The most mass of our Milky Way is contained in an inner regionclose to the core with radius R0. Because the mass outside thisinner region is almost constant, the density distribution can bewritten as following (assume a flat Milky Way with height z0):
Ï(r) = p0, when r< or = to R0
0, when r >R0
(b) Derive the expected rotational velocity of the Milky Wayv(r) at a radius r.
(c) Astronomical observations indicate that the rotational velocityfollows a different behaviour:
Draw the expected and observed rotational velocity into the plotbelow:
(d) Scientists believe the reasons for the difference to be darkmatter: Determine the rotational velocity due to dark matter vDM(r) from R0 and draw it into the plot above.
(e) Derive the dark matter mass MDM (r) enclosed in r and explainits distributed.
(f) Explain briefly three theories that provide explanations fordark matter.
(a) Derive an expression for the mass M (r) enclosed within theradius r.
