The synthetic rotation curves used a thin exponential disk model for the [OII] surface brightness distribution. In this model, the surface brightness 
as a function of radius from the center of a galaxy is given by the simple equation:
where 
and 
are the central surface brightness and scale length of the disk respectively. Equation 
provides a good fit to the light profiles of spiral disk galaxies. The central surface brightness of an exponential disk is related to the total luminosity 
of the disk by:
Equation is obtained by simply integrating equation from zero to infinity. In real disk galaxies, surface brightness profiles are influenced by complex internal absorption by dust lanes. Internal absorption by dust lanes was not taken into account in the fitting model since dust distributions vary from galaxy to galaxy, and they can only be mapped with HST's high spatial resolution at intermediate redshifts. Every point in the simulated disk was given an observed intensity 
following equation .
