57 research outputs found
Waves and granulation
Propagation of hydrodynamic waves is considered in frames of the one-dimensional model of granulation. An exact analytical solution of the problem is obtained. The theory is applied only to high-frequency p-modes, because the effect of gravity is neglected. It appears that acoustic waves in a structured atmosphere are not plane ones. Besides, there are hydrodynamic phonon and wave guide wave
modes. The results of calculations of the wave functions for high-frequency waves with periods 100â200 s are presented. Upgoing waves are captured in integranular lanes, while downgoing ones are trapped in granules. The effect of wave capture is of greater efficiency for phonon and wave guide modes. The phase velocities of waves differ from the mean sound speed in the photosphere
Calculation of Spectral Darkening and Visibility Functions for Solar Oscillations
Calculations of spectral darkening and visibility functions for the
brightness oscillations of the Sun resulting from global solar oscillations are
presented. This has been done for a broad range of the visible and infrared
continuum spectrum. The procedure for the calculations of these functions
includes the numerical computation of depth-dependent derivatives of the
opacity caused by p modes in the photosphere. A radiative-transport code was
used for this purpose to get the disturbances of the opacities from temperature
and density fluctuations. The visibility and darkening functions are obtained
for adiabatic oscillations under the assumption that the temperature
disturbances are proportional to the undisturbed temperature of the
photosphere. The latter assumption is the only way to explore any opacity
effects since the eigenfunctions of p-mode oscillations have not been obtained
so far. This investigation reveals that opacity effects have to be taken into
account because they dominate the violet and infrared part of the spectrum.
Because of this dominance, the visibility functions are negative for those
parts of the spectrum. Furthermore, the darkening functions show a
wavelength-dependent change of sign for some wavelengths owing to these opacity
effects. However, the visibility and darkening functions under the assumptions
used contradict the observations of global p-mode oscillations, but it is
beyond doubt that the opacity effects influence the brightness fluctuations of
the Sun resulting from global oscillations
Buoyancy-driven Magnetohydrodynamic Waves
Turbulent motions close to the visible solar surface may generate low-frequency internal gravity waves (IGWs) that propagate through the lower solar atmosphere. Magnetic activity is ubiquitous throughout the solar atmosphere, so it is expected that the behavior of IGWs is to be affected. In this article we investigate the role of an equilibrium magnetic field on propagating and standing buoyancy oscillations in a gravitationally stratified medium. We assume that this background magnetic field is parallel to the direction of gravitational stratification. It is known that when the equilibrium magnetic field is weak and the background is isothermal, the frequencies of standing IGWs are sensitive to the presence of magnetism. Here, we generalize this result to the case of a slowly varying temperature. To do this, we make use of the Boussinesq approximation. A comparison between the hydrodynamic and magnetohydrodynamic cases allows us to deduce the effects due to a magnetic field. It is shown that the frequency of IGWs may depart significantly from the BruntâVĂ€isĂ€lĂ€ frequency, even for a weak magnetic field. The mathematical techniques applied here give a clearer picture of the wave mode identification, which has previously been misinterpreted. An observational test is urged to validate the theoretical findings
Dynamics of the Solar Magnetic Network. II. Heating the Magnetized Chromosphere
We consider recent observations of the chromospheric network, and argue that
the bright network grains observed in the Ca II H & K lines are heated by an as
yet unidentified quasi-steady process. We propose that the heating is caused by
dissipation of short-period magnetoacoustic waves in magnetic flux tubes
(periods less than 100 s). Magnetohydrodynamic (MHD) models of such waves are
presented. We consider wave generation in the network due to two separate
processes: (a) by transverse motions at the base of the flux tube; and (b) by
the absorption of acoustic waves generated in the ambient medium. We find that
the former mechanism leads to an efficient heating of the chromosphere by slow
magnetoacoustic waves propagating along magnetic field lines. This heating is
produced by shock waves with a horizontal size of a few hundred kilometers. In
contrast, acoustic waves excited in the ambient medium are converted into
transverse fast modes that travel rapidly through the flux tube and do not form
shocks, unless the acoustic sources are located within 100 km from the tube
axis. We conclude that the magnetic network may be heated by magnetoacoustic
waves that are generated in or near the flux tubes.Comment: 30 pages, 8 figures, Accepted in Astrophysical Journa
Gravitational Instability in Radiation Pressure Dominated Backgrounds
I consider the physics of gravitational instabilities in the presence of
dynamically important radiation pressure and gray radiative diffusion, governed
by a constant opacity, kappa. For any non-zero radiation diffusion rate on an
optically-thick scale, the medium is unstable unless the classical gas-only
isothermal Jeans criterion is satisfied. When diffusion is "slow," although the
