Gravitational waves from dark matter collapse in a star

Abstract

We investigate the collapse of clusters of weakly interacting massive particles (WIMPs) in the core of a Sun-like star and the possible formation of mini-black holes and the emission of gravitational waves. When the number of WIMPs is small, thermal pressure balances the WIMP cluster's self gravity. If the number of WIMPs is larger than a critical number, thermal pressure cannot balance gravity and the cluster contracts. If WIMPs are collisionless and bosonic, the cluster collapses directly to form a mini-black hole. For fermionic WIMPs, the cluster contracts until it is sustained by Fermi pressure, forming a small compact object. If the fermionic WIMP mass is smaller than $4\times 10^2$ GeV, the radius of the compact object is larger than its Schwarzschild radius and Fermi pressure temporally sustains its self gravity, halting the formation of a black hole. If the fermionic WIMP mass is larger than $4\times 10^2$ GeV, the radius is smaller than its Schwarzschild radius and the compact object becomes a mini-black hole. If the WIMP mass is 1 TeV, the size of the black hole will be approximately 2.5 cm and ultra high frequency gravitational waves will be emitted during black hole formation. The central frequency $f_c$ of ringdown gravitational waves emitted from the black hole will be approximately 2 GHz. To detect the ringdown gravitational waves, the detector's noise must be below $\sqrt{S_h(f_c)}\approx 10^{-30}/\sqrt{\rm Hz}$.