Maximum Likelihood Fitting of Tidal Streams with Application to the Sagittarius Dwarf Tidal Tails

We present a maximum likelihood method for determining the spatial properties of tidal debris and of the Galactic spheroid. With this method we characterize Sagittarius debris using stars with the colors of blue F turnoff stars in SDSS stripe 82. The debris is located at (α, δ, R) = (31.37 ◦ ± 0.26 ◦ , 0.0, 29.22 ± 0.20 kpc), with a (spatial) direction given by the unit vector −0.991 ±0.007 kpc, 0.042 ± 0.033 kpc, 0.127±0.046 kpc, in Galactocentric Cartesian coordinates, and with FWHM = 6.74 ± 0.06 kpc. This 2.5 ◦-wide stripe contains 0.892 % as many F turnoff stars as the current Sagittarius dwarf galaxy. Over small spatial extent, the debris is modeled as a cylinder with a density that falls off as a Gaussian with distance from the axis, while the smooth component of the spheroid is modeled with a Hernquist profile. We assume that the absolute magnitude of F turnoff stars is distributed as a Gaussian, which is an improvement over previous methods which fixed the absolute magnitude at ¯ Mg0 = 4.2. The effectiveness and correctness of the algorithm is demonstrated on a simulated set of F turnoff stars created to mimic SDSS stripe 82 data, which shows that we have a much greater accuracy than previous studies. Our algorithm can be applied to divide the stellar data into two catalogs: one which fits the stream density profile and one with the characteristics of the spheroid. This allows us to effectively separate tidal debris from the spheroid population, both facilitating the study of the tidal stream dynamics and providing a test of whether a smooth spheroidal population exists.