Abstract
Strong magnetic fields inhibit degeneracy in Fermi gases, that is, they postpone degeneracy to higher densities or lower temperatures. We derive this principle, virtually unknown in the physical and astrophysical literature, for the case of an ideal Dirac electron gas. Its possible importance in astrophysics is due to the fact that the equations of state of Fermi gases at given density and temperature can be qualitatively changed by this degeneracy-inhibition by strong fields. All astrophysical work with strong fields up to the present has used the field-free equations of state and the usual MHD approximation: permeability ≈1. Their interest was focussed on the effects of a strong Lorentz force term. We consider an application to hypothetical degenerate stellar objects with arbitrarily strong fields to see what effects the changed equations of state would lead to. One result is that the luminosity-temperature relation of the star is changed: the luminosity is reduced for given mass and interior temperature.
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References
Azbel', M. Ya.: 1984,Phys. Rev. B30, 2273.
Canuto, V. and Chiu, H.: 1968a,Phys. Rev. 173, 1210.
Canuto, V. and Chiu, H.: 1968b,Phys. Rev. 173, 1220.
Canuto, V. and Chiu, H.: 1968c,Phys. Rev. 173, 1229.
Chiu, H., Canuto, V., and Fassio-Canuto, L.: 1968,Phys. Rev. 176, 1438.
Chandrasekhar, S.: 1931a,Phil. Mag. 11, 592.
Chandrasekhar, S.: 1931b,Astrophys. J. 74, 81.
Chanmugam, G.: 1978,Astrophys J. 221, 965.
Condon, J. H.: 1966,Phys. Rev. 145, 526.
Cowling, T. G.: 1957,Magneto-Hydrodynamics, Interscience, New York, p. 3.
Das, M. K. and Tandon, J. N.: 1978,Astrophys. J. 221, 958.
Delsante, A. and Frankel, N.: 1978,Phys. Letters A67, 435.
Gershuni, G. Z. and Zhukovitskii, E. M.: 1976,Convective Stability of Incompressible Fluids, Keter, Jerusalem, p. 145.
Greenstein, J. L. and Oke, J. B.: 1982,Astrophys. J. 252, 285.
Grot, R. A.: 1976, in A. C. Eringen (ed.), ‘Relativistic Continuum Physics: Electromagnetic, Interactions’,Continuum Physics, Academic Press, New York, Vol. 3.
Henry, R. J. and O'Connell, R. F.: 1984,Astrophys J. 282, L97.
Ingraham, R. L.: 1985,Am. J. Phys. 53, 119.
Ingraham, R. L.: 1986a,Astrophys. J. 309, 628.
Ingraham, R. L.: 1986b,J. Low Temp. Phys. (submitted).
Ingraham, R. L. and Wilkes, J. M.: 1985, ‘On Explicit Equations of State for an Ideal Electron Gas in an Arbitrarily Strong Magnetic Field’, N.M. State University, preprint.
Jeffreys, H. and Jeffreys, B.: 1956,Methods of Mathematical Physics, 3rd ed., Cambridge, p. 279.
Kichigan, D. A., Knyth, I. N., Pogrebnyak, V. A., and Khalameida, D. D.: 1984,Soviet Phys. Solid State 26, 1389.
Landau, L. D. and Lifshitz, E. M.: 1984,Electrodynamics of Continuous Media, 2nd ed., Pergamon, New York, Sec. 31.
Luryi, S. and Kazarinov, R.: 1983,Phys. Rev. B27, 1386.
Mestel, L.: 1965, in L. H. Aller and D. B. McLaughlin (eds.),Stellar Structure, University of Chicago Press, Chicago.
Ostriker, J. P. and Hartwick, F. D. A.: 1968,Astrophys. J. 153, 797.
Peierls, R.: 1955,Quantum Theory of Solids, Oxford University Press, Oxford.
Raadu, M. A.: 1971Astrophys. Space Sci. 14, 464.
Reif, F.: 1965,Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, Equation (9.8.5).
Shapiro, S. and Teukolsky, S.: 1983,Black Holes, White Dwarfs, and Neutron Stars, Wiley-Interscience, New York, Secs. 7.1 and 7.2.
Spitzer, L.: 1956,Physics of Fully Ionized Gases, Interscience, New York, Sec. 1.4.
Straumann, N.: 1984,General Relativity and Relativistic Astrophysics, Springer, New York, Sec. 6.10.5.
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Ingraham, R.L., Wilkes, J.M. Inhibition of degeneracy by intense magnetic fields: Derivation and astrophysical application. Astrophys Space Sci 135, 87–104 (1987). https://doi.org/10.1007/BF00644464
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DOI: https://doi.org/10.1007/BF00644464