| During the main-sequence stage of the Sun’s lifetime, its propertieschange so slowly. It is commonly accepted that the Sun is in dynamicalequilibrium and almost spherical. All physical quantities of the Sundepend just on the distance from its center. Based on these assumptions,the structure of the Sun can be described by four differential equations,i.e. equation of mass distribution, equation of hydrostatic equilibrium,equation of energy transport and energy equation. The main task of thestudy of stellar models is to solve these equations with certain boundaryconditions. With the development of computer technology, scientists haveeffectively got numerical solutions to these equations. However, thereare still many open questions about the interior of the Sun that cannotbe answered by the numerical solutions. In order to overcome suchdeficiencies of the numerical solutions, scientists have proposed manyanalytical solar models and some meaningful results have been got. Theexisting analytical solar models are confronted with the main problem thatthere are few adjustable parameters and the results show a significantdeviation from numerical results. Moreover, in some models (e.g. Steinmodel), the density function is introduced as an assumption and one cannotexplain why it should have such form. In this thesis, a new analyticalsolar model was proposed and discussed. According to the differences ofthe physical properties, the interior of the Sun can be divided into twozones, one of which is nuclear-fusion zone and the other of which isnon-nuclear-fusion zone. To begin with, based on fundamental laws ofphysics, the general properties of density functions are assumed. Theparameter λ indicates the relative difference of the density between thecenter of the Sun and the interface of the two zones. The parameter αindicates the ratio between the radius of the nuclear-fusion zone and theradius of the Sun. The density function of each zone can be representedby a Taylor series expansion. And, in the new model, only the first twoor three terms of the Taylor series expansion have been taken intoconsideration. After that, the specific expressions of the densityfunctions can be ascertained naturally according to the generalproperties of the density functions. The very essence of the new modelis that we simulate the density function in the nuclear-fusion zone withquadratic function and simulate the density function in thenon-nuclear-fusion zone with line function. If the equation of state and the density function of the Sun are given, we can solve the mass equationand hydrostatic equilibrium equation directly without paying anyattentions to the other two equations. And, it is generally accepted thatthe interior of the Sun can be well described by perfect gas law. Therefore,if we submit the density functions into the three equations, we can getthe analytical solutions of the Sun’s pressure and temperature. The valueof the central density, pressure and temperature can be got, ifconsidering the boundary conditions and giving a certain value of theparameter α and λ. After that, we study the effects of the parameterα and λ on the central thermodynamic parameters of the Sun and discussthe advantages of the new model respectively. The advantages of the newmodel are reflected in getting the analytical solutions of the Sun withoutpaying any attentions to the details of the nuclear fusion. Since the newmodel introduces two adjustable parameters, it is more flexible. Basedon the comparison with the former analytical solar models, we find thatthe new model is much improved in many aspects and it leads to a valueof the central density, pressure and temperature which is in conformitywith the numerical solutions. Moreover, it is possible to derive theanalytical expression of the internal energy of the nuclear fusion zonefrom the new model and it can also substantially simplify the calculationof the solar luminosity. Thus the new model has great significance inunderstanding the physical processes of the Sun’s interior. |
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