V. Nakariakov - Academia.edu (original) (raw)
Papers by V. Nakariakov
Advances in Space Research, 2015
The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiate... more The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at coordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere-a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA.
Plasma Physics and Controlled Fusion, 2009
Coronal seismology exploits the properties of magnetohydrodynamics (MHD) in the corona of the Sun... more Coronal seismology exploits the properties of magnetohydrodynamics (MHD) in the corona of the Sun to diagnose the local plasma. Therefore, seismology complements direct diagnostic techniques, which suffer from line-of sight integration or may not give access to all physical quantities. In particular, the seismological exploitation of fast magnetoacoustic oscillations in coronal loops provides information about the global magnetic and density structuring of those loops acting as wave guides. From the oscillation period and damping time it is shown how to obtain information about the local coronal magnetic field as well as the longitudinal and transverse structuring. Furthermore, such studies motivate the development of coronal wave theories, which are also relevant for the coronal heating problem.
A theoretical model interpreting propagating disturbances of EUV emission intensity, recently obs... more A theoretical model interpreting propagating disturbances of EUV emission intensity, recently observed in coronal loops, is constructed in terms of slow magnetoacoustic waves. The model is one-dimensional and incorporates effects of nonlinearity, dissipation due to finite viscosity and thermal conduction, and gravitational stratification of plasma in the loop. It has been found that, for the observationally detected parameters of the waves, the main factors influencing the wave evolution are dissipation and stratification. The upwardly propagating waves of observed periods (5-20 min) are found to decay significantly in the vicinity of the loop apex, explaining the rarity of observational detection of downwardly propagating waves. The model provides a theoretical basis for development of MHD seismology of the coronal loops.
Low-Frequency Waves in Space Plasmas, 2016
This document was created by the Solar Simulations for the Atacama Large Millimeter Observatory N... more This document was created by the Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) in preparation of the first regular observations of the Sun with the Atacama Large Millimeter/submillimeter Array (ALMA), which are anticipated to start in ALMA Cycle 4 in October 2016. The science cases presented here demonstrate that a large number of scientifically highly interesting observations could be made already with the still limited solar observing modes foreseen for Cycle 4 and that ALMA has the potential to make important contributions to answering long-standing scientific questions in solar physics. With the proposal deadline for ALMA Cycle 4 in April 2016 and the Commissioning and Science Verification campaign in December 2015 in sight, several of the SSALMON Expert Teams composed strategic documents in which they outlined potential solar observations that could be feasible given the anticipated technical capabilities in Cycle 4. These documents have been ...
The Astrophysical Journal
Please refer to published version for the most recent bibliographic citation information. If a pu... more Please refer to published version for the most recent bibliographic citation information. If a published version is known of, the repository item page linked to above, will contain details on accessing it.
The Astrophysical Journal
We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in th... more We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in the context of large-scale propagating waves in the solar atmosphere. We perform one-dimensional numerical simulations of fast wave pulses propagating perpendicular to a constant magnetic field in a low-β plasma with a random density profile across the field. Both linear and nonlinear regimes are considered. We study how the evolution of the pulse amplitude and width depends on their initial values and the parameters of the random structuring. Acting as a dispersive medium, a randomly structured plasma causes amplitude attenuation and width broadening of the fast wave pulses. After the passage of the main pulse, secondary propagating and standing fast waves appear. Width evolution of both linear and nonlinear pulses can be well approximated by linear functions; however, narrow pulses may have zero or negative broadening. This arises because narrow pulses are prone to splitting, while broad pulses usually deviate less from their initial Gaussian shape and form ripple structures on top of the main pulse. Linear pulses decay at an almost constant rate, while nonlinear pulses decay exponentially. A pulse interacts most efficiently with a random medium with a correlation length of about half of the initial pulse width. This detailed model of fast wave pulses propagating in highly structured media substantiates the interpretation of EIT waves as fast magnetoacoustic waves. Evolution of a fast pulse provides us with a novel method to diagnose the sub-resolution filamentation of the solar atmosphere.
