Transverse oscillations of systems of coronal loops

We study the collective kinklike normal modes of a system of several cylindrical loops using the T-matrix theory. Loops that have similar kink frequencies oscillate collectively with a frequency which is slightly different from that of the individual kink mode. On the other hand, if the kink frequency of a loop is different from that of the others, it oscillates individually with its own frequency. Since the individual kink frequency depends on the loop density but not on its radius for typical 1 MK coronal loops, a coupling between kink oscillations of neighboring loops take place when they have similar densities. The relevance of these results in the interpretation of the oscillations studied by \citet{schrijver2000} and \citet{verwichte2004}, in which transverse collective loop oscillations seem to be detected, is discussed. In the first case, two loops oscillating in antiphase are observed; interpreting this motion as a collective kink mode suggests that their densities are roughly equal. In the second case, there are almost three groups of tubes that oscillate with similar periods and therefore their dynamics can be collective, which again seems to indicate that the loops of each group share a similar density. All the other loops seem to oscillate individually and their densities can be different from the rest

Flare-generated acoustic oscillations in solar and stellar coronal loops

Long period longitudinal oscillations of a flaring coronal loop are studied numerically. In the recent work of Nakariakov et al. (2004) it has been shown that the time dependence of density and velocity in a flaring loop contain pronounced quasi-harmonic oscillations associated with the 2nd harmonic of a standing slow magnetoacoustic wave. In this work we investigate the physical nature of these oscillations in greater detail, namely, their spectrum (using the periodogram technique) and how heat positioning affects mode excitation. We found that excitation of such oscillations is practically independent of the location of the heat deposition in the loop. Because of the change of the background temperature and density, the phase shift between the density and velocity perturbations is not exactly a quarter of the period; it varies along the loop and is time dependent, especially in the case of one footpoint (asymmetric) heating

Electron versus Proton Timing Delays in Solar Flares

Both electrons and ions are accelerated in solar flares and carry nonthermal energy from the acceleration site to the chromospheric energy loss site, but the relative amount of energy carried by electrons versus ions is subject of debate. In this {\sl Letter} we test whether the observed energy-dependent timing delays of 20-200 keV HXR emission can be explained in terms of propagating electrons versus protons. For a typical flare, we show that the timing delays of fast (\lapprox 1 s) {\sl HXR pulses} is consistent with time-of-flight differences of directly precipitating electrons, while the timing delays of the {\sl smooth HXR} flux is consistent with collisional deflection times of trapped electrons. We show that these HXR timing delays cannot be explained either by $\le 1$ MeV protons (as proposed in a model by Simnett \& Haines 1990), because of their longer propagation and trapping times, or by $\approx 40$ MeV protons (which have the same velocity as $\approx 20$ keV electrons), because of their longer trapping times and the excessive fluxes required to generate the HXRs. Thus, the HXR timing results clearly rule out protons as the primary generators of $\ge 20$ keV HXR emission.Comment: 7 pages, TEX type, AASTeX macros, 1 Figure, to appear in Astrophysical Journal Letters, accepted 1996 July 2

Transverse oscillations of a multi-stranded loop

We investigate the transverse oscillations of a line-tied multi-stranded coronal loop composed of several parallel cylindrical strands. First, the collective fast normal modes of the loop are found with the T-matrix theory. There is a huge quantity of normal modes with very different frequencies and a complex structure of the associated magnetic pressure perturbation and velocity field. The modes can be classified as bottom, middle, and top according to their frequencies and spatial structure. Second, the temporal evolution of the velocity and magnetic pressure perturbation after an initial disturbance are analyzed. We find complex motions of the strands. The frequency analysis reveals that these motions are a combination of low and high frequency modes. The complexity of the strand motions produces a strong modulation of the whole tube movement. We conclude that the presumed internal fine structure of a loop influences its transverse oscillations and so its transverse dynamics cannot be properly described by those of an equivalent monolithic loop.Comment: Accepted in Ap

Radiative hydrodynamic modeling of the Bastille-Day flare (14 July, 2000). I, Numerical simulations

A 1D loop radiative hydrodynamic model that incorporates the effects of gravitational stratification, heat conduction, radiative losses, external heat input, presence of helium, and Braginskii viscosity is used to simulate elementary flare loops. The physical parameters for the input are taken from observations of the Bastille-Day flare of 2000 July 14. The present analysis shows that: a) the obtained maximum values of the electron density can be considerably higher (4.2 × 10 11 cm −3 or more) in the case of footpoint heating than in the case of apex heating (2.5 × 10 11 cm −3); b) the average cooling time after the flare peak takes less time in the case of footpoint heating than in the case of apex heating; c) the peak apex temperatures are significantly lower (by about 10 MK) for the case of footpoint heating than for apex heating (for the same average loop temperature of about 30 MK). This characteristic would allow to discriminate between different heating positioning; d) in both cases (of apex and footpoint heating), the maximum obtained apex temperature T max is practically independent of the heating duration σ t , but scales directly with the heating rate E H0 ; e) the maximum obtained densities at the loop apex, n max e, increase with the heating rate E H0 and heating duration σ t for both footpoint and apex heating. In Paper II we will use the outputs of these hydrodynamic simulations, which cover a wide range of the parameter space of heating rates and durations, as an input for forward-fitting of the multi-loop arcade of the Bastille-day flare