dynamical Jeans instability is stabilized by radiation pressure on scales
smaller than the adiabatic Jeans length, on these same spatial scales the
medium is unstable to a diffusive mode. In this regime, neglecting gas
pressure, the characteristic timescale for growth is independent of spatial
scale and given by (3 kappa c_s^2)/(4 pi G c), where c_s is the adiabatic sound
speed. This timescale is that required for a fluid parcel to radiate away its
thermal energy content at the Eddington limit, the Kelvin-Helmholz timescale
for a radiation pressure supported self-gravitating object. In the limit of
"rapid" diffusion, radiation does nothing to suppress the Jeans instability and
the medium is dynamically unstable unless the gas-only Jeans criterion is
satisfied. I connect with treatments of Silk damping in the early universe. I
discuss several applications, including photons diffusing in regions of extreme
star formation (starburst galaxies & pc-scale AGN disks), and the diffusion of
cosmic rays in normal galaxies and galaxy clusters. The former (particularly,
starbursts) are "rapidly" diffusing and thus cannot be supported against
dynamical instability in the linear regime by radiation pressure alone. The
latter are more nearly "slowly" diffusing. I speculate that the turbulence in
starbursts may be driven by the dynamical coupling between the radiation field
and the self-gravitating gas, perhaps mediated by magnetic fields. (Abridged)Comment: 15 pages; accepted to Ap
Excitation of Oscillations in the Magnetic Network on the Sun
We examine the excitation of oscillations in the magnetic network of the Sun
through the footpoint motion of photospheric magnetic flux tubes located in
intergranular lanes. The motion is derived from a time series of
high-resolution G band and continuum filtergrams using an object-tracking
technique. We model the response of the flux tube to the footpoint motion in
terms of the Klein-Gordon equation, which is solved analytically as an initial
value problem for transverse (kink) waves. We compute the wave energy flux in
upward propagating transverse waves. In general we find that the injection of
energy into the chromosphere occurs in short-duration pulses, which would lead
to a time variability in chromospheric emission that is incompatible with
observations. Therefore, we consider the effects of turbulent convective flows
on flux tubes in intergranular lanes. The turbulent flows are simulated by
adding high-frequency motions (periods 5-50 s) with an amplitude of 1 km
s^{-1}. The latter are simulated by adding random velocity fluctuations to the
observationally determined velocities. In this case we find that the energy
flux is much less intermittent and can in principle carry adequate energy for
chromospheric heating.Comment: 11 pages, 5 figures, figure 1 is in color, all files gzippe
Magneto-acoustic waves in a gravitationally stratified magnetized plasma: eigen-solutions and their applications to the solar atmosphere
Magneto-acoustic gravity (MAG) waves have been studied intensively in the context of astrophysical plasmas. There are three popular choices of analytic modeling using a Cartesian coordinate system: a magnetic field parallel, perpendicular, or at an angle to the gravitational field. Here, we study a gravitationally stratified plasma embedded in a parallel, so called vertical, magnetic field. We find a governing equation for the auxiliary quantity Î = p 1/Ï 0, and find solutions in terms of hypergeometric functions. With the convenient relationship between Î and the vertical velocity component, v z , we derive the solution for v z . We show that the four linearly independent functions for v z can also be cast as single hypergeometric functions, rather than the Frobenius series derived by Leroy & Schwartz. We are then able to analyze a case of approximation for a one-layer solution, taking the small wavelength limit. Motivated by solar atmospheric applications, we finally commence study of the eigenmodes of perturbations for a two-layer model using our solutions, solving the dispersion relation numerically. We show that, for a transition between a photospheric and chromospheric plasma embedded in a vertical magnetic field, modes exist that are between the observationally widely investigated three and five minute oscillation periods, interpreted as solar global oscillations in the lower solar atmosphere. It is also shown that, when the density contrast between the layers is large (e.g., applied to photosphere/chromosphere-corona), the global eigenmodes are practically a superposition of the same as in each of the separate one-layer systems
Transverse oscillations of coronal loops
On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probably caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this review we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist.
An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transition layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube.
Very often collective oscillations of an array of coronal magnetic loops are observed. It is natural to start studying this phenomenon from the system of two coronal loops. We describe very recent analytical and numerical results of studying collective oscillations of two parallel homogeneous coronal loops.
The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations.
In the last part of the review we summarise the most outstanding and acute problems in the theory of the coronal loop transverse oscillations
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