Book Directly Comparing Synthetic and Real Binary Black Hole Coalescence Sources with Numerical Solutions of Einstein's Equation PDF Free

Directly Comparing Synthetic and Real Binary Black Hole Coalescence Sources with Numerical Solutions of Einstein's Equation PDF
By:Jacob A. Lange
Published on 2016 by

|We compare real and synthetic data directly to complete numerical relativity simulations of binary black holes. Even though our method largely agrees with [2], our method goes beyond the existing semi-analytic models that were used. Comparisons with only the quadrupole modes constrain the redshifted mass Mz [epsilon] [64 M [circled dot] - 82 M [circled dot]], mass ratio 1/q=m2/m1 [epsilon] [0.6,1], effective aligned spin [chi]eff [epsilon] [-0.3,0.2], where [chi]eff = (S1/m1+S2/m2) · L̂/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 [2]. We found a final total black hole redshifted mass is consistent with Mf,z in the range 64.0 M [circled dot] -73.5 M [circled dot], and we found a final dimensionless spin parameter to be constrained to af = 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 (DKL) between PDFs derived from fits to our lnLmarg from our integrate_likelihood_extrinsic code (called ILE). The error due to Monte Carlo integration was found to have a insignificant effect on the PDFs giving DKL~10−5. The impact of extracting the waveform was also found to be minimal assuming a high enough extraction radius is possible; we found DKL~10−2 - 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 DKL10−4. Our most noticeable source of error was the low frequency cutoffs, which produced DKL ~2 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.|--Abstract.

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Download Directly Comparing Synthetic and Real Binary Black Hole Coalescence Sources with Numerical Solutions of Einstein's Equation PDF Free

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