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1.
An improved method of image segmentation is introduced. The object-tracking algorithm, originally developed by Sobotka, Brandt, and Simon (Astron. Astrophys. 328, 682, 1997) is modified with special attentions on splitting and merging of umbral dots (UDs), definition of the umbral boundary, and the birth-frames and the death-frames of UDs. By applying the new method of image segmentation and the object-tracking algorithm on a 67-min series of white-light images of a large pore (Sobotka et al., Astrophys. J. 511, 436, 1999), the physical characteristics of 20 “resolved” UDs with umbral origin were recorded. The most probable lifetime of the UDs is between 7 and 10 min. Umbral dots show a typical size of about 230 km. Their mean speeds are smaller than 2 km s−1 with a distribution around a value less than 1 km s−1. However, their average velocities are less than 0.8 km s−1. Brighter (fainter) UDs are formed in the brighter (dimmer) region of the pore. There is no correlation between time-averaged area or time-averaged speeds and lifetimes. Also, the time-averaged peak intensities of UDs do not show any well-defined dependence on the corresponding time-averaged areas. It seems that there is a relation between average velocities of UDs and their time-averaged peak intensities, with brighter UDs moving more slowly.  相似文献   

2.
Recent studies of NOAA active region 10953, by Okamoto et al. (Astrophys. J. Lett. 673, 215, 2008; Astrophys. J. 697, 913, 2009), have interpreted photospheric observations of changing widths of the polarities and reversal of the horizontal magnetic field component as signatures of the emergence of a twisted flux tube within the active region and along its internal polarity inversion line (PIL). A filament is observed along the PIL and the active region is assumed to have an arcade structure. To investigate this scenario, MacTaggart and Hood (Astrophys. J. Lett. 716, 219, 2010) constructed a dynamic flux emergence model of a twisted cylinder emerging into an overlying arcade. The photospheric signatures observed by Okamoto et al. (2008, 2009) are present in the model although their underlying physical mechanisms differ. The model also produces two additional signatures that can be verified by the observations. The first is an increase in the unsigned magnetic flux in the photosphere at either side of the PIL. The second is the behaviour of characteristic photospheric flow profiles associated with twisted flux tube emergence. We look for these two signatures in AR 10953 and find negative results for the emergence of a twisted flux tube along the PIL. Instead, we interpret the photospheric behaviour along the PIL to be indicative of photospheric magnetic cancellation driven by flows from the dominant sunspot. Although we argue against flux emergence within this particular region, the work demonstrates the important relationship between theory and observations for the successful discovery and interpretation of signatures of flux emergence.  相似文献   

3.
Umbral dots (UDs) are small isolated brightenings observed in sunspot umbrae. They are convective phenomena existing inside umbrae. UDs are usually divided into central UDs (CUDs) and peripheral UDs (PUDs) according to their positions inside an umbra. Our purpose is to investigate UD properties and analyze their relationships, and further to find whether or not the properties depend on umbral magnetic field strengths. Thus, we selected high-resolution TiO images of four active regions (ARs) taken under the best seeing conditions with the New Vacuum Solar Telescope in the Fuxian Solar Observatory of the Yunnan Astronomical Observatory, China. The four ARs (NOAA 11598, 11801, 12158, and 12178) include six sunspots. A total of 1220 CUDs and 603 PUDs were identified. Meanwhile, the radial component of the vector magnetic field of the sunspots taken with the Helioseismic and Magnetic Imager on-board the Solar Dynamics Observatory was used to analyze relationships between UD properties and umbral magnetic field strengths. We find that diameters and lifetimes of UDs exhibit an increasing trend with the brightness, but velocities do not. Moreover, diameters, intensities, lifetimes and velocities depend on the surrounding magnetic field. A CUD diameter was found larger, the CUD brighter, its lifetime longer, and its motion slower in a weak umbral magnetic field environment than in a strong one.  相似文献   

