Question

3. The Milky Way's Dark Matter Halo The Milky Way's rotation curve is approximately a constant, v(r) ~220 km/s, for 5 20 kpc, This constant circular velocity cannot be explained by the observed distribution of luminous mass Instead, we propose that the Milky Way is embedded in a roughly spherical dark matter halo. (a) Calculate M(r), the enclosed mass of the spherical dark matter halo as a function of r in the range 5< T < 20 kpc, assuming the contribution from luminous matter is negligible. (b) Let us model the density profile of the dark matter halo with a simple power-law polynomial 0 0 where r0-8 kpc is the distance of the Sun from the center of the Milky Way. Compute and n. (c) What is the density of the dark matter halo in the neighborhood of the Sun? What is the ratio of this density to the critical density, Pe (assume h 0.7)? Do you expect such a high value? (d) Could p(r) maintain the same power-law behavior out to infinity? Why or why not? What does this imply about the behavior of v(r) at large radius? (e) Let us assume that the dark matter halo is made up of grains of mass mg moving at a speed v220 km/s. Estimate how many dark matter grains would hit the Earth every second (leave your answer as a function of mg)

Answer 1

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