2nd Week: Properties of Astrophysical Plasmas

The remnant of "Tycho's Supernova", a huge ball of expanding plasma.

Plasma is a state of matter in which the atoms and molecules are so hot, that they have ionized into negatively charged electrons and positively charged ions. The plasma found in the universe, whose physical properties are studied in astrophysics is known as astrophysical plasma. To study the properties of astrophysical plasma the equation of state of matter is very important. Here, we will bring some basic tools from thermodynamics and derive the equation of state for non-relativistic and relativistic plasma.

Basic thermodynamics for quantum systems

The particle density is determined as follows

$n={\frac {N}{V}}=\int _{0}^{\infty }{w(p)f(p)dp}\ ,$

where $f(p)$ is the occupation probability and $w(p)$ is the state density per unit volume.

The energy density is given by

$u={\frac {U}{V}}=\int _{0}^{\infty }{Ew(p)f(p)dp}\ ,$

where $E$ in the energy of the particle.

The pressure is defined as

$P={\frac {1}{3}}\int _{0}^{\infty }{pvw(p)f(p)dp}\ ,$

where $p$ is the value of the momentum of the particle and $v$ is its velocity.