4.
Recent numerical investigations of wave propagation near coronal magnetic null points (McLaughlin and Hood: Astron. Astrophys. 459, 641, 2006) have indicated how a fast MHD wave partially converts into a slow MHD wave as the disturbance passes from a low-β plasma to a high-β plasma. This is a complex process and a clear understanding of the conversion mechanism requires the detailed investigation of a simpler model. An investigation of mode conversion in a stratified, isothermal atmosphere with a uniform, vertical magnetic field is carried out, both numerically and analytically. In contrast to previous investigations of upward-propagating waves (Zhugzhda and Dzhalilov: Astron. Astrophys. 112, 16, 1982a; Cally: Astrophys. J. 548, 473, 2001), this paper studies the downward propagation of waves from a low-β to high-β environment. A simple expression for the amplitude of the transmitted wave is compared with the numerical solution.  相似文献   

5.
One goal of helioseismology is to determine the subsurface structure of sunspots. In order to do so, it is important to understand first the near-surface effects of sunspots on solar waves, which are dominant. Here we construct simplified, cylindrically-symmetric sunspot models that are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun τ 5000=1 level to the lower chromosphere. We use a combination of existing semi-empirical models of sunspot thermodynamic structure (density, temperature, pressure): the umbral model of Maltby et al. (1986, Astrophys. J. 306, 284) and the penumbral model of Ding and Fang (1989, Astron. Astrophys. 225, 204). The OPAL equation-of-state tables are used to derive the sound-speed profile. We smoothly merge the near-surface properties to the quiet-Sun values about 1 Mm below the surface. The umbral and penumbral radii are free parameters. The magnetic field is added to the thermodynamic structure, without requiring magnetostatic equilibrium. The vertical component of the magnetic field is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by surface observations. The full magnetic-field vector is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen such that the field inclination is 45° at the umbral – penumbral boundary. We construct a particular sunspot model based on SOHO/MDI observations of the sunspot in active region NOAA 9787. The helioseismic signature of the model sunspot is studied using numerical simulations of the propagation of f, p 1, and p 2 wave packets. These simulations are compared against cross-covariances of the observed wave field. We find that the sunspot model gives a helioseismic signature that is similar to the observations.  相似文献   

6.
T. Hirayama 《Solar physics》1992,137(1):33-50
Joule heating in a slender magnetic flux tube is investigated. The distribution of the magnetic field and electric sheet current encircling a vertical cylindrical magnetic tube is determined by equating the converging magnetic flux, which results from the converging and downward flow of the granulation, and the dissipative expanding magnetic flux due to Ohmic decay. Here, to ensure the mass flux conservation, an overshooting convective flow pattern resembling recent simulations was assumed. Even with the electrical resistivity from neutral hydrogen, the width of the current sheet was found to be 2 km, being much smaller than the tube diameter of 150 km, either from an exact or approximate (Gaussian) field distribution.The resultant energy flux density due to Joule heating averaged over the cylindrical cross sectional area, is 1 × 109 erg cm-2 s-1 for an assumed photospheric magnetic field of 1500 G. This amount may supply enough energy to heat the temperature minimum region of the flux tube by T = 300 K in accord with observations, though our estimation of the excess radiation loss which should be supplied by the Joule heating to keep T = 300 K is rather uncertain.A possible role of the Joule heating on spicule formation is briefly discussed together with discussions on the slab geometry, general flow patterns, and non-constant field distributions inside the flux tube.  相似文献   

7.
Improvements to an existing method for calculating nonlinear force-free magnetic fields (Wheatland, Solar Phys. 238, 29, 2006) are described. In particular a solution of the 3-D Poisson equation using 2-D Fourier transforms is presented. The improved nonlinear force-free method is demonstrated in application to linear force-free test cases with localized nonzero values of the normal component of the field in the boundary. These fields provide suitable test cases for nonlinear force-free calculations because the boundary conditions involve localized nonzero values of the normal components of the field and of the current density, and because (being linear force-free fields) they have more direct numerical solutions. Despite their simplicity, fields of this kind have not been recognized as test cases for nonlinear methods before. The examples illustrate the treatment of the boundary conditions on current in the nonlinear force-free method, and in particular the limitations imposed by field lines that connect outside of the boundary region.  相似文献   

8.
We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys. 235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.  相似文献   

