We present a new method for constraining the Milky Way halo gravitational potential by simultaneously fitting multiple tidal streams. This method requires full three-dimensional positions and velocities for all stars to be fit, but does not require i
dentification of any specific stream or determination of stream membership for any star. We exploit the principle that the action distribution of stream stars is most clustered when the potential used to calculate the actions is closest to the true potential. Clustering is quantified with the Kullback-Leibler Divergence (KLD), which also provides conditional uncertainties for our parameter estimates. We show, for toy Gaia-like data in a spherical isochrone potential, that maximizing the KLD of the action distribution relative to a smoother distribution recovers the true values of the potential parameters. The precision depends on the observational errors and the number of streams in the sample; using KIII giants as tracers, we measure the enclosed mass at the average radius of the sample stars accurate to 3% and precise to 20-40%. Recovery of the scale radius is precise to 25%, and is biased 50% high by the small galactocentric distance range of stars in our mock sample (1-25 kpc, or about three scale radii, with mean 6.5 kpc). About 15 streams, with at least 100 stars per stream, are needed to obtain upper and lower bounds on the enclosed mass and scale radius when observational errors are taken into account; 20-25 streams are required to stabilize the size of the confidence interval. If radial velocities are provided for stars out to 100 kpc (10 scale radii), all parameters can be determined with 10% accuracy and 20% precision (1.3% accuracy in the case of the enclosed mass), underlining the need for ground-based spectroscopic follow-up to complete the radial velocity catalog for faint halo stars observed by Gaia.
The class of tidal features around galaxies known variously as shells or umbrellas comprises debris that has arisen from high-mass-ratio mergers with low impact parameter; the nearly radial orbits of the debris give rise to a unique morphology, a uni
versal density profile, and a tight correlation between positions and velocities of the material. As such they are accessible to analytical treatment, and can provide a relatively clean system for probing the gravitational potential of the host galaxy. In this work we present a simple analytical model that describes the density profile, phase-space distribution, and geometry of a shell, and whose parameters are directly related to physical characteristics of the interacting galaxies. The model makes three assumptions: that their orbit is radial, that the potential of the host is spherical at the shell radii, and that the satellite galaxy had a Maxwellian velocity distribution. We quantify the error introduced by the first two assumptions and show that selecting shells by their appearance on the sky is a sufficient basis to assume that these simplifications are valid. We further demonstrate that (1) given only an image of a shell, the radial gravitational force at the shell edge and the phase-space density of the satellite are jointly constrained, (2) that combining the image with measurements of either point line-of-sight velocities or integrated spectra will yield an independent estimate of the gravitational force at a shell, and (3) that an independent measurement of this force is obtained for each shell observed around a given galaxy, potentially enabling a determination of the galactic mass distribution.
