Fe XIII Research Articles

Solar Rotation and Activity for Cycle 24 from SDO/AIA Observations

Differential rotation plays a crucial role in the dynamics of the Sun. We study the solar rotation and its correlation with solar activity by applying a modified machine learning algorithm to identify and track coronal bright points (CBPs) from the Solar Dynamics Observatory/Atmospheric Imaging Assembly observations at 193 Å during cycle 24. For more than 321,440 CBPs, the sidereal and meridional velocities are computed. We find the occurring height of CBPs to be about 5627 km above the photosphere. We obtain a rotational map for the corona by tracking CBPs at the formation height of Fe xii (193 Å) emissions. The equatorial rotation (14.°40 to 14.°54 day−1) and latitudinal gradient of rotation (−3.°0 to −2.°64 day−1) show very slightly positive and negative trends with solar activity (sunspots and flares), respectively. For cycle 24, our investigations show that the northern hemisphere has more differential rotation than the southern hemisphere, confirmed by the asymmetry of the midlatitude rotation parameter. The asymmetry (ranked) of the latitudinal gradient of the rotation parameter is concordant with the sunspot numbers for 7 yr within the 9 yr of the cycle; however, for only 3 yr, it is concordant with the flare index. The minimum horizontal Reynolds stress changes from about −2500 m2 s−2 (corresponding to high activity) in 2012 and 2014 to −100 m2 s−2 (corresponding to low activity) in 2019 over 5° to 35° latitudes within cycle 24. We conclude that the negative horizontal Reynolds stress (momentum transfer toward the Sun’s equator) is a helpful indication of solar activity.

Global Coronal Plasma Diagnostics Based on Multislit Extreme-ultraviolet Spectroscopy

Full-disk spectroscopic observations of the solar corona are highly desired to forecast solar eruptions and their impact on planets and to uncover the origin of solar wind. In this paper, we introduce a new multislit design (five slits) to obtain extreme-ultraviolet (EUV) spectra simultaneously. The selected spectrometer wavelength range (184–197 Å) contains several bright EUV lines that can be used for spectral diagnostics. The multislit approach offers an unprecedented way to efficiently obtain the global spectral data but the ambiguity from different slits should be resolved. Using a numerical simulation of the global corona, we primarily concentrate on the optimization of the disambiguation process, with the objective of extracting decomposed spectral information of six primary lines. This subsequently facilitates a comprehensive series of plasma diagnostics, including density (Fe xii 195.12/186.89 Å), Doppler velocity (Fe xii 193.51 Å), line width (Fe xii 193.51 Å), and temperature diagnostics (Fe viii 185.21 Å, Fe x 184.54 Å, Fe xi 188.22 Å, and Fe xii 193.51 Å). We find a good agreement between the forward modeling parameters and the inverted results at the initial eruption stage of a coronal mass ejection, indicating the robustness of the decomposition method and its immense potential for global monitoring of the solar corona.

Spectroscopic Observations of the Solar Corona during the 2017 August 21 Total Solar Eclipse: Comparison of Spectral Line Widths and Doppler Shifts between Open and Closed Magnetic Structures

The spectroscopic observations presented here were acquired during the 2017 August 21 total solar eclipse (TSE) with a three-channel partially multiplexed imaging spectrometer operating at extremely high orders (>50). The 4 R ⊙ extent of the slit in the north–south direction scanned the corona starting from the central meridian out to approximately 1.0 R ⊙ off the east limb throughout totality. The line widths and Doppler shifts of the Fe x (637.4 nm) and Fe xiv (530.3 nm) emission lines, characteristic of 1.1 × 106 K and 1.8 × 106 K electron temperatures, respectively, varied across the different coronal structures intercepted by the slit. Fe xiv was the dominant emission in the closed fields of an active region and the base of a streamer, with relatively constant 20–30 km s−1 line widths independent of the height. In contrast, Fe x emission exhibited broader (>40 km s−1) line widths in open fields, which increased with height, in particular in the polar coronal hole. Inferences of line widths and Doppler shifts were consistent with extreme ultraviolet (EUV) observations from the Hinode/EUV Imaging Spectrograph, as well as with the near-infrared Fe xiii 1074 nm line observed by Coronal Multichannel Polarimeter. The differences in the spectral line widths between distinct coronal structures are interpreted as an indication of the predominance of wave heating in open structures versus localized heating in closed structures. This study underscores the unparalleled advantages and the enormous potential of TSE spectroscopy in measuring line widths simultaneously in open and closed fields at high altitudes, with minimal exposure times, stray light levels, and instrumental widths.

