432 research outputs found
Nonlinear Instability of kink oscillations due to shear motions
First results from a high-resolution three-dimensional nonlinear numerical
study of the kink oscillation are presented. We show in detail the development
of a shear instability in an untwisted line-tied magnetic flux tube. The
instability produces significant deformations of the tube boundary. An extended
transition layer may naturally evolve as a result of the shear instability at a
sharp transition between the flux tube and the external medium. We also discuss
the possible effects of the instability on the process of resonant absorption
when an inhomogeneous layer is included in the model. One of the implications
of these results is that the azimuthal component of the magnetic field of a
stable flux tube in the solar corona, needed to prevent the shear instability,
is probably constrained to be in a very specific range
Kelvin-Helmholtz instability in coronal magnetic flux tubes due to azimuthal shear flows
Transverse oscillations of coronal loops are often observed and have been
theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical
simulations by Terradas et al. (2008, ApJ 687, L115) suggest that shear flows
generated at the loop boundary during kink oscillations could give rise to a
Kelvin-Helmholtz instability (KHI). Here, we investigate the linear stage of
the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear
motions. We consider the basic, linearized MHD equations in the beta = 0
approximation, and apply them to a straight and homogeneous cylindrical flux
tube model embedded in a coronal environment. Azimuthal shear flows with a
sharp jump of the velocity at the cylinder boundary are included in the model.
We obtain an analytical expression for the dispersion relation of the unstable
MHD modes supported by the configuration, and compute analytical approximations
of the critical velocity shear and the KHI growth rate in the thin tube limit.
A parametric study of the KHI growth rates is performed by numerically solving
the full dispersion relation. We find that fluting-like modes can develop a KHI
in time-scales comparable to the period of kink oscillations of the flux tube.
The KHI growth rates increase with the value of the azimuthal wavenumber and
decrease with the longitudinal wavenumber. However, the presence of a small
azimuthal component of the magnetic field can suppress the KHI. Azimuthal
motions related to kink oscillations of untwisted coronal loops may trigger a
KHI, but this phenomenon has not been observed to date. We propose that the
azimuthal component of the magnetic field is responsible for suppressing the
KHI in a stable coronal loop. The required twist is small enough to prevent the
development of the pinch instability.Comment: Submitted in Ap
Three-Dimensional Propagation of Magnetohydrodynamic Waves in Solar Coronal Arcades
We numerically investigate the excitation and temporal evolution of
oscillations in a two-dimensional coronal arcade by including the
three-dimensional propagation of perturbations. The time evolution of
impulsively generated perturbations is studied by solving the linear, ideal
magnetohydrodynamic (MHD) equations in the zero-beta approximation. As we
neglect gas pressure the slow mode is absent and therefore only coupled MHD
fast and Alfven modes remain. Two types of numerical experiments are performed.
First, the resonant wave energy transfer between a fast normal mode of the
system and local Alfven waves is analyzed. It is seen how, because of resonant
coupling, the fast wave with global character transfers its energy to Alfvenic
oscillations localized around a particular magnetic surface within the arcade,
thus producing the damping of the initial fast MHD mode. Second, the time
evolution of a localized impulsive excitation, trying to mimic a nearby coronal
disturbance, is considered. In this case, the generated fast wavefront leaves
its energy on several magnetic surfaces within the arcade. The system is
therefore able to trap energy in the form of Alfvenic oscillations, even in the
absence of a density enhancement such as that of a coronal loop. These local
oscillations are subsequently phase-mixed to smaller spatial scales. The amount
of wave energy trapped by the system via wave energy conversion strongly
depends on the wavelength of perturbations in the perpendicular direction, but
is almost independent from the ratio of the magnetic to density scale heights.Comment: 27 pages, 11 figure
Transverse kink oscillations in the presence of twist
Magnetic twist is thought to play an important role in coronal loops. The
effects of magnetic twist on stable magnetohydrodynamic (MHD) waves is poorly
understood because they are seldom studied for relevant cases. The goal of this
work is to study the fingerprints of magnetic twist on stable transverse kink
oscillations. We numerically calculated the eigenmodes of propagating and
standing MHD waves for a model of a loop with magnetic twist. The azimuthal
component of the magnetic field was assumed to be small in comparison to the
longitudinal component. We did not consider resonantly damped modes or kink
instabilities in our analysis. For a nonconstant twist the frequencies of the
MHD wave modes are split, which has important consequences for standing waves.
This is different from the degenerated situation for equilibrium models with
constant twist, which are characterised by an azimuthal component of the
magnetic field that linearly increases with the radial coordinate. In the
presence of twist standing kink solutions are characterised by a change in
polarisation of the transverse displacement along the tube. For weak twist, and
in the thin tube approximation, the frequency of standing modes is unaltered
and the tube oscillates at the kink speed of the corresponding straight tube.
The change in polarisation is linearly proportional to the degree of twist.
This has implications with regard to observations of kink modes, since the
detection of this variation in polarisation can be used as an indirect method
to estimate the twist in oscillating loops
The statistical significance of the N-S asymmetry of solar activity revisited
The main aim of this study is to point out the difficulties found when trying
to assess the statistical significance of the North-South asymmetry (hereafter
SSNSA) of the most usually considered time series of solar activity. First of
all, we distinguish between solar activity time series composed by integer or
non-integer and dimensionless data, or composed by non-integer and dimensional
data. For each of these cases, we discuss the most suitable statistical tests
which can be applied and highlight the difficulties to obtain valid information
about the statistical significance of solar activity time series. Our results
suggest that, apart from the need to apply the suitable statistical tests,
other effects such as the data binning, the considered units and the need, in
some tests, to consider groups of data, affect substantially the determination
of the statistical significance of the asymmetry. Our main conclusion is that
the assessment of the statistical significance of the N-S asymmetry of solar
activity is a difficult matter and that an absolute answer cannot be given,
since many different effects influence the results given by the statistical
tests. In summary, the quantitative results about the statistical significance
of the N-S asymmetry of solar activity provided by different authors, as well
as the studies about its behaviour, must be considered with care because they
depend from the chosen values of different parameters or from the considered
units.Comment: Astronomy and Astrophysics Latex, 9 pages, 4 figure
The effect of longitudinal flow on resonantly damped kink oscillations
The most promising mechanism acting towards damping the kink oscillations of
coronal loops is resonant absorption. In this context most of previous studies
neglected the effect of the obvious equilibrium flow along magnetic field
lines. The flows are in general sub-Alfv\'enic and hence comparatively slow.
Here we investigate the effect of an equilibrium flow on the resonant
absorption of linear kink MHD waves in a cylindrical magnetic flux tube with
the aim of determining the changes in the frequency of the forward and backward
propagating waves and in the modification of the damping times due to the flow.
A loop model with both the density and the longitudinal flow changing in the
radial direction is considered. We use the thin tube thin boundary (TTTB)
approximation in order to calculate the damping rates. The full resistive
eigenvalue problem is also solved without assuming the TTTB approximation.
Using the small ratio of flow and Alfv\'en speeds we derive simple analytical
expressions to the damping rate. The analytical expressions are in good
agreement with the resistive eigenmode calculations. Under typical coronal
conditions the effect of the flow on the damped kink oscillations is small when
the characteristic scale of the density layer is similar or smaller than the
characteristic width of the velocity layer. However, in the opposite situation
the damping rates can be significantly altered, specially for the backward
propagating wave which is undamped while the forward wave is overdamped
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