9.
We studied the characteristics of the zebra-associated spike-like bursts that were recorded with high time resolution at 1420 MHz in four intervals (from 12:45 to 12:48 UT) during 5 August 2003. Our detailed analysis is based on the selection of more than 500 such spike-like bursts and it is, at least to our knowledge, the first study devoted to such short-lived bursts. Their characteristics are different from those pertinent to “normal” spike bursts, as presented in the paper by Güdel and Benz (Astron. Astrophys. 231, 202, 1990); in particular, their duration (about 7.4 ms at half power) is shorter, so they should be members of the SSS (super short structures) family (Magdalenić et al., Astrophys. J. 642, L77, 2006). The bursts were generally strongly R-polarized; however, during the decaying part of interval I a low R-polarized and L-polarized bursts were also present. This change of polarization shows a trend that resembles the peculiar form of the zebra lines in the spectral dominion (“V” like). A global statistical analysis on the bursts observed in the two polarimetric channels shows that the highest cross-correlation coefficient (about 0.5) was pertinent to interval I. The zebras and the bursts can be interpreted by the same double plasma resonance process as proposed by Bárta and Karlicky (Astron. Astrophys. 379, 1045, 2001) and Karlicky et al. (Astron. Astrophys. 375, 638, 2001); in particular, the spikes are generated by the interruption of this process by assumed turbulence (density or magnetic field variations). This process should be present in the region close to the reconnection site (e.g., in the plasma reconnection outflows) where the density and the magnetic field vary strongly.  相似文献   

10.
We compute the change in the Lorentz force integrated over the outer solar atmosphere implied by observed changes in vector magnetograms that occur during large, eruptive solar flares. This force perturbation should be balanced by an equal and opposite force perturbation acting on the solar photosphere and solar interior. The resulting expression for the estimated force change in the solar interior generalizes the earlier expression presented by Hudson, Fisher, and Welsch (Astron. Soc. Pac. CS-383, 221, 2008), providing horizontal as well as vertical force components, and provides a more accurate result for the vertical component of the perturbed force. We show that magnetic eruptions should result in the magnetic field at the photosphere becoming more horizontal, and hence should result in a downward (toward the solar interior) force change acting on the photosphere and solar interior, as recently argued from an analysis of magnetogram data by Wang and Liu (Astrophys. J. Lett. 716, L195, 2010). We suggest the existence of an observational relationship between the force change computed from changes in the vector magnetograms, the outward momentum carried by the ejecta from the flare, and the properties of the helioseismic disturbance driven by the downward force change. We use the impulse driven by the Lorentz-force change in the outer solar atmosphere to derive an upper limit to the mass of erupting plasma that can escape from the Sun. Finally, we compare the expected Lorentz-force change at the photosphere with simple estimates from flare-driven gasdynamic disturbances and from an estimate of the perturbed pressure from radiative backwarming of the photosphere in flaring conditions.  相似文献   

11.
Using nine years of solar wind plasma and magnetic field data from the Wind mission, we investigated the characteristics of both magnetic clouds (MCs) and magnetic cloud-like structures (MCLs) during 1995 – 2003. A MCL structure is an event that is identified by an automatic scheme (Lepping, Wu, and Berdichevsky, Ann. Geophys. 23, 2687, 2005) with the same criteria as for a MC, but it is not usually identifiable as a flux rope by using the MC (Burlaga et al., J. Geophys. Res. 86, 6673, 1981) fitting model developed by Lepping, Jones, and Burlaga (Geophys. Res. Lett. 95(11), 957, 1990). The average occurrence rate is 9.5 for MCs and 13.6 for MCLs per year for the overall period of interest, and there were 82 MCs and 122 MCLs identified during this period. The characteristics of MCs and MCL structures are as follows: (1) The average duration, Δt, of MCs is 21.1 h, which is 40% longer than that for MCLs (Δt=15 h); (2) the average (minimum B z found in MC/MCL measured in geocentric solar ecliptic coordinates) is −10.2 nT for MCs and −6 nT for MCLs; (3) the average Dstmin  (minimum Dst caused by MCs/MCLs) is −82 nT for MCs and −37 nT for MCLs; (4) the average solar wind velocity is 453 km s−1 for MCs and 413 km s−1 for MCLs; (5) the average thermal speed is 24.6 km s−1 for MCs and 27.7 km s−1 for MCLs; (6) the average magnetic field intensity is 12.7 nT for MCs and 9.8 nT for MCLs; (7) the average solar wind density is 9.4 cm−3 for MCs and 6.3 cm−3 for MCLs; and (8) a MC is one of the most important interplanetary structures capable of causing severe geomagnetic storms. The longer duration, more intense magnetic field and higher solar wind speed of MCs, compared to those properties of the MCLs, are very likely the major reasons for MCs generally causing more severe geomagnetic storms than MCLs. But the fact that a MC is an important interplanetary structure with respect to geomagnetic storms is not new (e.g., Zhang and Burlaga, J. Geophys. Res. 93, 2511, 1988; Bothmer, ESA SP-535, 419, 2003).  相似文献   

