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Extrapolated results shown in a 3D coordinate system. The Z-axis has been stretched. The X-Y plane image represents an MGN-enhanced AIA image with overplotted blue lines that are the projections of the extrapolated loops shown with green lines.
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How the solar corona is heated to high temperatures remains an unsolved mystery in solar physics. In the present study we analyse observations of 50 whole active-region loops taken with the Extreme-ultraviolet Imaging Spectrometer (EIS) on board the Hinode satellite. Eleven loops were classified as cool (<1 MK) and 39 as warm (1-2 MK) loops. We stu...
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... our analysis, the positive direction of the loop is from the east to the west footpoint of the loop. A 3D example of the extrapolated results for one of the data sets is shown in Figure 1. It presents three observational loops that conform well with the extrapolated magnetic field. ...
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... loops are distinguishable in AIA193Å in Figure 9(c). The 3D presentation of Loop22 is given in Figure 9( Figure 10. Figure 11 presents the physical parameter distributions along the loop. ...
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... 3D presentation of Loop22 is given in Figure 9( Figure 10. Figure 11 presents the physical parameter distributions along the loop. We found that the electron density decreases from ∼10 9.5 cm −3 in the loop east footpoint to ∼10 8.95 cm −3 at the loop top. ...
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... found that the electron density decreases from ∼10 9.5 cm −3 in the loop east footpoint to ∼10 8.95 cm −3 at the loop top. The density profile differs considerably from the one described by Equation (4), given by the red dashed curve in Figure 11(a). Figure 12 shows the EM curves for several points along the loop. ...
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... density profile differs considerably from the one described by Equation (4), given by the red dashed curve in Figure 11(a). Figure 12 shows the EM curves for several points along the loop. The temperature in the two loop footpoints has the same value of 1.25MK. ...
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... extrapolated magnetic field lines are identified at αL=2.5 that best agree with two loops. Only one loop, however, is clearly visible along its full length in the EIS Fe XII λ195.12 intensity image (Figure 13(b)) and was numbered as Loop29. We show in Figure 13(c) the AIA 193Å loop observations of both loops. ...
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... one loop, however, is clearly visible along its full length in the EIS Fe XII λ195.12 intensity image (Figure 13(b)) and was numbered as Loop29. We show in Figure 13(c) the AIA 193Å loop observations of both loops. The Loop29 3D positioning derived from the extrapolation can be seen in Figure 13(d). ...
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... show in Figure 13(c) the AIA 193Å loop observations of both loops. The Loop29 3D positioning derived from the extrapolation can be seen in Figure 13(d). ...
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... XII λ195.12, Fe XIII λ202.04, and Fe XIV λ264.79 lines ( Figure 14). The spectral line pair Fe XIII λ202.04/ ...
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... + λ203.83) was used to obtain the electron density, and all spectral lines shown in Figure 14 were used to derive the electron temperature. Figure 15 shows the derived physical parameter distributions along Loop29. ...
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... λ203.83) was used to obtain the electron density, and all spectral lines shown in Figure 14 were used to derive the electron temperature. Figure 15 shows the derived physical parameter distributions along Loop29. The loop length is 121Mm, and its height is 34Mm. ...
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... temperature distribution along Loop29 ranges from 1.49 to 1.75MK. Figure 15(b) shows the magnetic field intensity distribution along Loop29. The magnetic field values range from 23G at the loop top to 291G in the loop east footpoint, and 214G in the west. ...
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... magnetic field values range from 23G at the loop top to 291G in the loop east footpoint, and 214G in the west. The Doppler shifts along the loop are close to zero because of the orientation of the loop with respect to the observer (see Figure 13(d)). The nonthermal velocities obtained from Fe XII λ195.12 along the loop range from 27 to 41km s −1 . ...
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... factor 2 comes from the assumption that the loop plasma comprises primarily electrons and protons. Figure 16 shows the overpressure ratio Q as a function of loop length L for warm (left panel) and cool (right panel) loops. Note that 6 out of our 50 loops were not included because no suitable density-sensitive line pairs were available for us to derive the electron densities. ...
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... for the rest, five loops correspond to a Q in the range of 0.8-1.2. When it comes to the six cool loops we examine, the derived values of Q are exclusively larger than 2. In any case, Figure 16 suggests that neither the warm nor cool loops that we examine agree with the scaling law predicted by RTV78. We note that a similar discrepancy was also found for warm loops such as measured with STEREO by Aschwanden et al. (2008). ...
