Hair is complicated: Gravitational waves from stable and unstable boson-star mergers

TL;DR

The paper addresses how head-on mergers of equal-mass solitonic boson-star binaries emit gravitational waves, mapping the behavior across a two-parameter BS model space defined by $|phi_{\rm c}|$ and $\sigma$. Using 2D axisymmetric numerical relativity with the CCZ4 formulation, they show that BS mergers can be significantly louder than comparable BH mergers, with $E_{\rm GW}$ peaking near intermediate compactness before decreasing at high compactness due to reduced deformability; sharp discontinuities and needle-like features in $E_{\rm GW}(|\phi_{\rm c}|)$ arise from transitions between stable and unstable BS branches and from migrating to different BS configurations. The single-star stability analysis, via the mass-amplitude curve $M(|\phi_{\rm c}|)$, informs the merger outcomes, classified into stable, unstable migrating, and unstable collapsing branches, which in turn determine the remnants and GW signatures. The work highlights the need for dedicated boson-star waveform templates and surrogates for GW data analysis, and shows that finite infall time and initial separation can substantially affect the observed energy output and needle structure. Overall, the findings advance our understanding of exotic compact objects in gravitational-wave astronomy and provide a framework for distinguishing BSs from BHs in future detections.

Abstract

We explore the gravitational-wave emission from head-on collisions of equal-mass solitonic boson-star binaries from simulations spanning a two-dimensional parameter space, consisting of the central scalar-field amplitude of the stars and the solitonic potential parameter. We report the gravitational-wave energies emitted by boson-star binaries which, due to their combination of moderately high compactness with significant deformability, we often find to be louder by up to an order of magnitude than analogous black-hole collisions. The dependence of the radiated energy on the boson-star parameters exhibits striking needle-sharp features and discontinuous jumps to the value emitted by black-hole binaries. We explain these features in terms of the solitonic potential and the stability properties of the respective individual stars.

Figures (11)

• Figure 1: Left: The GW energy of the head-on collision of two BSs with a solitonic potential (\ref{['eq:Vsol']}) for $\sigma=0.27825 M_{\rm{Pl}}$ is shown as a function of the BSs' central scalar-field amplitude $|\phi_{\rm c}|$. Blue dots represent binaries completing their infall as BSs and forming a BH or BS at merger whereas red symbols denote systems where each BS collapses to a BH prior to merger. The numbers adjacent to the dots give the final digit of their $|\phi_{\rm c}|$ value. The purple line represents the mass curve $M(|\phi_{\rm c}|)$ for single spherical BSs with central scalar-field amplitude $|\phi_{\rm c}|$. Right: Zoom into the region around the sharp variations of $E_{\rm GW}(|\phi_{\rm c}|)$.
• Figure 2: Convergence analysis of the GW energy for the binary BS configuration $\sigma=0.25\,M_{\rm Pl}$, $|\phi_{\mathrm{c}}|=0.18\,M_{\rm Pl}$. The top panel displays the differences in the energy as a function of time for resolutions $N=256$, $N=512$ and $N=1024$ points with the higher-resolution differences magnified by factors $Q_2=4$ and $Q_3=8$ expected for second and third-order convergence. The bottom panel shows the radiated energy as a function of time for all resolutions together with the result for second-order Richardson extrapolation.
• Figure 3: Comparison of the $(2,0)$ GW mode generated by the head-on collision of equal-mass BSs with $|\phi_{\rm{c}}| = 0.086 M_{\rm{Pl}}$, $\sigma = 0.35 M_{\rm{Pl}}$ using the 2D and 3D versions of the GRChombo code. The inset shows the absolute difference $e_{\rm{diff}}$ between the two signals and demonstrates relative agreement $\lesssim 1\,\%$, well within the uncertainty of the simulations.
• Figure 4: $M(|\phi_{\rm c}|)$ diagrams for the one-parameter families of BSs obtained for $\sigma/M_{\rm Pl}=0.2$, $0.25$, $0.28725$, $0.3$, $0.5$ as well as the mini-BS limit $\sigma \rightarrow \infty$. For each one-parameter family of BS models, globally (perturbatively) stable models are displayed in light (dark) copper color while unstable stars are marked in black. The blue dashed curves, quantified in units of $m^2M_{\rm Pl}^2$ on the right vertical axis, represent the respective potential functions (\ref{['eq:Vsol']}). The vertical dotted lines mark the extrema of the potential (blue) and the mass-amplitude curves (orange).
• Figure 5: Schematic illustration of the $M(|\phi_{\rm c}|)$ curve and the resulting branches for stationary BSs. The local extrema naturally divide the $|\phi_{\rm c}|$ range into regions I and III with $\mathrm{d} M/\mathrm{d} |\phi_{\rm c}|>0$ and regions II and IV with $\mathrm{d} M/\mathrm{d} |\phi_{\rm c}|<0$. BSs of the former regions -- provided they are not extremely compact -- are stable (marked in blue) while the latter regions are exclusively comprised of unstable stars which, when perturbed, either collapse to BHs (red) or migrate to more compact stable BS configurations (yellow). We correspondingly call these branches S (stable), UB (unstable BH) and UM (unstable migrating).