TREEBANK: Differential Geometric Methods for Fast Template Bank Generation in Searches for Gravitational Waves

Open Access
Wang, Jonathan Zhu
Area of Honors:
Bachelor of Science
Document Type:
Thesis Supervisors:
  • Chad Hanna, Thesis Supervisor
  • Richard Robinett, Honors Advisor
  • LIGO
  • gravitational waves
  • matched filtering
  • template bank
  • treebank
  • physics
  • computational physics
  • astrophysics
Gravitational waves are propagating ripples in spacetime originating from non-spherically sym- metric accelerating systems. A fundamental prediction of Einstein’s theory of general relativity, they are the subject of the most sensitive scientific search in history due to fact the that their ef- fect on Earth is minuscule, with detectable waves squashing and stretching spacetime on the order of 1 × 10 −21 strain. On September 14, 2015, the advanced LIGO detectors made the first gravita- tional wave detection ever, observing the coalescence of two low-spin black holes of approximately 60M combined mass. On December 26, 2016, just a few months later, a second gravitational wave was observed from yet another black hole binary, this time of 22M total mass. The frequency of these events suggested that astrophysically significant sources of gravitational waves are even more prevalent than predictions estimated, indicating an extremely promising future for LIGO and grav- itational wave astronomy. With a possibly bountiful universe of gravitational waves to observe, it is in the interests of the LIGO Scientific Collaboration (LSC) to expand the parameter space across which they can detect gravitational waves. The matched filtering process applied to the detection of compact binary coalescences (CBCs) has proven to be effective so far, but is limited to searches across the mass and z-spin parameters of binaries. This is in large part due to the computational costs and large amounts of time currently required to generate template banks for use in matched filtering. For the rest of this thesis I summarize the motivation, algorithm, and initial results of a new template bank generator for use in matched filtering searches for gravitational waves origi- nating from CBCs. This method, dubbed ”treebank”, seeks to cut down on the computational cost and time required by the current template bank generator by orders of magnitude through clever applications of differential geometry and foundational ideas in computer science. Treebank utilizes a binary tree decomposition approach to split the bank into distinct hyper-rectangles of approxi- mately constant metric until the expected template density of each of these rectangles is sufficient to cover a user defined minimum match. The placement of templates in these hyper-rectangles can be handled using a geometric approach, a stochastic approach, or by splitting