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Citations
... For one active region loop observed by the EUV Imaging Spectrometer (EIS), Tripathi et al. (2009) found from the region near its footpoint toward its apex the temperatures and electron densities vary from 0.8 MK to 1.5 MK and from 10 9 cm −3 to 10 8.5 cm −3 , respectively. With EIS data, Xie et al. (2017) derived densities, temperatures, filling factors, nonthermal velocities, and magnetic strengths of 50 active region loops, and they found that most of the loops were in a state of overpressure compared to the prediction of Rosner et al. (1978), giving a constraint to a heating model. Transition region loops, which have temperatures from tens of thousands to hundreds of thousands of Kelvin, are usually difficult to identify owing to their dynamic nature, strong radiative background, and line-of-sight (LOS) contamination from other features. ...
Loops are fundamental structures in the magnetized atmosphere of the Sun. Their physical properties are crucial for understanding the nature of the solar atmosphere. Transition region loops are relatively dynamic and their physical properties have not yet been fully understood. With spectral data of the line pair of O iv 1399.8 Å and 1401.2 Å ( T max = 1.4 × 10 5 K) of 23 transition region loops obtained by IRIS, we carry out the first systematic analyses to their loop lengths ( L ), electron densities ( n e ), and effective temperatures. We found electron densities, loop lengths, and effective temperatures of these loops are in the ranges of 8.9 × 10 ⁹ –3.5 × 10 ¹¹ cm ⁻³ , 8–30 Mm, and 1.9 × 10 ⁵ –1.3 × 10 ⁶ K, respectively. At a significant level of 90%, regression analyses show that the relationship between electron densities and loop lengths is n e [cm ⁻³ ] ∝ ( L [Mm]) −0.78±0.42 , while the dependences of electron densities on effective temperatures and that on the line intensities are not obvious. These observations demonstrate that transition region loops are significantly different than their coronal counterparts. Further studies on the theoretical aspect based on the physical parameters obtained here are of significance for understanding the nature of transition region loops.
... According to Gupta et al. (2015), the electron density was measured to be 3.2 × 10 8 cm −3 in two loops, which is slightly lower than the value of about 5.0 × 10 8 cm −3 reported in this paper. However, Xie et al. (2017) reported a density range of 4.0 × 10 8 -2.8 × 10 9 cm −3 , while Huang (2018) found the density to fall between 1 × 10 9 cm −3 and 4 × 10 9 cm −3 . Both studies found higher densities at the top of loops in comparison to the value in this paper. ...
The solar type J radio burst is a variant of type III bursts, which are a probe for understanding solar energetic electrons and local electron density. This study investigates a type J burst event on 2017 September 9. We have combined the data from the extreme-ultraviolet (EUV) imaging and the EUV Imaging Spectrometer (EIS) to analyze the event. Within 4 minutes several type J bursts with similar morphology occur. Two of them, with clear fundamental and second harmonic bands, are studied in detail. We find a delay of 2 ± 0.5 s between their different harmonic bands. During type J bursts, only one coronal loop brightens significantly at its northern footpoint, in correlation with the continuous injection of erupting jets into the loop. The EUV intensity of the brightening footpoint is correlated with the radio flux at 245 and 410 MHz, with correlation coefficients of 0.2 and 0.4, respectively. These observations suggest that the type J bursts should originate from this coronal loop. By analyzing the electron number density distribution along the coronal loop diagnosed from the EIS data and the time evolution of the plasma frequency calculated from the type J burst, we determine that the velocities of the energetic electrons exciting the two type Js are 0.10 ± 0.02 c and 0.12 ± 0.02 c . Our results confirm previous studies on type J bursts.
... Such models have then subsequently been used to guide further investigations. As an example, Xie et al. (2017) used a LFF field model with optimized α to compute the plasma parameters of active-region magnetic loops. ...
Deriving the physical parameters of observed phenomena in the solar atmosphere has fundamental importance, as these parameters are then employed to constrain and validate models. Here we report the development of a new computational algorithm based on a magneto-hydro-static model that computes the magnetic field in the solar atmosphere and automatically matches individual magnetic-field lines with observed structures that appear with enhanced emission in extreme-ultraviolet (EUV) images. Presently, for the quiet-Sun regions, we can only measure the vertical photospheric magnetic field Bz, as accurate horizontal magnetic field measurements are not available. Thus, vertical photospheric magnetic-field measurements are extrapolated into the upper atmosphere, from the photosphere to the corona, with a magneto-hydro-static model. Free model parameters are then optimized with a downhill-simplex method by comparing quantitatively magnetic-field lines with the enhanced emission of loop structures composing the so-called coronal bright points recorded in EUV images taken with the Atmospheric Imaging Assembly on-board the Solar Dynamics Observatory. The algorithm will be applicable to any solar image data where individual structures with an enhanced emission can be resolved. Most importantly, the algorithm can be employed to obtain the magnetic properties of these structures above the photosphere.
