Gravitational waves and the deformation of compact objects: Topics in relativistic astrophysics

Open Access
Johnson-McDaniel, Nathan Kieran
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
June 27, 2011
Committee Members:
  • Benjamin J Owen, Dissertation Advisor
  • Benjamin J Owen, Committee Chair
  • Martin Bojowald, Committee Member
  • Irina Mocioiu, Committee Member
  • Steinn Sigur&Eth;Sson, Committee Member
  • summation formulae
  • binary white dwarfs
  • neutron stars
  • relativistic astrophysics
  • binary black holes
  • gravitational waves
<p>In this dissertation, we present various theoretical investigations of sources of gravitational waves, relevant to interpreting the data from current and planned gravitational wave detectors; an <i>idée fixe</i> is the deformation of compact objects.</p> <p>We begin in the strong field, vacuum regime, with a construction of initial data for the numerical simulation of black hole binaries (specializing to the case of nonspinning holes in a quasicircular orbit). The data we construct contain more of the binary's expected physics than any other current data set. In particular, they contain both the binary's outgoing radiation and the expected tidal deformations of the holes. Such improved initial data will likely be necessary for simulations to achieve the accuracy required to supply advanced gravitational wave detectors with templates for parameter estimation.</p> <p>We end in the weak field, hydrodynamic regime with a calculation of the expected accuracy with which one can combine standard electromagnetic and gravitational wave observations of white dwarf binaries to measure the masses of the binary's components. In particular, we show that this measurement will not be contaminated by finite size effects for realistic sources observed by LISA, though such effects could be important for exceptional sources and/or advanced mHz gravitational wave detectors.</p> <p>In the middle, we make a detour into the messy and poorly constrained realm of the physics of neutron star interiors, calculating the shear modulus of hadron–quark mixed phase in hybrid stars. Here we include a rough treatment of charge screening, dimensional continuation of the lattice, and the contributions from changing the cell volume when shearing lower-dimensional lattices. We find that the last of these contributions is necessary to stabilize the lattice for those dimensions, where it makes a considerable contribution to the shear modulus.</p> <p>We then move back to sounder theoretical footing in making a general relativistic calculation of the maximum elastic quadrupole deformation that could be sustained by a star with a known shear modulus and breaking strain (provided by, e.g., the hadron–quark mixed phase in the core, or the more standard lattice of nuclei in the crust). We find that the standard Newtonian calculation considerably overestimates the quadrupole, particularly for massive, compact stars.</p> <p>We also present the dimensionally continued Poisson summation formula we discovered while performing the shear modulus calculation, and thought interesting enough to prove rigorously. Our method of proof also provides a new way of proving other (Voronoi) summation formulae obtained from functions satisfying modular transformations, and allows one to relax certain of the standard hypotheses.</p>