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1.
We investigate the damping of longitudinal (i.e., slow or acoustic) waves in nonisothermal, hot (T≥ 5.0 MK), gravitationally stratified coronal loops. Motivated by SOHO/SUMER and Yohkoh/SXT observations, and by taking into account a range of dissipative mechanisms such as thermal conduction, compressive viscosity, radiative cooling, and heating, the nonlinear governing equations of one-dimensional hydrodynamics are solved numerically for standing-wave oscillations along a magnetic field line. A semicircular shape is chosen to represent the geometry of the coronal loop. It was found that the decay time of standing waves decreases with the increase of the initial temperature, and the periods of oscillations are affected by the different initial footpoint temperatures and loop lengths studied by the numerical experiments. In general, the period of oscillation of standing waves increases and the damping time decreases when the parameter that characterises the temperature at the apex of the loop increases for a fixed footpoint temperature and loop length. A relatively simple second-order scaling polynomial between the damping time and the parameter determining the apex temperature is found. This scaling relation is proposed to be tested observationally. Because of the lack of a larger, statistically relevant number of observational studies of the damping of longitudinal (slow) standing oscillations, it can only be concluded that the numerically predicted decay times are well within the range of values inferred from Doppler shifts observed by SUMER in hot coronal loops. 相似文献
2.
We investigate the propagation of MHD waves in a magnetised plasma in a weakly stratified atmosphere, representative of hot
coronal loops. In most earlier studies, a time-independent equilibrium was considered. Here we abandon this restriction and
allow the equilibrium to develop as a function of time. In particular, the background plasma is assumed to be cooling due
to thermal conduction. The cooling is assumed to occur on a time scale greater than the characteristic travel times of the
perturbations. We investigate the influence of cooling of the background plasma on the properties of magneto–acoustic waves.
The MHD equations are reduced to a 1D system modelling magneto–acoustic modes propagating along a dynamically cooling coronal
loop. A time-dependent dispersion relation that describes the propagation of the magneto–acoustic waves is derived using the
WKB theory. An analytic solution for the time-dependent amplitude of waves is obtained, and the method of characteristics
is used to find an approximate analytical solution. Numerical calculations of the analytically derived solutions are obtained
to give further insight into the behaviour of the MHD waves in a system with a variable, time-dependent background. The results
show that there is a strong damping of MHD waves and the damping also appears to be independent of the position along the
loop. Studies of MHD wave behaviour in a time-dependent backgrounds seem to be a fundamental and very important next step
in the development of MHD wave theory that is applicable to a wide range of situations in solar physics. 相似文献
3.
The damping of standing slow waves in hot (T>6 MK) coronal loops of semicircular shape is revisited in both the linear and nonlinear regimes. Dissipation by thermal conduction,
compressive viscosity, radiative cooling, and heating are examined for nonstratified and stratified loops. We find that for
typical conditions of hot SUMER loops, thermal conduction increases the period of damped oscillations over the sound-crossing
time, whereas the decay times are mostly shaped by compressive viscosity. Damping from optically thin radiation is negligible.
We also find that thermal conduction alone results in slower damping of the density and velocity waves compared to the observations.
Only when compressive viscosity is added do these waves damp out at the same rate as the observed rapidly decaying modes of
hot SUMER loop oscillations, in contrast to most current work, which has pointed to thermal conduction as the dominant mechanism.
We compare the linear predictions with numerical hydrodynamic calculations. Under the effects of gravity, nonlinear viscous
dissipation leads to a reduction of the decay time compared to the homogeneous case. In contrast, the linear results predict
that the damping rates are barely affected by gravity. 相似文献
4.
