Parametric excitation of acoustic oscillations in closed coronal magnetic loops

Quasi-periodic modulations of the microwave emission from solar outbursts at 37 GHz are studied based on 17 events observed in 1989–2000 at the Metsähovi Observatory. Low-frequency modulations with periods of ～5 min were found in approximately 90% of the observed microwave outbursts. The most likely origin of this modulation is modulation of the current flowing along a closed coronal magnetic loop due to the five-minute oscillations of the photospheric-convection velocity. In approximately 70% of the cases, oscillations with periods ～10 min were observed simultaneously with the five-minute oscillations in the same events. In 30% of the cases, simultaneous modulation of the microwave emission by three low-frequency signals with periods of 3, 5, and 10 min was observed. One possible origin of these “double” and “triple” modulations is parametric excitation of acoustic oscillations with periods of 10 and 3 min in a closed coronal magnetic loop as a result of coupling with the five-minute photospheric oscillations. This can occur when the period of the natural acoustic oscillations of the closed magnetic loop is about 10 min (the resonance condition). Since the ten-minute oscillations are excited more easily than the three-minute oscillations at the parametric instability, the latter are observed less frequently. For the same reason, the observed linewidth of the ten-minute oscillations is considerably greater than that of the three-minute oscillations.     

Dissipation of diamagnetic currents and plasma heating in coronal magnetic loops

SOHO and TRACE data have shown that the coronal plasma is heated most actively near sunspots, in magnetic loops that issue from the penumbral region. The source of heating is nonuniform in height, and its power is maximum near the footpoints of the magnetic loops. The heating process is typically accompanied by the injection of dense chromospheric plasma into the coronal parts of the magnetic loops. It is important that the radiative losses cannot be compensated for via electron thermal conduction in the loops, which have temperatures of 1.0–1.5 MK; therefore, some heating source must operate throughout the entire length of the loop, balancing radiative losses and maintaining a quasi-steady state of the loop over at least several hours. As observations show, the plasma density inside the loops exceeds the density of the ambient plasma by more than an order of magnitude. It is supposed that the enhanced plasma density inside the loops results from the development of the ballooning mode of a flute-type instability in the sunspot penumbra, where the plasma of the inner sunspot region, with β _i ? 1, comes into contact with the dense chromospheric plasma, which has β _e ? β _i (β is the gas-to-magnetic pressure ratio). As the chromospheric plasma penetrates into the potential field of the sunspot, the generated diamagnetic currents balance the excess gas pressure. These currents efficiently decay due to the Cowling conductivity. Even if neutrals are few in number in the plasma (accounting for less than 10^?5 of the total mass density), this conductivity ensures a heating rate that exceeds the rate of the normal Joule dissipation of diamagnetic currents by 7–8 orders of magnitude. Helium is an important factor in the context of plasma heating in magnetic loops. Its relatively high ionization potential, while not forbidding dielectronic recombination, ensures a sufficiently high number of neutrals in the coronal plasma and maintains a high heating rate due to the Cowling conductivity, even at coronal temperatures. The heating results from the “burning-out” of the nonpotential component of the magnetic field of the coronal magnetic loops. This mechanism provides the necessary heating rate for the plasma inside the loops if the loops are thin enough (with thickness of the order of 10⁵–10⁶ cm). This may imply that the observed (1–5) × 10⁸-cm-thick loops consist of numerous hot, thin threads. For magnetic loops in hydrostatic equilibrium, the calculated heating function exponentially decreases with height on characteristic scales a factor of 1.8 smaller than the total-pressure scale height, since the scale heights for the total pressure and for the ⁴He partial pressure are different. The heating rate is proportional to the square of the plasma pressure in the loop, in agreement with observational data.

     

Ballooning instability and oscillations of coronal loops

The excitation of the ballooning instability by the eigenoscillations of coronal loops is analyzed using the energy method. The second variation of the potential energy for the case of a plasma—plasma boundary is obtained via the linearized ideal MHD equations. It is shown that the eigenmodes of a magnetic tube and of a toroidal coronal loop coincide in a first approximation. The bending oscillations of the loops are able to excite the ballooning instability when β ? 1. The effects of the instability in solar coronal loops are discussed.     

