Title:

Oscillations and structure of the sun

Oscillations of the sun are an increasingly important tool for exploring the sun's internal structure. This is because the oscillation frequencies depend on the structure of the part of the sun where the oscillations are confined. It is possible to compute the oscillation frequencies of any candidate structure for the interior of the sun. So, in principle, the family of candidate structures which possess the known oscillation frequencies can be identified. The implications of the five minute oscillations of high degree are considered first. They are confined to the outer few thousand kilometres of the sun. However, they penetrate deep enough to experience the adiabatically stratified part of the convection zone. Careful calculations are made of the eigenfrequencies of the modes corresponding to the observed oscillations. It is shown that the oscillation frequencies place constraints on the convection zone adiabat. This conclusion is found to hold despite present ignorance of the details of some of the physical processes involved in the oscillations. It is shown that most of the oscillation frequencies are very insensitive to these various uncertainties so that the use of the oscillations to place bounds on the structure is legitimate. If a standard chemical composition is assumed (one which does not have a very low heavy element abundance) it follows that the convection zone is deep, that is of the order of 30% of the radius. In this investigation it is necessary to test the sensitivity of the oscillation frequencies to the, normally neglected, turbulent pressure of convection. To do this, solar envelope models including turbulent pressure must be constructed. It is found that including turbulent pressure in a local mixinglength formalism gives results which have unwanted discontinuities at the top boundary of the convection zone. A nonlocal mixinglength formalism is therefore used instead which does not have this disadvantage. The convection zone models calculated in this way have upper thermal boundary layers which have a similar structure to those found in more sophisticated modal treatments of stellar convection and also in laboratory experiments. One claim about the interior of the sun that has been made based upon the frequencies of oscillations is that the solar interior is considerably cooler than evolved solar models suggest. This conclusion results from identifying the observed 160 minute oscillation with the fundamental radial oscillation mode. It is shown that this identification is certainly incorrect as the sun cannot possibly have a radial mode period as long as 160 minutes. In fact the maximum possible period is not significantly greater than that of an n  3/2 polytrope (about 100 minutes). The geophysical inversion technique used to explore the internal structure of the earth is then applied to the sun in the form of simple model calculations. Two models are constructed. These are superposed polytropic models with an n = 3 polytrope at the centre and an outer n = 3/2 polytrope of depth 25% and 20% of the radius. This represents the sun's outer convection zone. The former model is supposed to represent the true structure and the latter a guess at that structure. The oscillation frequencies computed from the first model are used to attempt to infer its structure. This method makes it possible to obtain a good idea of what information about structure is contained in a particular set of oscillation mode frequencies. It is found that about a dozen modes of oscillation of low order and degree can provide useful information about much of the internal structure. It may soon be possible to obtain enough observed oscillation frequencies to apply this method to the actual sun.