Flares that are orders of magnitude larger than the most energetic solar flares are routinely obs... more Flares that are orders of magnitude larger than the most energetic solar flares are routinely observed on Sun-like stars, raising the question of whether the same physical processes are responsible for both solar and stellar flares. In this Letter, we present a white-light stellar superflare on the star KIC 9655129, observed by NASA's Kepler mission, with a rare multi-period quasi-periodic pulsation (QPP) pattern. Two significant periodic processes were detected using the wavelet and autocorrelation techniques, with periods of 78 ± 12 minutes and 32 ± 2 minutes. By comparing the phases and decay times of the two periodicities, the QPP signal was found to most likely be linear, suggesting that the two periodicities are independent, possibly corresponding either to different magnetohydrodynamic (MHD) modes of the flaring region or different spatial harmonics of the same mode. The presence of multiple periodicities is a good indication that the QPPs were caused by MHD oscillations and suggests that the physical processes in operation during stellar flares could be the same as those in solar flares.
Within the last decade, due to significant improvements in the spatial and temporal resolution of... more Within the last decade, due to significant improvements in the spatial and temporal resolution of chromospheric data, magnetohydrodynamic (MHD) wave studies in this fascinating region of the Sun's atmosphere have risen to the forefront of solar physics research. In this review we begin by reviewing the challenges and debates that have manifested in relation to MHD wave mode identification in fine-scale chromospheric magnetic structures, including spicules, fibrils and mottles. Next we go on to discuss how the process of accurately identifying MHD wave modes also has a crucial role to play in estimating their wave energy flux. This is of cardinal importance for estimating what the possible contribution of MHD waves is to solar atmospheric heating. Finally, we detail how such advances in chromospheric MHD wave studies have also allowed us, for the first time, to implement cutting-edge magnetoseismological techniques that provide new insight into the sub-resolution plasma structuri...
Astronomy & Geophysics
Seismology now includes study of the Sun's corona, a promising research target both in its ow... more Seismology now includes study of the Sun's corona, a promising research target both in its own right and for its role in the relationship between the Sun and the Earth and its links to the solar magnetic field. In addition, the corona, as a natural plasma, is itself an objective for fundamental physics. Observations using spacecraft such as SOHO and TRACE highlight the interrelationship between the magnetic field and corona.
Direct observational evidence of wave and oscillatory activity of the solar corona is abundant in... more Direct observational evidence of wave and oscillatory activity of the solar corona is abundant in all observational bands and includes recent discoveries of propagating compressible waves in polar plumes and near loop footpoints, flare-generated transverse oscillations of loops, and longitudinal and sausage standing oscillations within loops. These phenomena are successfully interpreted in terms of magnetohydrodynamic (MHD) waves. This observational breakthrough gave rise to the rapid development of a new method for the remote diagnostics of the coronal plasma, MHD coronal seismology, allowing for estimation of the absolute value of the magnetic field in coronal loops, Alfvén speeds, transport coefficients, fine structuring, heating function and other important coronal parameters. EIS and XRT instruments are excellent tools for the further development of coronal wave studies and especially flare generated oscillations and waves. We present the recent findings, theoretical estimation...
This paper focuses on forward modeling of spectroscopic data, as would be emitted by a coronal lo... more This paper focuses on forward modeling of spectroscopic data, as would be emitted by a coronal loop oscillating in the vertical fast kink mode. The Doppler shift, broadening and deformation of the observed spectral lines are investigated. It is concluded that the vertical kink mode causes strong line broadening, either inside the loop or at the edges of the loop, depending on the time integration and the oscillatory phase observed.
Research in Astronomy and Astrophysics
Solar radiophysics is a rapidly developing branch of solar physics and plasma astrophysics. Solar... more Solar radiophysics is a rapidly developing branch of solar physics and plasma astrophysics. Solar radiophysics has the goal of analyzing observations of radio emissions from the Sun and understanding basic physical processes operating in quiet and active regions of the solar corona. In the near future, the commissioning of a new generation of solar radio observational facilities, which include the Chinese Spectral Radio Heliograph (CSRH) and the upgrade of the Siberian Solar Radio Telescope (SSRT), and the beginning of solar observations with the Atacama Large Millimeter/submillimeter Array (ALMA), is expected to bring us new breakthrough results of a transformative nature. The Marie-Curie International Research Staff Exchange (MC IRSES) "RadioSun" international network aims to create a solid foundation for the successful exploitation of upcoming solar radio observational facilities, as well as intensive use of the existing observational tools, advanced theoretical modelin...
