Impact of star formation inhomogeneities on merger rates and interpretation of LIGO results

Within the next decade, ground based gravitational wave detectors are in principle capable of determining the compact object merger rate per unit volume of the local universe to better than 20% with more than 30 detections. We argue that the stellar models are sensitive to heterogeneities (in age and metallicity at least) in such a way that the predicted merger rates are subject to an additional 30-50% systematic errors unless these heterogeneities are taken into account. Without adding new electromagnetic constraints on massive binary evolution or relying on more information from each merger (e.g., binary masses and spins), as few as the $simeq 5$ merger detections could exhaust the information available in a naive comparison to merger rate predictions. As a concrete example, we use a nearby-universe catalog to demonstrate that no one tracer of stellar content can constrain merger rates without introducing a systematic error of order $O(30%)$ at 90% confidence. More generally, we argue that theoretical binary evolution can depend sufficiently sensitively on star-forming conditions -- even assuming no uncertainty in binary evolution model -- that the emph{distribution} of star forming conditions must be incorporated to reduce the systematic error in merger rate predictions below roughly 40%. (Abridged)