Cosmic and local mass density of ‘‘invisible’’ axions

Michael S. Turner

doi:10.1103/PhysRevD.33.889

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Cosmic and local mass density of ‘‘invisible’’ axions

Michael S. Turner

Departments of Physics and Astronomy and Astrophysics, Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637 and NASA/Fermilab Astrophysics Center, MS 209 Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510

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Phys. Rev. D 33, 889 – Published 15 February, 1986

DOI: https://doi.org/10.1103/PhysRevD.33.889

Abstract

If the Universe is axion dominated it may be possible to detect the axions which comprise the bulk of the mass density of the Universe. The feasibility of the proposed experiments depends crucially upon knowing the axion mass (or equivalently, the Peccei-Quinn symmetry-breaking scale) and the local mass density of axions. In an axion-dominated universe our galactic halo should be comprised primarily of axions. We calculate the local halo density to be at least 5× $10^{- 25}$ g ${cm}^{- 3}$ , and at most a factor of 2 larger. Unfortunately, it is not possible to pin down the axion mass, even to within an order of magnitude. In an axion-dominated universe we place an upper limit to the axion mass of about $10^{- 4}$ eV. We give precise formulas for the axion mass in an axion-dominated universe, and clearly point out all the uncertainties involved in determining the precise value of the mass.

References (23)

R. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977).
S. Weinberg, Phys. Rev. Lett. 40, 223 (1978); F. Wilczek, ibid. 40, 279 (1978).
J. Kim, Phys. Rev. Lett. 43, 103 (1979); M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104B, 199 (1981).
J. Preskill, M. Wise and F. Wilczek, Phys. Lett. 120B, 127 (1983); L. Abbott and P. Sikivie, ibid. 120B, 133 (1983); M. Dine and W. Fischler, ibid. 120B, 137 (1983).
P. Steinhardt and M. S. Turner, Phys. Lett. 129B, 51 (1983).
J. Ipser and P. Sikivie, Phys. Rev. Lett. 50, 925 (1983); M. S. Turner, F. Wilczek and A. Zee, Phys. Lett. 125B, 35 (1983); ibid. 125B, 519(E) (1983); G. Blumenthal, S. Faber, J. Primack and M. J. Rees, Nature (London) 311, 517 (1984).
P. Sikivie, Phys. Rev. Lett. 51, 1415 (1983); L. L. Krauss, J. Moody, D. Morris, and F. Wilczek, Report No. UCSB/ITP, 1985 (unpublished), have recently suggested a new type of axion detector which exploits the spin coupling of axions to matter. Several groups are designing experiments to detect axions in the halo of the Galaxy; they include Sikivie et al. (University of Florida), Lubin et al. (Lawrence Berkeley Laboratory, Melissinos et al. (Rochester), and Nezrick et al. (Fermi National Accelerator Laboratory).
P. Sikivie, Phys. Rev. Lett. 48, 1156 (1982).
S. Weinberg, Phys. Rev. Lett. 48, 1303 (1982); R. Scherrer and M. S. Turner, Phys. Rev. D 31, 681 (1985).
S.-Y. Pi, Phys. Rev. Lett. 52, 1725 (1984); in a recent paper, A. Linde has also emphasized the point that all values of $θ_{1}$ should occur with finite probability in an axion-dominated universe which is inflationary; A. Linde, Phys. Lett. 158B, 375 (1985).
D. Seckel and M. S. Turner, Phys. Rev. D 32, 3178 (1985).
D. Gross, R. Pisarski and L. Yaffe, Rev. Mod. Phys. 53, 43 (1981).
W. Unruh and R. Wald, Phys. Rev. D 32, 831 (1985); M. S. Turner, ibid. 32, 843 (1985).
The most convincing evidence for the existence of galactic halos are the flat rotation curves observed in spiral galaxies. See, e.g., V. Rubin et al., Astrophys. J. 225, L107 (1978); , ibid. 261, 439 (1980); , Science 220, 1339 (1983) A. Bosma, Astron. J. 86, 1721 (1981); ibid. 86, 1825 (1981).
J. Bahcall and R. M. Soneira, Astrophys. J. Suppl. 44, 73 (1980); J. Bahcall, M. Schmidt and R. M. Soneira, Astrophys. J. 265, 730 (1983).
D. Mihalas and J. Binney, Galactic Astronomy: Structure and Kinematics (Freeman, San Francisco, 1981). It is only fair to mention that for our Galaxy, $v_{rot}$ has only been measured out to about 15 kpc, which is not really >> R. This implies an additional uncertainty in determining $ρ_{0}$ (and in turn $ρ_{halo}$ ) as $ρ_{0}$ prop $v_{rot}^{2}$ .
J. Bahcall, Astrophys. J. 287, 926 (1984), and references cited therein.
J. Oort, Bull. Astron. Inst. Neth. 6, 249 (1932); ibid. 15, 45 (1965).
For a discussion of the constraints on the composition of the dark disk component, see D. Hegyi, E. W. Kolb, and K. Olive, Astrophys. J. (to be published); B. J. Carr, Fermilab report, 1985 (unpublished); J. Bahcall, P. Hut and S. Tremaine, Astrophys. J. 290, 15 (1985).
See, e.g., Dark Matter in the Universe, proceedings of the IAU Symposium No. 117, edited by J. Knapp and J. Kormendy (Reidel, Dordrecht, 1986).
J. Barnes (in preparation).
M. S. Turner, Phys. Rev. D 28, 1243 (1983).
T. DeGrand, T. Kephart and T. Weiler, this issue, Phys. Rev. D 33, 910 (1986).

