the 90% upper limit on $\Omega_{\rm BBH+BNS}(f)$, as a dotted line in Figure \[fig:cbc\].

We also show the power-law-integrated curves (PI curves) [@locus] of the O1 and O2 isotropic background searches. A power-law  that is tangent to a PI curve is detectable with ${\rm SNR} = 2$ by the given search. We additionally show a projected PI curve based on operating Advanced LIGO and Advanced Virgo at design sensitivity for 2 years, with 50% network duty cycle. By design sensitivity, we refer to a noise curve which is determined by fundamental noise sources. We use the Advanced LIGO design sensitivity projection given in [@new_design], which incorporates improved measurements of coating thermal noise relative to the one assumed in [@gw150914_stoch]. This updated curve introduces additional broadband noise at low frequencies relative to previous estimates. As a result, the updated design-sensitivity PI curve is less sensitive than the one shown in [@gw150914_stoch].

![Sensitivity curves for O1, combined O1+O2, and design sensitivity. A power law  which lies tangent to one of these curves is detectable with 2$\sigma$ significance. We have used the Advanced LIGO design sensitivity given in [@new_design], which incorporates improved measurements of coating thermal noise. Design sensitivity assumes that the LIGO 