# What polytropic index should I use for spherical accretion onto a degenerate object?

Take a degenerate object, such as a white dwarf, embedded in a gas cloud. The cloud is small enough such that the size of the object is non-negligible in comparison - that is, the white dwarf takes up a decent amount of space in the cloud. The white dwarf is stationary and is not rotating.

If I were the model the accreting gas as a polytrope - i.e. as $$p=K \rho^{1+\frac{1}{n}}$$ where $p$ is pressure, $\rho$ is density, $K$ is a constant and $n$ is the polytropic index - what value of $n$ should I choose?

Anyway for spherically symmetric accretion onto an object, one approach is to make an assumption that no heat is conducted or radiated away, in which case the adiabatic index is 5/3 for a perfect monatomic gas ($n=3/2$).