case. We see later that the squared bicoherence $b^2$ quantifies the fraction of power which is due to quadratic nonlinear coupling at $\bmm=\bk+\bl$. For such a coupling to be present in the data and a bispectral measurement to be significant, it is therefore necessary that the bicoherence be significantly different from zero. The variance of an estimator $\hat b$ of the bicoherence that is built by simply averaging [over independent]{} realizations for estimating expectation values in Equation  – see Appendix \[appBispecEst\] –, is bounded by [@Kim1979] $$\begin{aligned}
\Var[\hat b(\bk,\bl)] &\approx \frac{1}{N_B} (1-b(\bk,\bl)^2) \leq \frac{1}{N_B},\end{aligned}$$ where $N_B$ is the number of independent data realizations used in the estimate. The statistical $1\sigma$ error in the bicoherence estimate is therefore $\sigma_b = 1/\sqrt{N_B}$. Additionally, we average the results azimuthally – see Appendix \[appAzimAvg\] – which results in a typical $\sigma_b=0.0035$ at $|\bmm| R_\sun=155.5$.

A model with a weak quadratic nonlinearity {#secModel}
------------------------------------------

\[secgenerate\]

We here present a model that helps us to interpret the measured bispectrum signal and to generate synthetic data that have approximatively a given bispectrum. There are several ways to generate data with a given power spectrum and bispectrum; see for example [@Contaldi2001] and [@Wagner2010]. Such a method is not 