The Cycles of Alpha Centauri: Double Dipping of AB

Abstract In mid-2023, the Sunlike dwarfs of nearby α Centauri (HD 128620 (“A”): G2 V; HD 128621 (“B”): K1 V; hereafter “AB”) coincidentally both entered coronal (T ≈ 1–3 MK) low states in their long-term X-ray cycles, as captured by the Chandra Observatory and its High Resolution Camera (HRC-I). The assessment benefited from a sensitivity degradation model for HRC-I based on a “check star,” the F subgiant Procyon (α Canis Minoris A; HD 61421: F5 IV–V), further validated by Hubble Space Telescope time series of the Fe xii 1241.985 Å and 1349.396 Å coronal forbidden lines (T ≈ 1.6 MK) of all three stars. The AB starspot-cycle periods noted previously, 19 and 8 yr, appear to be holding. These deviate substantially from the 11 yr solar example, despite only modest differences in the stellar properties. The new cycle-minimum L X/L BOL of α Cen A is similar to that of the previous minimum observed by Chandra in 2005–2010, and close to solar-MIN X-ray levels in 2009 and 2019, with implications for the “basal” coronal flux of low-activity early G stars. The recent α Cen B X-ray MIN is similar to that in 2016 but higher than an earlier one in 2007–2009. Significantly, the B X-ray minima (in L X/L BOL) are comparable to the solar Cycle 24 maximum, suggesting plentiful starspots at the B-cycle MIN (contrary to the solar case). Tangentially, the current AB low states favor Doppler-reflex detections of planets, as opposed to the coronal high states, when elevated chromospheric activity can add nuisance signals to radial velocity time series.

Multipole rate coefficients for collisional excitation of Fe XIII by isotropic electrons

Multipole rate coefficients for collisional excitation of Fe XIII by isotropic electrons

Estimating Ion Temperatures at the Polar Coronal Hole Boundary

The temperatures of the heavy ions (T i ) in the solar corona provide critical information about the heating mechanism of the million-degree corona. However, the measurement of T i is usually challenging due to the nonthermal motion, instrumental limitations, and optically thin nature of the coronal emissions. We present the measurement of T i and its dependency on the ion charge-to-mass ratio (Z/A) at the polar coronal hole boundary, only assuming that heavy ions have the same nonthermal velocity. To improve the Z/A coverage and study the influence of the instrumental broadening, we used a coordinated observation from the EUV Imaging Spectrometer on board the Hinode satellite and the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) on board the Solar and Heliospheric Observatory. We found that the T i of ions with Z/A less than 0.20 or greater than 0.33 are much higher than the local electron temperature. We ran the Alfvén Wave Solar Model-realtime to investigate the formation of optically thin emissions along the line of sight (LOS). The simulation suggested that plasma bulk motions along the LOS broaden the widths of hot emission lines in the coronal hole (e.g., Fe xii, Fe xiii). We discussed other factors that might affect the T i measurement, including the non-Gaussian wings in some bright SUMER lines, which can be fitted by a double-Gaussian or a κ distribution. Our study confirms the preferential heating of heavy ions in coronal holes and provides new constraints on coronal heating models.

Evolution of the thermodynamic properties of a coronal mass ejection in the inner Corona

The thermodynamic evolution of Coronal Mass Ejections (CMEs) in the inner corona (≤1.5 Rsun) is not yet completely understood. In this work, we study the evolution of thermodynamic properties of a CME core observed in the inner corona on 20 July 2017, by combining the MLSO/K-Cor white-light and the MLSO/CoMP Fe XIII 10747 Å line spectroscopic data. We also estimate the emission measure weighted temperature (TEM) of the CME core by applying the Differential Emission Measure (DEM) inversion technique on the SDO/AIA six EUV channels data and compare it with the effective temperature (Teff) obtained using Fe XIII line width measurements. We find that the Teff and TEM of the CME core show similar variation and remain almost constant as the CME propagates from ∼1.05 to 1.35 Rsun. The temperature of the CME core is of the order of million-degree kelvin, indicating that it is not associated with a prominence. Further, we estimate the electron density of this CME core using K-Cor polarized brightness (pB) data and found it decreasing by a factor of ∼3.6 as the core evolves. An interesting finding is that the temperature of the CME core remains almost constant despite expected adiabatic cooling due to the expansion of the CME core, which suggests that the CME core plasma must be heated as it propagates. We conclude that the expansion of this CME core behaves more like an isothermal than an adiabatic process.

