Non-stationary quasi-periodic pulsations in solar and stellar flares |
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Valery Nakariakov Submitted: 2018-08-10 08:41
Often the enhanced electromagnetic radiation generated in solar and stellar flares shows a pronounced (quasi)-oscillatory pattern - quasi-periodic pulsations (QPP), with characteristic periods ranging from a fraction of a second to several tens of minutes. We review recent advances in the empirical study of QPP in solar and stellar flares, addressing the intrinsic non-stationarity of the signal, i.e. the variation of its amplitude, period or phase with time. This non-stationarity could form a basis for a classification of QPP, necessary for revealing specific physical mechanisms responsible for their appearance. We could identify two possible classes of QPP, decaying harmonic oscillations, and trains of symmetric triangular pulsations. Apparent similarities between QPP and irregular geomagnetic pulsations Pi offer a promising avenue for the knowledge transfer in both analytical techniques and theory. Attention is also paid to the effect of the flare trend on the detection and analysis of QPP.
Authors: Nakariakov, V.M., Kolotkov, D., Kupriyanova, E.G., Mehta, T., Pugh, C.E., Lee, D.-H., Broomhall, A.M.
Projects: None
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Publication Status: PPCF, accepted
Last Modified: 2018-08-10 08:56
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Quasi-periodic Pulsations in a Solar Microflare |
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Valery Nakariakov Submitted: 2018-06-07 11:07
Irregular time evolution of the radio emission generated in a B2-class microflare (SOL2017-01-25T10:15), occurring on 2017 January 25 in active region 12,628, is studied. The microflare was apparently initiated by an appearance of an s-shaped loop, observed in the EUV band. The radio emission is associated with the nonthermal electrons detected with Ramaty High Energy Solar Spectroscopic Imager, and originates simultaneously from two opposite footpoints of a magnetic fan structure beginning at a sunspot. According to the active region geometry, the footpoints are situated in the meridional direction, and hence are observed by RATAN-600 simultaneously. The radio emission intensity signal, as well as the left-hand and right-hand circular polarization signals in the low-frequency band (3-4 GHz) show good correlation with each other, with the average characteristic time of the variation 1.4 ± 0.3 s. The polarization signal shows a time variation with the characteristic time of about 0.7 ± 0.2 s. The irregular quasi-periodic pulsations of the radio emission are likely to be caused by the superposition of the signals generated at the local electron plasma frequencies by the interaction of nonthermal electrons with the plasma at the footpoints. In this scenario, the precipitation rate of the nonthermal electrons at the opposite footpoints could be modulated by the superposition of fundamental and second harmonic modes of sausage oscillations, resulting in the observed different characteristic times of the intensity and polarization signals. However, other mechanisms, e.g., the oscillatory regime of loop coalescence or magnetic null point oscillation could not be rigorously excluded.
Authors: Nakariakov, V. M., Anfinogentov, S., Storozhenko, A. A., Kurochkin, E. A., Bogod, V. M., Sharykin, I. N., Kaltman, T. I.
Projects: RATAN-600
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Publication Status: ApJ 859:154, 2018
Last Modified: 2018-06-07 12:36
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Effect of local thermal equilibrium misbalance on long-wavelength slow magnetoacoustic waves |
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Valery Nakariakov Submitted: 2017-11-03 05:51
Evolution of slow magnetoacoustic waves guided by a cylindrical magnetic flux tube that represents a coronal loop or plume, is modelled accounting for the effects of finite gas pressure, weak nonlinearity, dissipation by thermal conduction and viscosity, and the misbalance between the cooling by optically thin radiation and unspecified heating of the plasma. An evolutionary equation of the Burgers-Malthus type is derived. It is shown that the cooling/heating misbalance, determined by the derivatives of the combined radiative cooling and heating function, with respect to the density, temperature and magnetic field at the thermal equilibrium affect the wave rather strongly. This effect may either cause additional damping, or counteract it, or lead to the gradual amplification of the wave. In the latter case the coronal plasma acts as an active medium for the slow magnetoacoustic waves. The effect of the cooling/heating misbalance could be important for coronal slow waves, and could be responsible for certain discrepancies between theoretical results and observations, in particular the increased or decreased damping lengths and times, detection of the waves at certain heights only, and excitation of compressive oscillations. The results obtained open up a possibility for the diagnostics of the coronal heating function by slow magnetoacoustic waves.