... The solar corona contains many different types of magnetic tubes with hot plasma (Klimchuk & DeForest 2020;Litwin & Rosner 1993;Hara et al. 1992;Moses et al. 1997;Schrijver et al. 1999). Abrupt coronal plasma heating is a mystery for astrophysicists, and a great deal of work in this direction has appeared in the literature (Mandrini et al. 2000;Xie et al. 2017;Hollweg & Sterling 1984;Ionson 1983;Steinolfson & Davila 1993;Ofman et al. 1995;Poedts et al. 1989;Poedts et al. 1990;Poedts et al. 1994;Poedts & Goedbloed 1997;Vranjes & Poedts 2009;Vranjes & Poedts 2010;Saleem et al. 2012;Saleem et al. 2021). Plasma filaments in corona have different sizes (De Pontieu et al. 2007) and scale sizes of the order of 1 km in corona have been discussed (Woo 1996). ...
The 3D exact analytical solutions of ideal two-fluid plasma, single-fluid plasma, and neutral fluid equations have been found using physically justifiable assumptions. Surprisingly these solutions satisfy all nonlinearities in the systems. It is pointed out that these solutions explain the fundamental mechanism behind the creation of a vast variety of ordered structures in plasmas and fluids. In the limiting case of 2D dependence of fields, the theoretical model for plasma is applied to explain the formation of spicules in the solar chromosphere. It is pointed out that the main contribution of electron (ion) baroclinic vectors is to produce vorticity in the plasma, and that magnetic field generation is coupled with the flow of both electrons and ions.
... At lower electron densities ( 10 7.5 cm −3 ), the changes can be very pronounced at low heights, while also being important at the ∼3% level for heights ≥ 30 Mm. However, the active corona at heights low enough to be significantly affected by the presence of a sunspot, in particular active region loops, exhibit relatively high densities > 10 8.5 cm −3 (see, e.g., Aschwanden et al. (2013) and Xie et al. (2017)). In Li, Landi Degl'Innocenti, and Qu (2017), the symmetry-breaking effects of a sunspot on the forbidden line emission was considered, but the employed density stratification peaked at electron densities of ∼10 7.8 cm −3 . ...
Photoexcited forbidden lines at visible and infrared wavelengths provide important diagnostics for the coronal magnetic field via scattering induced polarization and the Zeeman effect. In forward models, the polarized formation of these lines is often treated assuming a simplified exciting radiation field consisting only of the photospheric quiet-Sun continuum, which is both cylindrically-symmetric relative to the solar vertical and unpolarized. In particular, this assumption breaks down near active regions, especially due to the presence of sunspots and other surface features that modify the strength and anisotropy of the continuum radiation field. Here we investigate the role of symmetry-breaking on the emergent polarized emission in high resolution models of the active corona simulated with the MURaM code. We treat the full 3D unpolarized continuum radiation field of the photosphere that excites the coronal ions and compare the cases where the symmetry-breaking effects of the photospheric features are included or ignored. Our discussion focuses on the key observables soon to be available by the National Science Foundation’s Daniel K Inouye Solar Telescope. The results indicate that while symmetry breaking can in principle have a large effect, its role is relatively minor for the simulated active region, largely due to the low inherent polarization fraction emitted by forbidden lines in denser active region plasmas.
... In our model, background subtraction can help recover the real oscillation velocities. This result highlights the necessity of background subtraction in observations (e.g., Del Zanna & Mason 2003;Xie et al. 2017) to get a more reliable velocity. In our idealized model, the POS oscillation and velocity are not influenced by the background emission. ...
We simulate transverse oscillations in radiatively cooling coronal loops and forward-model their spectroscopic and imaging signatures, paying attention to the influence of background emission. The transverse oscillations are driven at one footpoint by a periodic velocity driver. A standing kink wave is subsequently formed and the loop cross section is deformed due to the Kelvin–Helmholtz instability, resulting in energy dissipation and heating at small scales. Besides the transverse motions, a long-period longitudinal flow is also generated due to the ponderomotive force induced slow wave. We then transform the simulated straight loop to a semi-torus loop and forward-model their spectrometer and imaging emissions, mimicking observations of Hinode/EIS and SDO/AIA. We find that the oscillation amplitudes of the intensity are different at different slit positions, but are roughly the same in different spectral lines or channels. X-t diagrams of both the Doppler velocity and the Doppler width show periodic signals. We also find that the background emission dramatically decreases the Doppler velocity, making the estimated kinetic energy two orders of magnitude smaller than the real value. Our results show that background subtraction can help recover the real oscillation velocity. These results are helpful for further understanding transverse oscillations in coronal loops and their observational signatures. However, they cast doubt on the spectroscopically estimated energy content of transverse waves using the Doppler velocity.