First Infrared Coronal Spectra from DKIST/Cryo-NIRSP: Comparisons with Global MHD Models

The Cryogenic Near-Infrared Spectropolarimeter (Cryo-NIRSP) is now conducting science operations at the National Science Foundation’s Daniel K. Inouye Solar Telescope (DKIST). We report results obtained during instrument commissioning that advance multiwavelength coronagraphic observations in the infrared. This includes the first observations of the Fe xiii 1075 nm, Fe xiii 1079 nm, Si x 1430 nm, and Si ix 3934 nm forbidden lines. The Si ix observations, in particular, significantly improve upon the few previous ground-based detections and open up this diagnostic for more routine study. We analyse long-slit spectra in each line sampling elongations from 1.06 to 1.52 solar radii above the northeast solar limb on 2022 February 14. Line characteristics as a function of radial distance are derived and discussed in comparison to modeled emission emergent from global coronal magnetohydrodynamic models with different heating prescriptions. We find favorable correspondence between the observations and different aspects of these models, and further demonstrate the utility of infrared observations for constraining coronal models. Continued DKIST/Cryo-NIRSP observations including polarimetric data, together with ongoing improvements in data calibrations, promise significant value for coronal studies.

Scattered Light in the Hinode/EIS and SDO/AIA Instruments Measured from the 2012 Venus Transit

Observations from the 2012 transit of Venus are used to derive empirical formulae for long- and short-range scattered light at locations on the solar disk observed by the Hinode Extreme ultraviolet Imaging Spectrometer (EIS) and the Solar Dynamics Observatory Atmospheric Imaging Assembly (AIA) instruments. Long-range scattered light comes from the entire solar disk, while short-range scattered light is considered to come from a region within 50″ of the region of interest. The formulae were derived from the Fe xii 195.12 Å emission line observed by EIS and the AIA 193 Å channel. A study of the weaker Fe xiv 274.20 Å line during the transit and a comparison of scattering in the AIA 193 Å and 304 Å channels suggests the EIS scattering formula applies to other emission lines in the EIS wavebands. Both formulae should be valid in regions of fairly uniform emission such as coronal holes and quiet Sun, but may be less accurate for faint areas close (around 100″) to bright active regions. The formula for EIS is used to estimate the scattered light component of Fe xii λ195.12 for seven on-disk coronal holes observed between 2010 and 2018. Scattered light contributions of 56%–100% are found, suggesting that these features are dominated by scattered light, consistent with earlier work of Wendeln & Landi. Emission lines from the S x and Si x ions—formed at the same temperature as Fe xii and often used to derive the first ionization potential bias from EIS data—are also expected to be dominated by scattered light in coronal holes.

Contribution of Spicules to Solar Coronal Emission

Recent high-resolution imaging and spectroscopic observations have generated renewed interest in spicules’ role in explaining the hot corona. Some studies suggest that some spicules, often classified as type II, may provide significant mass and energy to the corona. Here we use numerical simulations to investigate whether such spicules can produce the observed coronal emission without any additional coronal heating agent. Model spicules consisting of a cold body and hot tip are injected into the base of a warm (0.5 MK) equilibrium loop with different tip temperatures and injection velocities. Both piston- and pressure-driven shocks are produced. We find that the hot tip cools rapidly and disappears from coronal emission lines such as Fe xii 195 and Fe xiv 274. Prolonged hot emission is produced by preexisting loop material heated by the shock and by thermal conduction from the shock. However, the shapes and Doppler shifts of synthetic line profiles show significant discrepancies with observations. Furthermore, spatially and temporally averaged intensities are extremely low, suggesting that if the observed intensities from the quiet Sun and active regions were solely due to type II spicules, one to several orders of magnitude more spicules would be required than have been reported in the literature. This conclusion applies strictly to the ejected spicular material. We make no claims about emissions connected with waves or coronal currents that may be generated during the ejection process and heat the surrounding area.

