Proc. Neutrino Astrophysics - MPP Theory Group

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62 scopic asymmetry can build up because the anisotropy of the neutrino flux increases with the average number of scatterings per neutrino, i.e. with the optical depth of the medium. The polarization term in the cross section represents a slightly different chance for a neutrino to be scattered into the direction of the external magnetic field than into the opposite direction, or means a tiny enhancement of the scattering probability of neutrinos moving into (or opposite to) the field direction. Formally, the neutrino flux is not only described by a diffusive propagation mode (proportional to the gradient of the neutrino energy density), but an additional “advective” vector component in the magnetic field direction (see [17, 18]). The ratio between advective and diffusive component grows approximately linearly with the scattering optical depth τ. Physically, this can be understood [15] by recalling that a diffusing particle has travelled a mean distance d = √ Nλ after N steps with (constant) scattering mean free path λ. If the particle has a tiny chance P to be scattered into the field direction, the distance it has propagated along the field after N scatterings is l = PNλ. Therefore the relative anisotropy increases as l/d ∝ P √ N ∝ τ (for P √ N ≪ 1). The second proportionality holds because the optical depth is defined as τ = d/λ, thus τ = √ N. The discussed process would be highly interesting if the magnetic fields required to create a few per cent anisotropy of the neutrino emission of a neutron star were much smaller than the very strong fields (> ∼ several 10 15 G) where the neutrino opacity is affected by the change of the electron phase space distribution. Horowitz and Li [15] have only considered very simple situations of scattering media to show the fundamental characteristics of the cumulative process and have disregarded essential complications of neutrino transport in neutron stars, e.g., neutrino absorption, transport of different neutrino types with opposite signs of the polarization terms, and the feedback of the transport on the energy distribution in the neutron star. The question must be asked whether the proposed cumulative process leads to a global anisotropy of the neutrino emission of the nascent neutron star and how large this anisotropy can be for a given magnetic field. The neutron star situation was more realistically investigated by Lai and Qian [18] who estimated a maximum recoil velocity of about 200km/s for average magnetic fields of ∼ 10 14 G, provided the magnetic field in a nascent neutron star possesses a strong dipole component. Their analysis, however, is based on the assumption that neutrinos and antineutrinos, in particular νe and ¯νe, have the same opacity for interactions with the stellar medium. Therefore their kicks are only produced by the deleptonization neutrinos which carry away only a minor fraction (∼ 10%) of the gravitational binding energy of the neutron star which is released by neutrino emission. This assumption, however, leads to a large underestimation of the recoil acceleration [19]. Monte Carlo simulations [19] which include neutrino production and absorption, different opacities and polarizations for different neutrino and antineutrino flavors (νe, ¯νe, and heavy lepton neutrinos νx and ¯νx), and the evolution of the stellar background in a simplified but reasonable, approximative description 1 , suggest that a polarization term in the neutrino-nucleon scattering opacity of κs,pol/κs ∼ 10 −5 can lead to a global asymmetry q of the integrated neutrino luminosity of about 16% for the one-dimensional (plane) case (Fig. 1). Taking into account projection effects by multiplying this result with 1/2, the corresponding threedimensional asymmetry q3D is estimated to about 8%, i.e. q3D ∼ 0.08· � (κs,pol/κs)/10 −5� . This 1 Monte Carlo simulations become extremely expensive and CPU-time consuming for high optical depths. Instead of considering a neutron star with neutrino optical depth of 10000–100000, a toy model with optical depth τ = 100 and correspondingly rescaled polarization terms of the neutrino interactions was investigated. The scaling of the results was tested by comparative computations for τ = 30 and for τ = 300.
Figure 1: <strong>Neutrino</strong> luminosity and emission anisotropy as functions of time step for two Monte Carlo simulations of the neutrino cooling of a one-dimensional toy model of a neutron star. L = L+ + L− is the total neutrino luminosity, ∆L = L+−L− ∆L = L+−L− the luminosity difference between the two hemispheres (both normalized to the maximum luminosity Lmax), E = E++E− the energy radiated in neutrinos, and ∆E = E+ − E− the energy difference (both normalized to the final energy Emax). The integral asymmetry of the neutrino emission is given by the parameter q = ∆E/E which approaches nearly 16% towards the end of the simulations. The three-dimensional asymmetry in the integrated neutrino luminosity, q3D, would be smaller by a factor 1/2 (for small anisotropies) compared to the displayed one-dimensional results. The Monte Carlo simulations were performed for models with total optical depths of τ = 30 (left) and τ = 100 (right), where the opacity polarizations were rescaled such that the results should be identical if the anisotropy grows linearly with the optical depth. The very good agreement between both calculations (left and right) thus confirms the scaling of the cumulative anisotropy with the optical depth of the star. can be related to the anisotropy parameter α3D for the momentum transfer to the neutron star: α3D = 2 3q3D ∼ 0.05 · � (κs,pol/κs)/10 −5� . The effective polarization of neutrino-nucleon scatterings depends on the magnetic field strength B, the plasma temperature T, and the abundances Yn and Yp of neutrons and protons, respectively: κs,pol κs ∼ � 6.4 × 10 −5 − 13.3 × 10 � � −5 Yp · 1 + 1.134 Yn Yp �−1 Yn · B14 T10 63 , (1) where B14 is measured in 10 14 G and T10 in 10MeV. Using representative values for temperature and composition during the phase when most of the gravitational binding energy of the neutron star is radiated away in neutrinos, T = 10...30MeV, Yn = 0.8...0.9, and Yp = 1 − Yn = 0.2...0.1, a space-time average of κs,pol/κs ∼ 10 −5 can be expected for a mean interior magnetic field 〈Bz〉 of the neutron star of ∼ 10 14 G. This leads to an estimated recoil velocity of � � � � � α3D 1.4M⊙ vns ∼ Eν = 1800 0.05 Mns 3 × 1053 � km s erg −1 � 〈Bz〉 ∼ 1800 1014 � � � � 1.4M⊙ Eν G 3 × 1053 � km s erg −1 . (2) Mns The reason for a nearly 10 times larger anisotropy compared to the result found by Lai and Qian [18] is twofold. During deleptonization and neutronization the neutron star plasma becomes increasingly asymmetric, i.e. the abundance of protons decreases and the plasma
