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

TL;DR

The paper investigates condensate dark stars formed from a dilute, ultracold Bose gas under general relativity, incorporating beyond-mean-field Lee-Huang-Yang corrections to the equation of state. Using the TOV equations together with a relativistic tidal Love-number formalism, the authors quantify how quantum fluctuations modify mass-radius relations, compactness, and tidal deformabilities, for two representative particle-physics models. They find that the LHY corrections can raise the maximum stellar mass and radius, reduce the factor of compactness $C$, and increase the tidal Love number at fixed $C$, with the magnitude of the effect depending on the underlying EoS. The work highlights the significance of quantum fluctuations in macroscopic gravitational objects and lays the groundwork for future studies on oscillations, rotation, and universal relations in condensate dark stars.

Abstract

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.

Figures (4)

• Figure 1: Mass-to-radius relationships (top panel) and factor of compactness versus stellar mass (lower panel) for model A ($m=0.50~GeV, \; a_s=0.10~fm$). Dashed curves correspond to the usual polytrope $p=K \rho^2$, while the solid curves correspond to the EoS including the LHY correction.
• Figure 2: Stellar mass versus central energy density (in units of $1/K$, top panel) and tidal Love numbers versus compactness (lower panel) for model A ($m=0.50~GeV, \; a_s=0.10~fm$). Dashed curves correspond to the usual polytrope $p=K \rho^2$, while the solid curves correspond to the EoS including the LHY correction.
• Figure 3: Mass-to-radius relationships (top panel) and factor of compactness versus stellar mass (lower panel) for model B ($m=0.45~GeV, \; a_s=0.11~fm$). Dashed curves correspond to the usual polytrope $p=K \rho^2$, while the solid curves correspond to the EoS including the LHY correction.
• Figure 4: Stellar mass versus central energy density (in units of $1/K$, top panel) and tidal Love numbers versus compactness (lower panel) for model B ($m=0.45~GeV, \; a_s=0.11~fm$). The dashed curve corresponds to the usual polytrope $p=K \rho^2$, while the solid curve corresponds to the EoS including the LHY correction.