Speaker
Mr
Sayantan Auddy
(Student)
Description
We develop an analytic formulation to find the internal structure of sub-stellar objects. This yields a value for a minimum stellar mass that denotes the boundary between brown dwarfs and stars. Our method employs an exact expression for the pressure of an ideal non-relativistic Fermi gas at finite temperature, meaning that the parameter $\psi$ is non zero. Our model gives a more accurate pressure than using the purely degenerate ($\psi =0$ ) limit. Integration of the Fermi distribution to yield an equation of state can be accomplished using the polylogrithm functions. This equation of state is used to solve the Lane-Emden equation to obtain the surface luminosity of a brown dwarf. On equating it with the luminosity for nuclear burning we find the maximum mass for a brown dwarf, $0.07M_o$. This result is in agreement with the results of the numerical models, but it is simple and provides maximum insight into the physics.
Primary author
Mr
Sayantan Auddy
(Student)
Co-authors
Dr
S.R. Valluri
(Professor)
Dr
Shantanu Basu
(Professor)
