A Solve Stellar Structure with Lane-Emden Equation

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The Lane-Emden equation (LEE) can be applied to the Standard Solar Model (SSM) for studying stellar structure, despite the complexities involved. It combines Newtonian gravity with the ideal gas law, using the polytropic index to relate pressure and density. Different polytropic indices yield various solutions known as polytropes, which can be combined to model the layered structure of stars. For example, the Sun features a convection zone with a polytropic index of 3/2 and a radiation zone with an index of 3. Overall, while the SSM is complex, the LEE remains accessible for educational purposes.
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HI, I have a question can Lane-Emden equation be use in SSM( standard stellar model) and overall for the study of stellar structure in todays latest research.
thanks
HI, I have a question can Lane-Emden equation be use in SSM( standard stellar model) and overall for the study of stellar structure in todays latest research.
thanks
 
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SSM is the standard solar model not the standard stellar model. How could there be a standard stellar model if there are so many different kinds of stars?
The Lane-Emden equation is an equation that merges Newtonian gravity with the ideal gas law. It is instructive to study its derivation. The critical parameter is called the polytropic index, used to relate pressure to density. For different polytropic indices, we get solutions to LEE called polytropes. A simple star model would assume a single index throughout the star, however the innards of stars are usually stratified into layers with different indices, so we have to create a composite polytrope, and graft different polytropes together smoothly. The Sun has a convection zone ( index = 3/2 ) and a radiation zone ( index = 3 ). The polytropic index is half the degrees of freedom of the substance.
The SSM is likely very complicated but the LEE is within the grasp of a college physics student.
 
Thanks a lot , it indeed clear my query to a great extent.
 

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