Abstract
Oscillations in velocity and intensity are detectable over a range of height in the solar atmosphere. Properties of the atmosphere can be deduced from the stratification revealed by the corresponding power and phase-difference spectra, potentially in a manner independent of optical spectroscopy. In this paper, published acoustic power spectra and phase-difference spectra, mainly derived from observations in the NaD2 line, are interpreted through a simple model of the oscillations in an exploratory investigation along these lines. The difference between the ‘heights of formation’ at two positions in the line profile is deduced from the ratio of oscillatory power. The corresponding phase difference between oscillations in velocity at the two heights is compared with the phase spectrum derived from observations. Deduced acoustically, the ‘height of formation’ of the core of the D2 line is about 700 km above that of the pressure-broadened wing. The indicated acoustic cut-off frequency is about 4.5 mHz, a value significantly lower than that usually quoted. A variety of observational evidence is consistent with this value. The low value is probably a consequence of radiative damping, with a relaxation time of about 55 s. The phase relations between the vertical and horizontal components of motion, the temperature and the pressure are considered. At low frequencies the velocity/intensity phase difference, for oscillations of moderate to high degree, is significantly affected by the horizontal motion, even if observations are restricted to a relatively small window at disc centre. There is evidence that at the edge of the Doppler cores of strong absorption lines, fluctuations in intensity are in anti-phase with fluctuations in temperature.
Highlights
Since the confirmation by Deubner (1975) that the oscillations with periods around 5 min in the solar atmosphere are the fringes of global modes, the oscillations have been exploited as a probe of the interior of the Sun
Because the oscillations can be observed at different heights in the atmosphere, there is the possibility of tracing the vertical profile of the waves of a particular frequency and horizontal scale
It is shown that even if observations are restricted to a fairly small region near disc centre, as for the results deduced from the Michelson Doppler Imager (MDI) on board SOHO, the horizontal component has a significant effect on the expected phase difference between velocity and temperature at lower frequencies
Summary
Since the confirmation by Deubner (1975) that the oscillations with periods around 5 min in the solar atmosphere are the fringes of global modes, the oscillations have been exploited as a probe of the interior of the Sun. The solution of this equation at a particular frequency, the wavefunction, determines the ratio of the amplitudes of, and the phase difference between, oscillations at any two different heights Each of these quantities can be determined from observations at two positions in the profile of an absorption line, and to be acceptable the wavefunction must be compatible with both. Schmitz (1990) studied the vertical propagation of plane waves in isothermal atmospheres, representative of late-type stars, with the height-dependent radiative relaxation time corresponding to a mean opacity approximated by a simple power law in pressure and temperature. Referring to the phase difference between intensity and velocity, the authors ‘find not exactly an adiabatic behaviour but close to it’ With these considerations in mind, it seems appropriate to explore the implications of the simplest feasible case: adiabatic oscillations in an isothermal atmosphere, so that simple analytical results are obtained as a baseline model. It is shown that even if observations are restricted to a fairly small region near disc centre, as for the results deduced from the Michelson Doppler Imager (MDI) on board SOHO, the horizontal component has a significant effect on the expected phase difference between velocity and temperature at lower frequencies
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