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Register a new userAn optimization-based approach to calculating neutrino flavor evolution
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We assess the utility of an optimization-based data assimilation (D.A.) technique for treating the problem of nonlinear neutrino flavor transformation in core collapse supernovae. D.A. uses measurements obtained from a physical system to estimate the state variable evolution and parameter values of the associated model. Formulated as an optimization procedure, D.A. can offer an integration-blind approach to predicting model evolution, which offers an advantage for models that thwart solution via traditional numerical integration techniques. Further, D.A. performs most optimally for models whose equations of motion are nonlinearly coupled. In this exploratory work, we consider a simple steady-state model with two mono-energetic neutrino beams coherently interacting with each other and a background medium. As this model can be solved via numerical integration, we have an independent consistency check for D.A. solutions. We find that the procedure can capture key features of flavor evolution over the entire trajectory, even given measurements of neutrino flavor only at the endpoint, and with an assumed known initial flavor distribution. Further, the procedure permits an examination of the sensitivity of flavor evolution to estimates of unknown model parameters, locates degeneracies in parameter space, and can identify the specific measurements required to break those degeneracies.
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Neutrino-neutrino refraction dominates the flavor evolution in core-collapse supernovae, neutron-star mergers, and the early universe. Ordinary neutrino flavor conversion develops on timescales determined by the vacuum oscillation frequency. However, when the neutrino density is large enough, collective flavor conversion may arise because of pairwise neutrino scattering. Pairwise conversion is deemed to be fast as it is expected to occur on timescales that depend on the neutrino-neutrino interaction energy (i.e., on the neutrino number density) and is regulated by the angular distributions of electron neutrinos and antineutrinos. The enigmatic phenomenon of fast pairwise conversion has been overlooked for a long time. However, because of the fast conversion rate, pairwise conversion may possibly occur in the proximity of the neutrino decoupling region with yet to be understood implications for the hydrodynamics of astrophysical sources and the synthesis of the heavy elements. We review the physics of this fascinating phenomenon and its implications for neutrino-dense sources.
The multi-messenger astrophysics of compact objects presents a vast range of environments where neutrino flavor transformation may occur and may be important for nucleosynthesis, dynamics, and a detected neutrino signal. Development of efficient techniques for surveying flavor evolution solution spaces in these diverse environments, which augment and complement existing sophisticated computational tools, could leverage progress in this field. To this end we continue our exploration of statistical data assimilation (SDA) to identify solutions to a small-scale model of neutrino flavor transformation. SDA is a machine learning (ML) formula wherein a dynamical model is assumed to generate any measured quantities. Specifically, we use an optimization formulation of SDA wherein a cost function is extremized via the variational method. Regions of state space in which the extremization identifies the global minimum of the cost function will correspond to parameter regimes in which a model solution can exist. Our example study seeks to infer the flavor transformation histories of two mono-energetic neutrino beams coherently interacting with each other and with a matter background. We require that the solution be consistent with measured neutrino flavor fluxes at the point of detection, and with constraints placed upon the flavor content at various locations along their trajectories, such as the point of emission, and the locations of the Mikheyev-Smirnov-Wolfenstein (MSW) resonances. We show how the procedure efficiently identifies solution regimes and rules out regimes where solutions are infeasible. Overall, results intimate the promise of this variational annealing methodology to efficiently probe an array of fundamental questions that traditional numerical simulation codes render difficult to access.
We propose a model-independent analysis of the neutrino mass matrix through an expansion in terms of the eigenvectors defining the lepton mixing matrix, which we show can be parametrized as small perturbations of the tribimaximal mixing eigenvectors. This approach proves to be powerful and convenient for some aspects of lepton mixing, in particular when studying the sensitivity of the mass matrix elements to departures from their tribimaximal form. In terms of the eigenvector decomposition, the neutrino mass matrix can be understood as originating from a tribimaximal dominant structure with small departures determined by data. By implementing this approach to cases when the neutrino masses originate from different mechanisms, we show that the experimentally observed structure arises very naturally. We thus claim that the observed deviations from the tribimaximal mixing pattern might be interpreted as a possible hint of a ``hybrid nature of the neutrino mass matrix.
A dense neutrino medium such as that inside a core-collapse supernova can experience collective flavor conversion or oscillations because of the neutral-current weak interaction among the neutrinos. This phenomenon has been studied in a restricted, stationary supernova model which possesses the (spatial) spherical symmetry about the center of the supernova and the (directional) axial symmetry around the radial direction. Recently it has been shown that these spatial and directional symmetries can be broken spontaneously by collective neutrino oscillations. In this paper we analyze the neutrino flavor instabilities in a time-dependent supernova model. Our results show that collective neutrino oscillations start at approximately the same radius in both the stationary and time-dependent supernova models unless there exist very rapid variations in local physical conditions on timescales of a few microseconds or shorter. Our results also suggest that collective neutrino oscillations can vary rapidly with time in the regimes where they do occur which need to be studied in time-dependent supernova models.
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