Figure 3.
The rotation curve of NGC 2403 derived from the diffusion model, km/sec vs. kpc. The squares are the observed velocities of rotation taken from the study by Albada and Sancisi (5). The fine dots are the calculation of the rotation curve expected from the diffusion model. The mass distribution for stars and gas was derived from the curve on figure 4 from the study of Albada and Sancisi (5). Mass was added near the center for agreement with the inner part of the rotation curve in a step that is essentially model independent. From this mass distribution (136 values) the rotation curve was calculated step-by-step: V(R) = sum (j = n to 136)[sqrt (m(j)/R + m(j)/2)], for 260 values of the radius R, the sum being taken from each mass element or shell, outwards. This form is derived from Eq. 3 as V2/r = Gm r−2 (1 + br/p)erfc[r/a(pct)0.5] where the erfc term is unity at these distances. The mean free path is taken to be 5 kpc and the constant b = 3.1. Figure 4 of Albada and Sancisi (5) shows a comparably good fit to the rotation curve, which is achieved by adding in an arbitrary curve for the mass of dark matter. Here, there is no such freedom and the parameters are the mean free path (5 kpc) and the mass of the galaxy NGC 2403, which, from the asymptotic value of V = 132 km/sec, is 6.5 E9 solar masses, which agrees with a brightness estimate (6).