The role of faculae in wave-energy transfer to upper layers of the solar atmosphere: Observations

The properties of Doppler-velocity oscillations in solar faculae are analyzed at the photospheric level (based on Fe I 6569 ? and Fe I 8536 ? lines) and chromospheric level (based on Hα and Ca II 8542 ? lines) to search for upward propagating waves. The similarity of the averaged power spectra at 2.5–4 mHz is not found to be convincing proof of the presence of unidirectional wave-energy transfer from the photosphere to the chromosphere. Phase relations between the photospheric and chromospheric oscillations that are indicative of either upward or downward propagating waves are obtained for various areas in many faculae. This suggests that the wave energy of the five-minute oscillations returns to the photosphere, at least partially. The derived properties suggest that the role of faculae in the transfer of the five-minute oscillations to the chromosphere and overlying layers is not as obvious as could be expected. The relatively typical presence of low-frequency (0.5–2 mHz) oscillations in faculae and their possible important role in this energy transfer are noted.     

The generation of magnetic field via convective motions in the photosphere,Alvén waves,and the origin of chromospheric spicules

The basis is laid out for a theory relating various phenomena in the solar atmosphere, including localized concentrations of magnetic field at the bases of coronal magnetic arches, chromospheric spicules, twisted coronal magnetic flux tubes, and flows of energy carried by Alfvén waves propagating upward into the corona. The structure of photospheric currents localized in the vicinity of supergranule boundaries and excited by convective motions is studied. These currents exist primarily in a “dynamo layer” of sharply enhanced transverse conductivity, which forms in the weakly ionized thermal photospheric plasma located in the solar gravitational field. The motions of the electrons and ions in this layer have appreciably different characters: the ions are collisionly driven by the flows of neutral atoms, while the electrons drift in the crossed electric and magnetic fields. The electric field supporting the current arises due to the polarization of the electrons and ions. This field also gives rise to Alfvén perturbations that propagate upward into the corona, together with their associated longitudinal currents. The character of this “loading” makes the system of fields and currents uniquely defined. Moreover, the momentum flux carried by these Alfvén waves should be transferred to the cool chromospheric gas, facilitating the vertical ejection of this gas in the form of spicules, as was first proposed in 1992 by Haerendel.     

Harmonic oscillations of the X-ray emission of a solar flare

An analysis is presented for the class-M9.3 solar flare of November 6, 2004, whose decay phase displayed weakly damped harmonic oscillations of the predominantly thermal X-ray flux detected by the RHESSI spacecraft (at energies ≲25 keV). The period of these oscillations was ≈78 s, and their characteristic decay time ≈100 min. Similar quasi-periodic pulsations were observed in the decimeter-centimeter radio flux (pulsations of a type-IV radio outburst), but were less pronounced in the non-thermal hard X-ray flux (≳25 keV). The area of the quasi-stationary X-ray source, which was located primarily at the apex of a set of flare loops (≲15 keV) that were cooled primarily via thermal conduction, was found to be in anti-phase with the oscillating X-ray flux it emitted. The observed oscillations are interpreted as harmonic modulations of the radiation flux emitted by the heated thermal flare-loop plasma, due to the global, standing, sausage mode of fast magnetoacoustic waves excited in the loop.     

Characteristics of oscillatory-wave processes in solar structures with various magnetic field topology

Recognizing that waves play an important role in energy-exchange processes between layers of the solar atmosphere, and that the characteristics of propagating waves are determined by the physical conditions of the medium, and, most importantly, the magnetic-field configuration, we have carried out a comparative analysis of the properties of oscillations in solar structures with various magnetic-field topologies: sunspots, faculae, and coronal holes. Simultaneous measurements of the Doppler velocities and intensities at the photospheric and chromospheric levels were accompanied by episodic measurements of the longitudinal magnetic field. In the chromosphere, spot umbrae dominate the three-minute oscillations, while lower-frequency modes are also observed in the penumbrae and at the outer parts of spots. Clear signs of propagating waves have been observed at the bases of coronal holes and in faculae only at frequencies close to 3 mHz.     

The relationship between coronal fan structures and oscillations above faculae regions

The power spectra of radial-velocity and intensity oscillations are analyzed using ground-based (the Si I 10 827 Å and He I 10 830 Å lines) and Solar Dynamics Observatory (the Fe I 6173, 1700 Å, He II 304 Å, and Fe IX 171 Å lines) data, with the aim of searching for frequency modes that most efficiently penetrate into the solar corona from the lower layers of solar faculae. Analysis of the spatial distribution of the oscillation power at various heights indicates that fan structures in the corona (at the height of the 171 Å emission) are better reproduced at frequencies of 1–1.5 mHz. This means that oscillations with periods of 10–15 min dominate in coronal loops above faculae regions. The five-minute oscillations that universally dominate in radial-velocity measurements in low layers of faculae are appreciable in coronal loops only in individual compact fragments.     

