Parameter estimation from the core-bounce phase of rotating core collapse supernovae in real interferometer noise

Abstract

In this work we propose an analytical model that reproduces the core-bounds phase of gravitational waves (GW) of Rapidly Rotating (RR) from Core Collapse Supernovae (CCSNe), as a function of three parameters, the arrival time $\tau$, the ratio of the kinetic and potential energy $\beta$ and a phenomenological parameter $\alpha$ related to rotation and equation of state (EOS). To validate the model we use 126 waveforms from the Richers catalog \cite{Richers_2017} selected with the criteria of exploring a range of rotation profiles, and involving EOS. To quantify the degree of accuracy of the proposed model, with a particular focus on the rotation parameter $\beta$, we show that the average Fitting Factor (FF) between the simulated waveforms with the templates is 94.4\%. In order to estimate the parameters we propose a frequentist matched filtering approach in real interferometric noise which does not require assigning any priors. We use the Matched Filter (MF) technique, where we inject a bank of templates considering simulated colored Gaussian noise and the real noise of O3L1. For example for A300w6.00\_BHBLP at 10Kpc we obtain a standar deviation of $\sigma = 3.34\times 10^{-3}$ for simulated colored Gaussian noise and $\sigma= 1.46\times 10^{-2}$ for real noise. On the other hand, from the asymptotic expansion of the variance we obtain the theoretical minimum error for $\hat{\beta}$ at 10 kpc and optimal orientation. The estimation error in this case is from $10^{-2}$ to $10^{-3}$ as $\beta$ increases. We show that the results of the estimation error of $\beta$ for the 3-parameter space (3D) is consistent with the single-parameter space (1D), which allows us to conclude that $\beta$ is decoupled from the others two parameters.