is the distance to the target, $\tau $ the assumed age of the target object, and $I$ a fiducial moment of inertia for a neutron star ($10^{38} \textup{kg} \cdot \textup{m}^{2}$). $G$ and $c$ are the gravitational constant and the speed of light, respectively. This age-based limit was then superimposed on a curve of expected upper limits in the absence of signal for the LIGO detectors, obtained from the noise harmonically averaged over all of and both interferometers. A running median with a 16-Hz window was further applied to smooth the curve. The curve is given by:

$$\label{senscurve}
h_{0}^{95\%} = \Theta \sqrt{ \frac{S_h} {T_\mathrm{data}} }$$

where $S_{h}$ is the harmonically averaged noise, $T_\mathrm{data}$ is the coherence time (the total data livetime searched coherently), initially estimated at two weeks, and $\Theta$ is a sensitivity factor that includes a trials factor, or number of templates searched, and uncertainty in the source orientation [@Wette2008]. For a directed search like ours, $\Theta$ is approximately 35 [@Wette2008; @WetteSens]. The intersection of this coherence-time adjusted upper limit curve and our indirect limit (Eq. (\[indirect1\])) gives an initial frequency band over which the indirect limit can be beaten. The braking index is related to the frequency parameters by 