Quasilinear theory has long been used to treat the problem of a weak electron beam interacting wi... more Quasilinear theory has long been used to treat the problem of a weak electron beam interacting with plasma and generating Langmuir waves. Its extension to weak-turbulence theory treats resonant interactions of these Langmuir waves with other plasma wave modes, in particular ion-sound waves. These are strongly damped in plasma of equal ion and electron temperatures, as sometimes seen in, for example, the solar corona and wind. Weak turbulence theory is derived in the weak damping limit, with a term describing ion-sound wave damping then added. In this paper we use the EPOCH particle-in-cell code to numerically test weak turbulence theory for a range of electron-ion temperature ratios. We find that in the cold ion limit the results agree well, but increasing ion temperature the three-wave resonance becomes broadened in proportion to the ion-sound wave damping rate. This may be important in, for example, the theory of solar radio bursts, where the spectrum of Langmuir waves is critical...
Quasi-periodic pulsations (QPP) are a common feature of flaring energy releases in the solar atmo... more Quasi-periodic pulsations (QPP) are a common feature of flaring energy releases in the solar atmosphere, observed in all bands, from radio to hard X-ray. In this review we concentrate on QPP with the periods longer than one second. Physical mechanisms responsible for the generation of long QPP split into two groups: "load/unload" mechanisms and MHD oscillations. Load/unload mechanisms are repetitive regimes of flaring energy releases by magnetic reconnection or by other means. MHD oscillations can affect all elements of the flaring emission generation: triggering of reconnection and modulation of its rate, acceleration and dynamics of non-thermal electrons, and physical conditions in the emitting plasmas. In the case of MHD oscillations, the periodicity of QPP is determined either by the presence of some resonances, e.g. standing modes of plasma structures, or by wave dispersion. Periods and other parameters of QPP are linked with properties of flaring plasmas and their morphology. Observational investigation of the QPP generation mechanisms based upon the use of spatial information, broadband spectral coverage and multi-periodicity is discussed.
ABSTRACT Impulsively generated magnetohydrodynamic waves in a typical EUV solar coronal loop are ... more ABSTRACT Impulsively generated magnetohydrodynamic waves in a typical EUV solar coronal loop are studied numerically with a use of the three-dimensional FLASH code. Our results reveal several 3D effects such as distinctive time signatures which are collected at a detection point inside the loop. A slow magnetosonic wave generates a significant variation in a mass density profile with a time-scale of the order of s. A fast kink wave affects a mass density too but its magnitude is much lower than in the case of a slow wave. Time-scales which are associated with the fast kink wave are generally lower than in the case of a slow wave; they are in the range of a dozen or so seconds. Temporal signatures of a fast sausage wave reveal s oscillations in the quasi-periodic phase. Impulses which are launched outside the loop excite few seconds oscillations in the mass density. Time-signatures depend on a position of the detection point; they are usually more complex further out from the exciter.
ABSTRACT We present the first identification of the global (or fundamental) fast magnetoacoustic ... more ABSTRACT We present the first identification of the global (or fundamental) fast magnetoacoustic sausage mode of a coronal loop in the X-ray band, based upon the detailed analysis of multi-wavelength spatially-resolving observations of the M9.3 solar flare on 6 November 2004 by RHESSI. High quality harmonic oscillations with the time period of about 78 s and Q=240 have been detected in the thermal X-ray (with energies lower than 25 keV) emission flux in the decay phase of the flare. Similar quasi-periodic pulsations were also observed in the decimetric-centimetric radio emission flux (as pulsations of type IV radio burst). In the non-thermal hard X-ray emission (higher than 25 keV) the oscillations were less pronounced. It is found that the area of the quasi-stationary and cooling soft X-ray source (lower than 15 keV), which was situated near the top of the flaring loop, varied in anti-phase with the oscillating flux of its radiation. The oscillation period remained constant during all the oscillations. The observed properties of the oscillations coincide with the theoretically predicted properties of standing sausage modes. Cooling of heated plasma during the oscillations is explained mainly by the conductive losses.
Advances in Space Research, 2015
The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiate... more The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at coordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere-a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA.
Plasma Physics and Controlled Fusion, 2009
Coronal seismology exploits the properties of magnetohydrodynamics (MHD) in the corona of the Sun... more Coronal seismology exploits the properties of magnetohydrodynamics (MHD) in the corona of the Sun to diagnose the local plasma. Therefore, seismology complements direct diagnostic techniques, which suffer from line-of sight integration or may not give access to all physical quantities. In particular, the seismological exploitation of fast magnetoacoustic oscillations in coronal loops provides information about the global magnetic and density structuring of those loops acting as wave guides. From the oscillation period and damping time it is shown how to obtain information about the local coronal magnetic field as well as the longitudinal and transverse structuring. Furthermore, such studies motivate the development of coronal wave theories, which are also relevant for the coronal heating problem.