The nuclear transient AT 2017gge: a tidal disruption event in a dusty and gas-rich environment and the awakening of a dormant SMBH

ABSTRACT We present the results from a dense multwavelength [optical/UV, near-infrared (IR), and X-ray] follow-up campaign of the nuclear transient AT 2017gge, covering a total of 1698 d from the transient’s discovery. The bolometric light curve, the blackbody temperature and radius, the broad H and He i λ5876 emission lines and their evolution with time, are all consistent with a tidal disruption event (TDE) nature. A soft X-ray flare is detected with a delay of ∼200 d with respect to the optical/UV peak and it is rapidly followed by the emergence of a broad He ii λ4686 and by a number of long-lasting high ionization coronal emission lines. This indicate a clear connection between a TDE flare and the appearance of extreme coronal line emission (ECLEs). An IR echo, resulting from dust re-radiation of the optical/UV TDE light is observed after the X-ray flare and the associated near-IR spectra show a transient broad feature in correspondence of the He i λ10830 and, for the first time in a TDE, a transient high-ionization coronal NIR line (the [Fe xiii] λ10798) is also detected. The data are well explained by a scenario in which a TDE occurs in a gas-and-dust rich environment and its optical/UV, soft X-ray, and IR emission have different origins and locations. The optical emission may be produced by stellar debris stream collisions prior to the accretion disc formation, which is instead responsible for the soft X-ray flare, emitted after the end of the circularization process.

Constraining the Physical Properties of Stellar Coronal Mass Ejections with Coronal Dimming: Application to Far-ultraviolet Data of ϵ Eridani

Coronal mass ejections (CMEs) are a prominent contributor to solar system space weather and might have impacted the Sun’s early angular momentum evolution. A signal diagnostic of CMEs on the Sun is coronal dimming: a drop in coronal emission, tied to the mass of the CME, that is the direct result of removing emitting plasma from the corona. We present the results of a coronal dimming analysis of Fe xii 1349 Å and Fe xxi 1354 Å emission from ϵ Eridani (ϵ Eri), a young K2 dwarf, with archival far-ultraviolet observations by the Hubble Space Telescope’s Cosmic Origins Spectrograph. Following a flare in 2015 February, ϵ Eri’s Fe xxi emission declined by 81 ± 5%. Although enticing, a scant 3.8 minutes of preflare observations allows for the possibility that the Fe xxi decline was the decay of an earlier, unseen flare. Dimming nondetections following each of three prominent flares constrain the possible mass of ejected Fe xii-emitting (1 MK) plasma to less than a few × 1015 g. This implies that CMEs ejecting this much or more 1 MK plasma occur less than a few times per day on ϵ Eri. On the Sun, 1015 g CMEs occur once every few days. For ϵ Eri, the mass-loss rate due to CME-ejected 1 MK plasma could be < 0.6 , well below the star’s estimated 30 mass-loss rate (wind + CMEs). The order-of-magnitude formalism we developed for these mass estimates can be broadly applied to coronal dimming observations of any star.

Properties of EUV Imaging Spectrometer (EIS) Slot Observations

The Extreme ultraviolet Imaging Spectrometer (EIS) on board the Hinode spacecraft has been operating since 2006, returning high-resolution data in the 170 – 212 and 246 – 292 Å wavelength regions. EIS has four slit options, with the narrow 1′′ and 2′′ slits used for spectroscopy and the wide 40′′ and 266′′ slits used for monochromatic imaging. In this article several properties of the 40′′ slit (or slot) are measured using the Fe xii 195.12 Å line, which is formed at 1.5 MK. The projected width of the slot on the detector shows a small variation along the slit with an average value of 40.949′′. The slot image is tilted on the detector and a quadratic formula is provided to describe the tilt. The tilt corresponds to four pixels on the detector and the slot centroid is offset mostly to the right (longer wavelengths) of the 1′′ slit by up to four pixels. Measurement of the intensity decrease at the edge of the slot leads to an estimate of the spatial resolution of the images in the x-direction. The resolution varies quadratically along the slot, with a minimum value of 2.9′′ close to the detector center. Intensities measured from the slot images are found to be on average 14% higher than those measured from the 1′′ slit at the same spatial location. Background subtraction is necessary to derive accurate intensities in quiet-Sun and coronal-hole regions. Prescriptions for deriving accurate slot intensities for different types of slot datasets are presented.

