Alexander V. Stepanov

Microwave Observations of the Rapid Propagation of Nonthermal Sources in a Solar Flare by the Nobeyama Radioheliograph

We report a Nobeyama Radioheliograph (NoRH) microwave observation of propagating features of nonthermal emission in a solar flare on 1999 August 28, an M2.8 event for the GOES soft X-ray class. The flare had a very extended source (≈4.5 × 104 km) that was well resolved by the NoRH, and it is confirmed to be a magnetic loop by comparison with the photospheric magnetic field. In the rising phase of the microwave burst, a nonthermal gyrosynchrotron source was observed by the high-rate (10 images per second) observation of the NoRH to propagate from one end of the loop to the other with a speed of 6 × 103 km s-1. We also found a 9 × 104 km s-1 propagation in the same apparent position, which is the first imaging observation of streaming electrons.

Oscillations of coronal loops and second pulsations of solar radio emission

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.

Pulsations of Microwave Emission and Flare Plasma Diagnostics

We consider the modulation of nonthermal gyrosynchrotron emission from solar flares by the ballooning and radial oscillations of coronal loops. The damping mechanisms for fast magnetoacoustic modes are analyzed. We suggest a method for diagnosing the plasma of flare loops that allows their main parameters to be estimated from peculiarities of the microwave pulsations. Based on observational data obtained with the Nobeyama Radioheliograph (17 GHz) and using a technique developed for the event of May 8, 1998, we determined the particle density n≈3.7×1010 cm−3, the temperature T≈4×107 K, and the magnetic field strength B≈220 G in the region of flare energy release. A wavelet analysis for the solar flare of August 28, 1999, has revealed two main types of microwave oscillations with periods P1≈7, 14 s and P2≈2.4 s, which we attribute to the ballooning and radial oscillations of compact and extended flare loops, respectively. An analysis of the time profile for microwave emission shows evidence of coronal loop interaction. We determined flare plasma parameters for the compact (T≈5.3×107 K, n≈4.8≈1010 cm−3, B≈280 G) and extended (T≈2.1≈107 K, n≈1.2≈1010 cm−3, B≈160 G) loops. The results of the soft X-ray observations are consistent with the adopted model.

Second-Harmonic Plasma Radiation of Magnetically Trapped Electrons in Stellar Coronae

Plasma radiation near the second harmonic of the plasma frequency driven by the loss-cone instability of magnetically trapped energetic electrons in stellar coronae is considered. Growth rates of longitudinal waves near the upper hybrid frequency are determined for warm background plasma and sufficiently high plasma densities, ωp > ωc, where the electrostatic instability prevails over the electromagnetic cyclotron maser instability, with particular attention given to the intermediate magnetic field condition, 1 < ω/ω 5. The plasma turbulence level and the brightness temperature of the second-harmonic plasma radiation arising from the coalescence of upper hybrid waves are estimated. The brightness temperature can reach ~1014 K for spontaneous conversion of the waves and ~1016 K for induced conversion. The radiation pattern of the second-harmonic plasma emission is also calculated; it shows a prevalence of the extraordinary mode. Analyzing the problem of the escape of radiation from stellar coronae, it is found that the escape window is wider for the o-mode because the x-mode radiation is strongly absorbed by the warm background plasma at the low harmonic gyrolevels, and thus the observed radiation can be polarized in the ordinary sense in the intermediate magnetic field case. Because of the high temperature of the plasma in the coronae of X-ray-emitting stars, the characteristic length scale of the wave conversion and the efficiency of the plasma radiation mechanism can be much higher than on the Sun. The results are discussed in the context of nonthermal quiescent and flare radio emission from active stars.

Radial oscillations of coronal loops and microwave radiation from solar flares

We consider the damping mechanisms for the radial oscillations of solar coronal loops in the approximation of a thin magnetic flux tube. We show that the free tube oscillations can have a high Q if the plasma density inside the magnetic flux tube is much higher than the density outside. We analyze the effect of radial coronal-loop magnetic-field oscillations on the modulation of the microwave radiation from solar flares. In the case of a nonthermal gyrosynchrotron mechanism, the fluxes from optically thin and optically thick sources are modulated in antiphase. Based on our model, we diagnose the flare plasma. For the event of May 23, 1990, we estimate the spectral index for accelerated electrons, α≈4.4, and the magnetic-field strength in the region of energy release, B≈190 G.

Pulsating Microwave Emission from the Star AD Leo

We have performed a spectral analysis of the quasi-periodic low-frequency modulation of microwave emission from a flare on the star AD Leo. We used the observations of the May 19, 1997 flare in the frequency range 4.5–5.1 GHz with a total duration of the burst phase of about 50 s obtained in Effelsberg with a time resolution of 1 ms. The time profile of the radio emission was analyzed by using the Wigner-Ville transformation, which yielded the dynamic spectrum of low-frequency pulsations with a satisfactory frequency-time resolution. In addition to the noise component, two regular components were found to be present in the low-frequency modulation spectrum of the stellar radio emission: a quasi-periodic component whose frequency smoothly decreased during the flare from ∼2 to ∼0.2 Hz and a periodic sequence of pulses with a repetition rate of about 2 Hz, which was approximately constant during the flare. We consider the possibility of the combined effect of MHD and LCR oscillations of the radio source on the particle acceleration in the stellar atmosphere and give estimates of the source’s parameters that follow from an analysis of the low-frequency modulation spectra.

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 ρe/ρi≈10−2, and the electrical current flowing along the loop I≈1012 A.

Sub-terahertz emission from solar flares: The plasma mechanism of chromospheric emission

We consider the plasma mechanism of sub-terahertz emission from solar flares and determine the conditions for its realization in the solar atmosphere. The source is assumed to be localized at the chromospheric footpoints of coronal magnetic loops, where the electron density should reach n ≈ 1015 cm−3. This requires chromospheric heating at heights h ⩾ 500 km to coronal temperatures, which provides a high degree of ionization needed for Langmuir frequencies νp ≈ 200–400 GHz and reduces the bremsstrahlung absorption of the sub-THz emission as it escapes from the source. The plasma wave excitation threshold for electron-ion collisions imposes a constraint on the lower density limit for energetic electrons in the source, n1 > 4 × 109 cm−3. The generation of emission at the plasma frequency harmonic ν ≈ 2νp rather than the fundamental tone turns out to be preferred. We show that the electron acceleration and plasma heating in the sub-THz emission source can be realized when the ballooning mode of the flute instability develops at the chromospheric footpoints of a flare loop. The flute instability leads to the penetration of external chromospheric plasma into the loop and causes the generation of an inductive electric field that efficiently accelerates the electrons and heats the chromosphere in situ. We show that the ultraviolet radiation from the heated chromosphere emerging in this case does not exceed the level observed during flares.

Oscillations of optical emission from flare stars and coronal loop diagnostics

Based on an analogy between stellar and solar flares, we investigate the ten-second oscillations detected in the U and B bands on the star EV Lac. The emission pulsations are associated with fast magnetoacoustic oscillations in coronal loops. We have estimated the magnetic field, B ≈ 320 G; the temperature, T ≈ 3.7 × 107 K; and the plasma density, n ≈ 1.6 × 1011 cm−3, in the region of energy release. We provide evidence suggesting that the optical emission source is localized at the loop footpoints.

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.