A Solve Stellar Structure with Lane-Emden Equation

[wasi-uz-zaman]

TL;DR Summary

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

 

[Helios]

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.

 

[wasi-uz-zaman]

Thanks a lot , it indeed clear my query to a great extent.