The figure below shows the rotation curves of galaxies NGC 2403 and NGC 2841, from Begeman et al. 1991 (MNRAS, 249, 523). The data points represent the measured rotation curves, while the dotted, dashed, and dash-dotted plots are models for the stellar and dark matter content of the galaxies. From the last data point in each rotation curve, use the expression for the orbital velocity to estimate the total enclosed mass, up to that point, in each galaxy. Express the result in M. Are these masses large or small? How do they compare to the stellar masses that you derived in the previous problem? What is making up the difference in mass?

200 400 NGC 2403 NGC 2841 300 ULL Ver (km s') 100 Vet (km s') 200 100 1 0 1 30 10 40 50 10 20 Radius (kpc) 20 30 Radius (kpc) 200 400 NGC 2403 NGC 2841 300 ULL Ver (km s') 100 Vet (km s') 200 100 1 0 1 30 10 40 50 10 20 Radius (kpc) 20 30 Radius (kpc)