... Cool loops with a temperature of 0.1-1 MK could be observed in ultraviolet (UV) spectral lines or narrowband images, and they have recently been intensively explored based on Interface Region Imaging Spectrograph (IRIS; De Pontieu et al. 2014) observations (e.g., Huang et al. 2015). Warm loops consist of plasma at a temperature of around 1-2 MK, and they are well observed by extreme-ultraviolet (EUV) imagers and spectrographs (e.g., Lenz et al. 1999;Xie et al. 2017). Loops with a temperature higher than 2 MK are defined as hot loops, which are typically observed in some spectral lines with a high formation temperature and filters with a high-temperature response, often at soft X-ray, EUV, and UV wavelengths (e.g., Winebarger et al. 2011). ...
Coronal loops are the building blocks of solar active regions. However, their formation mechanism remains poorly understood. Here we present direct observational evidence for the formation of coronal loops through magnetic reconnection as new magnetic fluxes emerge into the solar atmosphere. Extreme-ultraviolet observations by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) clearly show the newly formed loops following magnetic reconnection within a plasma sheet. Formation of the loops is also seen in the H α line-core images taken by the New Vacuum Solar Telescope. Observations from the Helioseismic and Magnetic Imager on board SDO show that a positive-polarity flux concentration moves toward a negative-polarity one with a speed of ∼0.4 km s ⁻¹ before the formation of coronal loops. During the loop formation process, we found signatures of flux cancellation and subsequent enhancement of the transverse field between the two polarities. The three-dimensional magnetic field structure reconstructed through a magnetohydrostatic model shows field lines consistent with the loops in AIA images. Numerous bright blobs with an average width of 1.37 Mm appear intermittently in the plasma sheet and move upward with a projected velocity of ∼114 km s ⁻¹ . The temperature, emission measure, and density of these blobs are about 3 MK, 2.0 × 10 ²⁸ cm ⁻⁵ , and 1.2 × 10 ¹⁰ cm ⁻³ , respectively. A power spectral analysis of these blobs indicates that the observed reconnection is likely not dominated by a turbulent process. We have also identified flows with a velocity of 20–50 km s ⁻¹ toward the footpoints of the newly formed coronal loops.
... Coupled to the Extreme Ultraviolet Imaging Spectrometer (EIS: Culhane et al., 2007) on Hinode, the resulting work on solar atmospheric loops is extensive (e.g. McIntosh and De Pontieu, 2009;Brooks, Warren, and Ugarte-Urra, 2012;Reale, 2014;Xie et al., 2017). Subsequently, the superior resolution images from NASA's sounding rocket High-resolution Coronal imager (Hi-C: Kobayashi et al., 2014, 0.1 pixel) has led to observational assertions of the detection of magnetic braiding , nanoflares in inter-moss flares , and the determination of plasma loop parameters (Brooks et al., 2013;Peter et al., 2013;Scullion et al., 2014;Aschwanden and Peter, 2017;Williams et al., 2020b). ...
... Subsequently, the superior resolution images from NASA's sounding rocket High-resolution Coronal imager (Hi-C: Kobayashi et al., 2014, 0.1 pixel) has led to observational assertions of the detection of magnetic braiding , nanoflares in inter-moss flares , and the determination of plasma loop parameters (Brooks et al., 2013;Peter et al., 2013;Scullion et al., 2014;Aschwanden and Peter, 2017;Williams et al., 2020b). It is still not fully settled whether the loop structures we observe with our current capabilities are actually spatially resolved or if they may be comprised of several individually isolated sub-resolution strands (Peter et al., 2013;Xie et al., 2017;Williams et al., 2020a). ...
... Additionally, given the large number of parameters at play (loop aspect ratio, loop length, temperature, geometry, Doppler/flow velocities, etc.) it is likely this analysis would need to be performed on a loopby-loop basis. This will be explored further in a future study analysing Hinode/EIS loops (see Xie et al., 2017). ...
