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Register a new userBayesian parameter estimation of core collapse supernovae using gravitational wave simulations
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Matthew Charles Edwards
Publication date
2014
fields
Physics
and research's language is
English
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Using the latest numerical simulations of rotating stellar core collapse, we present a Bayesian framework to extract the physical information encoded in noisy gravitational wave signals. We fit Bayesian principal component regression models with known and unknown signal arrival times to reconstruct gravitational wave signals, and subsequently fit known astrophysical parameters on the posterior means of the principal component coefficients using a linear model. We predict the ratio of rotational kinetic energy to gravitational energy of the inner core at bounce by sampling from the posterior predictive distribution, and find that these predictions are generally very close to the true parameter values, with $90%$ credible intervals $sim 0.04$ and $sim 0.06$ wide for the known and unknown arrival time models respectively. Two supervised machine learning methods are implemented to classify precollapse differential rotation, and we find that these methods discriminate rapidly rotating progenitors particularly well. We also introduce a constrained optimization approach to model selection to find an optimal number of principal components in the signal reconstruction step. Using this approach, we select 14 principal components as the most parsimonious model.
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Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the model, the model error as well as the statistics of the model error. This method relies on the usage of many data sets in a simultaneous analysis in order to overcome the problems caused by the degeneracy between model parameters and model error. Errors in the modeling of the measurement instrument can be absorbed in the model error allowing for applications with complex instruments.
We summarize our current understanding of gravitational wave emission from core-collapse supernovae. We review the established results from multi-dimensional simulations and, wherever possible, provide back-of-the-envelope calculations to highlight the underlying physical principles. The gravitational waves are predominantly emitted by protoneutron star oscillations. In slowly rotating cases, which represent the most common type of the supernovae, the oscillations are excited by multi-dimensional hydrodynamic instabilities, while in rare rapidly rotating cases, the protoneutron star is born with an oblate deformation due to the centrifugal force. The gravitational wave signal may be marginally visible with current detectors for a source within our galaxy, while future third-generation instruments will enable more robust and detailed observations. The rapidly rotating models that develop non-axisymmetric instabilities may be visible up to a megaparsec distance with the third-generation detectors. Finally, we discuss strategies for multi-messenger observations of supernovae.
Gravitational wave (GW) detection is now commonplace and as the sensitivity of the global network of GW detectors improves, we will observe $mathcal{O}(100)$s of transient GW events per year. The current methods used to estimate their source parameters employ optimally sensitive but computationally costly Bayesian inference approaches where typical analyses have taken between 6 hours and 5 days. For binary neutron star and neutron star black hole systems prompt counterpart electromagnetic (EM) signatures are expected on timescales of 1 second -- 1 minute and the current fastest method for alerting EM follow-up observers, can provide estimates in $mathcal{O}(1)$ minute, on a limited range of key source parameters. Here we show that a conditional variational autoencoder pre-trained on binary black hole signals can return Bayesian posterior probability estimates. The training procedure need only be performed once for a given prior parameter space and the resulting trained machine can then generate samples describing the posterior distribution $sim 6$ orders of magnitude faster than existing techniques.
Recent core-collapse supernova (CCSN) simulations have predicted several distinct features in gravitational-wave (GW) spectrograms, including a ramp-up signature due to the g-mode oscillation of the proto-neutron star (PNS) and an excess in the low-frequency domain (100-300 Hz) potentially induced by the standing accretion shock instability (SASI). These predictions motivated us to perform a sophisticated time-frequency analysis (TFA) of the GW signals, aimed at preparation for future observations. By reanalyzing a gravitational waveform obtained in a three-dimensional general-relativistic CCSN simulation, we show that both the spectrogram with an adequate window and the quadratic TFA separate the multimodal GW signatures much more clearly compared with the previous analysis. We find that the observed low-frequency excess during the SASI active phase is divided into two components, a stronger one at 130 Hz and an overtone at 260 Hz, both of which evolve quasi-statically during the simulation time. We also identify a new mode whose frequency varies from 700 to 600 Hz. Furthermore, we develop the quadratic TFA for the Stokes I, Q, U, and V parameters as a new tool to investigate the GW circular polarization. We demonstrate that the polarization states that randomly change with time after bounce are associated with the PNS g-mode oscillation, whereas a slowly changing polarization state in the low-frequency domain is connected to the PNS core oscillation. This study demonstrates the capability of the sophisticated TFA for diagnosing the polarized CCSN GWs in order to explore their complex nature.
We present gravitational wave (GW) signal predictions from four 3D multi-group neutrino hydrodynamics simulations of core-collapse supernovae of progenitors with 11.2 Msun, 20 Msun, and 27 Msun. GW emission in the pre-explosion phase strongly depends on whether the post-shock flow is dominated by the standing accretion shock instability (SASI) or convection and differs considerably from 2D models. SASI activity produces a strong signal component below 250 Hz through asymmetric mass motions in the gain layer and a non-resonant coupling to the proto-neutron star (PNS). Both convection- and SASI-dominated models show GW emission above 250 Hz, but with considerably lower amplitudes than in 2D. This is due to a different excitation mechanism for high-frequency l=2 motions in the PNS surface, which are predominantly excited by PNS convection in 3D. Resonant excitation of high-frequency surface g-modes in 3D by mass motions in the gain layer is suppressed compared to 2D because of smaller downflow velocities and a lack of high-frequency variability in the downflows. In the exploding 20 Msun model, shock revival results in enhanced low-frequency emission due to a change of the preferred scale of the convective eddies in the PNS convection zone. Estimates of the expected excess power in two frequency bands suggests that second-generation detectors will only be able to detect very nearby events, but that third-generation detectors could distinguish SASI- and convection-dominated models at distances of ~10 kpc.
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