minutesby 3 pixels ( ∼ ±
15 minutes (31 minutes). For eachsub-image, we calculate the lagged cross-correlations between the profile at the distance of 50 Mmand profiles for different distances. The average cross-correlation is presented in Figure 3b. Thepositive and negative lags represent that the profiles at different distances lead and trail the profileat the distance of 50 Mm, respectively, hence the migration of the lag showing maximum correlationsfrom negative to positive indicates the upward propagation.In Figure 3b, we plot the weighted-mean lag for a given distance (gray circle). It is clearly shownthat the instantaneous slope of distance evolution ( h ( t )) are different from different times (see redsolid lines). We perform the linear least-square fittings for the distances at low and high altitudes, Cho et al.
Figure 3.
Perturbations of electron number density ( δn e ≡ d ( n e / < n e > t − and found that the speeds are 111 km s − and 161 km s − , respectively. Hence, h(t) is likely toaccelerate. To quantify the evolution, h ( t ) were fitted with the 2nd-order polynomial as a functionof lag time. As a result, the evolution of the propagation of perturbations is described by a constantacceleration model. The acceleration ( a ) is calculated to be 183 ±
12 m s − . The initial speed ( v )at zero height ( h ) is found to be 67 km s − .In Figure 3c, we plot the fitted speed ( v ) as a function of distance together with the sound speed( c S ). The speed is given by p v + 2 a ( h − h ) and its error q v δv + ( h − h ) δa + a ( δh + δh ) v +2 a ( h − h ) ,where δv , δa , δh are the errors of the fitting parameters, and δh is taken to be the standarddeviation of residuals between h and the observed distance. The speed is compared with the soundspeed which could be the propagation speed of slow magnetoacoustic waves in a static medium oflow plasma- β . The sound speed ( c S ) is q γk B Tµm H , and equivalent to 90.9 q γ
67) is the adiabatic index, k B is the Boltzmann constant, m H is the proton mass,and µ (= 0 .
6) is the mean molecular weight. It is shown that the speed of the density perturbationbecomes faster than the sound speed from ∼ ∼
35 Mm) and has an excess of ∼ ropagating Density Fluctuations in Solar Coronal Holes Figure 4.
The average speed is extrapolated up to 2 solar radii using the fitting parameters and thensubtracted by the mean sound speed which corresponds to the phase speed of slow waves. The horozontal-dashed line indicates the sound speed. The vertical-solid line indicates the distance where the extrapolatedspeed becomes supersonic. km s − relative to the sound speed at 1.23 solar radii ( ∼
160 Mm) (see a difference between black lineand dashed line in Figure 3c). The excess speed seems to be consistent with radial speeds derived bythe Doppler dimming technique (Gabriel et al. 2003; Teriaca et al. 2003). Hence, the excess speed inour study is likely to be the speed of flowing background.In Figure 4, we present the flow speed defined as the observed speed after subtracting off the meansound speed, which is assumed to be wave speed. Interestingly, the distance where the flow speedbecomes supersonic is 1.27 solar radii when extrapolated using the fitting parameters. This distanceis lower than sonic heights of solar winds (Telloni et al. 2019; Griton et al. 2020). This may becausethe extrapolation is based on the constant acceleration motion, which may not adequately describecomplex dynamic evolution of solar wind such as deceleration at low altitude (Bemporad 2017).3.2.
Mass flux
We apply spectral analysis to the density profile at the distance of 50 Mm as indicated in Figure 3a.We assume that the profile is embedded in red noise because a perturbed medium at a certaintime might be influenced by previous perturbations via dissipation or heating. This may result in afrequency dependent power which is to be an additional noise. A red noise is defined as σ (1 − ρ )(1 − ρ cos ffN + ρ ) (Schulz & Mudelsee 2002) where σ is the standard deviation of the density profile in Figure 5a, ρ isthe autoregressive parameter of the autoregressive process of the order 1, f is the frequency (min − ),and f N is the Nyquist frequency, respectively. The autoregressive parameter is defined by e − ∆ tτd ,where ∆ t is the sampling interval and τ d is the decorrelation time which makes the autocorrelationto be e as shown in Figure 5b. This noise follows the chi-square distribution with two degrees of Cho et al.
Figure 5.
