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Dynamics of Binary Black Holes and Dark Matter Density Profiles in Galactic Centers

This study investigates the dynamics of binary black holes and their relationship with dark matter density profiles in galactic centers. Observations reveal that black hole masses are correlated with their host galaxies' properties. We classify early-type galaxies into power-law or core types based on their density profiles. By analyzing the motion equations, we identify multiple equilibrium points for different models of density profiles, enhancing our understanding of how binary black holes interact with dark matter in their galaxies.

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Dynamics of Binary Black Holes and Dark Matter Density Profiles in Galactic Centers

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  1.  The Dark-Matter Density Profiles and Binary Black Holes Li-Chin Yeh(1) and Ing-Guey Jiang(2) (1)Department of Applied Mathematics, National Hsinchu University of Education, Taiwan; (2)Department of Physics & Institute of Astronomy, National Tsing-Hua University, Hsin-Chu City, Taiwan

  2. Abstract It is known that galactic centers could host single or binary black holes, and observations show that black-hole masses are correlated with the properties of galaxies. Moreover, in terms of center's density profiles, early-type galaxies can be classified into power-law or core galaxies. Therefore, in this project, we study the dynamics near galactic centers with given galactic dark-matter density profiles and binary black holes. Our results could constrain the properties of binary black holes or dark-matter density profiles in their host galaxies.

  3. Density Profiles

  4. Equations of Motion

  5. Model A: n=1equilibrium points on the x-axis

  6. The First Property

  7. Model B: equilibrium points on the x-axis

  8. The 2nd Property

  9. Conclusions • Depending on density profiles, number of equilibrium points could be different, and combine with the general properties proved in Jiang & Yeh (2006), we have: • For Model A, if below condition is satisfied, there are 6 equilibrium points (4 collinear and 2 triangular); if not, there are 5 equilibrium points (3 collinear and 2 triangular) • For Model B, there are always 6 equilibrium points

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