12.
The decrease in the rms contrast of time-averaged images with the averaging time is compared between four data sets: (1) a series of solar granulation images recorded at La Palma in 1993, (2) a series of artificial granulation images obtained in numerical simulations by Rieutord et al. (Nuovo Cimento 25, 523, 2002), (3) a similar series computed by Steffen and his colleagues (see Wedemeyer et al. in Astron. Astrophys. 44, 1121, 2004), (4) a random field with some parameters typical of the granulation, constructed by Rast (Astron. Astrophys. 392, L13, 2002). In addition, (5) a sequence of images was obtained from real granulation images by using a temporal and spatial shuffling procedure, and the contrast of the average of n images from this sequence as a function of n is analysed. The series (1) of real granulation images exhibits a considerably slower contrast decrease than do both the series (3) of simulated granulation images and the series (4) of random fields. Starting from some relatively short averaging times t, the behaviour of the contrast in series (3) and (4) resembles the t −1/2 statistical law, whereas the shuffled series (5) obeys the n −1/2 law from n=2 on. Series (2) demonstrates a peculiarly slow decline of contrast, which could be attributed to particular properties of the boundary conditions used in the simulations. Comparisons between the analysed contrast-variation laws indicate quite definitely that the brightness field of solar granulation contains a long-lived component, which could be associated with locally persistent dark intergranular holes and/or with the presence of quasi-regular structures. The suggestion that the random field (4) successfully reproduces the contrast-variation law for the real granulation (Rast in Astron. Astrophys. 392, L13, 2002) can be dismissed.  相似文献   

13.
With viscous dissipation and Joule heating taken into account, solution of the energy equation is obtained for unsteady hydromagnetic thermal boundary layer flow past a porous wall (e.g., surface of a star) in presence of a transverse magnetic field, under the condition of zero heat transfer between the fluid and the boundary — the so-called plate thermometer problem in MHD. Solution of the problem, in the form of power series, is obtained under certain valid simplifying assumptions, when (i) the wall is subjected to a normal velocity of suction/injection which is proportional tot –1/2, and (ii) the wall has a velocity given by t n . The variation of temperature is shown graphically and is followed by a quantitative discussion therein also signifying the importance of retaining the Joule heating term in the energy equation.Part I is the article inAstrophysics and Space Science, Vol.45, No. 2, 1976, pp. 397–410.On study-leave from Defence Science Laboratory, Delhi, India.  相似文献   

14.
In this paper, two semi-analytical solutions of force-free fields (Low and Lou, Astrophys. J. 352, 343, 1990) have been used to test two nonlinear force-free extrapolation methods. One is the boundary integral equation (BIE) method developed by Yan and Sakurai (Solar Phys. 195, 89, 2000), and the other is the approximate vertical integration (AVI) method developed by Song et al. (Astrophys. J. 649, 1084, 2006). Some improvements have been made to the AVI method to avoid the singular points in the process of calculation. It is found that the correlation coefficients between the first semi-analytical field and extrapolated field using the BIE method, and also that obtained by the improved AVI method, are greater than 90% below a height 10 of the 64×64 lower boundary. For the second semi-analytical field, these correlation coefficients are greater than 80% below the same relative height. Although differences between the semi-analytical solutions and the extrapolated fields exist for both the BIE and AVI methods, these two methods can give reliable results for heights of about 15% of the extent of the lower boundary.  相似文献   

