Abstract
We present a modification of the original GalIC code, which is designed to generate equilibrium initial conditions for numerical $N$-body models of collisionless, gravitationally bound systems. The proposed approach focuses on improving the procedure for assigning initial particle velocities, which is crucial for ensuring the stability and physical consistency of equilibrium models. Instead of drawing trial velocities from a uniform distribution bounded by the local escape velocity, we introduce a Gaussian-like distribution with compact support. Its dispersion is adapted to the local properties of the system and is derived from the Jeans equations. This choice provides a more physically motivated sampling of velocity space while preserving the bound nature of the system. A detailed comparison with the original GalIC method is performed using isotropic Hernquist models. We demonstrate that the modified algorithm converges significantly faster and produces well-resolved time-averaged mass profiles and velocity distributions. The resulting models show improved convergence toward the target distribution function while maintaining a comparable computational cost per iteration. Overall, the proposed modification provides a more efficient and physically realistic framework for generating equilibrium $N$-body initial conditions in collisionless stellar dynamical systems.