Coronal loops form the basic building blocks of the magnetically closed solar corona yet much is still to be determined concerning their possible fine-scale structuring and the rate of heat deposition within them. Using an improved multi-stranded loop model to better approximate the numerically challenging transition region, this article examines synthetic NASA Solar Dynamics Observatory's (SDO) Atmospheric Imaging Assembly (AIA) emission simulated in response to a series of prescribed spatially and temporally random, impulsive and localised heating events across numerous sub-loop elements with a strong weighting towards the base of the structure: the nanoflare heating scenario. The total number of strands and nanoflare repetition times is varied systematically in such a way that the total energy content remains approximately constant across all the cases analysed. Repeated time-lag detection during an emission time series provides a good approximation for the nanoflare repetition time for low-frequency heating. Furthermore, using a combination of AIA 171/193 and 193/211 channel ratios in combination with spectroscopic determination of the standard deviation of the loop-apex temperature over several hours alongside simulations from the outlined multi-stranded loop model, it is demonstrated that both the imposed heating rate and number of strands can be realised.
... Cool loops with a temperature of 0.1-1 MK could be observed in ultraviolet (UV) spectral lines or narrow-band images, and they have been intensively explored recently based on the Interface Region Imaging Spectrograph (IRIS, De Pontieu et al. 2014) observations (e.g., Huang et al. 2015). Warm loops consist of plasma at a temperature of around 1-2 MK, and they are well observed by extreme ultraviolet (EUV) imagers and spectrographs (e.g., Lenz et al. 1999;Xie et al. 2017). Loops with a temperature higher than 2 MK are defined as hot loops, which are typically observed in some spectral lines with a high formation temperature and filters with a hightemperature response, often at the wavelengths of soft X-ray, EUV and UV (e.g., Winebarger et al. 2011). ...
Coronal loops are building blocks of solar active regions. However, their formation mechanism is still not well understood. Here we present direct observational evidence for the formation of coronal loops through magnetic reconnection as new magnetic fluxes emerge into the solar atmosphere. Extreme-ultraviolet observations of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) clearly show the newly formed loops following magnetic reconnection within a plasma sheet. Formation of the loops is also seen in the h{\alpha} line-core images taken by the New Vacuum Solar Telescope. Observations from the Helioseismic and Magnetic Imager onboard SDO show that a positive-polarity flux concentration moves towards a negative-polarity one with a speed of ~0.4 km/s, before the formation of coronal loops. During the loop formation process, we found signatures of flux cancellation and subsequent enhancement of the transverse field between the two polarities. The three-dimensional magnetic field structure reconstructed through a magnetohydrostatic model shows field lines consistent with the loops in AIA images. Numerous bright blobs with an average width of 1.37 Mm appear intermittently in the plasma sheet and move upward with a projected velocity of ~114 km/s. The temperature, emission measure and density of these blobs are about 3 MK, 2.0x10^(28) cm^(-5) and 1.2x10^(10) cm^(-3), respectively. A power spectral analysis of these blobs indicates that the observed reconnection is likely not dominated by a turbulent process. We have also identified flows with a velocity of 20 to 50 km/s towards the footpoints of the newly formed coronal loops.
... Let L 0 denote the length of the coronal loop and B 0 denote the magnetic field magnitude of the loop. The predictions of how the effective temperature dependence varies with respect to the B 0 /L 0 ratio are in agreement with the observational estimates of those quantities obtained by Xie et al. (2017), who examined 50 coronal loops in the <1-2 MK range. A larger observational temperature range is needed to determine the slope of the temperature dependence. ...
Parker first proposed (1972) that coronal heating was the necessary outcome of an energy flux caused by the tangling of coronal magnetic field lines by photospheric flows. In this paper we discuss how this model has been modified by subsequent numerical simulations outlining in particular the substantial differences between the “nanoflares” introduced by Parker and “elementary events,” defined here as small-scale spatially and temporally isolated heating events resulting from the continuous formation and dissipation of field-aligned current sheets within a coronal loop. We present numerical simulations of the compressible 3D MHD equations using the HYPERION code. We use two clustering algorithms to investigate the properties of the simulated elementary events: an IDL implementation of a density-based spatial clustering of applications with noise technique, and our own physical distance clustering algorithm. We identify and track elementary heating events in time, both in temperature and in Joule heating space. For every event we characterize properties such as density, temperature, volume, aspect ratio, length, thickness, duration, and energy. The energies of the events are in the range of 10 ¹⁸ –10 ²¹ erg, with durations shorter than 100 s. A few events last up to 200 s and release energies up to 10 ²³ erg. While high temperatures are typically located at the flux tube apex, the currents extend all the way to the footpoints. Hence, a single elementary event cannot at present be detected. The observed emission is due to the superposition of many elementary events distributed randomly in space and time within the loop.
