THE PLANNING AND ANALYSIS OF GALACTIC DISK TRACER OBSERVATIONS

The Bahcall method of determining the Galactic disk potential (and so its missing mass) from tracer observations ≲ 1 kpc is analyzed systematically. A mathematical measure of the effectiveness of observations is introduced and is used to determine the optimal observation strategy and optimal binning of the data. The following rules of thumb are demonstrated. First, every effort should be made to increase the " effective scale height of the observations" (denned precisely in the text) so long as this parameter is below 1, but there is little to be gained by increasing it above 1. Second, given the choice between doing additional velocity and additional distance measurements, the former is far more productive. Third, distance errors will be the main uncertainty unless the mean (not root mean square) distance error is reduced below 0.06(N/500)-1/2, where N is the number of tracers. Fourth, tracer data should be divided into about four bins rather than the approximately 10 bins used by Bahcall. Fifth, the effectiveness of a survey deteriorates greatly the more the tracers deviate from being isothermal. Sixth, a few hundred tracers are sufficient to determine whether the disk has a substantial quantity of missing matter, but script O sign(104) are required to make statements about the velocity dispersion of the missing component. However, this latter number can be reduced to ∼ 2000 if the tracers are drawn from two distinct populations with substantially different velocity dispersions.