Asymptotic expansions for the maximum likelihood estimation errors of the rotating parameter of the gravitational wave from core-collapse supernovae

In this work, we obtain the error estimate of the rotation parameter $\beta$ from the core bounce phase of the characteristic gravitational wave signal of a rapidly rotating core collapse supernova (CCSN). We quantify the error with asymptotic expansions of the covariance of a Maximum Likelihood Estimator (MLE) in terms of inverse powers of Signal-Noise Ratio (SNR), this method has been previously applied to parameter estimation for compact binary coalescences. When the second order of this expansion is negligible, it indicates that the first order is a good approximation of the error that will have a matching filter approach when estimating $\beta$. The analysis indicates that we should be able to resolve the presence of rotation for the galactic and nearby extragalactic progenitors. We show that the estimation error $\Delta \beta$ can be as small as a few percent and is larger for small values of $\beta$.