Abstract
The equations of neutrino hydrodynamics are derived in two different approximations taking into consideration the neutrino scattering from stellar material. In a thermal-conductivity approximation which holds good when neutrino optical depth with respect to absorption exceeds 1, the neutrino scattering is taken into account, analogously with photon radiative conductivity, by introducing the transport cross-section in the neutrino mean free path. In a practically important case when the neutrino optical thickness with respect to scattering is high enough, whereas that concerning absorption is sufficiently low, another approximation of ‘Comptonized’ neutrinos is valid. In this case, the neutrino and antineutrino chemical potentials are independent of each other. They have to be calculated from equations of continuity established for neutrino and antineutrino alongside with the diffusion equation expressing the law of lepton-charge conservation. The equations of neutrino hydrodynamics are written out both with and without inclusion of muon neutrinos and antineutrinos.
The equations obtained are established to deal properly with neutrino diffusion inside collapsing stars.
Similar content being viewed by others
References
Bludman, S. A.: 1977,Diffusion Approximation to Neutrino Fluxes Out of Collapsing Stars, Preprint.
Bludman, S. A. and Van Piper, K. A.: 1978,Astrophys. J. 224, 631.
Chiu, H.-Y.: 1968,Transport Processes in Stars, Stellar Physics. IV, Blaisdell Publishing Co., Waltham, Mass., U.S.A.
Colgate, S. A. and White, R. H.: 1966,Astrophys. J. 143, 626.
Domogatsky, G. V.: 1969,Nauch. Inform. Astron. Sovieta U.S.S.R. Acad. Sci. 13, 94.
Frank-Kamenetsky, D. A.: 1959,Fizicheskie Processy Vnutri Zvezd (in Russian), ‘Fizmatgiz’, Moscow.
Gershtein, S. S., Imshennik, V. S., Nadyozhin, D. K., Folomeshkin, V. N., Khlopov, M. Yu., Chechetkin, V. M., and Eramzhyan, R. A.: 1975,Zh. Eksp. Teor. Fiz. 69, 1473. See also a short communication inPhys. Letters 62B (1976), 100.
Gershtein, S. S., Ivanova, L. N., Imshennik, V. S., Khlopov, M. Yu., and Chechetkin, V. M.: 1977,Pis'ma JETP 26, 189.
Gershtein, S. S., Khlopov, M. Yu., Ivanova, L. N., Imshennik, V. S., and Chechetkin, V. M.: 1978,Proceedings of Neutrino-77 International Conference, ‘Nauka’ Publ. House, Moscow,1, 106.
Imshennik, V. S.: 1976,Compton Radiative Gasdynamics (in Russian), Institute of Applied Mathematics of the U.S.S.R. Academy of Sciences, Preprint No. 86.
Imshennik, V. S. and Nadyozhin, D. K.: 1972,Zh. Eksp. Teor. Fiz. 63, 1548, Translation in English:Soviet Phys. — JETP 36, 821.
Ivanova, L. N., Imshennik, V. S., and Nadyozhin, D. K.: 1969,Nauch. Inform. Astron. Sovieta U.S.S.R. Acad. Sci. 13, 3.
Ivanova, L. N., Imshennik, V. S., and Chechetkin, V. M.: 1977,Astron. Zh. 54, 1009, Translation in English:Soviet Astron. — AJ 21, 571.
Lamb, D. Q. and Pethick, C. J.: 1976,Astrophys. J. 209, L77.
Mazurek, T. J.: 1975,Astrophys. Space Sci. 35, 117.
Nadyozhin, D. K.: 1977,Astrophys. Space Sci. 49, 399;51, 283.
Nadyozhin, D. K.: 1978,Astrophys. Space Sci. 53, 131.
Rhodes, P.: 1950,Proc. Roy. Soc. A204, No. 1078, 396.
Weinberg, S.: 1974,Rev. Mod. Phys. 46, 255.
Yueh, W. R. and Buchler, J. R.: 1976,Astrophys. Space Sci. 39, 429.
Yueh, W. R. and Buchler, J. R.: 1977,Astrophys. J. 217, 565.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Imshennik, V.S., Nadyozhin, D.K. Neutrino chemical potential and neutrino heat conductivity with allowance for neutrino scattering. Astrophys Space Sci 62, 309–333 (1979). https://doi.org/10.1007/BF00645472
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00645472