A theoretical model interpreting propagating disturbances of EUV emission intensity, recently obs... more A theoretical model interpreting propagating disturbances of EUV emission intensity, recently observed in coronal loops, is constructed in terms of slow magnetoacoustic waves. The model is one-dimensional and incorporates effects of nonlinearity, dissipation due to finite viscosity and thermal conduction, and gravitational stratification of plasma in the loop. It has been found that, for the observationally detected parameters of the waves, the main factors influencing the wave evolution are dissipation and stratification. The upwardly propagating waves of observed periods (5-20 min) are found to decay significantly in the vicinity of the loop apex, explaining the rarity of observational detection of downwardly propagating waves. The model provides a theoretical basis for development of MHD seismology of the coronal loops.
Low-Frequency Waves in Space Plasmas, 2016
This document was created by the Solar Simulations for the Atacama Large Millimeter Observatory N... more This document was created by the Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) in preparation of the first regular observations of the Sun with the Atacama Large Millimeter/submillimeter Array (ALMA), which are anticipated to start in ALMA Cycle 4 in October 2016. The science cases presented here demonstrate that a large number of scientifically highly interesting observations could be made already with the still limited solar observing modes foreseen for Cycle 4 and that ALMA has the potential to make important contributions to answering long-standing scientific questions in solar physics. With the proposal deadline for ALMA Cycle 4 in April 2016 and the Commissioning and Science Verification campaign in December 2015 in sight, several of the SSALMON Expert Teams composed strategic documents in which they outlined potential solar observations that could be feasible given the anticipated technical capabilities in Cycle 4. These documents have been ...
The Astrophysical Journal
Please refer to published version for the most recent bibliographic citation information. If a pu... more Please refer to published version for the most recent bibliographic citation information. If a published version is known of, the repository item page linked to above, will contain details on accessing it.
The Astrophysical Journal
We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in th... more We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in the context of large-scale propagating waves in the solar atmosphere. We perform one-dimensional numerical simulations of fast wave pulses propagating perpendicular to a constant magnetic field in a low-β plasma with a random density profile across the field. Both linear and nonlinear regimes are considered. We study how the evolution of the pulse amplitude and width depends on their initial values and the parameters of the random structuring. Acting as a dispersive medium, a randomly structured plasma causes amplitude attenuation and width broadening of the fast wave pulses. After the passage of the main pulse, secondary propagating and standing fast waves appear. Width evolution of both linear and nonlinear pulses can be well approximated by linear functions; however, narrow pulses may have zero or negative broadening. This arises because narrow pulses are prone to splitting, while broad pulses usually deviate less from their initial Gaussian shape and form ripple structures on top of the main pulse. Linear pulses decay at an almost constant rate, while nonlinear pulses decay exponentially. A pulse interacts most efficiently with a random medium with a correlation length of about half of the initial pulse width. This detailed model of fast wave pulses propagating in highly structured media substantiates the interpretation of EIT waves as fast magnetoacoustic waves. Evolution of a fast pulse provides us with a novel method to diagnose the sub-resolution filamentation of the solar atmosphere.
Flares that are orders of magnitude larger than the most energetic solar flares are routinely obs... more Flares that are orders of magnitude larger than the most energetic solar flares are routinely observed on Sun-like stars, raising the question of whether the same physical processes are responsible for both solar and stellar flares. In this Letter, we present a white-light stellar superflare on the star KIC 9655129, observed by NASA's Kepler mission, with a rare multi-period quasi-periodic pulsation (QPP) pattern. Two significant periodic processes were detected using the wavelet and autocorrelation techniques, with periods of 78 ± 12 minutes and 32 ± 2 minutes. By comparing the phases and decay times of the two periodicities, the QPP signal was found to most likely be linear, suggesting that the two periodicities are independent, possibly corresponding either to different magnetohydrodynamic (MHD) modes of the flaring region or different spatial harmonics of the same mode. The presence of multiple periodicities is a good indication that the QPPs were caused by MHD oscillations and suggests that the physical processes in operation during stellar flares could be the same as those in solar flares.