15.
The Theory of Alfven drag (Drell et al. in J Geophys Res 70: 3131–3145 1965; Anselmo and Farinella in Icarus, 58, 182–185 1983) is applied here to show that the existence of a possible solar ring structure at a radial distance of 0.02 AU (~4R , R  = radius of the sun) predicted by earlier authors (Brecher et al. in Nature 282, 50–52 1979; Rawal in Bull. Astr. Soc. India 6, 92–95 1978, Moon Planets 24, 407–414 1981, Moon Planets 31, 175–182 1984, J Astrophys Astr 10, 257–259 1989) may not survive Alfven drag produced during even moderate solar magnetic storms which take place from time to time through the age of the sun, but a possible solar ring structure at a radial distance of 0.13 AU (~27R ) (Brecher et al. in Nature 282, 50–52 1979; Rawal in Bull. Astr. Soc. India 6, 92–95 1978, Moon Planets 24, 407–414 1981, Moon Planets 31, 175–182 1984, J Astrophys Astr 10, 257–259 1989) may survive intense Alfven drag produced during even strong magnetic storms of magnetic field value up to 1,000 G.  相似文献   

16.
It is well known that the parallel cuts of the parallel and perpendicular electric field in electron phase-space holes (electron holes) have bipolar and unipolar structures, respectively. Recently, electron holes in the Earth’s plasma sheet have been observed by THEMIS satellites to have detectable fluctuating magnetic field with regular structures. Du et al. (2011) investigated the evolution of a one-dimensional (1D) electron hole with two-dimensional (2D) electromagnetic particle-in-cell (PIC) simulations in weakly magnetized plasma (Ω e <ω pe , where Ω e and ω pe are the electron gyrofrequency and electron plasma frequency, respectively), which initially exists in the simulation domain. The electron hole is unstable to the transverse instability and broken into several 2D electron holes. They successfully explained the observations by THEMIS satellites based on the generated magnetic structures associated with these 2D electron holes. In this paper, 2D electromagnetic particle-in-cell (PIC) simulations are performed in the xy plane to investigate the nonlinear evolution of the electron two-stream instability in weakly magnetized plasma, where the background magnetic field (B0 = B0[(e)\vec] x)(\mathbf{B}_{0} =B_{0}\vec{\mathbf{e}} _{x}) is along the x direction. Several 2D electron holes are formed during the nonlinear evolution, where the parallel cuts of E x and E y have bipolar and unipolar structures, respectively. Consistent with the results of Du et al. (2011), we found that the current along the z direction is generated by the electric field drift motion of the trapped electrons in the electron holes due to the existence of E y , which produces the fluctuating magnetic field δB x and δB y in the electron holes. The parallel cuts of δB x and δB y in the electron holes have unipolar and bipolar structures, respectively.  相似文献   

17.
An expression for the vertical velocity of the neutral atmosphere in the F-region is derived for Joule heating by the electric field that drives the auroral electrojet. When only vertical expansion is allowed, it is found that the vertical wind must always increase monotonically with altitude. The heating rate is proportional to the F-region ion density, so that appreciable heating, even during high electric fields, requires some production mechanism of ionization such as auroral secondary ionization or solar photoionization, in the lower F-region. Once started at night, when an ionizing source is present in the lower F-region, the expansion of the atmosphere transports ionization upward, thereby increasing the heating rate, and hence the expansion rate, i.e. positive feedback. Electric field strengths and F-region ion densities of 50 mV/m and 2 × 1011e/m3, respectively, will produce vertal neutral wind speeds of several tens of m/sec in the 300–500 km altitude range. During periods of high magnetic activity, i.e. high electric field, Joule heating can produce large increases in the relative N2 concentration in the upper F-region; computations made with a simple model suggest that tenfold increases can occur at 400 km altitude 12?1 hr after the onset of magnetic activity, a result in agreement with satellite observations. When the Joule heating theory is applied to incoherent scatter data taken during one period of high heating, the horizontal electric field in the F-region is found to decrease markedly, possibly approaching zero as the field penetrates a weak, discrete auroral arc; the decrease began 10–20 km from the arc.  相似文献   

