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 Brunt–Väisälä 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 Θ = p 1/ρ 0, and find solutions in terms of hypergeometric functions. With the convenient relationship between Θ 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

Photospheric observations of surface and body modes in solar magnetic pores

Over the past number of years, great strides have been made in identifying the various low-order magnetohydrodynamic wave modes observable in a number of magnetic structures found within the solar atmosphere. However, one aspect of these modes that has remained elusive, until now, is their designation as either surface or body modes. This property has significant implications for how these modes transfer energy from the waveguide to the surrounding plasma. Here, for the first time to our knowledge, we present conclusive, direct evidence of these wave characteristics in numerous pores that were observed to support sausage modes. As well as outlining methods to detect these modes in observations, we make estimates of the energies associated with each mode. We find surface modes more frequently in the data, as well as that surface modes appear to carry more energy than those displaying signatures of body modes. We find frequencies in the range of ~2–12 mHz, with body modes as high as 11 mHz, but we do not find surface modes above 10 mHz. It is expected that the techniques we have applied will help researchers search for surface and body signatures in other modes and in differing structures from those presented here

An Inside Look at Sunspot Oscillations with Higher Azimuthal Wavenumbers

Solar chromospheric observations of sunspot umbrae offer an exceptional view of magneto-hydrodynamic wave phenomena. In recent years, a wealth of wave signatures related to propagating magneto-acoustic modes have been presented, which demonstrate complex spatial and temporal structuring of the wave components. Theoretical modelling has demonstrated how these ubiquitous waves are consistent with an m=0 slow magneto-acoustic mode, which are excited by trapped sub-photospheric acoustic (p-mode) waves. However, the spectrum of umbral waves is broad, suggesting that the observed signatures represent the superposition of numerous frequencies and/or modes. We apply Fourier filtering, in both spatial and temporal domains, to extract chromospheric umbral wave characteristics consistent with an m=1 slow magneto-acoustic mode. This identification has not been described before. Angular frequencies of 0.037 +/- 0.007 rad/s (2.1 +/- 0.4 deg/s), corresponding to a period approximately 170 s for the m=1 mode are uncovered for spatial wavenumbers in the range of 0.45<k<0.90 arcsec^-1 (5000-9000 km). Theoretical dispersion relations are solved, with corresponding eigenfunctions computed, which allows the density perturbations to be investigated and compared with our observations. Such magnetohydrodynamic modelling confirms our interpretation that the identified wave signatures are the first direct observations of an m=1 slow magneto-acoustic mode in the chromospheric umbra of a sunspot

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review

Propagating spectropolarimetric disturbances in a large sunspot

We present results derived from the analysis of spectropolarimetric measurements of active region AR12546, which represents one of the largest sunspots to have emerged onto the solar surface over the last 20 years. The region was observed with full-Stokes scans of the Fe I 617.3 nm and Ca II 854.2 nm lines with the Interferometric BIdimensional Spectrometer (IBIS) instrument at the Dunn Solar Telescope over an uncommon, extremely long time interval exceeding three hours. Clear circular polarization (CP) oscillations localized at the umbra-penumbra boundary of the observed region were detected. Furthermore, the multi-height data allowed us to detect the downward propagation of both CP and intensity disturbances at 2.5−3~mHz, which was identified by a phase delay between these two quantities. These results are interpreted as a propagating magneto-hydrodynamic surface mode in the observed sunspot