Condensate Dark Stars beyond the Mean-Field Approximation: The Lee-Huang-Yang correction

We study structural properties of self-gravitating fluid spheres made of a dilute, homogeneous and ultracold Bose gas assuming repulsive, short-range interactions. For the first time we include the Lee-Huang-Yang correction to the usual polytropic equation-of-state of index $n=1$, which goes beyond the Hartree mean-field approximation taking into account quantum fluctuations. We find that the correction has a considerable impact on the M-R relationships and other properties of condensate dark stars, such as factor of compactness and tidal Love numbers. The impact is more significant for equation-of-states that support larger highest stellar masses.