Modelling stellar streams around the Milky Way

Abstract: Stellar streams around the Milky Way (MW) have been observed by wide sky surveys, and studied to understand the mass distribution of the MW. This is because streams are formed by a disruption of a globular cluster or a dwarf galaxy under the influence of the gravitational field of the MW. Moreover, the streams can provide an understanding of dark matter because they orbit in the far outer region of the MW, where dark matter dominates. However, we would not know the gravitational field without dynamical modeling of a stream even though we know the exact positions and velocities of all stars in the stream from the observational data. One of the typical methods in dynamical modeling is using N-body integration, but it is computationally expensive due to the different orbits of each star in the stream. Thus, we modeled a stellar stream with a faster and more flexible method than the N-body integration, called an action-angle formalism, to study the gravitational field of the MW. As a substitute for the observational data, we built an N-body model, which integrated orbits of stars in a globular cluster to form a stellar stream. From the comparison with the N-body model, we validated our stellar stream model based on the action-angle formalism, which we call an action-angle model. The first method to generate the action-angle model was using the eigenvectors of the Hessian matrix to distribute actions for the stream. However, the action distributions of this model did not match with the N-body model. Therefore, we found another method, using a separation vector to split actions along the stream. The action distributions from this method resulted in a good fit with the N-body model, and we also found an appropriate offset between the leading and trailing arms of our stellar stream. We concluded that the second method is suitable to model a stellar stream. Moreover, we compared our action-angle models with the second method to the N-body model in two widely used galactic potentials, named McMillan17 and BT08 in this thesis. While the action-angle model was generated in the BT08 galactic potential model, the N-body model was generated in the McMillan17 galactic potential model. However, the positions and velocities of the N-body model were transformed to actions and angles using the Stäckel fudge in the BT08 potential. The action distributions of the action-angle model and the N-body model were significantly different showing that the action-angle model can be used to find an appropriate galactic potential of the MW. Further, the action-angle model can also determine parameters of the galactic potential. Action-angle models of streams in versions of the McMillan17 potential with varying halo masses were generated and compared to the N-body model in the original McMillan17 model. The comparisons showed that a $\chi^2$-like value, characterizing the difference from the N-body model, becomes lower as the halo mass gets close to the original mass. This means that the positions and velocities of the stream models become similar as the parameter becomes similar to the original value. We also compared action distributions of two action-angle models with low $\chi^2$-like values to the N-body model. The two models have higher $\chi^2$-like values in action distributions than the action-angle model in the original McMillan17 model. Therefore, the action-angle model can be used to study the galactic potential of the real MW from the comparison with the observed stellar streams.