Spherical gravitational collapse of annihilating dark matter and the minimum mass of colddark matter black holes

Abstract

Spherical gravitational collapse of a cold gas of annihilating particles involves a competitionbetween two density dependent rates: the free fall rate and the (s-wave) annihilation rate . Thus, there is a critical densityρann above which annihilation proceeds faster than free fall. Gravitational collapse of a cloud of (initial)mass M to a black hole is only possible if , which implies that . We compute the collapse and annihilation of cold, spherical gas clouds witheither a homogeneous density profile or a specific radially dependent profilethat would lead to self-similar collapse if there were no annihilation. Thesecalculations verify that there exists a lower bound to the range of possible black holemasses that can form in cold dark matter (CDM) collapse. For a particle massm and freeze-outtemperature Tf = m/xf, the minimum black hole mass is , where and are degeneracy factors. Moreover, the formation of a black hole is accompanied by the annihilation ofabout Mann of the original mass. Most of the annihilated mass is released in a burst lasting a time∼GMBH,where MBH is the black hole mass when collapse first occurs. A total annihilation luminosity∼1059 erg s−1 could easily bereached, lasting a time ∼100 s. The absence of astronomical observations of such spectacularevents suggests that: (i) the branching ratio for CDM annihilation toe+e− pairs or quarks is , while the branching ratio to is ; or (ii) CDM is not made of annihilating particles, but may be in some non-annihilatingform, such as axions; or (iii) CDM black holes never form.