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arXiv:astro-ph/9801320v1 30 Jan 199
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Preface This was the fourth worksho
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vi S.J. Hardy Quasilinear Diffusion
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viii
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History of Neutrino Physics: Pauli
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Brief an Oskar Klein, Stockholm, vo
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Recent observations with the Hubble
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MACHO sample of ∼100,000 light cu
Page 19: Solar Neutrinos
Page 22 and 23: 14 In the depth range where an abun
Page 24 and 25: 16 as follows: (1) All the detector
Page 26 and 27: 18 [3] J.N. Bahcall and H.A. Bethe,
Page 28 and 29: 20 the opacity has a very slowly ch
Page 30 and 31: 22 Status of the Radiochemical Gall
Page 32 and 33: 24 known true source activity. The
Page 34 and 35: 26 Solar Neutrino Observation with
Page 36 and 37: 28 Events/day/kton/bin 0.3 0.25 0.2
Page 38 and 39: 30 log(Δm 2 (eV 2 log(Δm )) 2 (eV
Page 40 and 41: 32 Table 1: Neutrino event rates in
Page 42 and 43: 34 tank and sphere high purity wate
Page 44 and 45: 36 Measurements of Low Energy Nucle
Page 46 and 47: 38 Figure 1: The S(E) factor of 3 H
Page 48 and 49: 40 Solar Neutrinos: Where We Are an
Page 50 and 51: 42 [9] B. Pontecorvo, Chalk River R
Page 52 and 53: 44 Figure 2: The difference between
Page 55 and 56: Phenomenology of Supernova Explosio
Page 57 and 58: Figure 2: Theoretical classificatio
Page 59 and 60: Supernova Rates Bruno Leibundgut Eu
Page 61 and 62: galaxies, however, and the statisti
Page 63 and 64: Figure 1: The motions of pulsars re
Page 65 and 66: Convection in Newly Born Neutron St
Page 67 and 68: a b Figure 2: Panel a shows the rec
Page 69: ference). The angular variations of
Page 73 and 74: [9] G.S. Bisnovatyi-Kogan, Astron.
Page 75 and 76: and the mass-to-luminosity ratio of
Page 77 and 78: Figure 1: Time variation of superno
Page 79 and 80: Figure 3: Energy spectra of the sup
Page 81 and 82: Supernova Neutrino Opacities G.G. R
Page 83 and 84: Quasilinear Diffusion of Neutrinos
Page 85 and 86: Assuming a saturated thermal distri
Page 87 and 88: Anisotropic Neutrino Propagation in
Page 89 and 90: So far the damping rate corresponds
Page 91 and 92: Cherenkov Radiation by Massless Neu
Page 93 and 94: on ω so that they are well approxi
Page 95: 2 2 / meff,e m eff 1.0 0.5 0.0 elec
Page 99 and 100: Gamma-Ray Burst Observations D.H. H
Page 101 and 102: Figure 1: The cumulative distributi
Page 103 and 104: [7] Lilly, S., in Critical Dialogue
Page 105 and 106: ) Phase Transitions in Neutron Star
Page 107 and 108: after the collapse began (nb., no e
Page 109 and 110: Models of Coalescing Neutron Stars
Page 111 and 112: Figure 2: Contour plots of the mass
Page 113 and 114: From our torus models we find that
Page 115: High-Energy Neutrinos
Page 118 and 119: 110 in gamma-rays. However, the acc
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112 Atmospheric Muons and Neutrinos
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114 Today, however, charm productio
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116 Atmospheric Neutrinos in Super-
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118 number of events 300 200 100 (a
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120 Acknowledgements D.K. is suppor
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122 Key signatures for νµ nucleon
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124 (a.u) 0.5 0.4 0.3 0.2 0.1 0 0 1
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126 However, in order to operate th
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128 could be gravitationally captur
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130 Ground-Based Observation of Gam
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132 Figure 2: Sensitivities in unit
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134 Crab flux Figure 4: Gamma-ray f
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136
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Helium Absorption and Cosmic Reioni
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Non-Standard Big Bang Nucleosynthes
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) Non-standard Neutrino Properties
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some heating of the plasma. In cont
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Big Bang Nucleosynthesis With Small
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Neutrinos and Structure Formation i
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Photon and Neutrino Backgrounds The
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The (photon) temperature at aeq is
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spectrum has therefore changed to 1
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Figure 4: Growth of structure in CD
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Future Prospects
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162 Figure 1: Calorimetric β − s
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164 References [1] F. Gatti: Procee
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166 The frequency of Galactic super
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168 Table 1: Comparison of proposed
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170 Neutrinos in Astrophysics José
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172 N eq 7 6.5 6 5.5 5 4.5 4 3.5 3
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174 Figure 4: SN 1987A bounds on FC
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176 [5] A. Joshipura and J. W. F. V
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178 Some Neutrino Events of the 21s
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180 2099: Relic Neutrinos And last
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182
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184 Tuesday, Oct. 21: Supernova Neu
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186 Michael Altmann Technische Univ
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188 Paolo Gondolo Max-Planck-Instit
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190 Patrizia Meunier Max-Planck-Ins
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192 Torsten Soldner Technische Univ
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194 A Experimental Particle Physics
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196 C Astrophysics and Cosmology C1
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