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)
We estimate binary compact object merger detection rates for LIGO, including the binaries formed in ellipticals long ago. Specifically, we convolve hundreds of model realizations of elliptical- and spiral-galaxy population syntheses with a model for
elliptical- and spiral-galaxy star formation history as a function of redshift. Our results favor local merger rate densities of 4times 10^{-3} {Mpc}^{-3}{Myr}^{-1} for binary black holes (BH), 3times 10^{-2} {Mpc}^{-3}{Myr}^{-1} for binary neutron stars (NS), and 10^{-2} {Mpc}^{-3}{Myr}^{-1} for BH-NS binaries. Mergers in elliptical galaxies are a significant fraction of our total estimate for BH-BH and BH-NS detection rates; NS-NS detection rates are dominated by the contribution from spiral galaxies. Using only models that reproduce current observations of Galactic NS-NS binaries, we find slightly higher rates for NS-NS and largely similar ranges for BH-NS and BH-BH binaries. Assuming a detection signal-to-noise ratio threshold of 8 for a single detector (as part of a network), corresponding to radii Cv of the effective volume inside of which a single LIGO detector could observe the inspiral of two 1.4 M_sun neutron stars of 14 Mpc and 197 Mpc, for initial and advanced LIGO, we find event rates of any merger type of 2.9* 10^{-2} -- 0.46 and 25-400 per year (at 90% confidence level), respectively. We also find that the probability P_{detect} of detecting one or more mergers with this single detector can be approximated by (i) P_{detect}simeq 0.4+0.5log (T/0.01{yr}), assuming Cv=197 {Mpc} and it operates for T years, for T between 2 days and 0.1 {yr}); or by (ii) P_{detect}simeq 0.5 + 1.5 log Cv/32{Mpc}, for one year of operation and for $Cv$ between 20 and 70 Mpc. [ABRIDGED]
