Energy and energy flux in axisymmetric slow and fast waves

Abstract

Aims. We aim to calculate the kinetic, magnetic, thermal, and total energy densities and the flux of energy in axisymmetric sausage modes. The resulting equations should contain as few parameters as possible to facilitate applicability for different observations. Methods. The background equilibrium is a one-dimensional cylindrical flux tube model with a piecewise constant radial density profile. This enables us to use linearised magnetohydrodynamic equations to calculate the energy densities and the flux of energy for axisymmetric sausage modes.Results. The equations used to calculate the energy densities and the flux of energy in axisymmetric sausage modes depend on the radius of the flux tube, the equilibrium sound and Alfvén speeds, the density of the plasma, the period and phase speed of the wave, and the radial or longitudinal components of the Lagrangian displacement at the flux tube boundary. Approximate relations for limiting cases of propagating slow and fast sausage modes are also obtained. We also obtained the dispersive first-order correction term to the phase speed for both the fundamental slow body mode under coronal conditions and the slow surface mode under photospheric conditions.

Magnetoacoustic wave energy dissipation in the atmosphere of solar pores

“…The authors used wavelet and Fourier techniques to detect oscillations in both the intensity and cross-sectional area of the pore, and observed periods in the range of 3–7 min, remaining consistent with a global p -mode driver suggested by Morton et al [12]. The energy flux was calculated [18] to drop rapidly with height from the solar surface, with the initial energy flux of approximately 35 kW m −2 dropping by three orders of magnitude over an atmospheric height separation of approximately 800 km, confirming that the pore was indeed able to guide wave energy into higher atmospheric layers of the solar atmosphere. Standing slow sausage waves have also been detected in pores by Freij et al [19], who characterized the waves as ‘standing’ due to the estimated vertical wavelengths that would indicate strong reflection at the transition region boundary—i.e.…”

Photospheric Observations of Surface and Body Modes in Solar Magnetic Pores.

“…It has also been suggested that pores can support a significant amount of wave energy (Grant et al 2015), with the potential to power the local dynamics of the lower solar atmosphere. Utilizing the theoretical framework for energy flux estimates (Moreels et al 2015b), we suggest that at the photospheric level the surface modes transport at least twice the energy (22 ± 10 kW m −2 ) as the observed body modes (11 ± 5 kW m −2 ). This may be significant in determining which mode contributes more to localized atmospheric heating as a function of waveguide height.…”

“…Here we only employ one bandpass in our analysis. Therefore, we utilize a technique demonstrated previously (Grant et al 2015;Moreels et al 2015b) to yield accurate estimates of the phase speed of a sausage mode oscillation using the equation…”

“…Grant et al (2015) employed multiple passbands and instruments to observe an upwardly propagating sausage mode from the lower photosphere to the upper photosphere/low chromosphere. They used the energy equations of Moreels et al (2015b) to determine that the energy carried by the modes decreases substantially with height and, thus, may release significant energy into the surrounding chromospheric plasma. A recent study of two pores (Freij et al 2016) using magnetoseismology techniques suggested that sausage modes in pores can be standing harmonics, with strong reflection at the transition region, indicating a chromospheric resonator.…”

Chromospheric Heating by Magnetohydrodynamic Waves and Instabilities

“…In-phase relation between oscillations in cross sectional area and intensity categorises the waves as slow sausage waves. The energy flux of the waves was estimated at different heights using the theoretical tool of Moreels et al (2015a). They found the energy flux of the waves at the solar surface to be 35 kW m −2 , which rapidly decreased to 100 W m −2 at the height of 800 km (see the upper right panel of Figure 3).…”