Long-period oscillations of the solar microwave emission

Modulations of the microwave emission of the Sun at 11.7 GHz have been studied using more than 40 events observed in 2001 at the Mets?hovi Radio Observatory. In nearly all the observed events, low-frequency modulations with periods of 3–90 min were detected. As a rule, simultaneous modulation of the emission at several frequencies was observed. One possible origin of such modulations with periods 5–10 min is parametric resonance arising in coronal magnetic loops as a result of interactions with the 5-min photospheric oscillations, while the long-period modulations could be a manifestation of sunspot oscillations. Torsional (ϑ-mode) and radial (r-mode) oscillations have such periods. The frequency of occurrence of oscillations with the determined periods is considered, and a lower limit for the brightness temperature of the oscillations is estimated.     

Spectral-temporal evolution of low-frequency pulsations in the microwave radiation of solar flares

Low-frequency pulsations of 22 and 37 GHz microwave radiation detected during solar flares are analyzed. Several microwave bursts observed at the Metsähovi Radio Observatory are studied with time resolutions of 100 and 50 ms. A fast Fourier transformation with a sliding window and the Wigner-Ville method are used to obtain frequency-time diagrams for the low-frequency pulsations, which are interpreted as natural oscillations of coronal magnetic loops; the dynamical spectra of the pulsations are synthesized for the first time. Three types of low-frequency fluctuations modulating the flare microwave radiation can be distinguished in the observations. First, there are fast and slow magneto-acoustic oscillations with periods of 0.5–0.8 s and 200–280 s, respectively. The fast magneto-acoustic oscillations appear as trains of narrow-band signals with durations of 100–200 s, a positive frequency drift dν/dt=0.25 MHz/min, and frequency splitting δν=0.01–0.05 Hz. Second, there are natural oscillations of the coronal magnetic loops as equivalent electrical circuits. These oscillations have periods of 0.5–10 s and positive or negative frequency drift rates dν/dt=8×10^?3 Hz/min or dν/dt=?1.3×10^?2 Hz/min, depending on the phase of the radio outburst. Third, there are modulations of the microwave radiation by short periodic pulses with a period of 20 s. The dynamical spectra of the low-frequency pulsations supply important information about the parameters of the magnetic loops: the ratio of the loop radius to its length r/L≈0.1, the plasma parameter β≈10^?3, the ratio of the plasma densities outside and inside the loop ρ_e/ρ_i≈10^?2, and the electrical current flowing along the loop I≈10¹² A.     

Spectral Observations of the Eruption of a Filament

Results of studies of motions in a filament during its slow ascent and eruption based on spectral observations obtained at the Sayan Solar Observatory are presented. SDO/HMI data on the longitudinal magnetic field and SDO/AIA images in the EUV are also considered. Short-period (∼5 min) vertical oscillations of the filament as a whole were detected during its ascent. An acceleration of the rise of the filament was accompanied by the rupture of an orthogonal loop above the filament, which was observed in 193 A EUV images obtained with SDO/AIA over a long time preceding the event. Two hours before the partial eruption of the filament, SDO/HMI data indicate an increase in the magnetic flux by 2 × 10¹⁹ Mx at the footpoints of the loop. The emission from the loop rupture piont propagated toward the east and west along a neutral line, and brightenings were observed at the boundaries of the filament channel. Emission loops were visible in all SDO/AIA channels, testifying to strong heating of the filament plasma. During the rapid phase of the eruption, the filament moved with an acceleration ∼21 m/s². Hα images show the filament splitting into fragments parallel to its axis during the eruption. The results of these studies of the eruption of the filament are in agreement with other results in the literature, and are supplemented by new observational facts. Vertical oscillations (∼5 min) of the filament as a whole are observed before the ascent phase. During the ascent phase, an interaction of the filament with a higher-lying coronal loop is observed.