The effect of temperature inhomogeneity on the periods, their ratios (fundamental versus first overtone), and the damping times of the standing slow modes in gravitationally stratified solar coronal loops are studied. The effects of optically thin radiation, compressive viscosity, and thermal conduction are considered. The linearized one-dimensional magnetohydrodynamic (MHD) equations (under low-?? condition) were reduced to a fourth-order ordinary differential equation for the perturbed velocity. The numerical results indicate that the periods of nonisothermal loops (i.e., temperature increases from the loop base to apex) are smaller compared to those of isothermal loops. In the presence of radiation, viscosity, and thermal conduction, an increase in the temperature gradient is followed by a monotonic decrease in the periods (compared with the isothermal case), while the period ratio turns out to be a sensitive function of the temperature gradient and the loop lengths. We verify that radiative dissipation is not a main cooling mechanism in both isothermal and nonisothermal hot coronal loops and has a small effect on the periods. Thermal conduction and compressive viscosity are primary mechanisms in the damping of slow modes of the hot coronal loops. The periods and damping times in the presence of compressive viscosity and/or thermal conduction dissipation are consistent with the observed data in specific cases. By tuning the dissipation parameters, the periods and the damping times could be made consistent with the observations in more general cases. 相似文献
5.
TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived. 相似文献
6.
TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived. 相似文献
7.
We use linear analysis to simulate the evolution of a coronal loop in response to a localized impulsive event. The disturbance is modeled by injecting a narrow Gaussian velocity pulse near one footpoint of a loop in equilibrium. Three different damping mechanisms, namely viscosity, thermal conduction, and optically thin radiation, are included in the loop calculations. We consider homogeneous and gravitationally stratified, isothermal loops of varying length (50≤L≤400 Mm) and temperature (2≤T≤10 MK). We find that a localized pulse can effectively excite slow magnetoacoustic waves that propagate up along the loop. The amplitudes of the oscillations increase with decreasing loop temperature and increasing loop length and size of the pulse width. At T≥4 MK, the waves are dissipated by the combined effects of viscosity and thermal conduction, whereas at temperatures of 2 MK, or lower, wave dissipation is governed by radiative cooling. We predict periods in the range of 4.6?–?41.6 minutes. The wave periods remain unaltered by variations of the pulse size, decrease with the loop temperature, and increase almost linearly with the loop length. In addition, gravitational stratification results in a small reduction of the periods and amplification of the waves as they propagate up along the loop. 相似文献
8.
Many coronal heating mechanisms have been suggested to balance the losses from this tenuous medium by radiation, conduction, and plasma mass flows. A previous paper (Walsh, Bell, and Hood, 1995) considered a time-dependent heating supply where the plasma evolved isobarically along the loop length. The validity of this assumption is investigated by including the inertial terms in the fluid equations making it necessary to track the sound waves propagating in a coronal loop structure due to changes in the heating rate with time. It is found that the temperature changes along the loop are mainly governed by the variations in the heating so that the thermal evolution can be approximated to a high degree by the simple isobaric case. A typical isobaric evolution of the plasma properties is reproduced when the acoustic time scale is short enough. However, the cooling of a hot temperature equilibrium to a cool one creates supersonic flows which are not allowed for in this model. 相似文献
9.
In this paper, we give a detailed discussion of the parameters of longitudinal oscillations in coronal loops, described in Paper I. We found a surprising absence of correlations between the measured variables, with the exception of a relation between the estimated damping length and the period of the intensity variations. Only for 2 out of the 38 cases presented in Paper I did we find a significant perturbation in the 195 Å TRACE data. The loops supporting the propagating disturbances were typically stable, quiescent loops and the total luminosity of the analyzed structures generally varied by no more than 10%. The observed density oscillations are unlikely to be flare-driven and are probably caused by an underlying driver exciting the loop footpoints. It was demonstrated that the rapid damping of the perturbations could not simply be explained as a consequence of the decreasing intensity along the loops. However, we found that (slightly enhanced) thermal conduction alone could account for the observed damping lengths and wavelengths, and, additionally, explain the correlation between propagation period and damping length. 相似文献
10.