Perturbations of the electron number density at the distance of 50 Mm as indicated in 3a (a), andthe corresponding autocorrelation (b) and the Fourier power (c). The red cross indicates the decorrelationtime (e-folding time). The solid line in panel c represents 99.9% significance level of the red noise. Fourcolored circles represent the powers higher than the significance level. Their peak peirods range from ∼ ∼ freedom. It is shown that the Fourier power at 4.8, 5.9, 8.9 minutes are above the 99% noise level.The observed periods will be used to estimate a temporal filling factor ( f T ).The mass flux is defined as 4 πd µm p n e vf T f CH f S (Tian et al. 2014), where d is the heliocentricdistance, µ is the mean molecular weight, m p is the proton mass, n e is the electron number density, v is the flow speed, f T is the temporal filling factor, f CH is the fractional area of the coronal hole, f S is the spatial filling factor. In Figure 3b, the perturbation is observed from -300 seconds to 300seconds, hence the lifetime is at least 10 minutes. The temporal filling factor, defined by the ratioof the lifetime ( ∼
10 minutes) to the period (5 – 9 minutes), could be taken as the unity. We use f CH = 0 .
05 and f S = 0 .
1, indicating that plumes occupy 10% of a coronal hole and the coronal holecovers 5% area of the solar surface. The mass flux is calculated to be 5.6 × g s − (8.8 × − M ⊙ yr − ), if we apply n e = 2 . × cm − and v = 66 . − at the height of 100 Mm ( d ∼ ∼ SUMMARY AND DISCUSSIONIn this study, we analyzed the kinematics of perturbations of the electron number density in plumestructures above the limb, as a function of time and heliocentric distance, and find that the densityperturbations are accelerating up to supersonic speeds for a given temperature. We interpreted themas slow magnetoacoustic waves in a low plasma- β background which is flowing with subsonic speedsand exhibiting acceleration. The acceleration of the subsonic flows is estimated to be 183 ±
12 m − inthe distance range from 1.02 to 1.23 solar radii. The extrapolated sonic height is calculated to be 1.27 ropagating Density Fluctuations in Solar Coronal Holes ∼ ∼ ∼
30 solar radii (Griton et al. 2020), which were ubiquitouslyobserved in the coronagraphic images (Cho et al. 2018; DeForest et al. 2018).If the density perturbations are repeated supersonic solar winds, the mass flux corresponds to134.6% on the global solar wind. The repetition periods are in the narrow range from ∼ ∼ − (Threlfall et al.2013).The apparent variation of the phase speed could also be connected with the variation of the poly-tropic index γ , and hence the effective sound speed with height in an isothermal and static plasma,caused by the misbalance of heating and cooling processes (Zavershinskii et al. 2019). A robust mea-surment of γ as a function of height would be helpful to examine the possibility, but such measurementseems only to be allowed on-disk where the signal-to-noise is high (e.g., Krishna Prasad et al. 2018).Coronal holes are possibly in nonequilibrium ionization (NEI) states (e.g., Bradshaw & Raymond2013). It is shown that the measured plasma density and temperature could be affected by NEI in arapidly heated system (e.g., Lee et al. 2019), while the NEI significantly affects the FIP and abun-dance in a coronal hole (Shi et al. 2019). Possible effects of NEI modulated by a MHD wave wereexplored through a foward modeling (Shi et al. 2019). An attempt to fomulate MHD waves undera NEI condition have been performed only recently (Ballai 2019), which potentially could provide atool for interpreting observations.We appreciate helpful comments from an anonymous reviewer, which improve the originalmanuscript. The SDO data is (partly) provided by the Korean Data Center (KDC) for SDO inthe Korea Astronomy and Space Science Institute (KASI) in cooperation with NASA/SDO andthe AIA, EVE, and HMI science teams. This work is supported by KASI under the R&Dprogram’Development of a Solar Coronagraph on International Space Station’ (Project No. 2020-1-850-07)supervised by the Ministry of Science, ICT and Future Planning, the BK 21 plus program funded bythe Korean Government, the Basic Science Research Program through the National Research Foun-dation (NRF) of Korea (grant No. NRF-2020R1I1A0107814) funded by the Ministry of Education,and also the Research Program (grant No. NRF-2019R1C1C1006033, NRF-2019R1C1C1004778,NRF-2019R1A2C1002634) funded by the Ministry of Science, ICT and Future Planning. This workis also supported by the Institute for Information & communications Technology Promotion (IITP)grant funded by the Korean government (2018-0-0142). V.M.N.acknowledges support from the STFC0 Cho et al. consolidated grant ST/T000252/1. V.Y. acknowledges support from NSF AST-1614457, AFOSRFA9550-19-1-0040, and NASA80NSSC17K0016, 80NSSC19K0257, and 80NSSC20K0025 grantsREFERENCES
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