Within the last decade, due to significant improvements in the spatial and temporal resolution of... more Within the last decade, due to significant improvements in the spatial and temporal resolution of chromospheric data, magnetohydrodynamic (MHD) wave studies in this fascinating region of the Sun's atmosphere have risen to the forefront of solar physics research. In this review we begin by reviewing the challenges and debates that have manifested in relation to MHD wave mode identification in fine-scale chromospheric magnetic structures, including spicules, fibrils and mottles. Next we go on to discuss how the process of accurately identifying MHD wave modes also has a crucial role to play in estimating their wave energy flux. This is of cardinal importance for estimating what the possible contribution of MHD waves is to solar atmospheric heating. Finally, we detail how such advances in chromospheric MHD wave studies have also allowed us, for the first time, to implement cutting-edge magnetoseismological techniques that provide new insight into the sub-resolution plasma structuri...
Astronomy & Geophysics
Seismology now includes study of the Sun's corona, a promising research target both in its ow... more Seismology now includes study of the Sun's corona, a promising research target both in its own right and for its role in the relationship between the Sun and the Earth and its links to the solar magnetic field. In addition, the corona, as a natural plasma, is itself an objective for fundamental physics. Observations using spacecraft such as SOHO and TRACE highlight the interrelationship between the magnetic field and corona.
Direct observational evidence of wave and oscillatory activity of the solar corona is abundant in... more Direct observational evidence of wave and oscillatory activity of the solar corona is abundant in all observational bands and includes recent discoveries of propagating compressible waves in polar plumes and near loop footpoints, flare-generated transverse oscillations of loops, and longitudinal and sausage standing oscillations within loops. These phenomena are successfully interpreted in terms of magnetohydrodynamic (MHD) waves. This observational breakthrough gave rise to the rapid development of a new method for the remote diagnostics of the coronal plasma, MHD coronal seismology, allowing for estimation of the absolute value of the magnetic field in coronal loops, Alfvén speeds, transport coefficients, fine structuring, heating function and other important coronal parameters. EIS and XRT instruments are excellent tools for the further development of coronal wave studies and especially flare generated oscillations and waves. We present the recent findings, theoretical estimation...
This paper focuses on forward modeling of spectroscopic data, as would be emitted by a coronal lo... more This paper focuses on forward modeling of spectroscopic data, as would be emitted by a coronal loop oscillating in the vertical fast kink mode. The Doppler shift, broadening and deformation of the observed spectral lines are investigated. It is concluded that the vertical kink mode causes strong line broadening, either inside the loop or at the edges of the loop, depending on the time integration and the oscillatory phase observed.
Research in Astronomy and Astrophysics
Solar radiophysics is a rapidly developing branch of solar physics and plasma astrophysics. Solar... more Solar radiophysics is a rapidly developing branch of solar physics and plasma astrophysics. Solar radiophysics has the goal of analyzing observations of radio emissions from the Sun and understanding basic physical processes operating in quiet and active regions of the solar corona. In the near future, the commissioning of a new generation of solar radio observational facilities, which include the Chinese Spectral Radio Heliograph (CSRH) and the upgrade of the Siberian Solar Radio Telescope (SSRT), and the beginning of solar observations with the Atacama Large Millimeter/submillimeter Array (ALMA), is expected to bring us new breakthrough results of a transformative nature. The Marie-Curie International Research Staff Exchange (MC IRSES) "RadioSun" international network aims to create a solid foundation for the successful exploitation of upcoming solar radio observational facilities, as well as intensive use of the existing observational tools, advanced theoretical modelin...
Quasilinear theory has long been used to treat the problem of a weak electron beam interacting wi... more Quasilinear theory has long been used to treat the problem of a weak electron beam interacting with plasma and generating Langmuir waves. Its extension to weak-turbulence theory treats resonant interactions of these Langmuir waves with other plasma wave modes, in particular ion-sound waves. These are strongly damped in plasma of equal ion and electron temperatures, as sometimes seen in, for example, the solar corona and wind. Weak turbulence theory is derived in the weak damping limit, with a term describing ion-sound wave damping then added. In this paper we use the EPOCH particle-in-cell code to numerically test weak turbulence theory for a range of electron-ion temperature ratios. We find that in the cold ion limit the results agree well, but increasing ion temperature the three-wave resonance becomes broadened in proportion to the ion-sound wave damping rate. This may be important in, for example, the theory of solar radio bursts, where the spectrum of Langmuir waves is critical...