Yu. G. Kopylova A. V. Melnikov A. V. Stepanov Yu. T. Tsap T. B. Goldvarg 《Astronomy Letters》2007,33(10):706-713
The dispersion properties of the sausage eigenmodes of oscillations in a thin magnetic flux tube are numerically analyzed in terms of ideal magnetohydrodynamics (MHD). The period of the modes accompanied by the emission of MHD waves into the surrounding medium, which leads to acoustic damping of oscillations, is determined by the radius of the tube, not by its length. The dissipation of the sausage oscillations in comparatively high (?0.7R ⊙) and tenuous (?6 × 108 cm?3) coronal loops is considered. Their Q factor has bound found to be determined by the acoustic damping mechanism. The ratio of the plasma densities outside and inside the loop and the characteristic height of the emission source have been estimated by assuming the quasi-periodic pulsations of meter-wavelength radio emission to be related to the sausage oscillations. 相似文献
11.
We consider the flare oscillations from the active red dwarf AT Mic detected with the XMM-Newton space observatory in the soft X-ray energy range (0.2–12 keV). Following Mitra-Kraev et al. (2005a), we associate the observed oscillations with a period of ≈750 s with the excitation of a standing slow magnetoacoustic (SMA) wave in a coronal loop. The damping of flare loop SMA oscillations is shown to be governed by electron thermal conduction. We have estimated the plasma density (≈3 × 1010 cm?3) and the minimum magnetic field strength (≈100 G) in the region of flare energy release. The adopted model is consistent with the results of a spectral analysis of the soft X-ray emission. The piston mechanism is assumed to be responsible for the excitation of loop SMA oscillations. 相似文献
12.
A. Abedini 《Solar physics》2018,293(2):22
The excitation and damping of the transversal coronal loop oscillations and quantitative relation between damping time, damping property (damping time per period), oscillation amplitude, dissipation mechanism and the wake phenomena are investigated. The observed time series data with the Atmospheric Imaging Assembly (AIA) telescope on NASA’s Solar Dynamics Observatory (SDO) satellite on 2015 March 2, consisting of 400 consecutive images with 12 s cadence in the 171 \(\mathring{\mathrm{A}}\) pass band is analyzed for evidence of transversal oscillations along the coronal loops by the Lomb–Scargle periodgram. In this analysis signatures of transversal coronal loop oscillations that are damped rapidly were found with dominant oscillation periods in the range of \(\mathrm{P}=12.25\,\text{--}\,15.80\) min. Also, damping times and damping properties of the transversal coronal loop oscillations at dominant oscillation periods are estimated in the range of \({\tau_{\mathrm{d}}=11.76}\,\text{--}\,{21.46}\) min and \({\tau_{\mathrm{d}}/\mathrm{P}=0.86}\,\text{--}\,{1.49}\), respectively. The observational results of this analysis show that damping properties decrease slowly with increasing amplitude of the oscillation, but the periods of the oscillations are not sensitive functions of the amplitude of the oscillations. The order of magnitude of the damping properties and damping times are in good agreement with previous findings and the theoretical prediction for damping of kink mode oscillations by the dissipation mechanism. Furthermore, oscillations of the loop segments attenuate with time roughly as \(t^{-\alpha}\) and the magnitude values of \(\alpha\) for 30 different segments change from 0.51 to 0.75. 相似文献
13.
The damping of fast kink oscillations of solar coronal loops attributable to the radiation of MHD waves into the surroundings is considered in the thin-tube approximation. The oscillation damping decrement is calculated both by using a new energy method and by solving the dispersion equation for magnetic-tube eigenmodes. The two approaches are in good agreement under appropriate assumptions. The damping is negligible if MHD waves are radiated perpendicular to the magnetic field. The low Q factor of the loop oscillations in active regions found with the TRACE space telescope is associated with the generation of running waves that propagate along magnetic field lines. 相似文献
14.
M. S. Ruderman 《Solar physics》2011,271(1-2):41-54
In this paper we study kink oscillations of coronal loops with the density varying along the loop and also slowly changing with time. Using the Wentzel?CKramers?CBrillouin (WKB) method we obtain the adiabatic invariant that determines the time dependence of the oscillation amplitude. The obtained general results are applied to kink oscillations of cooling loops. The main conclusion of this study is that cooling causes the amplification of kink oscillations. 相似文献
15.