     

Periodic processes and plasma motions in solar coronal holes

Episodic observations of coronal holes were carried out simultaneously in several spectral lines during the 2002–2005 observational seasons. An analysis of eighteen time series is used to obtain the amplitude—spectral properties of oscillatory wave motions of the solar plasma at the bases of coronal holes. It is found that the amplitudes of the 5-min and 3-min line-of-sight velocity oscillations increase in coronal holes. Low-frequency (1–2 mHz) oscillations are concentrated at the boundaries of the chromospheric network, while the 3-mHz and 5-mHz oscillations dominate in the network cells. Clear indications of propagating waves have been found at the bases of coronal holes. The 3 mHz phase velocities are 45 ± 5 km/s and 80–100 km/s for the equatorial and polar coronal holes, respectively.     

Initial formation of an “impulsive” coronal mass ejection

An “impulsive” coronal mass ejection (CME) observed on August 24, 2014 is analyzed using ultraviolet images obtained in the SDO/AIA 193, 304, 1600, and 1700 Å channels and Hα (6562.8 Å) data obtained with the EI Teide and Big Bear telescopes. The formation of this impulsive CME was related to a magnetic tube (rope) moving with a velocity of ≈35 km/s and containing plasma that was cooler than the photospheric material. Moving in the corona, the magnetic tube collides with a quasi-stationary coronal magnetic rope, with its two bases rooted in the photosphere. This interaction results in the formation of the CME, with the surface of the coronal magnetic rope becoming the CME frontal structure. According to SDO/HMI data, no enhancements or changes in magnetic flux were detected in the vicinity of the CME bases during its formation. This may support the hypothesis that the magnetic tube starts its motion from layers in the vicinity of the temperature minimum.     

Pulsating evershed flows and propagating waves in a sunspot

A comparative analysis of oscillatory spectra based on 66 time series for 14 active regions observed in 2001 shows that, although the chromospheric and photospheric oscillations in the Evershed flow zone possess many common features, there is no firm evidence that the direct and inverse flows have the same physical origin. The interactions between the various oscillation modes and stationary flows results in a complex pattern of wave motions in a sunspot. We studied the Doppler-velocity variations in the sunspot NOAA 0051 during its motion over the disk. The spatial-temporal distribution of the line-of-sight velocity in the chromospheric umbra displays a chevron structure, clearly indicating the presence of propagating waves. These waves move from the center of the umbra to outer regions with a phase speed of 45–60 km/s, a period of 2.8 min, and a measured Doppler speed of 2 km/s. The amplitude of these oscillations decreases abruptly at the boundary between the umbra and penumbra, and the observed waves are not directly related to propagating penumbral waves. Furthermore, the observed pattern of the photospheric velocities shows periodic motions (with a period of 5 min) directed from the inner boundary of the penumbra and superpenumbra toward the line of maximum Evershed velocity.     

Common features in the development of powerful long-duration solar X-ray flares

We have begun an investigation of the possible origins of considerable of powerful solar flares. This effect is manifest, first and foremost, in the existence of high-temperature plasma in flare loops over many hours. Analysis of the soft X-ray emission in two energy bands detected by the GOES satellites for about 20 powerful solar flares reveals long time intervals during the decay phase when the source temperature decreases, in general, exponentially. The characteristic time t _i for a decrease in the temperature by a factor of ten is 3–10 hours for most powerful events. In addition, another interval of very slow decrease with a characteristic time t _i of tens of hours can be identified in some cases. We found a gradual change in the dependence of the temperature on the square root of the emission measure for the source as a whole, which characterizes the transition from purely coronal processes to powerful flares with a prolonged inflow of plasma from the chromosphere. Modeling the energy balance in a loop can yield the requirements for the source of plasma heating in a long-lived arch system. A necessary condition for the development of prolonged flares seems to be a powerful coronal mass ejection, which initiates the formation of a source of plasma heating at coronal heights. Our analysis shows that a considerable fraction of the energy is often released in the region of the cusp, and that systems of giant coronal arches rising to heights of about 100 000 km above the limb are formed in most prolonged events (called dynamical flares in the terminology of Svestka).     

Solar flares with long soft X-ray decays: Energy balance in giant loops

Solar flares with long X-ray decays (Long-Decay Flars, LDF) are studied. X-ray and radio observations can be used to trace the active phase of an LDF and the subsequent development of a system of giant coronal loops. The energy balance in a giant loop is modeled for the events of January 24, 1992 (an elementary LDF, considered earlier), November 2, 1991, and March 15, 1993; the modeling shows that energy flow into the loop over the entire life time of the LDF is necessary to account for the duration of the events. The total energy of the LDF was confined within rather narrow limits and was comparable to the energy of major impulsive flares. The results are consistent with the concept (developed in connection with Yohkoh observations) that an LDF in a posteruptive process results in magnetic reconnection in a vertical current sheet, with the subsequent formation of new loops and their specific evolution.     

