  Cold stellar streams---produced by tidal disruptions of clusters---are
long-lived, coherent dynamical features in the halo of the Milky Way. Due to
their different ages and different positions in phase space, different streams
tell us different things about the Galaxy. Here we employ a Cramer--Rao (CRLB)
or Fisher-matrix approach to understand the quantitative information content in
eleven known streams (ATLAS, GD-1, Hermus, Kwando, Orinoco, PS1A, PS1C, PS1D,
PS1E, Sangarius and Triangulum). This approach depends on a generative model,
which we have developed previously, and which permits calculation of
derivatives of predicted stream properties with respect to Galaxy and stream
parameters. We find that in simple analytic models of the Milky Way, streams on
eccentric orbits contain the most information about the halo shape. For each
stream, there are near-degeneracies between dark-matter-halo properties and
parameters of the bulge, the disk, and the stream progenitor, but simultaneous
fitting of multiple streams will constrain all parameters at the percent level.
At this precision, simulated dark matter halos deviate from simple analytic
parametrizations, so we add an expansion of basis functions to give the
gravitational potential more freedom. As freedom increases, the information
about the halo reduces overall, and it becomes more localized to the current
position of the stream. In the limit of high model freedom, a stellar stream
appears to measure the local acceleration at its current position; this
motivates thinking about future non-parametric approaches. The CRLB formalism
also permits us to assess the value of future measurements of stellar
velocities, distances, and proper motions. We show that kinematic measurements
of stream stars are essential for producing competitive constraints on the
distribution of dark matter, which bodes well for stream studies in the age of
Gaia.
