Quantification of the parameter estimation error from Rotating Core Collapse supernovae

In this paper, we perform parameter estimation with an analytical model to simulate the gravitational wave emission during the core bounce phase of a rapidly rotating core collapse supernova progenitor. This approach enables us to estimate the parameter $\beta$, defined as the ratio of rotational kinetic energy to gravitational potential energy in core collapse supernovae. To verify the reliability of both the analytical model and the inferred value of $\beta$, we use a numerical template bank constructed from Abylkairov\'s gravitational waveform catalog and simulate O4 noise, characterized by the interferometers power spectral density. An average fitting factor of 94\% over the interval 0.02 $< \beta <$ 0.14 shows that our analytical model reproduces the key characteristics of the core-bounce waveform with high accuracy, leading to only a 6\% reduction in the optimal signal to noise ratio. This provides a quantitative measure of how well the analytical model performs. Subsequently, we analyze the error in estimating $\beta$ using a Matched Filter method and compare it to the corresponding Cram\'er Rao Lower Bound. The results obtained by considering noise and waveforms at distances of 5, 10, and 50 kpc enable an assessment of how accurately the selected statistical model fits the observed data. From the asymptotic expansion of the variance, we derive a theoretical lower bound for the error that falls below $10^{-1}$ when the parameter $\beta$ decreases with distance.