Maximize correlation between $\Theta$ and $\Omega$ structure of stream

Maximizes the mutual information of the action distribution of stream stars to determine the best-fit potential.

Needs:

• full phase-space coordinates for stars in more than one stream (preferably at least 10-15, depending on observational errors)
• at least ~100 stars in the largest stream
• Enough stars per stream that the largest stream does not solely determine the fit
• the major component of the sample to be accreted streams (i.e. background must be <50%)

Does not need:

• number of streams in sample or stream membership assignments
• all stars to be in streams
• complete sampling of any particular stream

Steps:

1. Compute actions from phase-space coordinates given a potential
2. Maximize mutual information by varying potential to obtain best-fit
3. Use the KLD again to compare action distribution in best-fit potential to distribution in other potentials to get uncertainty

From present-day position & velocity of the progenitor of interest, integrate the orbit of a cluster particle of a given mass in a test potential backwards for several Gyr. Then integrate forward to present time. While doing so, generate test stream particles. Compare the present-day distribution of stream test particles to the observations. Define likelihood, calculate likelihood, put in MCMC, stirr, ready.

Need:

• Observations of progenitor (can have missing data): l,b,dist.,μ,RV
• Constraint on the mass of the progenitor
• Observations of a sample of stars stripped from the progenitor: (again) l,b,dist.,μ,RV
• A flag to specify which tail (leading/trailing) each star belongs to

Integrate orbits of progenitor and stars back in time; the stars recombine into the progenitor in the correct potential, but their orbits diverge in an incorrect potential. See Price-Whelan & Johnston (2013) for the basic idea, or Price-Whelan et al. (2014) for the new idea for accounting for observational uncertainties.

Minimize scatter/entropy of tidal streams.

We model the stream as though it is generated by the orbit of a single particle in a fixed potential. We find the full PDF of a particular model using a Bayesian analysis. See http://adsabs.harvard.edu/abs/2014arXiv1401.4070D for a full description of the technique.

Look at evolution of galaxy potential and streams. For now: look at “progenitor” orbit compared with stream.

• Stream finder: modified great circle cell method (Mateu et al 11)
• Method for revocering local potential based on energy conservation

Working on recovery of stellar streams using a phase-space halo finder ROCKSTAR (Behroozi et al. 2013), with some parameters modified.