Authors: Nakariakov, V.M., Afanasyev, A.N., Kumar, S., Moon, Y.-J.
Projects: None
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Publication Status: ApJ 849:62, 2017
Last Modified: 2017-11-03 13:41
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Comparison of damped oscillations in solar and stellar X-ray flares |
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Valery Nakariakov Submitted: 2016-08-09 20:18
We explore the similarity and difference of the quasi-periodic pulsations (QPPs) observed in the decay phase of solar and stellar flares at X-rays. We identified 42 solar flares with pronounced QPPs, observed with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) and 36 stellar flares with QPPs, observed with X-ray Multi Mirror Newton observatory (XMM-Newton). The Empirical Mode Decomposition (EMD) method and least-square fit by a damped sine function were applied to obtain the periods (P) and damping times (τ) of the QPPs. We found that (1) the periods and damping times of the stellar QPPs are 5.00+70.45-4.57 min and 17.29+60.80-17.02 min, which are comparable with those of the solar QPPs (0.57+3.01-0.30 and 1.20+2.77-0.76 min). (2) The ratio of the damping times to the periods (τ/P) observed in the stellar QPPs (1.46+2.54-0.48) are statistically identical to those of solar QPPs (1.49+2.49-0.66). (3) The scalings of the QPP damping time with the period are well described by the power law in both solar and stellar cases. The power indices of the solar and stellar QPPs are 0.96±{0.10} and 0.98±{0.05}, respectively. This scaling is consistent with the scalings found for standing slow magnetoacoustic and kink modes in solar coronal loops. Thus, we propose that the underlying mechanism responsible for the stellar QPPs is the natural magnetohydrodynamic oscillations in the flaring or adjacent coronal loops, as in the case of solar flares.
Authors: Cho, I.-H., Cho, K.-S., Nakariakov, V.M., Kim, S., Kumar, P.
Projects: RHESSI
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Publication Status: Astrophysical Journal, 2016, accepted
Last Modified: 2016-08-10 16:05
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Undamped transverse oscillations of coronal loops as a self-oscillatory process |
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Valery Nakariakov Submitted: 2016-05-18 13:18
Context. Standing transverse oscillations of coronal loops are observed to operate in two regimes, the rapidly decaying large amplitude oscillations, and undamped small amplitude oscillations. In the latter regime the damping should be compensated by energy supply, which allows the loop to perform almost monochromatic oscillations with almost constant amplitude. Different loops oscillate with
different periods. The oscillation amplitude does not show dependence on the loop length or the oscillation period.
Aims. We aim to develop a low-dimensional model explaining the undamped kink oscillations as a self-oscillatory process caused by the effect of negative friction. The source of energy is an external quasi-steady flow, e.g. supergranulation motions near the loop footpoints or external flows in the corona.
Methods. We demonstrate that the interaction of a quasi-steady flow with a loop can be described by a Rayleigh oscillator equation that is a nonlinear ordinary differential equation, with the damping and resonant terms determined empirically.
Results. Low-amplitude self-oscillatory solutions to the Rayleigh oscillator equation are harmonic signals of constant amplitude, which is consistent with the observed properties of undamped kink oscillations. The period of self-oscillations is determined by the frequency of the kink mode. The damping by dissipation and mode conversion is compensated by the continuous energy deposition
at the frequency of the natural oscillation.
Conclusions. We propose that undamped kink oscillations of coronal loops may be caused by the interaction of the loops with quasi-steady flows, and hence are self-oscillations, in analogy with producing a tune by a stick moving across a violin string.
Authors: Nakariakov, V. M., Anfinogentov, S., Nistico, G., Lee, D.-H.
