2014 CAP Congress / Congrès de l'ACP 2014

Analytic derivation of the substellar mass limit for a non-zero degeneracy parameter

17 Jun 2014, 15:00

15m

C-309 (Laurentian University / Université Laurentienne)

Oral (Student, In Competition) / Orale (Étudiant(e), inscrit à la compétition) Theoretical Physics / Physique théorique (DTP-DPT) (T2-1) Theoretical Astrophysics - DTP / Astrophysique théorique - DPT

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.

Presentation materials

Slides

Analytic_derivation_of_the_sub_stellar_mass_limit.pdf