DUE TUESDAY MARCH 21 IN CLASS.

The Milky Way's Rotation Curve

In Sofue (2013, "Rotation Curve and Mass Distribution in the Galactic Center -- from Black Hole to Entire Galaxy") you will find a table (Table 3) that lists values for the rotation curve of the Milky Way along with their error bars. This table can be downloaded in ascii format from the author's website (2nd file in list) where the velocity is in km/s and the radius is in kpc. Note that Sofue has taken R_0 = 8.0 kpc and V_0 = 200 km/s.

a) Plot the Milky Way's rotation curve along with its error bars out to 20 kpc radius [FIG. 1]

b) Refer to Sofue (2013, "The Mass Distribution and Rotation Curve in the Galaxy". In particular, read sections 3.2, 3.3, 3.4, and 4.1.1. Note that Table 2 has been provided to you as a hand-out in an earlier class. To model a rotation curve, one should ideally enter a potential for each component and work out the contributions to the rotation curve for each. However, we will take an approach that starts with a surface mass distribution (except for the halo) as described in these sections.

c) Find a fit (by eye is okay) to the total rotation curve using bulge and disk components only. If you can handle this with all of the mathematics provided, then please do so. However, this is not meant to be solely an exercise in your analytic and coding skills. Therefore, I will accept some approximations. For example, for the bulge, you may use Eqns. 27, 28 and 30. For the disk, you may wish to eschew Eqn. 33 and instead use a simple form for the disk that was first proposed by Lequeux in 1983, namely M(R) = 0.6 R[V(R)^2]/G. (Note, though, that the more your equations depart from those specified, the farther will be your fitted parameters from those listed in Table 2.) Specify the equations and parameters that you've used and plot the result on a single graph showing the contribution of each component as well as the total [FIG. 2].

d) Repeat part c) but now include the dark halo as well [FIG. 3].

e) If R_0 were increased, how would the results change? If V_0 were increased, how would the results change?

f) Write a brief paragraph summarizing your results and conclusions from the above exercise.

In Sofue (2013, "Rotation Curve and Mass Distribution in the Galactic Center -- from Black Hole to Entire Galaxy") you will find a table (Table 3) that lists values for the rotation curve of the Milky Way along with their error bars. This table can be downloaded in ascii format from the author's website (2nd file in list) where the velocity is in km/s and the radius is in kpc. Note that Sofue has taken R_0 = 8.0 kpc and V_0 = 200 km/s.

a) Plot the Milky Way's rotation curve along with its error bars out to 20 kpc radius [FIG. 1]

b) Refer to Sofue (2013, "The Mass Distribution and Rotation Curve in the Galaxy". In particular, read sections 3.2, 3.3, 3.4, and 4.1.1. Note that Table 2 has been provided to you as a hand-out in an earlier class. To model a rotation curve, one should ideally enter a potential for each component and work out the contributions to the rotation curve for each. However, we will take an approach that starts with a surface mass distribution (except for the halo) as described in these sections.

c) Find a fit (by eye is okay) to the total rotation curve using bulge and disk components only. If you can handle this with all of the mathematics provided, then please do so. However, this is not meant to be solely an exercise in your analytic and coding skills. Therefore, I will accept some approximations. For example, for the bulge, you may use Eqns. 27, 28 and 30. For the disk, you may wish to eschew Eqn. 33 and instead use a simple form for the disk that was first proposed by Lequeux in 1983, namely M(R) = 0.6 R[V(R)^2]/G. (Note, though, that the more your equations depart from those specified, the farther will be your fitted parameters from those listed in Table 2.) Specify the equations and parameters that you've used and plot the result on a single graph showing the contribution of each component as well as the total [FIG. 2].

d) Repeat part c) but now include the dark halo as well [FIG. 3].

e) If R_0 were increased, how would the results change? If V_0 were increased, how would the results change?

f) Write a brief paragraph summarizing your results and conclusions from the above exercise.