Modelling stellar streams around the Milky Way
(2021) In Lund Observatory Examensarbeten ASTM31 20211Lund Observatory
 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 Nbody integration, but it is computationally... (More)
 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 Nbody 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 Nbody integration, called an actionangle formalism, to study the gravitational field of the MW. As a substitute for the observational data, we built an Nbody model, which integrated orbits of stars in a globular cluster to form a stellar stream. From the comparison with the Nbody model, we validated our stellar stream model based on the actionangle formalism, which we call an actionangle model. The first method to generate the actionangle 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 Nbody 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 Nbody 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 actionangle models with the second method to the Nbody model in two widely used galactic potentials, named McMillan17 and BT08 in this thesis. While the actionangle model was generated in the BT08 galactic potential model, the Nbody model was generated in the McMillan17 galactic potential model. However, the positions and velocities of the Nbody model were transformed to actions and angles using the Stäckel fudge in the BT08 potential. The action distributions of the actionangle model and the Nbody model were significantly different showing that the actionangle model can be used to find an appropriate galactic potential of the MW. Further, the actionangle model can also determine parameters of the galactic potential. Actionangle models of streams in versions of the McMillan17 potential with varying halo masses were generated and compared to the Nbody model in the original McMillan17 model. The comparisons showed that a $\chi^2$like value, characterizing the difference from the Nbody 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 actionangle models with low $\chi^2$like values to the Nbody model. The two models have higher $\chi^2$like values in action distributions than the actionangle model in the original McMillan17 model. Therefore, the actionangle model can be used to study the galactic potential of the real MW from the comparison with the observed stellar streams. (Less)
 Popular Abstract
 Our galaxy is wrapped around ribbons of stars, called stellar streams. The stellar stream was not originally shaped like a ribbon. It was a group of stars in a spherelike shape, such as a globular cluster or a dwarf galaxy. The group of stars orbits around the galaxy and is tidally stretched by the mass of the galaxy, as the Earth feels a tidal force from the Moon, which causes the tide to go in and out. The stars closer to the galaxy orbit faster while other stars farther from the galaxy orbit slower with respect to the center of the stretched group of stars. Therefore, stars leave the group on slightly different orbits and different velocities during their evolution. A few gigayears later, a long and thin shape of stars is formed around... (More)
 Our galaxy is wrapped around ribbons of stars, called stellar streams. The stellar stream was not originally shaped like a ribbon. It was a group of stars in a spherelike shape, such as a globular cluster or a dwarf galaxy. The group of stars orbits around the galaxy and is tidally stretched by the mass of the galaxy, as the Earth feels a tidal force from the Moon, which causes the tide to go in and out. The stars closer to the galaxy orbit faster while other stars farther from the galaxy orbit slower with respect to the center of the stretched group of stars. Therefore, stars leave the group on slightly different orbits and different velocities during their evolution. A few gigayears later, a long and thin shape of stars is formed around the galaxy, a stellar stream. Stellar streams have been observed by wide and deepsky surveys, such as the Sloan Digital Sky Survey, 2MASS, and WISE. Many scientists have studied the observed stellar streams to understand the mass distribution of the galaxy because the dynamics of the stellar streams are determined by the gravitational field of the galaxy. However, studying the gravitational field requires an understanding of the dynamics of the stellar stream. Thus, scientists have used computational modeling of stellar streams with Nbody integration, but this method takes too much time to calculate the positions and velocities of each star in the stream. Therefore, we study an actionangle formalism that makes it possible for us to build models of the stellar stream quickly.
In the actionangle formalism, we only need three constant actions, representing orbits of stars, and three initial angles, representing a point on its orbit. One convenient feature about the angles is that they have a linear relationship with time. Thus, it is easy to track the angles over time. For modeling stellar streams based on the actionangle formalism, hereafter an actionangle model, we use eigenvectors of the Hessian matrix, which explains the curvature of the stellar stream, to generate actions for the stellar stream. However, the generated actions do not match with an Nbody model, a model of the stellar stream by Nbody integration we built as a substitute for the observational data. Thus, we are encouraged to find 'a separation vector' that split actions along the stellar stream for leading and trailing arms. From the comparison with the Nbody model, we conclude the actionangle model with the separation vector corresponds to the Nbody model.
Furthermore, the actionangle model can be used to determine the galactic potential of the MW, which represents the mass distribution of the MW. We generate the actionangle model in a different galactic potential model from the Nbody model. The comparisons in positionvelocity and actionangle between the actionangle model and the Nbody model show significant differences. Thus, the actionangle model only matches with the Nbody model when the galactic potential for both models is the same. In addition, the actionangle model can also determine parameters of a galactic potential. Using the same galactic potential model, named McMillan17, we varied the halo mass used when computing the actionangle model and compared the results with the Nbody model in the original halo. The actionangle model and the Nbody model become more and more similar as the changed halo mass comes closer to the original value. Therefore, the actionangle model is useful for studying the overall shape and parameters of the galactic potential. If the actionangle model is compared with the observational data, we can study the real structures of the galactic potential of the MW. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/9050901
 author
 Jang, Hyerin ^{LU}
 supervisor

 Paul McMillan ^{LU}
 organization
 course
 ASTM31 20211
 year
 2021
 type
 H2  Master's Degree (Two Years)
 subject
 publication/series
 Lund Observatory Examensarbeten
 report number
 2021EXA181
 language
 English
 id
 9050901
 date added to LUP
 20210609 15:32:05
 date last changed
 20210609 15:32:05
@misc{9050901, 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 Nbody 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 Nbody integration, called an actionangle formalism, to study the gravitational field of the MW. As a substitute for the observational data, we built an Nbody model, which integrated orbits of stars in a globular cluster to form a stellar stream. From the comparison with the Nbody model, we validated our stellar stream model based on the actionangle formalism, which we call an actionangle model. The first method to generate the actionangle 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 Nbody 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 Nbody 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 actionangle models with the second method to the Nbody model in two widely used galactic potentials, named McMillan17 and BT08 in this thesis. While the actionangle model was generated in the BT08 galactic potential model, the Nbody model was generated in the McMillan17 galactic potential model. However, the positions and velocities of the Nbody model were transformed to actions and angles using the Stäckel fudge in the BT08 potential. The action distributions of the actionangle model and the Nbody model were significantly different showing that the actionangle model can be used to find an appropriate galactic potential of the MW. Further, the actionangle model can also determine parameters of the galactic potential. Actionangle models of streams in versions of the McMillan17 potential with varying halo masses were generated and compared to the Nbody model in the original McMillan17 model. The comparisons showed that a $\chi^2$like value, characterizing the difference from the Nbody 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 actionangle models with low $\chi^2$like values to the Nbody model. The two models have higher $\chi^2$like values in action distributions than the actionangle model in the original McMillan17 model. Therefore, the actionangle model can be used to study the galactic potential of the real MW from the comparison with the observed stellar streams.}}, author = {{Jang, Hyerin}}, language = {{eng}}, note = {{Student Paper}}, series = {{Lund Observatory Examensarbeten}}, title = {{Modelling stellar streams around the Milky Way}}, year = {{2021}}, }