Benjamin Burch, Ramanath Cowsik
The distributions of normal matter and of dark matter in the Galaxy are coupled to each other as they both move in the common gravitational potential. In order to fully exploit this interplay and to derive the various properties of dark matter relevant to their direct and indirect detection, we have comprehensively reviewed the astronomical observations of the spatial and velocity distributions of the components of normal matter. We then postulate that the phase-space distribution of dark matter follows a lowered-isothermal form and self-consistently solve Poisson's equation to construct several models for the spatial and velocity distributions of dark matter. In this paper, we compute the total gravitational potential of the normal and dark matter components and investigate their consistency with current observations of the rotation curve of the Galaxy and of the spatial and velocity distributions of blue horizontal-branch and blue straggler stars. Even with this demand of consistency, a large number of models with a range of parameters characterizing the dark matter distribution remain. We find the best choice of parameters, within the range of allowed values, for the surface density of the disk 55 M$_\odot$ pc$^{-2}$, are the following: the dark matter density at the Galactic center $\rho_{DM0}\approx 500$ GeV cm$^{-3}$, the local dark matter density $\rho_{DM}(R_\odot) \approx 0.66$ GeV cm$^{-3}$, and the root-mean-speed of dark matter particles $< v_{DM}^{2}(R_\odot)> ^{1/2}\approx490$ km s$^{-1}$. We also discuss possible astronomical observations that may further limit the range of the allowed models. The predictions of the allowed models for direct and indirect detection will be discussed separately in a companion paper.
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http://arxiv.org/abs/1306.1920
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