Fundamental oscillations as a tool to distinguish boson stars from neutron stars and black holes

TL;DR

This work establishes scaling relations for the fundamental ($f$-)mode frequencies and damping times of massive boson stars in the strong-interaction limit, showing that scaled quantities $f'$ and $\tau'$ are independent of microscopic DM parameters. By expressing $f$-mode properties as functions of mass and compactness, the authors derive universal relations, including $f_{BS}=f'(C)\,M'(C)\,(M_{Pl}^{2}/M_{BS})$, and identify a fixed offset relative to black hole QNMs ($\mathcal{R}_{BS/BH}=0.22$) that provides a smoking-gun GW signature for boson stars. They further quantify maximum frequencies and minimum damping times, yielding a minimum of $N_{min}=406$ $f$-mode oscillations for BSs, and discuss detectability with current and future GW observatories across a broad mass spectrum. These results enhance the capability to distinguish boson stars from neutron stars and black holes through gravitational-wave spectroscopy, especially in post-merger and isolated-burst scenarios.

Abstract

Massive boson stars are self-gravitating configurations of self-interacting scalar fields and can be modeled by a massive scalar field with a quartic self-interaction potential. It has been shown that the equation of state and static structure properties, such as mass and radius, follow scaling relations independent of microscopic dark matter properties. In this work, we demonstrate for the first time that non-radial fundamental ($f$-)mode characteristics also follow a scaling in the strong interaction limit, opening up the outstanding prospect of evaluating the mode properties for boson stars for arbitrary masses spanning the scalar dark matter parameter space allowed by current observations. We provide the scaling relations within full general relativity and obtain the mode characteristics corresponding to the maximum boson star mass configuration. We apply these to determine the $f$-mode properties for boson stars solely as a function of their mass and compactness, which allows distinguishing them from those of neutron stars and black hole quasinormal modes in comparable mass range. In particular, we show that the frequencies are always lower than those of corresponding black holes of the same mass by a factor of 4.5. This provides a smoking gun for the distinguishability of boson stars from other compact objects using gravitational wave observations.

Figures (3)

• Figure 1: The scaled $f$-mode frequency ($f'=f(xM_{Pl})$) for massive BSs in the strong interaction limit ($\Lambda \gg 1$) as a function of scaled mass $M'=M/(xM_{Pl}^3)$ and compactness $C$. These are unique curves and the scaling relations can be used to obtain the corresponding $f-M$ and $f-C$ for any microscopic parameters ($\lambda$, $m$). For a given set of parameters, the $f$-mode frequency corresponding to the maximum compactness configuration is the highest and is given by $f_{max}=f'_{max}/(xM_{Pl}) = 0.21/(xM_{Pl})$.
• Figure 2: The scaled $f$-mode damping time ($\tau'=\tau/(xM_{Pl})$) for massive BSs in the strong interaction limit ($\Lambda \gg 1$) as a function of scaled mass $M'=M/(xM_{Pl}^3)$ and compactness $C$. These are unique curves and the scaling relations can be used to obtain the corresponding $\tau-M$ and $\tau-C$ for any microscopic parameters ($\lambda$, $m$). For a given set of parameters, the $f$-mode damping time corresponding to the maximum compactness configuration is the lowest and is given by $\tau_{min}=\tau'_{min}(xM_{Pl}) = 1900(xM_{Pl})$.
• Figure 3: $f$-mode frequency as a function of mass for (a) NS, (b) stellar-mass BH, and (c) SMBH mass range for massive BSs. The blue region is the part where BSs admit a solution. The blue curve corresponds to the case with maximum compactness. The black line is the corresponding BH QNM frequency Kokkotas1999Berti2009. The BS frequencies satisfy $f_{BS}/f_{BH} < 0.22$ (see text for more details). The silver curves are indicative of the region spanned by NSs Pradhan2022.