The cooling of plasmas in closed coronal loops by thermal conduction is important when considering their detectability at
X-ray and EUV wavelengths. A non-local formalism of thermal conduction originating in laboratory plasmas is used and it is
shown that while the effect is unlikely to be important for loops that are in a steady state, it does play a significant role
in loops that are impulsively heated (e.g., by nanoflares). Such loops are “under-dense”, and so hot electrons have a relatively long mean free path. Analytic and numerical
models are presented, and it is shown that conduction cooling times are lengthened quite considerably. A comparison of various
cooling times with ionisation times is also presented, and it is noted that this conductive physics may enhance the chances
of observing hot nanoflare-heated plasma. 相似文献
16.
We present a detailed study of coronal loop brightenings observed in an active region on the solar limb. These brightening loops show expanding and shrinking motions in EUV coronal line images and also show downflow along the loops in Lα and Hα images. By means of time-slice analysis of the images, we found that both the expanding and shrinking motions of the loops are not real motions of plasma but apparent motions like post-flare loops, where the loops at the different height are successively heated and cooled. From a temperature analysis, the time delay between the brightenings of hot 195 Å and cool Lα loops is found to be nearly equal to the time-scale of the conduction cooling. We conclude that these loop brightenings are sources of so called Hα coronal rains. 相似文献
17.
The damping of ducted, fast, magnetohydrodynamic (MHD) waves by ion viscosity and electron heat conduction in a radiating, optically thin, warm, structured atmosphere has been evaluated. Dissipation is more effective in a warm plasma than in a cold one but, for waves ducted by solar coronal loops, dissipation is only efficient if the periods of the waves are shorter than a few tens of seconds and only if the background magnetic field is less than about 15 G. It appears that MHD waves of longer periods and in stronger magnetic fields will survive the dissipative mechanisms considered here and may be manifest as observable coronal oscillations. 相似文献
18.
G. Verth 《Astronomische Nachrichten》2007,328(8):764-768
Magnetohydrodynamic (MHD) waves in solar coronal loops, which were previously only predicted by theory have actually been detected with space‐borne instruments. These observations have given an important and novel tool to measure fundamental parameters in the magnetically embedded solar corona. This paper will illustrate how information about the magnetic and density structure along coronal loops can be determined by measuring the frequency or amplitude profiles of standing fast kink mode oscillations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
The effect of radiation losses on the dispersion and damping of magnetohydrodynamic waves in the solar corona is studied. The conditions are determined under which radiation losses are most appreciable. A damping of kink modes of coronal loops with plasma temperatures within 106–106.3 K and 106.3–107 K are compared. It is concluded that the radiation damping dominates in the temperature range 106–106.3 K, which can cause the observed fast damping of kink oscillations of coronal loops. Radiation losses should be taken into account in full magnetohydrodynamic equations with radiative transfer. 相似文献
20.
Nagendra Kumar Pradeep Kumar Shiv Singh Anil Kumar 《Journal of Astrophysics and Astronomy》2008,29(1-2):243-248
We study the propagation and dissipation of slow magnetoacoustic waves in an inhomogeneous viscous coronal loop plasma permeated by uniform magnetic field. Only viscosity and thermal conductivity are taken into account as dissipative processes in the coronal loop. The damping length of slow-mode waves exhibit varying behaviour depending upon the physical parameters of the loop in an active region AR8270 observed by TRACE. The wave energy flux associated with slow magnetoacoustic waves turns out to be of the order of 106 erg cm?2 s?1 which is high enough to replace the energy lost through optically thin coronal emission and the thermal conduction below to the transition region. It is also found that only those slow-mode waves which have periods more than 240s provide the required heating rate to balance the energy losses in the solar corona. Our calculated wave periods for slow-mode waves nearly match with the oscillation periods of loop observed by TRACE. 相似文献