Decay of Boson Stars with Application to Glueballs and Other Real Scalars

Abstract

One of the most interesting candidates for dark matter are massive real scalar particles. A well-motivated example is from a pure Yang-Mills hidden sector, which locks up into glueballs in the early universe. The lightest glueball states are scalar particles and can act as a form of bosonic dark matter. If self-interactions are repulsive this can potentially lead to very massive boson stars, where the inward gravitational force is balanced by the repulsive self-interaction. This can also arise from elementary real scalars with a regular potential. In the literature it has been claimed that this allows for astrophysically significant boson stars with high compactness, which could undergo binary mergers and generate detectable gravitational waves. Here we show that previous analyses did not take into proper account $3 \to 2$ and $4 \to 2$ quantum mechanical annihilation processes in the core of the star, while other work misinterpreted the classical $3 \to 1$ process. In this work, we compute the annihilation rates, finding that massive stars will rapidly decay from the $3 \to 2$ or $4 \to 2$ processes (while the $3 \to 1$ process is typically small). Using the Einstein-Klein-Gordon equations, we also estimate the binding energy of these stars, showing that even the densest stars do not have quite enough binding energy to prevent annihilations. For such boson stars to live for the current age of the universe and to be consistent with bounds on dark matter scattering in galaxies, we find the following upper bound on their mass for $O(1)$ self-interaction couplings: $M_*<10^{-18}M_{sun}$ when $3 \to 2$ processes are allowed and $M_*<10^{-11}M_{sun}$ when only $4 \to 2$ processes are allowed. We also estimate destabilization from parametric resonance which can considerably constrain the phase space further. Furthermore, such stars are required to have very small compactness to be long lived.