Improved Supernova Model and Neutrino Oscillation

There are a lot of unresolved problems concerning to the mechanism of core-collapsed supernova explosions and supernova neutrinos. Though the explosions succeed in nature, the shock wave stalls and optical supernovae do not occur in most numerical supernova simulations. How the core-collapsed supernovae explode is one of the biggest mysteries in astrophysics. Since 99 % of the gravitational energy of the collapsed core is released as neutrinos, it is expected that the neutrinos are important keys to solve how supernova explosions succeed. The neutrino oscillation was discovered in various neutrino experiments, for example Super Kamiokande (SK) and Sudbury Neutrino Observatory(SNO). However, it is still very diffcult to determine three neutrino oscillation parameters of the mass difference between 1-3 mass eigenstates, <small>Δ</small>m<small>13</small><sup><small>2</sup></small>, the 1-3 mixing angle, θ<sup><small>13</sup></small>, and the CP violating phase, δ. It is one of the most important research topics of particle physics, nuclear physics and astrophysics to determine these parameter values.<br /><br /> The purpose of this thesis is to constrain the neutrino oscillation parameters theoretically from the supernova neutrinos by studying the neutrino matter effect on the neutrino oscillation which is called the MSW (Mikheyev-Sminov-Wolfenstein) effect. We examine the influence of the shock wave on the neutrinos in the MSW effect, and the influence on the dependence of direction in 2-Dimensional model. The supernova neutrinos are generated in the supernova core and propagate through the envelope. It is pointed out that shock wave propagation has strong influences on the supernova neutrino oscillation through changing density profile.<br /><br /> We studied in this thesis how the influence of the shock wave appears in the neutrino spectrum using density profile of adiabatic explosion model of a core-collapse supernova which is calculated in an implicit Lagrangian code for general relativistic spherical hydrodynamics. We found that the influence of the shock wave appears from low-energy side and moves toward high-energy side according to the shock propagation. In addition, we found that this manner of the neutrino signal depends remarkably on the neutrino oscillation parameters.<br /><br /> We calculated the expected event rate of neutrino detection at Super-Kamiokande. The time evolution of the event rate was calculated for various θ<sup><small>13</sup></small> values. The observed event rate of anti-electron type neutrino depends on the mixing angle θ <sup><small>13</sup></small> in the case of the inverted mass hierarchy, while the event rate of electron type neutrino depends on θ <sup><small>13</sup></small><br />in the case of the normal mass hierarchy. When sin<sup><small>2</sup></small> 2θ <sup><small>13</sup></small> is larger than 1×10<sup><small>-3</sup></small>, the influence of the shock wave appears after 3 seconds in the observation of neutrinos. Therefore, observing the time evolution of the event rate would constrain the mixing parameter θ <sup><small>13</sup></small>, and eventually helps understanding the propagation of the shock wave inside the star if sin <sup><small>2</sup></small> 2 θ <sup><small>13</sup></small> is larger than 1×10<sup><small>-3</sup></small>.<br /><br /> We studied how non-spherical symmetric supernovae (Type-Ic supernovae) affect the neutrino spectrum. In order to clarify the difference of the neutrino spectrum which depends on the direction, we calculated the neutrino spectra in two typical directions of the equator and the pole, and compared them with each other. Moreover, we predicted the event rates of the supernova neutrinos to be observed in the Super-Kamiokande by assuming a supernova at the center of Milky Way. We found that the survival probabilities and neutrino spectra are different from one another depending on the direction from the axis for asymmetric Type-Ic supernova explosion. The event rate of the polar direction decreases when the shock wave is propagating the H-resonance (～10<sup><small>3</sup></small>g/cm <sup><small>3</sup></small>). If we obtain the inclination from axis of the supernova by optical observation, we can find the asymmetric diverse of core explosion from the neutrino observation, and the explosion mechanism in detail.<br /><br /> From these theoretical studies it is expected to obtain detailed information of supernova neutrinos in future supernova events. If information of the mass hierarchy and mixing angle are understood, we can examine by using the neutrino where the shock wave in the star is. In addition, if the non-spherical supernova explodes and the angle from the polar axis of the supernova will be determined from the optical observation, we can examine by using event rate how the asymmetry of the core explosion is. Moreover, it would provide many feed back on the construction of theoretical models of supernovae to tie up with clarification of explosion mechanism.

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