Quasi-periodic pulsations (QPP) are a common feature of flaring energy releases in the solar atmo... more Quasi-periodic pulsations (QPP) are a common feature of flaring energy releases in the solar atmosphere, observed in all bands, from radio to hard X-ray. In this review we concentrate on QPP with the periods longer than one second. Physical mechanisms responsible for the generation of long QPP split into two groups: "load/unload" mechanisms and MHD oscillations. Load/unload mechanisms are repetitive regimes of flaring energy releases by magnetic reconnection or by other means. MHD oscillations can affect all elements of the flaring emission generation: triggering of reconnection and modulation of its rate, acceleration and dynamics of non-thermal electrons, and physical conditions in the emitting plasmas. In the case of MHD oscillations, the periodicity of QPP is determined either by the presence of some resonances, e.g. standing modes of plasma structures, or by wave dispersion. Periods and other parameters of QPP are linked with properties of flaring plasmas and their morphology. Observational investigation of the QPP generation mechanisms based upon the use of spatial information, broadband spectral coverage and multi-periodicity is discussed.
ABSTRACT Impulsively generated magnetohydrodynamic waves in a typical EUV solar coronal loop are ... more ABSTRACT Impulsively generated magnetohydrodynamic waves in a typical EUV solar coronal loop are studied numerically with a use of the three-dimensional FLASH code. Our results reveal several 3D effects such as distinctive time signatures which are collected at a detection point inside the loop. A slow magnetosonic wave generates a significant variation in a mass density profile with a time-scale of the order of s. A fast kink wave affects a mass density too but its magnitude is much lower than in the case of a slow wave. Time-scales which are associated with the fast kink wave are generally lower than in the case of a slow wave; they are in the range of a dozen or so seconds. Temporal signatures of a fast sausage wave reveal s oscillations in the quasi-periodic phase. Impulses which are launched outside the loop excite few seconds oscillations in the mass density. Time-signatures depend on a position of the detection point; they are usually more complex further out from the exciter.
ABSTRACT We present the first identification of the global (or fundamental) fast magnetoacoustic ... more ABSTRACT We present the first identification of the global (or fundamental) fast magnetoacoustic sausage mode of a coronal loop in the X-ray band, based upon the detailed analysis of multi-wavelength spatially-resolving observations of the M9.3 solar flare on 6 November 2004 by RHESSI. High quality harmonic oscillations with the time period of about 78 s and Q=240 have been detected in the thermal X-ray (with energies lower than 25 keV) emission flux in the decay phase of the flare. Similar quasi-periodic pulsations were also observed in the decimetric-centimetric radio emission flux (as pulsations of type IV radio burst). In the non-thermal hard X-ray emission (higher than 25 keV) the oscillations were less pronounced. It is found that the area of the quasi-stationary and cooling soft X-ray source (lower than 15 keV), which was situated near the top of the flaring loop, varied in anti-phase with the oscillating flux of its radiation. The oscillation period remained constant during all the oscillations. The observed properties of the oscillations coincide with the theoretically predicted properties of standing sausage modes. Cooling of heated plasma during the oscillations is explained mainly by the conductive losses.
Impulsively excited sausage oscillations of a plasma cylinder with a smooth radial profile of Alf... more Impulsively excited sausage oscillations of a plasma cylinder with a smooth radial profile of Alfvén speed are analyzed with a numerical solution of the initial-value problem for a partial differential equation of the Klein-Gordon type, describing linear magnetoacoustic oscillations with a fixed axial wavelength and an azimuthal mode number. The range of analyzed ratios of Alfvén speeds outside and inside the cylinder is from 2 to 10. Both trapped and leaky regimes of the oscillations are considered. It is shown that even in the long-wavelength limit, i.e., for axial wavenumbers much smaller than the cutoff values, damping times of higher radial sausage harmonics could be significantly greater than the oscillation periods, i.e., several oscillation cycles could be present in the signal. The quality factors decrease with decfreasing ratios of Alfvén speeds outside and inside the cylinder. Oscillation periods of the second and third radial harmonics remain practically independent of the axial wavelength even when the wavelength is shorter than the radius of the cylinder. The ratios of oscillation periods of fundamental and higher radial and axial harmonics are found to be significantly different, up to a factor of two in the long-wavelength limit. It is concluded that higher radial harmonics could be responsible for the departure of observed sausage oscillation signals from a harmonic shape, especially during the first several cycles of the oscillation. Even in the absence of spatially resolved data, higher axial and radial harmonics can be distinguished from each other by the period ratios.