Thomson Scattering above Solar Active Regions and an Ad Hoc Polarization Correction Method for the Emissive Corona

Thomson-scattered photospheric light is the dominant constituent of the lower solar corona’s spectral continuum viewed off-limb at optical wavelengths. Known as the K-corona, it is also linearly polarized. We investigate the possibility of using the a priori polarized characteristics of the K-corona, together with polarized emission lines, to measure and correct instrument-induced polarized crosstalk. First we derive the Stokes parameters of the Thomson scattering of unpolarized light in an irreducible spherical tensor formalism. This allows forward synthesis of the Thomson-scattered signal for the more complex scenario that includes symmetry-breaking features in the incident radiation field, which could limit the accuracy of our proposed technique. For this, we make use of an advanced 3D radiative magnetohydrodynamic coronal model. Together with synthesized polarized signals in the Fe xiii 10746 Å emission line, we find that an ad hoc correction of telescope- and instrument-induced polarization crosstalk is possible under the assumption of a nondepolarizing optical system.

A Spectroscopic Survey of Infrared 1–4 μm Spectra in Regions of Prominent Solar Coronal Emission Lines of Fe XIII, Si X, and Si IX

The infrared solar spectrum contains a wealth of physical data about the Sun and is being explored using modern detectors and technology with new ground-based solar telescopes. One such instrument will be the ground-based Cryogenic Near-IR Spectro-Polarimeter of the Daniel K. Inouye Solar Telescope (DKIST), which will be capable of sensitive imaging of the faint infrared solar coronal spectra with full Stokes I, Q, U, and V polarization states. Highly ionized magnetic dipole emission lines have been observed in galaxies and the solar corona. Quantifying the accuracy of spectral inversion procedures requires a precise spectroscopic calibration of observations. A careful interpretation of the spectra around prominent magnetic dipole lines is essential for deriving physical parameters and particularly for quantifying the off-limb solar coronal observations from DKIST. In this work, we aim to provide an analysis of the spectral regions around the infrared coronal emission lines of Fe xiii 1074.68 nm, Fe xiii 1079.79 nm, Si x 1430.10 nm, and Si ix 3934.34 nm, aligning with the goal of identifying solar photospheric and telluric lines that will help facilitate production of reliable inversions and data products from four sets of solar coronal observations. The outputs can be integrated in processing pipelines to produce level 2 science-ready data.

Diagnostics of Non-Maxwellian Electron Distributions in Solar Active Regions from Fe xii Lines Observed by the Hinode Extreme Ultraviolet Imaging Spectrometer and Interface Region Imaging Spectrograph

We present joint Hinode Extreme Ultraviolet Imaging Spectrometer (EIS) and Interface Region Imaging Spectrograph (IRIS) observations of Fe xii lines in active regions, both on-disk and off-limb. We use an improved calibration for the EIS data, and find that the 192.4 Å/1349 Å observed ratio is consistent with the values predicted by CHIANTI and the coronal approximation in quiescent areas, but not in all active-region observations, where the ratio is often lower than expected by up to a factor of about two. We investigate a number of physical mechanisms that could affect this ratio, such as opacity and absorption from cooler material. We find significant opacity in the EIS Fe xii 193 and 195 Å lines, but not in the 192.4 Å line, in agreement with previous findings. As we cannot rule out possible EUV absorption by H, He, and He ii in the on-disk observations, we focus on an off-limb observation where such absorption is minimal. After considering these, as well as possible nonequilibrium effects, we suggest that the most likely explanation for the observed low Fe xii 192.4 Å/1349 Å ratio is the presence of non-Maxwellian electron distributions in the active regions. This is in agreement with previous findings based on EIS and IRIS observations independently.

