Discreteness effects in $N$-body simulations of warm dark matter

Understand

In cosmological $N$-body simulations of warm dark matter, thermal velocities of dark-matter particles are sometimes taken into account by adding random initial velocities to the particles of simulation.

• However, a particle in the $N$-body system represents a huge collection of dark-matter particles, whose average thermal velocity is very close to zero.
• We consider justification of the procedure of adding thermal velocities in $N$-body simulations and build a simple model of their influence on the power spectrum.
• Our model captures the physical effect of suppression of the power spectrum at small wave numbers and also explains its artificial enhancement at large wave numbers, observed in numerical simulations with added thermal velocities.