Spherical Einstein-Friedberg-Lee-Sirlin boson stars: Self-interacting solutions and their astrophysical appearance

TL;DR

We investigate static, spherically symmetric boson stars in the self-interacting Einstein-Friedberg-Lee-Sirlin (E-FLS) model, featuring a quartic self-interaction for the complex field. Using COLSYS to solve the coupled Einstein-scalar equations, we map how the ADM mass, particle number, and stability indicators vary with the real-field mass parameter $\mu$, the self-interaction strength $\lambda$, and the central complex-field value $\phi_0$, finding that positive $\lambda$ raises the maximum mass and increases compactness, even allowing $\mu=0$ configurations to exist with large radii. Timelike and null geodesics reveal that only sufficiently compact configurations (EFLS5, EFLS6) can support light rings, influencing the lensing and shadow structure. Backward ray-tracing of optically thick and thin disks shows that these self-interacting E-FLS stars can produce shadows and photon-ring features that mimic black holes, with shadow sizes scaling with $\lambda$ and mass, suggesting potential observational signatures in current and upcoming surveys.

Abstract

We investigate boson stars within the framework of the self-interacting Einstein-Friedberg-Lee-Sirlin (E-FLS) model, constituted by a complex scalar field with a quartic self-interaction and a real scalar field. Our analysis explores the family of static solutions across a broad range of parameters, including the self-interaction of the complex scalar field. We obtain that positive self-interaction terms increase the maximum mass and compactness of E-FLS stars, allowing them to reach masses comparable to the Chandrasekhar limit without the need of ultralight bosonic masses. Moreover, in the limit where the real scalar field becomes massless, the solutions present larger effective radii and allow a broader range of stable solutions. Astrophysical images, generated via backward ray-tracing, show that these compact, self-interacting E-FLS stars produce strong gravitational lensing, yielding shadows that could visually mimic black holes, thus providing potential observational signatures detectable in ongoing electromagnetic surveys.

Figures (16)

• Figure 1: The complex scalar field at the origin $\phi_{0}$ as a function of the eigenvalues $\omega$ for six different values of the self-interaction term $\lambda$. We also vary the value of the mass parameter $\mu$ to investigate the impact on self-interacting E-FLS stars solutions.
• Figure 2: The total mass $M$ of E-FLS stars, for different values of $\mu$ and $\lambda$, as a function of the normalized frequency ${\omega}$. Each point in these panels represents a self-interacting E-FLS star solution with a given $\phi_0$. The set of solutions with negative values of $\lambda$ are the ones with smaller maximum total mass. Increasing the value of $\lambda$ leads to an increase in the total mass limit of the stars.
• Figure 3: The total mass $M$ as a function of the effective radius for five different values of the self-interaction parameter $\lambda$, considering $\mu=0$. Increasing the value of $\lambda$ also increases the total mass of E-FLS stars.
• Figure 4: The total mass $M$ and the number of particles $N$ for self-interacting E-FLS stars as a function of the field at the origin $\phi_{0}$, considering four different combinations of $\mu$ and $\lambda$. The regions where the number of particles $N$ is larger than the values of $M$ describe stable solutions.
• Figure 5: The inverse compactness as a function of the oscillation frequency for distinct values of the self-interaction parameter $\lambda$ and $\mu=0$. As we increase the values of $\lambda$, we obtain a set of solutions that are more compact than the ones with smaller $\lambda$.