One of the National Science Foundation’s largest funded experiments is the Laser Interferometer Gravitational-Wave Observatory (LIGO), which will directly detect the gravitational waves (GWs) theorized in Einstein’s General Theory of Relativity. Compact binary coalescences (CBCs), such as those from black holes and neutron stars, are some of the strongest sources of GWs for ground-based gravitational-wave observatories. These GW signals tell us more about the initial and final properties of black holes, such as masses, spins, and also sky orientation, and eccentricity.
Now that Advanced LIGO has become more sensitive to a wider range of frequencies, we are closer to detecting the first GWs. The detection of these signatures will open a new field in astronomy since we will be able to get a picture of the GW sky for the first time. In preparation for this groundbreaking detection, numerical relativists have been analyzing theoretical waveforms and trying to recover as much information as possible from these signals.
At the moment, my aim is to analyze and understand CBC results coming from the LIGO detectors by tracking power spectral density variations over small time steps. These variations, plotted in a frequency versus time spectrogram, provide an easier way to check for regions of excess power, which is characteristic of a GW signal.
My past research at Georgia Tech focused on providing theoretical models of the gravitational wave radiation from the merger of two black holes. The data used comes from the GT Maya code, which solves initial value problems of Einstein’s equations of general relativity for the dynamical spacetime and radiation of binary black hole coalescence. These equations are a set of non-linear, coupled, partial differential equations that generate the theoretical gravitational wave data for a range of physical black hole parameters.
These models are necessary in detecting the gravitational radiation signal embedded in noise. The challenge is to recognize patterns in the data that reveal how the information about the originating binary is encoded on the gravitational waves over the nine dimensional parameter space. I found the total energy radiated to be as high as 10% of the total initial mass of the system. However, this is the energy radiated summed over all modes (l,m). These modes come from the spin-weighted spherical harmonics that allow us to recast the radiation from a function of theta and phi into a function to l and m. Decomposing a waveform into modes gives us sky orientation and studying the modes uncovers interesting trends.
As expected, the (2,2) mode is the most dominant. By fitting a line to the (2,2) mode, we are able to extrapolate to larger mass ratios — an important result since the numerical challenge increases substantially with increasing mass ratio. More interestingly, the (2,2) mode is the only one that monotonically decreases with an increasing mass ratio while the other modes contain turning points. This turning off and on of modes can be traced back to the initial values of the parameters and the symmetry they cause. With this predictive power, my research results are playing a role in understanding how the geometry of the system impacts the excitation of the radiation modes. This study was done for both precessing and non-precessing systems.