Nonrelativistic Boson stars as N-body quantum systems

In this work, we show that the structural configuration of a collection of generic nonrelativistic bosons forming a gravitationally bound Bose-Einstein condensate can be interpreted as a nonrelativistic boson star. With the approach followed in this work, we can analyze with a concise and straightforward procedure the equilibrium properties of nonrelativistic boson stars viewed as a Bose-Einstein condensate. The system's behavior is obtained by analyzing its fundamental constituent properties, i.e. the associated single-particle properties. Additionally, we show that by expressing the corresponding Newtonian gravitational potential, under certain circumstances, as a harmonic oscillator potential one, we can describe the conditions in which the nonrelativistic boson star can form equilibrium configurations. In order to analyze the boson star's structural configuration, we employ four different ansatzes commonly used in the literature. These ansatzes allow us to compare the cloud's structural properties of the boson star, which leads us to obtain several gravitational equilibrium configurations from compact objects matching the size of typical stars to gigantic systems comparable to the size of galaxy cluster dark matter halos. Finally, we show that these ansatzes predict, qualitatively speaking, the same structural and gravitational equilibrium configurations for different values of the parameters involved.