The figure above shows the rotation curve data and model for UGC 5166 that we sa

Question

The figure above shows the rotation curve data and model for UGC 5166 that we saw in class. The different components are as follows: short-dash (green) = bulge, long-dash (dark blue) = stellar disk, dotted (cyan) = gas. dot-dash (magenta) = dark matter, solid (red) = total. Total represents the sum of the masses of the various components, and the masses are not directly proportional to the velocities (as we saw in lecture, or page 110 of your text). This is why the velocities of the various model components at a given radius sum to more than the total velocity. The velocity plotted for each component Ls what would be generated by the mass of that component alone. (a) What is the mass of dark matter within 10 kpc? (b) What fraction of the total mass within 45 kpc Ls dark matter? (c) What is the total mass of the bulge? (d) Assuming an isothermal density distribution, what is the total mass density at 10 kpc (in M_/pc^3)?

Explanation / Answer

Answer:1

As it is the flat rotational curve which means mass increases with increase in radius.

Answer:2

Dark matter mass will also increases as total mass increases because both follow flat rotational curve.

Answer: 3

As bulge is not following the flat rotational curve therefore their mass would be decrease as on increase radius.

Answer:4

For isothermal sphere, following formula can be use;

D= d*(r/e)-2

Where, D= total mass density, d= central density, r= radius, e= scale length

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