In this work, we present a novel methodology for estimating the ratio of kinetic energy to gravitational potential energy of a core collapse supernova progenitor and assess the equation of state (EOS). We estimated this ratio by reconstructing the three peaks of a gravitational wave (GW) in real interferometric data. For this purpose, we extend a previous phenomenological analytical model for the core bounce phase by introducing an additional parameter associated with its timescale. We assess the agreement of our phenomenological template with numerical waveform databases through fitting factor (see Sec. V) and Bayesian model comparison. The improved phenomenological analytical model raised the median fitting factors from 88.88% to 90.83%. Parameter estimation (PE) is performed using a Markov chain Monte Carlo implementation in real O3a interferometric noise. We find that the rotational parameter $\beta$ estimation for 452 Abylkairov signals has a median absolute relative error of 11.93% with a 95th percentile of 38.41%, an overall uncertainty of ${\sigma }_{\beta }=1.083\times {10}^{-3}$ at 10 kpc. This was an improvement compared to estimated values using maximum likelihood estimator (MLE). In that work, at 10 kpc, a value of ${\sigma }_{\beta }=1.46\times {10}^{-2}$ was reported, i.e., an order of magnitude improvement in the standard deviations. We further investigate the impact of the Bayesian prior selection on the posteriors, injecting signals in Gaussian colored noise and real interferometric noise. Real noise would introduce non-Gaussian and nonstationary features that worsen the estimation accuracy. For example, the estimation for $\beta$ yielded a maximum bias of 11.9% at 10 kpc for a uniform in ${\beta }^2$ prior and a minimum bias of 0.6% with a triangular prior.

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• Gravitation
• Gravitational waves