Jet structure of electric currents in coronal magnetic loops

We analyze the properties of the electric-current distribution over the cross sections of fairly dense coronal magnetic flux tubes in which the plasma pressure exceeds the magnetic pressure, so that the equilibrium is maintained by the ambient magnetic field. If the plasma is fully ionized, the distributions of the longitudinal and azimuthal currents over the cross section of the loop have the same spatial scale as the pressure distribution. However, even a small number of neutral atoms in the corona (with a mass fraction of the order of 10^?5, taking into account the partial ionization of helium) substantially modifies the current distribution over the tube cross section: in this case, a considerable fraction of the full current flowing along the tube is concentrated in a thin region near the axis with a radius of the order of (10^?2–10^?3)r ₀ (where r ₀ is the characteristic scale of the plasma-pressure distribution over the tube), thus forming a sort of a jet current. This comes about because the pattern of the conductivity anisotropy is substantially modified in the presence of ion-atom collisions in the magnetoactive plasma of the tube, and the Cowling conductivity dominates over the Hall and Pedersen conductivities. The high current density near the axis of the tube can ensure heating of the plasma to coronal temperatures via Joule dissipation.     

Numerical MHD simulations of post-flare loop formation on the sun: Allowing for thermal-conductivity anisotropy

The process of post-flare loop formation, including the heating of flux tubes by hot chromospheric sources and their filling with plasma, is demonstrated by simulations in an MHD approximation. The loop is additionally heated at its apex by the interaction of oppositely directed plasma streams. Local coronal heating over the loop is also possible due to magnetic-field-line reconnection. A new version of the PERESVET code that can take into account anisotropy of the thermal conductivity of a plasma in a magnetic field was used for the computations.     

The three-dimensional structure of the corona above active region NOAA 9591 from microwave observations

We study the active region NOAA 9591 using observations at 1.92–10.17 cm obtained on two large Russian radio instruments: the RATAN-600 radio telescope and the Siberian Solar Radio Telescope. The active region was associated with an isolated spot at the photospheric level, whose magnetic field had a well-defined Delta configuration. The radio observations show that the structure of the coronal source located above the spot cannot be described in a simple (unipolar) cyclotron model. A comparison with X-ray observations indicates that the three-dimensional structure of the corona above the spot can be represented as a strongly elongated loop whose apex resembles a cusp brightening (a qualitative model for the structure is presented). Unexpectedly, radiation with a high degree of polarization (～25%) was detected far (～100 000 km) from the photosphere. The need for a quantitative model for coronal sources above the strong Delta-configuration magnetic fields, which are known to play an important role in active solar processes (flares, phenomena such as coronal-mass ejections) is outlined. Thanks to its simple morphology, which enabled the identification of a pure Delta configuration, the active region NOAA 9591 provides high-quality observational material for the creation of such a model.     

Origin of prolonged X-ray flares on active late-type stars

Soft X-ray data for prolonged flares in subgiants in RS CVn binary systems and some other active late-type stars (AB Dor, Algol) are analyzed. During these nonstationary events, a large amount of hot plasma with temperatures exceeding 10⁸ K exists for many hours. Numerical simulations of gas-dynamical processes in the X-ray source—giant loops—can yield reliable estimates of the plasma parameters and flare-source size. This confirms that such phenomena exist while considerable energy is supplied to the top part of a giant loop or system of loops. Refined estimates of the flare energy (up to 10³⁷ erg) and scales contradict the widely accepted idea that prolonged X-ray flares are associated with the evolution of local magnetic fields. The energy of the current component of the large-scale magnetic field arising during the ejection of magnetic field by plasma jets or stellar wind is estimated. Two cases are considered: a global stellar field and fields connecting regions with oppositely directed unipolar magnetic fields. The inferred energy of the current component of the magnetic field associated with distortion of the initial MHD configuration is close to the total flare energy, suggesting that large-scale magnetic fields play an important role in prolonged flares. The flare process encompasses some portion of a streamer belt and may propagate along the entire magnetic equator of the star during the most powerful prolonged events.