Projects: SDO-AIA
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Publication Status: A&A, Letter, Accepted
Last Modified: 2016-05-18 15:32
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Dependence of kink oscillation damping on the amplitude |
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Valery Nakariakov Submitted: 2016-05-15 14:00
Context. Kink oscillations of coronal loop are one of the most intensively studied oscillatory phenomena in the solar corona. In the large-amplitude rapidly damped regime these oscillations are observed to have a low quality-factor, with only a few cycles of oscillation detected before they are damped. The specific mechanism responsible for the rapid damping is commonly accepted to be associated with the linear coupling between collective kink oscillations and localised torsional oscillations, the phenomenon ofresonant absorption of the kink mode. However, the role of finite amplitude effects is still not clear. Aims. We investigated the empirical dependence of the kink oscillation damping time and its quality factor, defined as the ratio of the damping time to the oscillation period, on the oscillation amplitude. Methods. We analysed decaying kink oscillation events detected previously with TRACE, SDO/AIA and and STEREO/EUVI in the EUV 171 Å band. Results. We found that the ratio of the kink oscillation damping time to the oscillation period systematically decreases with the oscillation amplitude. The quality factor dependence on the oscillation displacement amplitude has been approximated by the powerlaw dependence with the exponent of -1/2, however we stress that this is a "by eye" estimate, and a more rigorous estimation of the scaling law requires more accurate measurements and increased statistics. We conclude that damping of kink oscillations of coronal loops depends on the oscillation amplitude, indicating the possible role of nonlinear mechanisms for damping.
Authors: Goddard, C.R., Nakariakov, V.M.
Projects: SDO-AIA
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Publication Status: A&A, accepted, DOI:10.1051/0004-6361/201628718
Last Modified: 2016-05-16 09:09
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Magnetohydrodynamic oscillations in the solar corona and Earth's magnetosphere: Towards consolidated understanding |
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Valery Nakariakov Submitted: 2016-05-13 03:25
Magnetohydrodynamic (MHD) oscillatory processes in different plasma systems, such as the corona of the Sun and the Earth's magnetosphere, show interesting similarities
and differences, which so far received little attention and remain under-exploited. The successful commissioning within the past ten years of THEMIS, Hinode, STEREO and SDO
spacecraft, in combination with matured analysis of data from earlier spacecraft (Wind, SOHO, ACE, Cluster, TRACE and RHESSI) makes it very timely to survey the breadth
of observations giving evidence for MHD oscillatory processes in solar and space plasmas, and state-of-the-art theoretical modelling. The paper reviews several important topics, such as Alfvénic resonances and mode conversion; MHD waveguides, such as the magnetotail, coronal loops, coronal streamers; mechanisms for periodicities produced in energy releases during substorms and solar flares, possibility of Alfvénic resonators along open field lines;
possible drivers of MHD waves; diagnostics of plasmas with MHD waves; interaction of MHD waves with partly-ionised boundaries (ionosphere and chromosphere). The review is
mainly oriented to specialists in magnetospheric physics and solar physics, but not familiar with specifics of the adjacent research fields.
Authors: V.M. Nakariakov, V. Pilipenko, B. Heilig, P. Jelínek, M. Karlický́, D.Y. Klimushkin, D.Y. Kolotkov, D.-H. Lee, G. Nisticò, T. Van Doorsselaere, G. Verth, I.V. Zimovets
Projects: None
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Publication Status: Space Science Reviews, published
Last Modified: 2016-05-14 07:55
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Solar and Heliospheric Physics with the Square Kilometre Array |
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Valery Nakariakov Submitted: 2014-12-23 05:09
The fields of solar radiophysics and solar system radio physics, or radio heliophysics, will benefit immensely from an instrument with the capabilities projected for SKA. Potential applications include interplanetary scintillation (IPS), radio-burst tracking, and solar spectral radio imaging with a superior sensitivity. These will provide breakthrough new insights and results in topics of fundamental importance, such as the physics of impulsive energy releases, magnetohydrodynamic oscillations and turbulence, the dynamics of post-eruptive processes, energetic particle acceleration, the structure of the solar wind and the development and evolution of solar wind transients at distances up to and beyond the orbit of the Earth. The combination of the high spectral, time and spatial resolution and the unprecedented sensitivity of the SKA will radically advance our understanding of basic physical processes operating in solar and heliospheric plasmas and provide a solid foundation for the forecasting of space weather events.
