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Dynamics of Tangential and Radial Dispersion Velocity in Spherical Collapse Through Analytical Methods and Simulation

Shaker Arani, Mohammad Javad | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58479 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Abolhassani, Ali Akbar
  7. Abstract:
  8. The spherical collapse model is one of the simplest analytical frameworks for studying the formation of halos, which are key components of cosmic structures. The basic spherical collapse model predicts that particles freely fall toward the center of an overdense region, leading to a singularity at the center. However, it is evident that velocity dispersion—particularly tangential velocity dispersion—acts as an angular momentum barrier that ultimately halts the collapse, resulting in a virialized structure. By taking into account both radial and tangential velocity dispersions, the average statistical evolution of the infall velocity can be derived from the spherically symmetric Jeans equation. In this equation, the terms involving radial and tangential velocity dispersions prevent the complete collapse of halos and predict a finite size for them. Solving the Jeans equation and studying the evolution of the radial velocity require knowledge of the dynamics of radial and tangential velocity dispersions. For simplicity, it is often assumed that in virialized structures the radial and tangential velocity dispersions are equal; however, simulations show that this assumption only approximately holds in the dense central regions of halos and breaks down toward their outskirts. In this work, we aim to determine the dynamics of radial and tangential velocity dispersions using N-body simulations and employ them to study the Jeans equation. To accelerate the N-body computations, instead of relying on conventional simulation codes, we intend to develop an optimized algorithm for parallel processing on GPUs, enabling faster and more cost-efficient simulations
  9. Keywords:
  10. Spherical Collapse ; Graphics Procssing Unit (GPU) ; Universe Large-Scale Structure ; N-Body Simulations ; Barnes–Hut Algorithm ; Tangential Velocity

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