# 2014 CAP Congress / Congrès de l'ACP 2014

15-20 June 2014
Laurentian University / Université Laurentienne
America/Toronto timezone
Welcome to the 2014 CAP Congress! / Bienvenue au 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)

### C-309

#### Laurentian University / Université Laurentienne

Sudbury, Ontario
Oral (Student, In Competition) / Orale (Étudiant(e), inscrit à la compétition) Theoretical Physics / Physique théorique (DTP-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.

### Primary author

Mr Sayantan Auddy (Student)

### Co-authors

Dr S.R. Valluri (Professor) Dr Shantanu Basu (Professor)

 Slides