Authors: Valery M. Nakariakov, Mario M. Bisi, Philippa K. Browning, Dalmiro Maia, Eduard P. Kontar, Divya Oberoi, Peter T. Gallagher, Iver H. Cairns, Heather Ratcliffe
Projects: None
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Publication Status: Proc. of Science (in press), 2015
Last Modified: 2014-12-23 14:49
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Multi-mode quasi-periodic pulsations in a solar flare |
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Valery Nakariakov Submitted: 2014-12-18 09:53
Context. Quasi-periodic pulsations (QPP) of the electromagnetic radiation emitted in solar and stellar flares are often detected in microwave, white light, X-ray and gamma-ray bands. Mechanisms for QPP are intensively debated in the literature. Previous studies revealed that QPP may manifest nonlinear, non-stationary and, perhaps, multi-modal processes operating in flares.
Aims. We study QPP of the microwave emission generated in an X3.2-class solar flare on 14 May, 2013, observed with the Nobeyama Radioheliograph (NoRH), aiming to reveal signatures of the nonlinear, non-stationary, and multi-modal processes in the signal.
Methods. The NoRH correlation signal obtained at the 17 GHz intensity has a clear QPP pattern. The signal was analysed with the Hilbert?Huang transform (HHT) that allows one to determine its instant amplitude and frequency, and their time variation.
Results. It was established that the QPP consists of at least three well-defined intrinsic modes, with the mean periods of 15, 45 and 100 seconds. All the modes have quasi-harmonic behaviour with different modulation patterns. The 100-second intrinsic mode is a decaying oscillation, with
the decay time of 250 seconds. The 15-second intrinsic mode shows a similar behaviour, with the decay time of 90 seconds. The 45-s mode has a wave-train behaviour.
Conclusions. Dynamical properties of detected intrinsic modes indicate that the 100-s and 15-s modes are likely to be associated with fundamental kink and sausage modes of the flaring loop, respectively. The 100-s oscillation could also be caused by the fundamental longitudinal mode,while this interpretation requires the plasma temperature of about 30 million K and hence is not likely. The 45-s mode could be the second standing harmonics of the kink mode.
Authors: Kolotkov, D. Y., Nakariakov, V. M., Kupriyanova, E. G., Ratcliffe, H., Shibasaki, K.
Projects: Nobeyama Radioheliograph
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Publication Status: A&A, accepted
Last Modified: 2014-12-21 19:19
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Wave dynamics in a sunspot umbra |
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Valery Nakariakov Submitted: 2014-09-01 02:05
Context. Sunspot oscillations are one of the most frequently studied wave phenomena in the solar atmosphere. Understanding the
basic physical processes responsible for sunspot oscillations requires detailed information about their fine structure.
Aims. We aim to reveal the relationship between the fine horizontal and vertical structure, time evolution, and the fine spectral structure
of oscillations in a sunspot umbra.
Methods. The high spatial and time resolution data obtained with SDO/AIA for the sunspot in active region NOAA 11131 on 08
December 2010 were analysed with the time-distance plot technique and the pixelised wavelet filtering method. Different levels of
the sunspot atmosphere were studied from the temperature minimum to the corona.
