#### Abstract

We compare real and synthetic data directly to complete numerical relativity simulations of binary black holes. Even though our method largely agrees with \cite{PEPaper}, our method goes beyond the existing semi-analytic models that were used. Comparisons with only the quadrupole modes constrain the redshifted mass $M_{z}\in[64 M_{\bigodot}-82 M_{\bigodot}]$, mass ratio $1/q=m_2/m_1\in[0.6,1]$, effective aligned spin $\chi_{eff}\in[-0.3,0.2]$, where $\chi_{eff}=(\mathbf{S}_1/m_1+\mathbf{S_2}/m_2)\cdot\mathbf{\hat{L}}/M$. If we include the octopole modes, we can constrain the mass ratio even better. Even though the spins are correlated, both magnitude and directions are not significantly constrained by the data. We determine that an upper limit for the spin magnitudes up to at least 0.8 but with random orientations. When we interpolate between nonprecessing binaries and reconstruct the posterior distribution, we find it is consistent with the results in \cite{PEPaper}. We found a final total black hole redshifted mass is consistent with $M_{f,z}$ in the range $64.0 M_{\bigodot}-73.5 M_{\bigodot}$, and we found a final dimensionless spin parameter to be constrained to $a_f=0.62-0.73$. To better understand and quantify the impact of potential sources of error, we calculated mismatches between waveforms and the KL Divergence($D_{KL}$) between PDFs derived from fits to our $\lnLmarg$ from our \textit{integrate\_likelihood\_extrinsic} code (called \textit{ILE}). The error due to Monte Carlo integration was found to have a insignificant effect on the PDFs giving $D_{KL}\sim10^{-5}$. The impact of extracting the waveform was also found to be minimal assuming a high enough extraction radius is possible; we found $D_{KL}\sim10^{-2}-10^{-3}$ for PDFs corresponding to sources with different extraction radii. The resolution of a simulation was also found to have an extremely low impact with $D_{KL}\sim10^{-4}$. Our most noticeable source of error was the low frequency cutoffs, which produced $D_{KL}\sim2$ for two PDFs with the biggest differences; however, this effect becomes less significant after marginalizing over all dimensions. We also use different sources for three end-to-end runs: zero spin, equal mass; aligned spin, unequal mass; and precessing, unequal mass. For all three cases, we were able to constrain the same parameters as with the analysis of the real event. For all three cases, the true system parameters lied within our reconstructed posterior. For the aligned case, we ran comparisons using the octopole modes and found, as in the real event analyses, we could further constrain the mass ratio.

#### Library of Congress Subject Headings

Black holes (Astronomy)--Mathematics; General relativity (Physics)

#### Publication Date

9-7-2016

#### Document Type

Thesis

#### Student Type

Graduate

#### Degree Name

Astrophysical Sciences and Technology (MS)

#### Department, Program, or Center

School of Physics and Astronomy (COS)

#### Advisor

Richard O’Shaughnessy

#### Advisor/Committee Member

Carlos Lousto

#### Advisor/Committee Member

John Whelan

#### Recommended Citation

Lange, Jacob A., "Directly comparing synthetic and real binary black hole coalescence sources with numerical solutions of Einstein’s equation" (2016). Thesis. Rochester Institute of Technology. Accessed from

https://scholarworks.rit.edu/theses/9323

#### Campus

RIT – Main Campus

#### Plan Codes

ASTP-MS

## Comments

Physical copy available from RIT's Wallace Library at QB843.B55 L36 2016