The Missing Massive Sector: Massive Boson Stars -- Stability and GW Emission in Head-on Mergers

TL;DR

The study investigates stability and gravitational-wave signatures of quartically self-interacting massive boson stars in head-on mergers. It constructs equilibrium sequences $M(|\phi_c|)$ for several $\lambda$ and evolves them using a 2D Cartoon reduction in GRChombo, analyzing stability and collision outcomes through $E_{\rm GW}$ and compactness $\mathcal{C}$. Key findings include stability changes only at the first mass maximum, absence of a second stable window, and a rich collision phenomenology with BS post-merger, BH post-merger, and BH pre-merger channels; high-$\lambda$ cases exhibit a non-monotonic $E_{\rm GW}/M_{\rm TOT}$ in the BH pre-merger branch linked to near-critical dynamics. The work provides an extensive waveform catalogue to enable AI-assisted initial-data improvements and rapid surrogate models across an extended parameter space, advancing gravitational-wave searches for exotic compact objects.

Abstract

We investigate quartically self-interacting massive boson stars by constructing equilibrium sequences and performing dynamical evolutions. The mass curve $M(|φ_c|)$ along these sequences develops multiple extrema, yet stability changes only at the first maximum; configurations beyond it become highly compact and collapse under numerically induced perturbations, with near-critical models displaying a short-lived double-dive behaviour. Head-on collisions of equal-mass stars yield three distinct outcomes - boson star remnants, black hole formation at contact, and collapse of each star to a black hole prior to contact. The associated gravitational-wave energies reflect the competition between increasing compactness and decreasing tidal deformability, and at large self-interaction strengths the collapse-before-contact branch exhibits a pronounced non-monotonic structure. The simulations reported here constitute a substantial catalogue of initial conditions and waveforms, providing a natural basis for neural-network techniques aimed at improving boson star initial data and constructing surrogate models capable of rapidly predicting gravitational-wave signals across an extended parameter space.

Figures (7)

• Figure 1: Illustration of the evolution scheme used in the two-dimensional boson star code. The evolution is performed in Cartesian coordinates $(x, y, z)$. In the setup shown, two boson stars undergo a head-on collision in the region where $x > 0$.
• Figure 2: Mass curves $M(|\phi_{\rm c}|)$ and compactness curves $\mathcal{C}(|\phi_{\rm c}|)$ for $\lambda = 10, 50, 100,$ and $300$. The extrema of the mass curves are used to divide each panel into several regions: region I denotes the first segment with $\mathrm{d}M/\mathrm{d}|\phi_{\rm c}| > 0$, region II the first segment with $\mathrm{d}M/\mathrm{d}|\phi_{\rm c}| < 0$, region III the second segment with $\mathrm{d}M/\mathrm{d}|\phi_{\rm c}| > 0$, and region IV (for $\lambda = 100, 300$) the second segment with $\mathrm{d}M/\mathrm{d}|\phi_{\rm c}| < 0$. Different regions are highlighted by different background colours. The numbers indicated in the panels denote the compactness $\mathcal{C}$ at the boundary between regions II and III.
• Figure 3: The $M(|\phi_{\rm c}|)$ curves for $\lambda = 10,~50,~100,~300$, colour–coded by the compactness $\mathcal{C}$. The left vertical axis shows the migration/collapse time. Coloured symbols indicate the stability class of selected configurations: blue markers denote stable S-branch stars, red markers UB models that collapse to a black hole. Orange markers indicate special UB-type boson stars that collapse to a black hole after undergoing two dives. The vertical position of each symbol encodes the corresponding collapse or migration time; for the special orange markers the time is defined as the instant when the central amplitude $|\phi_c|$ has changed by $1\%$. The number adjacent to each symbol indicates the last digit of the associated $|\phi_{\rm c}|$ value.
• Figure 4: Evolution of the central amplitude for $\lambda=300$, $|\phi_{\rm c}|= 0.05$ (left panel), and $\lambda=500$, $|\phi_{\rm c}|= 0.04$ (right panel). For each case, the upper subplot shows the full time evolution, while the lower subplot presents a zoomed–in view of the "double–dive" behaviour. The red labels indicate the coordinate times at which the amplitude reaches the bottom of each "valley".
• Figure 5: Head-on collisions of massive boson stars for four values of the self-coupling parameter $\lambda$. Green markers denote binaries that merge into a boson star remnant (BS post-merger), blue markers correspond to direct formation of a single black hole (BH post-merger), and red markers represent cases in which each star collapses individually prior to contact, followed by a subsequent BH--BH merger (BH pre-merger). The vertical axis shows the total emitted gravitational-wave energy, normalized by the initial total mass, $E_{\rm GW}/M_{\rm TOT}$. The dashed curve shows the sequence $M(|\phi_{\rm c}|)$ as a function of the central field amplitude $|\phi_{\rm c}|$, with the colour of the curve encoding the compactness of the corresponding equilibrium solution. The panels on the right provide zoomed-in views of the panels on the left.