Results. Oscillations in the 3 min band dominate in the umbra. The integrated spectrum of umbral oscillations contains distinct
narrowband peaks at 1.9 min, 2.3 min, and 2.8 min. The power significantly varies in time, forming distinct 12?20 min oscillation
trains. The oscillation power distribution over the sunspot in the horizontal plane reveals that the enhancements of the oscillation
amplitude, or wave fronts, have a distinct structure consisting of an evolving two-armed spiral and a stationary circular patch at the
spiral origin, situated near the umbra centre. This structure is seen from the temperature minimum at 1700? to the 1.6 MK corona at
193?. In time, the spiral rotates anti-clockwise. The wave front spirality is most pronounced during the maximum amplitude phases
of the oscillations, and in the bandpasses where umbral oscillations have the highest power, 304? and 171?. In the low-amplitude
phases the spiral breaks into arc-shaped patches. The 2D cross-correlation function shows that the oscillations at higher atmospheric
levels occur later than at lower layers. The phase speed is estimated to be about 100 km s-1. The fine spectral analysis shows that the
central patch corresponds to the high-frequency oscillations, while the spiral arms highlight the lower-frequency oscillations in the
3-min band.
Conclusions. The vertical and horizontal radial structure of the oscillations is consistent with the model that interprets umbral oscillations
as slow magnetoacoustic waves filtered by the atmospheric temperature non-uniformity in the presence of the magnetic field
inclination from the vertical. The mechanism for the polar-angle structure of the oscillations, in particular the spirality of the wave
fronts, needs to be revealed.
Authors: Sych, R., Nakariakov, V.M.
Projects: SDO-AIA
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Publication Status: A&A, accepted
Last Modified: 2014-09-03 13:12
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Sausage oscillations of coronal plasma slabs |
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Valery Nakariakov Submitted: 2014-05-15 06:41
Context. Sausage oscillations are observed in plasma non-uniformities of the solar corona as axisymmetric perturbations of the nonuniformity. Often, these non-uniformities can be modelled as field-aligned slabs of the density enhancement.
Aims. We perform parametric studies of sausage oscillations of plasma slabs, aiming to determine the dependence of the oscillation period on its parameters, and the onset of leaky and trapped regimes of the oscillations.
Methods. Slabs with smooth transverse profiles of the density of a zero-beta plasma are perturbed by an impulsive localised perturbation of the sausage symmetry. In particular, the slab can contain an infinitely thin current sheet in its centre. The initial value problem is then solved numerically. The numerical results are subject to spectral analysis. The results are compared with analytical solutions for a slab with a step-function profile and also with sausage oscillations of a plasma cylinder.
Results. We established that sausage oscillations in slabs generally have the same properties as in plasma cylinders. In the trapped regime, the sausage oscillation period increases with the increase in the longitudinal wavelength. In the leaky regime, the dependence of the period on the wavelength experiences saturation, and the period becomes independent of the wavelength in the long-wavelength
limit. In the leaky regime the period is always longer than in the trapped regime. The sausage oscillation period in a slab is always longer than in a cylinder with the same transverse profile. In slabs with steeper transverse profiles, sausage oscillations have longer periods. The leaky regime occurs at shorter wavelengths in slabs with smoother profiles.
Authors: Hornsey, C., Nakariakov, V.M. and Fludra, A.
Projects: None
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Publication Status: A&A, accepted
Last Modified: 2014-05-15 15:19
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The decaying long-period oscillation of a stellar megaflare |
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Valery Nakariakov Submitted: 2013-08-06 00:11
We analyze and interpret the oscillatory signal in the decay phase of the U-band light curve of a stellar megaflare observed on 2009 January 16 on the dM4.5e star YZ CMi. The oscillation is well approximated by an exponentially decaying harmonic function. The period of the oscillation is found to be 32 minutes, the decay time about 46 minutes, and the relative amplitude 15%. As this observational signature is typical of the longitudinal oscillations observed in solar flares at extreme ultraviolet and radio wavelengths, associated with standing slow magnetoacoustic waves, we suggest that this megaflare may be of a similar nature. In this scenario, macroscopic variations of the plasma parameters in the oscillations modulate the ejection of non-thermal electrons. The phase speed of the longitudinal (slow magnetoacoustic) waves in the flaring loop or arcade, the tube speed, of about 230 km s?1 would require a loop length of about 200 Mm. Other mechanisms, such as standing kink oscillations, are also considered.
