Ridgelines and Catastrophes: Analysis of LISA signals reveals how source parameter estimates sharpen non-linearly as observed signal duration increases

We have used a grid search technique to analyze simulated LISA gravitational wave signals to extract source parameters. We present parameter space graphs that illustrate the highly non-Gaussian nature of the probability distributions, and the high degree of correlation among various parameters. These correlations show up as ``ridgelines'' in the multidimensional parameter space. These graphs also illustrate the highly nonlinear rate with which the accuracy of the parameters extracted increases as a function of the duration of signal observed. The accuracy levels show plateaus followed by sudden jumps, which mathematicians call ``catastrophes.'' These extracted parameters can be used to perform the Ryan* test of the black hole uniqueness theorem. Results obtained to date support estimates that the Ryan test may be performed to an accuracy of better than 10{\%} if favorable cases of extreme-mass-ratio inspirals are observed for periods exceeding one year. Analysis of simulated LIGO cases suggests much less precise results for parameter extraction and much weaker limits on black hole non-uniqueness. \newline \newline * Ryan, F. D., \textit{Phys. Rev. D} \textbf{52}, 5707 (1995).