  We study whether binary black hole template banks can be used to search for
the gravitational waves emitted by general binary coalescences. To recover
binary signals from noisy data, matched-filtering techniques are typically
required. This is especially true for low-mass systems, with total mass $M
\lesssim 10 \, M_\odot$, which can inspiral in the LIGO and Virgo frequency
bands for thousands of cycles. In this paper, we focus on the detectability of
low-mass binary systems whose individual components can have large spin-induced
quadrupole moments and small compactness. The quadrupole contributes to the
phase evolution of the waveform whereas the compactness affects the merger
frequency of the binary. We find that binary black hole templates (with
dimensionless quadrupole $\kappa=1$) cannot be reliably used to search for
objects with large quadrupoles ($\kappa\gtrsim 20$) over a wide range of
parameter space. This is especially true if the general object is highly
spinning and has a larger mass than its binary companion. A binary that
consists of objects with small compactness could merge in the LIGO and Virgo
frequency bands, thereby reducing its accumulated signal-to-noise ratio during
the inspiraling regime. Template banks which include these more general
waveforms must therefore be constructed. These extended banks would allow us to
realistically search for the existence of new astrophysical and beyond the
Standard Model compact objects.
