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Modelling stellar streams around the Milky Way

Jang, Hyerin LU (2021) In Lund Observatory Examensarbeten ASTM31 20211
Lund 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 N-body 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 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. (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 sphere-like 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 sphere-like 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 deep-sky 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 N-body integration, but this method takes too much time to calculate the positions and velocities of each star in the stream. Therefore, we study an action-angle formalism that makes it possible for us to build models of the stellar stream quickly.
In the action-angle 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 action-angle formalism, hereafter an action-angle 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 N-body model, a model of the stellar stream by N-body 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 N-body model, we conclude the action-angle model with the separation vector corresponds to the N-body model.
Furthermore, the action-angle model can be used to determine the galactic potential of the MW, which represents the mass distribution of the MW. We generate the action-angle model in a different galactic potential model from the N-body model. The comparisons in position-velocity and action-angle between the action-angle model and the N-body model show significant differences. Thus, the action-angle model only matches with the N-body model when the galactic potential for both models is the same. In addition, the action-angle 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 action-angle model and compared the results with the N-body model in the original halo. The action-angle model and the N-body model become more and more similar as the changed halo mass comes closer to the original value. Therefore, the action-angle model is useful for studying the overall shape and parameters of the galactic potential. If the action-angle 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:
author
Jang, Hyerin LU
supervisor
organization
course
ASTM31 20211
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Lund Observatory Examensarbeten
report number
2021-EXA181
language
English
id
9050901
date added to LUP
2021-06-09 15:32:05
date last changed
2021-06-09 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 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.}},
  author       = {{Jang, Hyerin}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Lund Observatory Examensarbeten}},
  title        = {{Modelling stellar streams around the Milky Way}},
  year         = {{2021}},
}