Line Profile Studies of Coronal Active Regions in Fe xii λ195.12 Using Hinode/EIS

Coronal active regions are studied using Hinode/EIS observations in the EUV line Fe xii λ195.12 by analyzing their line profiles from 2006 December to 2019 December. The period covers the last 2 yr of solar cycle 23 and solar cycle 24 fully. Active regions are the main source of magnetic field in the solar atmosphere, important in its heating and dynamics. Line profiles were obtained from various active regions spread across the Sun on a monthly basis from which we obtained the intensity, line width, Doppler velocity, and centroid and examined their variation during the solar cycle. The histograms of the Doppler velocity and centroid show that they behave in six different ways with respect to the position of rest wavelength. In addition, the shifts in the centroid were found to be more compared to the Doppler velocity. The variation of the line width with respect to the Doppler velocity or the centroid mostly follows a second-degree polynomial. A multicomponent line profile is simulated to explain the difference in the behavior of the Doppler velocity and the centroid with respect to the line width. We also find that the intensity and the line width of the different data sets show a global dependence on the solar cycle with a good correlation. The implications of the results for the coronal heating and dynamics are pointed out.

Data pipeline architecture and development for VELC onboard Space Solar Mission AdityaL1

ADITYA L-1 is India's first dedicated mission to study Sun and its atmosphere with Visible Emission Line Coronagraph (VELC), a major payload on ADITYA-L1. VELC has provision to make imaging and spectroscopic observations of the corona, simultaneously. Imaging with the Field of View (FOV) from 1.05Ro to 3Ro will be done in continuum at 500nm. The spectroscopic observations of solar corona in three emission lines, namely 5303 {\AA} [Fe XIV], 7892 {\AA} [Fe XI], 10747 {\AA} [Fe XIII], and Spectro-polarimetry at 10747 {\AA} [Fe XIII] will be performed with FOV of 1.05-1.5Ro. In this work, the end-to-end data pipeline architecture and development of the VELC payload are presented. The VELC proposal submission form, satellite observation parameters, data products, level definitions, data pipeline and analysis software to process the big raw data sets obtained using VELC instruments onboard satellite to science-ready data are discussed.

Benchmarking Multiconfiguration Dirac–Hartree–Fock Calculations for Astrophysics: Si-like Ions from Cr xi to Zn xvii

Abstract The multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction methods are used to provide excitation energies, lifetimes, and radiative transition data for the 604 (699, 702, 704, 704, 704, and 699) lowest levels of the 3s 23p 2, 3s3p 3, 3s 23p3d, 3p 4, 3s3p 23d, 3s 23d 2, 3p 33d, 3s3p3d 2, 3s3d 3, 3p3d 3, 3p 23d 2, 3s 23p4s, 3s 23p4p, 3s 23p4d, 3s 23p4f, 3s3p 24s, 3s3p 24p, 3s3p 24d, 3s3p 24f, 3s 23d4s, 3s 23d4p, 3p 34s, 3p 34p, 3s3p3d4s, 3s 23p5s, and 3s 23p5p configurations in Cr xi, (Mn xii, Fe xiii, Co xiv, Ni xv, Cu xvi, and Zn xvii). Previous line identifications of Fe xiii and Ni xv in the EUV and X-ray wavelength ranges are reviewed by comprehensively comparing the MCDHF theoretical results with available experimental data. Many recent identifications of Fe xiii and Ni xv lines are confirmed, and several new identifications for these two ions are proposed. A consistent atomic data set with spectroscopic accuracy is provided for the lowest hundreds of levels for Si-like ions of iron-group elements of astrophysical interest, for which experimental values are scarce. The uncertainty estimation method suggested by Kramida, applied to the comparison of the length and velocity line strength values, is used for ranking the transition data. The correlation of the latter with the gauge dependency patterns of the line strengths is investigated.

How Does Transverse MHD Wave-driven Turbulence Influence the Density Filling Factor in the Solar Corona?

Abstract It is well established that transverse MHD waves are ubiquitous in the solar corona. One of the possible mechanisms for heating both open (e.g., coronal holes) and closed (e.g., coronal loops) magnetic field regions of the solar corona is MHD wave-driven turbulence. In this work, we study the variation of the filling factor of overdense structures in the solar corona due to the generation of transverse MHD wave-driven turbulence. Using 3D MHD simulations, we estimate the density filling factor of an open magnetic structure by calculating the fraction of the volume occupied by the overdense plasma structures relative to the entire volume of the simulation domain. Next, we perform forward modeling and generate synthetic spectra of Fe xiii 10749 Å and 10800 Å density-sensitive line pairs using FoMo. Using the synthetic images, we again estimate the filling factors. The estimated filling factors obtained from both methods are in reasonable agreement. Also, our results match fairly well with the observations of filling factors in coronal holes and loops. Our results show that the generation of turbulence increases the filling factor of the solar corona.