18.
Predictions of Energy and Helicity in Four Major Eruptive Solar Flares   总被引:1,自引:0,他引:1  
In order to better understand the solar genesis of interplanetary magnetic clouds (MCs), we model the magnetic and topological properties of four large eruptive solar flares and relate them to observations. We use the three-dimensional Minimum Current Corona model (Longcope, 1996, Solar Phys. 169, 91) and observations of pre-flare photospheric magnetic field and flare ribbons to derive values of reconnected magnetic flux, flare energy, flux rope helicity, and orientation of the flux-rope poloidal field. We compare model predictions of those quantities to flare and MC observations, and within the estimated uncertainties of the methods used find the following: The predicted model reconnection fluxes are equal to or lower than the reconnection fluxes inferred from the observed ribbon motions. Both observed and model reconnection fluxes match the MC poloidal fluxes. The predicted flux-rope helicities match the MC helicities. The predicted free energies lie between the observed energies and the estimated total flare luminosities. The direction of the leading edge of the MC’s poloidal field is aligned with the poloidal field of the flux rope in the AR rather than the global dipole field. These findings compel us to believe that magnetic clouds associated with these four solar flares are formed by low-corona magnetic reconnection during the eruption, rather than eruption of pre-existing structures in the corona or formation in the upper corona with participation of the global magnetic field. We also note that since all four flares occurred in active regions without significant pre-flare flux emergence and cancelation, the energy and helicity that we find are stored by shearing and rotating motions, which are sufficient to account for the observed radiative flare energy and MC helicity.  相似文献   

19.
The solar wind quasi-invariant (QI) has been defined by Osherovich, Fainberg, and Stone (Geophys. Res. Lett. 26, 2597, 1999) as the ratio of magnetic energy density and the energy density of the solar wind flow. In the regular solar wind QI is a rather small number, since the energy of the flow is almost two orders of magnitude greater than the magnetic energy. However, in magnetic clouds, QI is the order of unity (less than 1) and thus magnetic clouds can be viewed as a great anomaly in comparison with its value in the background solar wind. We study the duration, extent, and amplitude of this anomaly for two groups of isolated magnetic clouds: slow clouds (360<v<450 km s−1) and fast clouds (450≤v<720 km s−1). By applying the technique of superposition of epochs to 12 slow and 12 fast clouds from the catalog of Richardson and Cane (Solar Phys. 264, 189, 2010), we create an average slow cloud and an average fast cloud observed at 1 AU. From our analysis of these average clouds, we obtain cloud boundaries in both time and space as well as differences in QI amplitude and other parameters characterizing the solar wind state. Interplanetary magnetic clouds are known to cause major magnetic storms at the Earth, especially those clouds which travel from the sun to the Earth at high speeds. Characterizing each magnetic cloud by its QI value and extent may help in understanding the role of those disturbances in producing geomagnetic activity.  相似文献   

20.
The sunspot-associated sources at the frequency of 17 GHz give information on plasma parameters in the regions of magnetic field about B=2000 G at the level of the chromosphere-corona transition region. The observations of short period (from one to ten minutes) oscillations in sunspots reflect propagation of magnetohydrodynamic (MHD) waves in the magnetic flux tubes of the sunspots. We investigate the oscillation parameters in active regions in connection with their flare activity. We confirm the existence of a link between the oscillation spectrum and flare activity. We find differences in the oscillations between pre-flare and post-flare phases. In particular, we demonstrate a case of powerful three-minute oscillations that start just before the burst. This event is similar to the cases of the precursors investigated by Sych et al. (Astron. Astrophys. 505, 791, 2009). We also found well-defined eight-minute oscillations of microwave emission from sunspot. We interpret our observations in terms of a relationship between MHD waves propagating from sunspots and flare processes.  相似文献   

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