The mass distribution and gravitational potential of the Milky Way

We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to \(\sim N^2\) for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation and API. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the MIT License.

We use N-body simulations to investigate the structure of dark halos in the standard Cold Dark Matter cosmogony. Halos are excised from simulations of cosmologically representative regions and are resimulated individually at high resolution. We study objects with masses ranging from those of dwarf galaxy halos to those of rich galaxy clusters. The spherically averaged density profiles of all our halos can be fit over two decades in radius by scaling a simple ``universal'' profile. The characteristic overdensity of a halo, or equivalently its concentration, correlates strongly with halo mass in a way which reflects the mass dependence of the epoch of halo formation. Halo profiles are approximately isothermal over a large range in radii, but are significantly shallower than \(r^{-2}\) near the center and steeper than \(r^{-2}\) near the virial radius. Matching the observed rotation curves of disk galaxies requires disk mass-to-light ratios to increase systematically with luminosity. Further, it suggests that the halos of bright galaxies depend only weakly on galaxy luminosity and have circular velocities significantly lower than the disk rotation speed. This may explain why luminosity and dynamics are uncorrelated in observed samples of binary galaxies and of satellite/spiral systems. For galaxy clusters, our halo models are consistent both with the presence of giant arcs and with the observed structure of the intracluster medium, and they suggest a simple explanation for the disparate estimates of cluster core radii found by previous authors. Our results also highlight two shortcomings of the CDM model. CDM halos are too concentrated to be consistent with the halo parameters inferred for dwarf irregulars, and the predicted abundance of galaxy halos is larger than the observed abundance of galaxies.

The cold dark matter model has become the leading theoretical paradigm for the formation of structure in the Universe. Together with the theory of cosmic inflation, this model makes a clear prediction for the initial conditions for structure formation and predicts that structures grow hierarchically through gravitational instability. Testing this model requires that the precise measurements delivered by galaxy surveys can be compared to robust and equally precise theoretical calculations. Here we present a novel framework for the quantitative physical interpretation of such surveys. This combines the largest simulation of the growth of dark matter structure ever carried out with new techniques for following the formation and evolution of the visible components. We show that baryon-induced features in the initial conditions of the Universe are reflected in distorted form in the low-redshift galaxy distribution, an effect that can be used to constrain the nature of dark energy with next generation surveys.