[c1] R. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977).

[c2] S. Weinberg, Phys. Rev. Lett. 40, 223 (1978); F. Wilczek, ibid. 40, 279 (1978).

[c3] J. Kim, Phys. Rev. Lett. 43, 103 (1979); M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104B, 199 (1981).

[c4] J. Preskill, M. Wise and F. Wilczek, Phys. Lett. 120B, 127 (1983); L. Abbott and P. Sikivie, ibid. 120B, 133 (1983); M. Dine and W. Fischler, ibid. 120B, 137 (1983).

[c5] P. Steinhardt and M. S. Turner, Phys. Lett. 129B, 51 (1983).

[c6] J. Ipser and P. Sikivie, Phys. Rev. Lett. 50, 925 (1983); M. S. Turner, F. Wilczek and A. Zee, Phys. Lett. 125B, 35 (1983); ibid. 125B, 519(E) (1983); G. Blumenthal, S. Faber, J. Primack and M. J. Rees, Nature (London) 311, 517 (1984).

[c7] P. Sikivie, Phys. Rev. Lett. 51, 1415 (1983); L. L. Krauss, J. Moody, D. Morris, and F. Wilczek, Report No. UCSB/ITP, 1985 (unpublished), have recently suggested a new type of axion detector which exploits the spin coupling of axions to matter. Several groups are designing experiments to detect axions in the halo of the Galaxy; they include Sikivie et al. (University of Florida), Lubin et al. (Lawrence Berkeley Laboratory, Melissinos et al. (Rochester), and Nezrick et al. (Fermi National Accelerator Laboratory).

[c8] P. Sikivie, Phys. Rev. Lett. 48, 1156 (1982).

[c9] S. Weinberg, Phys. Rev. Lett. 48, 1303 (1982); R. Scherrer and M. S. Turner, Phys. Rev. D 31, 681 (1985).

[c10] S.-Y. Pi, Phys. Rev. Lett. 52, 1725 (1984); in a recent paper, A. Linde has also emphasized the point that all values of $θ_{1}$ should occur with finite probability in an axion-dominated universe which is inflationary; A. Linde, Phys. Lett. 158B, 375 (1985).

[c11] D. Seckel and M. S. Turner, Phys. Rev. D 32, 3178 (1985).

[c12] D. Gross, R. Pisarski and L. Yaffe, Rev. Mod. Phys. 53, 43 (1981).

[c13] W. Unruh and R. Wald, Phys. Rev. D 32, 831 (1985); M. S. Turner, ibid. 32, 843 (1985).

[c14] The most convincing evidence for the existence of galactic halos are the flat rotation curves observed in spiral galaxies. See, e.g., V. Rubin et al., Astrophys. J. 225, L107 (1978); , ibid. 261, 439 (1980); , Science 220, 1339 (1983) A. Bosma, Astron. J. 86, 1721 (1981); ibid. 86, 1825 (1981).

[c15] J. Bahcall and R. M. Soneira, Astrophys. J. Suppl. 44, 73 (1980); J. Bahcall, M. Schmidt and R. M. Soneira, Astrophys. J. 265, 730 (1983).

[c16] D. Mihalas and J. Binney, Galactic Astronomy: Structure and Kinematics (Freeman, San Francisco, 1981). It is only fair to mention that for our Galaxy, $v_{rot}$ has only been measured out to about 15 kpc, which is not really >> R. This implies an additional uncertainty in determining $ρ_{0}$ (and in turn $ρ_{halo}$ ) as $ρ_{0}$ prop $v_{rot}^{2}$ .

[c17] J. Bahcall, Astrophys. J. 287, 926 (1984), and references cited therein.

[c18] J. Oort, Bull. Astron. Inst. Neth. 6, 249 (1932); ibid. 15, 45 (1965).

[c19] For a discussion of the constraints on the composition of the dark disk component, see D. Hegyi, E. W. Kolb, and K. Olive, Astrophys. J. (to be published); B. J. Carr, Fermilab report, 1985 (unpublished); J. Bahcall, P. Hut and S. Tremaine, Astrophys. J. 290, 15 (1985).

[c20] See, e.g., Dark Matter in the Universe, proceedings of the IAU Symposium No. 117, edited by J. Knapp and J. Kormendy (Reidel, Dordrecht, 1986).

[c21] J. Barnes (in preparation).

[c22] M. S. Turner, Phys. Rev. D 28, 1243 (1983).

[c23] T. DeGrand, T. Kephart and T. Weiler, this issue, Phys. Rev. D 33, 910 (1986).

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