Authors: S. Anfinogentov, V. M. Nakariakov, M. Mathioudakis, T. Van Doorsselaere and A. F. Kowalski
Projects: None
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Publication Status: ApJ 773, 156, 2013; doi:10.1088/0004-637X/773/2/156
Last Modified: 2013-08-06 14:52
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Sausage oscillations of coronal plasma structures |
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Valery Nakariakov Submitted: 2012-10-30 16:08
Dependence of the period of sausage oscillations of coronal loops on its length and the radial profile depth and steepness is determined. We performed a parametric study of linear axisymmetric fast magnetoacoustic (sausage) oscillations of coronal loops modelled as a field-aligned low-beta plasma cylinder with a smooth inhomogeneity of the plasma density in the radial direction. The density decreases smoothly in the radial direction. Sausage oscillations are impulsively excited by a perturbation of the radial velocity, localised at the cylinder axis and having a harmonic dependence on the longitudinal coordinate.
The initial perturbation results either in a leaky or trapped sausage oscillation, depending upon whether the longitudinal wavenumber is smaller or greater than a cut-off value, respectively. The period of the sausage oscillations was found to always grow with the increase in the longitudinal wavelength, with the saturation of this dependence in the long-wavelength limit. Deeper and steeper radial profiles of the Alfvén speed correspond to more efficient trapping of sausage modes: the cutoff value of the wavelength increases with the steepness and the density (or Alfvén speed) contrast ratio. In the leaky regime, the period is always longer than the period of a trapped mode of a shorter wavelength in the same cylinder.
For shallow profiles of the density and shorter wavelengths, the period grows with the wavelength. In the long wavelength limit, the period becomes independent
of the wavelength, and increases with the depth and steepness of the radial profile of the Alfvén speed.
Authors: Nakariakov, V.M., Hornsey, C., Melnikov, V.F.
Projects: None
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Publication Status: accepted
Last Modified: 2012-10-30 19:45
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Slow Magnetoacoustic Waves in Two-Ribbon Flares |
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Valery Nakariakov Submitted: 2011-02-24 11:05
We demonstrate that disturbances observed to propagate along the axis of the arcade in two-ribbon solar flares at the speed of a few tens km s-1, well below the Alfvén and sound speeds, can be interpreted in terms of slow magnetoacoustic waves. The waves can propagate across the magnetic field, parallel to the magnetic neutral line, because of the wave-guiding effect due to the reflection from the footpoints. The perpendicular group speed of the perturbation is found to be a fraction of the sound speed, which is consistent with observations. The highest value of the group speed grows with the increase in the ratio of the sound and Alfvén speeds. For a broad range of parameters, the highest value of the group speed corresponds to the propagation angle of 25-28 degrees to the magnetic field. This effect can explain the temporal and spatial structure of quasi-periodic pulsations observed in two-ribbon flares.
Authors: Nakariakov, V.M., Zimovets, I.V.
Projects: None
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Publication Status: ApJ L, accepted
Last Modified: 2011-02-24 19:33
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Oscillatory processes in solar flares |
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Valery Nakariakov Submitted: 2010-10-05 07:21
Electromagnetic (radio, visible-light, UV, EUV, X-ray and gamma-ray) emission generated by solar and stellar flares often contains pronounced quasi-periodic pulsations (QPP). Physical mechanisms responsible for the generation of long-period QPP (with the periods longer than one second) are likely to be associated with MHD processes. The observed modulation depths, periods and anharmonicity of QPP suggest that they can be linked with some kind of MHD auto-oscillations, e.g. an oscillatory regime of magnetic reconnection. Such regimes, of both spontaneous and induced nature, have been observed in resistive-MHD numerical simulations. The oscillations are essentially nonlinear and non-stationary. We demonstrate that a promising novel method for their analysis is the Empirical Mode Decomposition technique.
Authors: Authors: V.M. Nakariakov, A.R. Inglis, I.V. Zimovets, C. Foullon, E. Verwichte, R. Sych, I. N. Myagkova
Projects: RHESSI
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Publication Status: Plasma Phys. Controlled Fusion (in press)
Last Modified: 2010-10-05 08:00
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