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Estimates of the density of dark matter near the center of the Galaxy

1987; American Physical Society; Volume: 35; Issue: 12 Linguagem: Inglês

10.1103/physrevd.35.3695

1538-4500

James R. Ipser, P. Sikivie,

Astrophysics and Cosmic Phenomena

It was recently pointed out by Silk and Bloemen that the COS-B satellite observations of the cosmic \ensuremath{\gamma}-ray flux are sensitive to \ensuremath{\gamma} rays from dark-matter annihilation at the center of the Galaxy if the dark matter is composed of stable weakly interacting particles such as photinos, Higgs fermions, scalar neutrinos, or heavy neutrinos and if the dark-matter content of the central component of the Galaxy is more than about 2%. Motivated by this remark, we have studied how much dark matter is expected to be near the center of the Galaxy under two different assumptions which we call the isothermal and adiabatic models. In the first model, the dark matter is assumed to be isothermally distributed. In the second model, it is assumed that while the central component forms the adiabatic invariant for the radial motion of each dark-matter particle, as well as its angular momentum, is conserved. In the isothermal model, the typical dark-matter density enhancement near the center of the Galaxy is large enough to make the COS-B data sensitive to the hypothesis that the dark matter is composed of stable weakly interacting particles, whereas in the adiabatic model it is about a factor of 5 too small. We show that in the adiabatic model the density of dark-matter particles near the center of the Galaxy is proportional to [-${\ensuremath{\varphi}}_{c}$(r${)]}^{3/2}$ where ${\ensuremath{\varphi}}_{c}$(r) is the gravitational potential due to the central component.