A maximum likelihood method for determining the spatial properties of tidal debris and of the Galactic spheroid is presented. Over small spatial extent, the tidal debris is modeled as a cylinder with density that falls off as a Gaussian with distance from its axis while the smooth component of the stellar spheroid is modeled as a Hernquist profile. The method is designed to use 2.5° wide stripes of data that follow great circles across the sky in which the tidal debris within each stripe is fit separately.

A probabilistic separation technique which allows for the extraction of the optimized tidal streams from the input data set is presented. This technique allows for the creation of separate catalogs for each component fit in the stellar spheroid: one catalog for each piece of tidal debris that fits the density profile of the debris and a single catalog which fits the density profile of the smooth stellar spheroid component. This separation technique is proven to be effective by extracting the simulated tidal debris from the simulated datasets. A method to determine the statistical errors is also developed which utilizes a Hessian matrix to determine the width of the peak at the maximum of the likelihood surface. This error analysis method serves as a means of testing the the algorithm with regard to the simulated datasets as well as determining the statistical errors of the optimizations over observational data. An heuristic method is also defined for determining the numerical error in the optimizations.

The maximum likelihood algorithm is then used to optimize spatial data taken from the Sloan Digital Sky Survey. Stars having the color of blue F turnoff stars 0.1 < (g − r)₀ < 0.3 and (u − g)₀ > 0.4 are extracted from the Sloan Digital Sky Survey database. In the algorithm, the absolute magnitude distribution of F turnoff stars is modeled as a Gaussian distribution, which is an improvement over previous methods which utilize a fixed absolute magnitude M_g0 = 4.2 value to estimate stellar distances. Fifteen stripes were extracted and used to trace the Sagittarius Dwarf Spheroidal galaxy tidal stream. These analyses characterize the Sagittarius tidal stream in both the trailing tidal tail and the leading tidal tail.

Comparing these detections with that of the current models for the Sagittarius dwarf galaxy disruption shows that there is considerable disagreement. The positions along the trailing tidal tail correspond well with the model disruption; however, the leading tidal tail positions differ greatly from those seen in the model disruptions indicating that new models need to be created to better fit the observations.

A new orbital plane of the Sagittarius dwarf galaxy has been calculated, using the fifteen detections of the Sgr stream, with equation −0.207 X+ 0.925Y+ 0.319Z − 1.996 = 0. The leading tidal tail lies along this plane while the Sgr core and the trailing tail do not. A second plane was fit to the three southern detections and the Sagittarius dwarf position and is described by equation 0.024 X + 03990Y + 0.136Z − 1.801 = 0. The leading and trailing tails are fit well with these two planes, respectively. There is approximately a 17° difference in orientation of these two planes and may imply a strong precession of the orbit of the Sagittarius dwarf.

The separation technique was applied to the analyzed data to successfully create a catalog of stars matching the density profile of the Sagittarius tidal streams; however, these stars do not explicitly represent stars drawn from the Sagittarius tidal stream. The stream was then successfully extracted from the data resulting in a much smoother spheroid. Therefore, through the fitting and extraction of all tidal debris in the data using this method, the smooth component of the spheroid may be recovered for uncontaminated study to determine the true structure of the smooth spheroid. (Abstract shortened by UMI.)